Difference between revisions of "751.40 LFD Widening and Repair"

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<div style="float: right; width: 500px; margin-top: 5px; margin-left: 30px; margin-bottom: 30px;">__TOC__</div>
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== 751.40.1 General ==
 
== 751.40.1 General ==
 
 
=== 751.40.1.1 Widening and Repair of Existing Structures ===
 
=== 751.40.1.1 Widening and Repair of Existing Structures ===
  
 
The Federal Highway Administration and the States have established a goal that the LRFD standards be used on all new bridge designs after October 2007.  For modification to existing structures and with the approval of the Structural Project Manager or Structural Liaison Engineer, the LRFD Specifications or the specifications which were used for the original design, may be used by the designer.
 
The Federal Highway Administration and the States have established a goal that the LRFD standards be used on all new bridge designs after October 2007.  For modification to existing structures and with the approval of the Structural Project Manager or Structural Liaison Engineer, the LRFD Specifications or the specifications which were used for the original design, may be used by the designer.
  
==751.40.2 Typical Sections of Concrete Repairs==
+
==751.40.2 Deck Treatments==
 
===751.40.2.1 Resurfacing===
 
===751.40.2.1 Resurfacing===
  
 +
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40_Resurfacing_Plan.gif|center]]
 +
|-
 +
| <big>'''PLAN'''</big>
 +
|}
  
<center>[[Image:751.40_Resurfacing_Plan.gif]]</center>
 
 
<center>'''PLAN'''</center>
 
 
 
 
<center>[[Image:751.40_Resurfacing_Section_Thru_Roadway.gif]]</center>
 
 
<center>'''SECTION THRU ROADWAY'''</center>
 
  
 +
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40_Resurfacing_Section_Thru_Roadway.gif|center]]
 +
|-
 +
| <big>'''SECTION THRU ROADWAY'''</big>
 +
|}
  
 
Place the following notes on plans.
 
Place the following notes on plans.
  
:The existing Asphaltic Concrete surface shall be removed to a uniform grade line (*) below the existing control grade line as noted.
+
: The existing asphaltic concrete surface shall be removed to a uniform grade line * below the existing control grade line as noted.
 
+
: Resurface with * Asphaltic Concrete.
:Resurface with (*) Asphaltic Concrete.
+
: <nowiki>*</nowiki> Depth of asphaltic concrete as specified in the Bridge Memorandum.
 
 
:(*) Depth of Asphaltic Concrete as specified in the Design Layout.
 
  
 
===751.40.2.2 Special Repair Zones===
 
===751.40.2.2 Special Repair Zones===
  
The following order of repair zones are to be used for the deck repair on continuous concrete structures.
+
The following order of repair zones shall be used for the deck repair on continuous concrete structures.
  
Zones with the same letter designation may be repaired at the same time.  Sequence of repairs follows zone A, zone B then zone C.
+
'''Hydro Demolition Projects (Case 1 and 2)'''
  
Zone A is to be completed before Zone B and Zone B before Zone C, etc.
+
Conventional deck repair required in the areas designated as special repair zones shall be completed before demolition in alphabetical sequence beginning with Zone A. Zones with the same letter designation may be repaired at the same time.
  
Any repair in the remainder of the bridge that is adjacent to Zone A shall be completed prior to work in Zone A.
+
Any deck repair in areas not designated as a special repair zone shall be completed after hydro demolition. Case 1 is primarily monolithic deck repair after hydro demolition. Case 2 is primarily conventional deck repair after hydro demolition.
  
If an excessive number of zones are required at one bent, See the Structural Project Manager.
+
Note:
 +
:- Case 1 shall not be used for polyester polymer and low slump concrete wearing surfaces (too stiff for monolithic repairs).
 +
:- Conventional deck repair is required with void tube replacement after hydro demolition with both Case 1 and Case 2.
 +
:- If an excessive number of zones are required at any bent, see the Structural Project Manager or Structural Liaison Engineer.
 +
:- Consider combining zones if the length of a zone in the longitudinal direction of the bridge is less than 24 inches.
  
Consider combining zones if it is ≤ 24".
+
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[image:751.40.2.2_hydro_part-plan.png|center|750px]]
 +
|-
 +
| <big>'''PART PLAN OF SLAB SHOWING REPAIR ZONES (A, B, C and D)'''</big>
 +
|}
 +
:::(1) Development Length.
 +
:::See [[751.50_Standard_Detailing_Notes|EPG 751.50 Standard Detailing Notes]] for appropriate notes.
  
 +
'''Non-Hydro Demolition Projects'''
  
<center>[[Image:751.40_Repair_Zones.gif]]</center>
+
Any deck repair in areas not designated as a special repair zone shall be completed prior to work in Zone A. Zones with the same letter designation may be repaired at the same time.
  
 +
Note:
 +
:- If an excessive number of zones are required at any bent, see the Structural Project Manager or Structural Liaison Engineer.
 +
:- Consider combining zones if the length of a zone in the longitudinal direction of the bridge is less than 24 inches.
  
<center>'''PART PLAN OF SLAB SHOWING REPAIR ZONES'''</center>
+
{| style="text-align: center; margin: 0 auto;"
 
+
|-
 
+
| [[image:751.40.2.2_nonhydro_part-plan.png|center|750px]]
(1) Development Length.
+
|-
 
+
| <big>'''PART PLAN OF SLAB SHOWING REPAIR ZONES (A, B and C)'''</big>
See [[751.50_Standard_Detailing_Notes|EPG 751.50 Standard Detailing Notes]] for appropriate notes.
+
|}
 +
:::(1) Development Length.
 +
:::See [[751.50_Standard_Detailing_Notes|EPG 751.50 Standard Detailing Notes]] for appropriate notes.
  
===751.40.2.3 Substructure Repair===
+
===751.40.2.3 Deck Repair and Filled Joints===
  
<center>[[Image:751.40_Substructure_Repair.gif]]</center>
+
<div style="float: right; margin-top: 5px; margin-bottom: 5px; padding: 5px; text-align:center; border: 1px solid black; border-radius:5px; box-shadow:5px 5px 5px #888888">
 +
'''Bridge Deck, Repair'''</br>
 +
[https://spexternal.modot.mo.gov/sites/cm/CORDT/RDT02002.pdf Report 2002]</br>
 +
'''See also:''' [https://www.modot.org/research-publications Research Publications]
 +
</div>
  
 
+
{| border="1" class="wikitable" style="margin: 0 auto; text-align: center"
<center>'''DETAILS SHOWING SUBSTRUCTURE REPAIR AREAS'''</center>
+
|+
 
+
| style="background:#BEBEBE" | '''[https://www.modot.org/bridge-standard-drawings Bridge Standard Drawings]'''
===751.40.2.4 Deck Repair===
 
{|style="padding: 0.3em; margin-left:15px; border:1px solid #a9a9a9; text-align:center; font-size: 95%; background:#ffddcc" width="210px" align="right"
 
|-
 
|'''Bridge Deck, Repair'''
 
|-
 
|[http://library.modot.mo.gov/RDT/reports/Ri97025/RDT02002.pdf Report 2002]
 
 
|-
 
|-
|'''See also:''' [http://www.modot.gov/services/OR/byDate.htm Innovation Library]
+
| Rehabilitation, Surfacing & Widening – RHB; Deck Rehab (Deck Repair and Wearing Surface Details)
 
|}
 
|}
'''DECKS WITHOUT AN EXISTING WEARING SURFACE (NEAR CENTERLINE SPAN)'''
 
  
 +
===751.40.2.4 Wearing Surfaces===
  
<center>[[Image:751.40_Deck_Repair_(without_exist_wearing_surface_CL_span).gif]]</center>
+
'''Replacement of Typical Expansion Joint Systems (Strip Seal Shown, Other Systems Similar)'''
  
 +
[[image:751.40.3.1 wearing surfaces.jpg|center|650px]]
  
<center>'''SECTION THRU ROADWAY'''</center>
+
When concrete is removed and armor is replaced, see [[751.13 Expansion Joint Systems|EPG 751.13 Expansion Joint Systems]] for the appropriate expansion joint system details and [[751.50 Standard Detailing Notes#H5. Expansion Joint Systems|EPG 751.50 H5]] for the appropriate notes.
  
 +
For chip seals and polymer wearing surfaces, see [[751.50 Standard Detailing Notes#I1. General|EPG 751.50 I1]] for the appropriate notes.
  
'''TOTAL SURFACE HYDRO DEMOLITION DECK REPAIR'''
+
'''Elastomeric Expansion Joint System'''
  
 +
When a thick wearing surface (low slump, latex, silica fume, CSA cement, steel fiber reinforced, asphaltic) is used, the elastomeric joint must be replace by another type of expansion joint system.
  
<center>[[Image:751.40_Deck_Repair_(total_surface_hydro_demolition).gif]]</center>
+
[[image:751.40.3.1 elastomeric.jpg|center|375px]]  
  
 +
'''Flat Plate Expansion Joint System '''
  
<center>'''SECTION THRU ROADWAY'''</center>
+
[[image:751.40.3.1 flat thick.jpg|center|575px]]
 +
::: '''*''' When this dimension exceeds 3" and a concrete wearing surface is used, tack weld a one inch bar chair to the plate for each 3" of plate to be covered by the wearing surface.
 +
::: '''**''' Scarify existing slab. See the Bridge Memorandum for the minimum depth of scarification. Scarification not required for asphaltic concrete wearing surface.
 +
::: Note: See standard plans for Steel Dams at Expansion Joints.
  
  
 +
[[image:751.40.3.1 flat thin.jpg|center|400px]]
  
'''DECKS WITHOUT AN EXISTING WEARING SURFACE (NEAR CENTERLINE SPAN)'''
+
===751.40.2.5 Edge Treatments===
 +
====751.40.2.5.1 Epoxy Coating====
  
 +
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40.3.1 latex section.jpg|center|540px]]
 +
|-
 +
| <big>'''TYPICAL SECTION OF EXISTING CURB<br/>OUTLET SHOWING LIMITS OF EPOXY COATING'''</big>
 +
|}
 +
::: Note:
 +
::: '''*''' Dimension to edge of girder or stringer &plusmn;. For bridges that do not have girders or stringers use 2'-6", except that if with thrie beam rail, then use 4'-0".
 +
::: Consult with Structural Project Manager or Liaison for making work incidental to another item or use of pay item "Cleaning and Epoxy Coating".
  
<center>[[Image:751.40_Deck_Repair_(without_exist_wearing_surface_CL_span)_Half-Soled_Area.gif]]</center>
 
  
 +
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40.3.1 latex elevation.jpg|440px]]
 +
|-
 +
| <big>'''TYPICAL ELEVATION OF EXISTING CURB<br/>OUTLET SHOWING LIMITS OF EPOXY COATING'''</big><br/>(Wearing surface not shown for clarity)
 +
|}
  
<center>'''HALF-SOLED AREA'''</center>
+
====751.40.2.5.2 Edge Repair====
  
 +
If slab edge repair is specified on the Bridge Memorandum when the barrier or railing is not removed or when full depth repair is not a pay item, the following detail shall be provided.
  
<center>[[Image:751.40_Deck_Repair_(without_exist_wearing_surface_CL_span)_Full_Depth_Area.gif]]</center>
+
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40_Concrete_Wearing_Surface_Slab_Edge_Repair_(Concrete_Edge_Repair)_no_1.gif|center]]
 +
|-
 +
| <big>'''CONCRETE EDGE REPAIR'''</big>
 +
|}
 +
:::If the barrier or railing is removed when full depth repair and slab edge repair are pay items, the following detail shall be provided.
  
  
<center>'''FULL DEPTH AREA'''</center>
+
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40_Concrete_Wearing_Surface_Slab_Edge_Repair_(Concrete_Edge_Repair)_no_1.gif|center]]
 +
|-
 +
| <big>'''CONCRETE EDGE REPAIR'''</big>
 +
|}
 +
::: '''*''' If the dimension exceeds 4 inches, the repair extending to the edge of slab will be paid for as Full Depth Repair.
  
 +
===751.40.2.6 Longitudinal Joints===
  
<center>[[Image:751.40_Deck_Repair_(without_exist_wearing_surface_CL_span)_Full_Depth_Repair_in_Half-Soled_Area.gif]]</center>
+
'''REPLACEMENT OF EXISTING EXPANSION DEVICE'''
  
 +
'''MEDIAN BARRIER '''
  
<center>'''FULL DEPTH AREA IN HALF-SOLED AREA'''</center>
+
{| style="text-align: center; margin: 0 auto;"
 
+
|-
 +
| [[Image:751.40.2.6_section_thru_barrier.jpg|center|400px]]
 +
|-
 +
| <big>'''SECTION THRU BARRIER'''</big>
 +
|}
  
{|border="0" cellpadding="3"
 
  
|valign="top"|(1)||Scarify existing slab.  See the Design Layout for the minimum depth of scarification for the Concrete Wearing Surface.  Scarification not required for Asphaltic Concrete Wearing Surface and Epoxy Polymer Concrete Overlay.
+
{| style="text-align: center; margin: 0 auto;"
 
|-
 
|-
|valign="top"|(2)||One inch vertical side shall be established outside the deteriorated area.  See Sec 704.
+
| [[Image:751.40.2.6_detail_A.jpg|center|400px]]
 
|-
 
|-
|valign="top"|(3)||1/4" (min.) for Epoxy Polymer Concrete Overlay.<br/>1-3/4" (min.) for Latex Modified Concrete.<br/>2-1/4" (min.) for Low Slump Concrete or Silica Fume Concrete.
+
| <big>'''DETAIL A'''</big>
 
|}
 
|}
 +
::: (1) May be cast vertical and saw cut to slant.
 +
::: * Latex Concrete Wearing Surface = 1-3/4".<br/>Low Slump Concrete Wearing Surface = 2-1/4".
 +
::: ** Cut minimum 1/2" support notch (rough finish). Remove any existing compression seal.
  
 +
===751.40.2.7 Temporary Traffic Control Device===
  
 +
Show Barrier as per district recommendation. Typically Barrier is shown when structure is on interstate and/or the rail is being removed. Otherwise, show the dimension lines with 2'-0" dimension.
  
'''DECKS WITH AN EXISTING WEARING SURFACE (NEAR CENTERLINE SPAN)'''
+
[[image:751.40.2.5.jpg|center|700px]]
  
 +
::: '''*''' If this dimension is less than 3 feet, the temporary concrete traffic barrier shall be attached with tie-down straps, with the approval of the Structural Project Manager or Structural Liaison Engineer. Where lateral deflection cannot be tolerated, the temporary concrete traffic barrier shall be attached with the bolt through deck detail (to be used only on existing decks). See [[617.1 Temporary Traffic Barriers|EPG 617.1 Temporary Traffic Barriers]] and [[751.1 Preliminary Design#751.1.2.12 Temporary Barriers|EPG 751.1.2.12 Temporary Barriers]].
 +
::: '''**''' Where slab removal represents small and discontinuous openings in the deck along the bridge length (e.g. expansion device replacement) use of either a flat steel plate, a 22 ½” temporary traffic control device or a temporary concrete traffic barrier may be more appropriate. Consult with the Structural Project Manager or Structural Liaison Engineer.
  
<center>[[Image:751.40_Deck_Repair_(with_exist_wearing_surface_CL_span)_Half-Soled_Area.gif]]</center>
+
==751.40.3 Substructure Repair==
 +
===751.40.3.1 Formed and Unformed Repair Areas===
  
 +
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40.3.1_elev_int_bent.png|center|700px]]
 +
|-
 +
| <big>'''Elevation of Int. Bent'''</big>
 +
|}
  
<center>'''HALF-SOLED AREA'''</center>
 
  
 +
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40.3.1_sec_through_end_bent.png|center|400px]]
 +
|-
 +
| <big>'''Section through End Bent'''</big>
 +
|}
  
 +
===751.40.3.2 Bent Cap Shear Strengthening using FRP Wrap===
  
<center>[[Image:751.40_Deck_Repair_(with_exist_wearing_surface_CL_span)_Full_Depth_Repair.gif]]</center>
+
{| border="1" class="wikitable" style="margin: 0 auto; text-align: center"
 +
|+
 +
| style="background:#BEBEBE" | '''[https://www.modot.org/bridge-standard-drawings Bridge Standard Drawings]'''
 +
|-
 +
| Rehabilitation, Surfacing & Widening; Fiber Reinf. Polymer (FRP) Wrap for Bent Cap Strengthening [RHB08]
 +
|}
  
 +
Fiber Reinforced Polymer (FRP) wrap may be used for Bent Cap Shear Strengthening.
  
<center>'''FULL DEPTH REPAIR'''</center>
+
'''When to strengthen:''' When increased shear loading on an existing bent cap is required and a structural analysis shows insufficient bent cap shear resistance, bent cap shear strengthening is an option.  An example of when strengthening a bent cap may be required:  removing existing girder hinges and making girders continuous will draw significantly more force to the adjacent bent. An example of when strengthening a bent cap is not required:  redecking a bridge  where analysis shows that the existing bent cap cannot meet capacity for an HS20 truck loading, and the new deck is similar to the old deck and the existing beam is in good shape.
  
 +
'''How to strengthen:'''  Using FRP systems for shear strengthening follows from the guidelines set forth in ''NCHRP Report 678, Design of FRP System for Strengthening Concrete Girders in Shear''. The method of strengthening, using either discrete strips or continuous sheets, is made optional for the contractor in accordance with ''NCHRP Report 678''.  A Bridge Standard Drawing and Bridge Special Provision have been prepared for including this work on jobs. They can be revised to specify a preferred method of strengthening if desired, strips or continuous sheet.
  
<center>[[Image:751.40_Deck_Repair_(with_exist_wearing_surface_CL_span)_Full_Depth_Repair_in_Half-Soled_Area.gif]]</center>
+
'''What condition of existing bent cap required for strengthening:'''  If a cap is in poor shape where replacement should be considered, FRP should not be used. Otherwise, the cap beam can be repaired before applying FRP.  Perform a minimum load check using (1.1DL + 0.75(LL+I))'''*''' on the existing cap beam to prevent catastrophic failure of the beam if the FRP fails (''ACI 440.2R, Guide for the Design and Construction of Externally Bonded FRP, Sections 9.2 and 9.3.3''). If the factored shear resistance of the cap beam is insufficient for meeting the factored minimum load check, then FRP strengthening should not be used.
 +
   
 +
:: '''*''' ACI 440.2R: ''Guide for the Design and Construction of Externally Bonded FRP''
  
 +
'''Design force (net shear strength loading):'''  Strengthening a bent cap requires determining the net factored shear loading that the cap beam must carry in excess of its unstrengthened factored shear capacity, or resistance. The FRP system is then designed by the manufacturer to meet this net factored shear load, or design force.  The design force for a bent cap strengthening is calculated considering AASHTO LFD where the factored load is the standard Load Factor Group I load case.  To determine design force that the FRP must carry alone, the factored strength of the bent cap, which is 0.85 x nominal strength according to LFD design, is subtracted out to give the net factored shear load that the FRP must resist by itself.  ''NCHRP Report 678'' is referenced in the special provisions as guidelines for the contractor and the manufacturer to follow.  The report and its examples use AAHTO LRFD.  <u>Regardless, the load factor case is given and it is left to the manufacturer to provide for a satisfactory factor of safety based on their FRP system.</u>
  
<center>'''FULL DEPTH REPAIR IN HALF-SOLED AREA'''</center>
+
Other References:
 +
:: '''*''' ACI 201.1R: ''Guide for Making a Condition Survey of Concrete in Service''
 +
:: '''*''' ACI 224.1R: ''Causes, Evaluation, and Repair of Cracks in Concrete''
 +
:: '''*''' ACI 364.1R-94: ''Guide for Evaluation of Concrete Structures Prior to Rehabilitation''
 +
:: '''*''' ACI 440.2R-08: ''Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures''
 +
:: '''*''' ACI 503R: ''Use of Epoxy Compounds with Concrete''
 +
:: '''*''' ACI 546R: ''Concrete Repair Guide''
 +
:: '''*''' International Concrete Repair Institute (ICI) ICI 03730: ''Guide for Surface Preparation for the Repair of Deteriorated Concrete Resulting from Reinforcing Steel Corrosion''
 +
:: '''*''' International Concrete Repair Institute (ICI) ICI 03733: ''Guide for Selecting and Specifying Materials for Repairs of Concrete Surfaces''
 +
:: '''*''' NCHRP Report 609: ''Recommended Construction Specifications Process Control Manual for Repair and Retrofit of Concrete Structures Using Bonded FRP Composites''
  
 +
===751.40.3.3 Steel HP Pile Maintenance and Repair===
 +
 +
'''Maintenance/Repair Guidelines'''
  
{|border="0" cellpadding="3"
+
Piles are primary structural members and are compressively loaded all the time which makes it important to safely inspect, maintain and repair them if necessary. Pile inspection will require an assessment of pile performance by looking for pile deterioration and measuring pile section loss in order to determine the level of pile maintenance/repair required. The following schedule may be used for selecting the level of maintenance/repair required:
  
|valign="top"|(1)||Remove existing wearing surface plus 1/4" removal not required for Asphaltic Concrete Wearing Surface and Epoxy Polymer Concrete Overlay.
+
{| class="wikitable" style="cellpadding="5" align="center"
 
|-
 
|-
|valign="top"|(2)||One inch vertical side shall be established outside the deteriorated area.  See Sec 704.
+
! Pile Percent Section Loss !! Method'''*''' !! Level
 
|-
 
|-
|valign="top"|(3)||1/4" (min.) for Epoxy Polymer Concrete Overlay.<br/>1-3/4" (min.) for Latex Modified Concrete.<br/>2-1/4" (min.) for Low Slump Concrete or Silica Fume Concrete.
+
| 0% through 25% || Clean and recoat existing piles || Maintenance
 +
|-
 +
| >25% through 40% || Encasement of deteriorated section || Maintenance
 +
|-
 +
| >40% through 75% or holes in any element or local buckling of any element || Plating ** of deteriorated section OR replacement *** of section (splicing), AND encasement of the repaired section || Repair
 +
|-
 +
| >75% || Contact the Bridge Division || Repair
 +
|-
 +
| colspan="3" | '''*''' Method may also include cleaning and recoating all exposed piles, and cleaning and recoating all remaining exposed pile sections after encasement and/or repair.
 +
|-
 +
| colspan="3" | '''**''' Plating can be for both flanges only, web only or both flanges and web. Overall symmetry of the pile cross-section shall be maintained when plating.  
 +
|-
 +
| colspan="3" | '''***''' Based on additional factors other than just the percent of pile section loss, a replacement pile section (splicing) may be considered. Minimizing or eliminating traffic loading, adding falsework or just having support conditions such as integral bents (where both the pile cap beam and the superstructure concrete diaphragm are connected by more than just dowel bars – see bridge plans) can help to determine the method of repair. A replacement pile section can be coated or galvanized. See Structural Project Manager.
 
|}
 
|}
  
 +
'''Estimating Pile Percent Section Loss in the Field'''
  
'''DECKS WITHOUT AN EXISTING WEARING SURFACE (NEAR CENTERLINE SPAN)'''<br/>'''HYDRO DEMOLITION'''
+
Quantifying pile section loss can be inexact. To encourage uniform application of the maintenance/repair guidelines, the following procedure is recommended:
  
 +
:1. Pile section loss should be determined using a thickness meter.
 +
:2. Remove deteriorated material and clean pile for measurement.
 +
:3. At any point along a pile (cross-section) where there are three elements to be considered independently, e.g. two flanges and a web.
 +
:4. Estimate the actual cross-section area of each element at its most deteriorated point along the length of pile. Using the thickness meter, measure the thickness at several points along a horizontal line across the element. From this data, estimate the actual cross-section area of each element.
 +
:5. The fraction of section remaining (PSR) is the actual cross-section area of each element at its most deteriorated point along the length of pile divided by the original area of same element.
 +
:6. Percent section loss is 100(1 – PSR) for each element.
 +
:7. The greatest PSR dictates the maintenance/repair method.
 +
:8. Examine continuity at flange/web intersections. Section loss along these intersections along the length of pile of more than 6 linear inches should be repaired using encasement as either the only method or part of plating/replacing repair method regardless of a low percent section loss.
 +
:9. Interference from cross bracing at pile sections to be repaired will need special consideration not detailed on the standard drawings.
  
<center>[[Image:751.40_Deck_Repair_(without_exist_wearing_surface_CL_span)(Hydro_demolition)_Partial_Depth_Repair.gif]]</center>
+
{| class="wikitable" style="margin: 0 auto; text-align: center"
 +
|+
 +
| style="background:#BEBEBE" | '''[https://www.modot.org/bridge-standard-drawings Bridge Standard Drawings]'''
 +
|-
 +
| Rehabilitation, Surfacing & Widening – RHB; Steel HP Pile Maintenance and Repair
 +
|}
  
 +
Additional types of maintenance and repairs may be considered which include but are not limited to:
 +
:* Zinc tape coating
 +
:* FRP strengthening
 +
:* Corrosion inhibitor
  
<center>'''PARTIAL DEPTH REPAIR'''</center>
+
==751.40.4 Barriers and Railings==
  
 +
===751.40.4.1 End Post Modification for 12-inch Vertical Barrier (Safe & Sound Bridges)===
  
<center>[[Image:751.40_Deck_Repair_(without_exist_wearing_surface_CL_span)(Hydro_demolition)_Full_Depth_Repair.gif]]</center>
+
The 12-inch vertical barrier requires modification to allow attachment of the transition for the Midwest Guardrail System.
  
 +
{| class="wikitable" style="margin: 0 auto; text-align: center"
 +
|+
 +
| style="background:#BEBEBE" | '''[https://www.modot.org/bridge-standard-drawings Bridge Standard Drawings]'''
 +
|-
 +
| Barrier End Modifications – BEM & CBO/Barrier End Modification – BEM
 +
|}
  
<center>'''FULL DEPTH AREA'''</center>
+
===751.40.4.2 Replacement of Existing Type B Barrier Using Anchor Systems===
  
  
<center>[[Image:751.40_Deck_Repair_(without_exist_wearing_surface_CL_span)(Hydro_demolition)_Full_Depth_Repair_in_Partial_Depth_Repair.gif]]</center>
+
'''NEW BARRIER ON SLAB'''
  
 +
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40_Replacement_of_Existing_Curb_(Safety_Barrier_Curb_on_Slab)_Section_Thru_Curb.gif]]
 +
|-
 +
| '''SECTION THRU BARRIER'''
 +
|}
  
<center>'''FULL DEPTH AREA IN PARTIAL DEPTH REPAIR'''</center>
 
  
 
+
{| style="text-align: center; margin: 0 auto;"
{|border="0" cellpadding="3"
 
 
 
|valign="top"|(1)||Scarify existing slab.  See the Design Layout for the minimum depth of scarification for the Concrete Wearing Surface.  Scarification not required for Asphaltic Concrete Wearing Surface and Epoxy Polymer Concrete Overlay.
 
 
|-
 
|-
|valign="top"|(2)||Total surface hydro demolition of existing slab.  See the Design Layout for the minimum depth of total surface hydro demolition.
+
| [[Image:751.40_Replacement_of_Existing_Curb_(Safety_Barrier_Curb_on_Slab)_Section_Thru_Curb_Optional_Anchoring_System.gif]]
 
|-
 
|-
|valign="top"|(3)||One inch vertical side shall be established outside the deteriorated area.  See Sec 704.
+
| '''SECTION THRU BARRIER'''<br/>'''(OPTIONAL ANCHORING SYSTEM)'''
 
|-
 
|-
|valign="top"|(4)||1-3/4" (min.) for Latex Modified Concrete.<br/>2-1/4" (min.) for Low Slump Concrete or Silica Fume Concrete.
+
| See [[751.50 Standard Detailing Notes#I2. Resin & Cone Anchors|EPG 751.50 I2. Resin & Cone Anchors]] for appropriate notes.
|-
 
|&nbsp;||Partial Depth Repair is not allowed for Low Slump Concrete.  Repairing Concrete Deck (Half-Soling) shall be substituted for Partial Depth Repair in the above details and not monolithically with the wearing surface.
 
 
|}
 
|}
  
  
 +
'''NEW BARRIER ON WING'''
  
'''DECKS WITH AN EXISTING WEARING SURFACE (NEAR CENTERLINE SPAN)'''<br/>'''HYDRO DEMOLITION'''
+
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40_Replacement_of_Existing_Curb_(Safety_Barrier_Curb_on_Wing)_Section_Thru_Curb.gif]]
 +
|-
 +
| '''SECTION THRU BARRIER(*)'''
 +
|}
  
  
<center>[[Image:751.40_Deck_Repair_(with_exist_wearing_surface_CL_span)(Hydro_demolition)_Partial_Depth_Repair.gif]]</center>
+
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40_Replacement_of_Existing_Curb_(Safety_Barrier_Curb_on_Wing)_Section_Thru_Curb_Optional_Anchoring_System.gif]]
 +
|-
 +
| '''SECTION THRU BARRIER(*)'''<br/>'''(OPTIONAL ANCHORING SYSTEM)'''
 +
|}
 +
:Note:  See [[751.50 Standard Detailing Notes#I2. Resin & Cone Anchors|EPG 751.50 I2. Resin & Cone Anchors]] for appropriate notes.  For details not shown, see [[751.12 Barriers, Railings, Curbs and Fences|EPG 751.12 Barriers, Railings, Curbs and Fences]].
  
  
<center>'''PARTIAL DEPTH REPAIR'''</center>
+
'''REPLACEMENT OF EXISTING BARRIER AT END OF WING USING ANCHOR SYSTEMS'''
  
 +
'''INTEGRAL END BENTS'''
  
<center>[[Image:751.40_Deck_Repair_(with_exist_wearing_surface_CL_span)(Hydro_demolition)_Full_Depth_Repair.gif]]</center>
+
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| style="text-align:left; width: 250px" | (*)Extend existing horizontal bars 2'-3" into new concrete.</br>(**) Fit bar to follow transition face of barrier.</br>Note: For details of guardrail attachment, see barrier standard drawings. || rowspan="2" | [[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Integral_End_Bents)_Part_Elevation.gif]]
 +
|-
 +
| [[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Integral_End_Bents)_Anchor_Systems_at_Section_CC.gif]]
 +
|-
 +
| '''ANCHOR SYSTEMS AT SECTION C-C''' || '''PART ELEVATION'''
 +
|-
 +
|}
  
  
<center>'''FULL DEPTH AREA'''</center>
+
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Integral_End_Bents)_Section_AA.gif]] || [[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Integral_End_Bents)_Section_BB.gif]] || [[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Integral_End_Bents)_Section_CC.gif]]
 +
|-
 +
| '''SECTION A-A''' || '''SECTION B-B''' || '''SECTION C-C'''
 +
|-
 +
|}
  
  
<center>[[Image:751.40_Deck_Repair_(with_exist_wearing_surface_CL_span)(Hydro_demolition)_Full_Depth_Repair_in_Partial_Depth_Repair.gif]]</center>
+
'''REPLACEMENT OF EXISTING BARRIER AT END OF WING USING ANCHOR SYSTEMS'''
  
 +
'''NON-INTEGRAL END BENTS'''
  
<center>'''FULL DEPTH AREA IN PARTIAL DEPTH REPAIR'''</center>
+
{| style="text-align: center; margin: 0 auto;"
 
 
 
 
{|border="0" cellpadding="3"
 
 
 
|valign="top"|(1)||Remove existing wearing surface plus 1/4" of existing deck.  1/4" removal not required for Asphaltic Concrete Wearing Surface and Epoxy Polymer Concrete Overlay.
 
 
|-
 
|-
|valign="top"|(2)||Total surface hydro demolition of existing slab. See the Design Layout for the minimum depth of total surface hydro demolition.
+
| style="text-align:left; width: 250px" | (*)Extend existing horizontal bars 2'-3" into new concrete.</br>(**) Fit bar to follow transition face of barrier.</br>Note: For details of guardrail attachment, see barrier standard drawings. || rowspan="2" | [[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Non-Integral_End_Bents)_Part_Elevation.gif]]
 
|-
 
|-
|valign="top"|(3)||One inch vertical side shall be established outside the deteriorated area.  See Sec 704.
+
| [[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Non-Integral_End_Bents)_Anchor_Systems_at_Section_CC.gif]]
 
|-
 
|-
|valign="top"|(4)||1-3/4" (min.) for Latex Modified Concrete.<br/>2-1/4" (min.) for Low Slump Concrete or Silica Fume Concrete.
+
| '''ANCHOR SYSTEMS AT SECTION C-C''' || '''PART ELEVATION'''
 
|-
 
|-
|&nbsp;||Partial Depth Repair is not allowed for Low Slump Concrete.  Repairing Concrete Deck (Half-Soling) shall be substituted for Partial Depth Repair in the above details and not monolithically with the wearing surface.
 
 
|}
 
|}
  
===751.40.2.5 Filled Joints===
 
  
 +
{| style="text-align: center; margin: 0 auto;"
 +
|-
 +
| [[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Non-Integral_End_Bents)_Section_AA.gif]] || [[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Non-Integral_End_Bents)_Section_BB.gif]] | [[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Non-Integral_End_Bents)_Section_CC.gif]]
 +
|-
 +
| '''SECTION A-A''' || '''SECTION B-B''' || '''SECTION C-C'''
 +
|-
 +
|}
  
'''LATEX, LOW SLUMP OR SILICA FUME'''
 
  
 +
===751.40.4.3 Replacement of Existing Rail with Thrie Beam Rail===
  
<center>[[Image:751.40_Filled_Joints_Section_Thru_Joint.gif]]</center>
+
As a matter of policy, blockouts for thrie beam railings are required while FHWA does show similar systems without blockouts as NCHRP 350 approved. See the Structural Project Manager (SPM) or the Structural Liaison Engineer (SLE), if practical, to omit blockout. A design exception shall be required. Blockouts shall always be required on major routes.
  
 +
There are four systems for use on state routes.  In these four systems the connection design load used is 1.5 times plastic moment capacity (Mp) of W6 x 20 Post. The vertical clearance of System 3 shall be checked due to the obtruding lower connection.
  
<center>'''SECTION THRU JOINT'''</center>
+
{| class="wikitable" style="margin: 0 auto; text-align: center"
 +
|+
 +
| style="background:#BEBEBE" | '''[https://www.modot.org/bridge-standard-drawings Bridge Standard Drawings]'''
 +
|-
 +
| Thrie Beam Rails - THRIE
 +
|}
  
 +
===751.40.4.4 End Treatment Using Thrie Beam Rail===
  
 +
[[image:751.40.4.4.jpg|center|700px]]
  
'''ASPHALTIC CONCRETE OVERLAY'''
 
  
 +
[[image:751.40.4.4 clearance.jpg|center|700px]]
  
<center>[[Image:751.40_Filled_Joints_Section_Thru_Joint_(Asphaltic_Concrete_Overlay)_no_1.gif]]</center>
 
  
 +
Guidance for Design:
 +
:Adequate clearance to first post off bridge shall be required. (See also [https://www.modot.org/media/16893 Standard Plan 617.10] for new bridges.)
  
<center>'''SECTION THRU JOINT'''</center>
+
===751.40.4.5 Curb Blockouts===
  
 +
See [[751.1_Preliminary_Design#751.1.3.4_Barrier_or_Railing_Type.2C_Height_and_Guidelines_for_Curb_Blockouts | EPG 751.1.3.4 Barrier or Railing Type, Height and Guidelines for Curb Blockouts]] for usage guidance.
  
<center>[[Image:751.40_Filled_Joints_Section_Thru_Joint_(Asphaltic_Concrete_Overlay)_no_2.gif]]</center>
+
{| class="wikitable" style="margin: 0 auto; text-align: center"
 +
|+
 +
| style="background:#BEBEBE" | '''[https://www.modot.org/bridge-standard-drawings Bridge Standard Drawings]'''
 +
|-
 +
| Barrier Modifications – BEM & CBO/Curb Blockouts - CBO
 +
|}
  
 +
==751.40.5 Drainage==
  
<center>'''SECTION THRU JOINT'''</center>
+
===751.40.5.1 Structure with Wearing Surface Slab Drains - Details===
  
 +
'''Two material options may be used for slab drains:
  
 +
:'''1. Steel Slab Drains''' and inserts are only shown in the following details.
  
(*) Saw cut 1" deep and fill with concrete and asphalt joint sealer, hot-poured elastic type.
+
:'''2. Fiberglass Reinforced Polymer (FRP)''' drains may be used with the approval of the Structural Project Manager or Structural Liaison Engineer. See [https://epg.modot.org/index.php?title=751.10_General_Superstructure#751.10.3.2.1_New_Structure_Without_Wearing_Surface_Slab_Drains_-_Details EPG 751.10.3.2.1 New Structure Without Wearing Surface Slab Drains - Details] for guidance and details of FRP drains on new structures as an aid.
  
 +
:A positive mechanical connection must be used for attaching FRP drains to either existing steel drains or to new FRP inserts since welding cannot be used as is shown in the following details for steel drains. For example, using at least four bolt-through connectors (one per side) from new FRP drains into a new wearing surface or an existing steel drain, or using an epoxy adhesive in conjunction with at least two bolt-through connectors is required.  It has been shown that using a more viscous epoxy or anchoring gel is beneficial in order to avoid dripping during placement. Using epoxy adhesive or an anchoring gel by itself is not acceptable.
  
 +
:FRP drain may not fit exactly to the inside or to the outside of existing steel drain. The looseness of fit can be addressed by considering a combination of attachment details like mechanical connectors (to existing slab drain) plus either a viscous epoxy adhesive or a positive attachment to an exterior girder depending on the length of the slab drain extension.
  
'''EPOXY POLYMER CONCRETE OVERLAY'''
+
'''For new wearing surface over new slab, note on plans:'''
  
 +
:Piece "A" shall be cast in the concrete slab. Prior to placement of wearing surface, piece "B" shall be inserted into piece "A".
  
<center>[[Image:751.40_Filled_Joints_Section_Thru_Joint_(Epoxy_Polymer_Concrete_Overlay)_no_1.gif]]</center>
 
  
 +
'''FOR STRUCTURE WITH WEARING SURFACE'''<br/>'''(GIRDER DEPTH LESS THAN 48")'''
  
<center>'''SECTION THRU JOINT'''</center>
 
  
 +
<center>[[Image:751.40_Slab_Drain_Details_(Girder_Depth_Less_than_48_in.)_Part_Elev_of_Slab_at_Drain.gif]]</center>
  
  
<center>[[Image:751.40_Filled_Joints_Section_Thru_Joint_(Epoxy_Polymer_Concrete_Overlay)_no_2.gif]]</center>
+
<center>'''PART ELEVATION OF SLAB AT DRAIN'''</center>
  
  
<center>'''SECTION THRU JOINT'''</center>
 
  
===751.40.2.6 Temporary Traffic Control Device===
+
<center>[[Image:751.40_Slab_Drain_Details_(Girder_Depth_Less_than_48_in.)_Elev_of_Drain.gif]]</center>
  
  
 +
<center>'''ELEVATION OF DRAIN'''</center>
  
<center>[[Image:751.40_Temporary_Traffic_Control_Device_Section_Thru_Roadway.jpg]]</center>
+
{|border="0" align="center"
 
 
 
 
{|border="0" cellpadding="3"
 
  
|valign="top"|(*)||Show Barrier Curb as per District recommendation.  Typically Barrier Curb is shown when structure is on interstate and/or the rail is being removed.  Otherwise, show the dimension lines with 2' 0" dimension.
+
|*||Deck thickness minus 1/8" minus the depth of the scarification.
 
|-
 
|-
|valign="top"|(**)||If this dimension is less than 48", the temporary curb may have to be doweled in, check with Structural Project Manager.
+
|**||Do not include the depth of the scarification.
 
|}
 
|}
<center>'''PART SECTION THRU ROADWAY'''</center>
 
  
==751.40.3 Dimensions==
+
&nbsp;
===751.40.3.1 Concrete Wearing Surface===
+
&nbsp;
 +
&nbsp;
  
'''REPLACEMENT OF EXISTING EXPANSION DEVICE'''
 
'''PREFORMED COMPRESSION JOINT SEAL'''
 
'''(STRIP SEAL & SILICONE EXPANSION SEALANT DETAILS ARE SIMILAR)'''
 
  
  
  
<center>[[Image:751.40_Concrete_Wearing_Surface_(Low_Slump,_Silica_Fume,_Latex_or_Asphaltic).gif]]</center>
+
<center>[[Image:751.40_Slab_Drain_Details_(Girder_Depth_Less_than_48_in.)_Plan_of_Drain.gif]]</center>
  
  
<center>'''LOW SLUMP, SILICA FUME, LATEX OR ASPHALTIC CONCRETE WEARING SURFACE'''</center>
+
<center>'''PLAN OF DRAIN'''</center>
  
  
<center>[[Image:751.40_Concrete_Wearing_Surface_(Epoxy_Polymer).gif]]</center>
 
  
 +
'''FOR STRUCTURE WITH WEARING SURFACE'''<br/>'''(GIRDER DEPTH 48" AND OVER)'''
  
Note:  The contractor shall exercise care to ensure that spillage over joint edges is prevented and that a neat line is obtained along any terminating edge of the epoxy polymer concrete.
 
  
 +
{|border="0" cellpadding="5" align="center" style="text-align:center"
  
<center>'''EPOXY POLYMER CONCRETE WEARING SURFACE'''</center>
+
|rowspan="3"|[[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Part_Elevation_of_Slab_at_Drain.gif]]
 +
|[[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Elev_of_Drain.gif]]
 +
|-
 +
|'''ELEVATION OF DRAIN'''<!--cell a occupied by [[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Part_Elevation_of_Slab_at_Drain.gif]]-->
 +
|-
 +
|[[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Plan_of_Drain.gif]]<!--cell a occupied by [[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Part_Elevation_of_Slab_at_Drain.gif]]-->
 +
|-
 +
|'''PART ELEVATION OF SLAB AT DRAIN'''||'''PLAN OF DRAIN'''
 +
|}
  
 +
::{|border="0"
 +
 +
|valign="top"|*||If dimension is less than 1", drains shall be placed parallel to roadway.  Otherwise, place drains transverse to roadway.
 +
|-
 +
|valign="top"|**||Do not include the depth of the scarification.
 +
|-
 +
|valign="top"|***||Deck thickness minus 1/8" minus the depth of the scarification.
 +
|}
  
Note:
 
Concrete overlay shall be forced into the cavity under the armor angle.  Proper consolidation of the concrete shall be achieved by localized internal vibration.
 
  
When concrete is removed and expansion device armor is replaced, see Section 3.35 of this manual for the appropriate expansion device.
+
{|border="0" align="center" style="text-align:center"
  
 +
|colspan="2"|[[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Part_Plans_Showing_Bracket_Assembly.gif]]
 +
|-
 +
|'''DRAIN TRANSVERSE TO ROADWAY'''||'''DRAIN PARALLEL TO ROADWAY'''
 +
|-
 +
|&nbsp;
 +
|-
 +
|colspan="2"|'''PART PLANS SHOWING BRACKET ASSEMBLY'''
 +
|}
  
  
 +
'''FOR STRUCTURE WITH WEARING SURFACE'''<BR/>'''(CONTINUOUS CONCRETE STRUCTURES)'''
  
'''TYPICAL SECTION OF ELASTOMERIC EXPANSION DEVICE'''
 
  
 +
<center>[[Image:751.40_Slab_Drain_Details_(Continuous_Concrete_Structures)_Part_Section_Near_Drain.gif]]</center>
  
When Low Slump, Silica Fume, Latex or Asphaltic Concrete wearing surface is used, the elastomeric joint must be replace by another type of expansion device.
 
  
 +
<center>'''PART SECTION NEAR DRAIN'''</center>
  
<center>[[Image:751.40_Concrete_Wearing_Surface_(Epoxy_Polymer)_Typ_Section_of_Elastomeric_Exp_Device.gif]]</center>
 
  
  
<center>'''EPOXY POLYMER CONCRETE WEARING SURFACE'''</center>
+
<center>[[Image:751.40 Slab Drain Details (Continuous Concrete Structures) Elevation of Drain.gif]]</center>
  
  
 +
<center>'''ELEVATION OF DRAIN'''</center>
  
'''TYPICAL SECTIONS OF FLAT PLATE EXPANSION DEVICE'''
 
  
  
<center>[[Image:751.40_Concrete_Wearing_Surface_(Low_Slymp,_Silica_Fume,_Latex_or_Asphaltic)_Typ_Section_of_Flat_Plate_Exp_Device.gif]]</center>
+
<center>[[Image:751.40_Slab_Drain_Details_(Continuous_Concrete_Structures)_Plan_of_Drain.gif]]</center>
  
  
<center>'''LOW SLUMP, SILICA FUME, LATEX OR ASPHALTIC CONCRETE WEARING SURFACE'''</center>
+
<center>'''PLAN OF DRAIN'''</center>
  
  
{|border="0" cellpadding="3"
+
{|border="0" align="center"
  
|valign="top"|(*)||Latex, Low Slump or Silica Fume Concrete Wearing Surface.
+
|*||Deck thickness minus 1/8" minus the depth of the scarification.
|-
 
|valign="top"|(**)||When this dimension exceeds 3" and a Concrete Wearing Surface is used, tack weld a one inch bar chair to the plate for each 3" of plate to be covered by the Wearing Surface.
 
 
|-
 
|-
|valign="top"|(***)||Scarify existing slab.  See the Design Layout for the minimum depth of scarification.  Scarification not required for Asphalt Concrete Wearing Surface.
+
|**||Do not include the depth of scarification.
|-
 
|valign="top"|Note:||See Standard Plans for Steel Dams at Expansion Devices for Resurfacing Bridge Floors.
 
 
|}
 
|}
  
  
  
 +
'''FOR STRUCTURE WITH WEARING SURFACE'''<BR/>'''(VARIABLE DEPTH GIRDERS)'''
  
<center>[[Image:751.40_Concrete_Wearing_Surface_(Epoxy_Polymer)_Typ_Section_of_Flat_Plate_Exp_Device.gif]]</center>
 
  
 +
<center>[[Image:751.40_Slab_Drain_Details_(Variable_Depth_Girders)_Part_Elevation_of_Slab_at_Drain.gif]]</center>
  
<center>'''EPOXY POLYMER CONCRETE WEARING SURFACE'''</center>
 
  
 +
<center>'''PART ELEVATION OF SLAB AT DRAIN'''</center>
  
  
'''LATEX, LOW SLUMP, SILICA FUME, ASPHALTIC OR EPOXY POLYMER'''
+
Note:  For variable depth girders with drains in deeper section, let the deeper section control and use throughout the structure.
  
  
<center>[[Image:751.40 concrete wearing surface-typical section of exist curb outlet showing limits of epoxy seal.gif]]</center>
 
  
 +
<center>[[Image:751.40_Slab_Drain_Details_(Variable_Depth_Girders)_Typ_Section_Straight_Drain.gif]]</center>
  
<center>'''TYPICAL SECTION OF EXISTING CURB<br/>OUTLET SHOWING LIMITS OF EPOXY SEAL'''</center>
 
  
 +
<center>'''TYPICAL SECTION STRAIGHT DRAIN'''</center>
  
Note:
+
===751.40.5.2 Structure with Wearing Surface Round Slab Drains - Details===
  
(*) Dimension to edge of girder or stringer &plusmn;. For bridges that do not have girders or stringers use 2'-6", except that if with thrie beam rail, then use 4'-0".
+
'''FOR STRUCTURE WITH WEARING SURFACE'''<BR/>'''MISCELLANEOUS DETAILS - ROUND DRAINS'''
 
Consult with Structural Project Manager or Liaison for making work incidental to another item or use of pay item "Clean and Epoxy Seal".
 
  
 +
FRP round drains may be used optionally unless otherwise specified. See [https://epg.modot.org/index.php?title=751.10_General_Superstructure#751.10.3_Bridge_Deck_Drainage_-_Slab_Drains EPG 751.10.3 Bridge Deck Drainage – Slab Drains] for guidance and details as an aid. Specify nominal pipe size as needed referencing ASTM D2996. Specify outer diameter based on nominal pipe size necessary for drainage for coring the correct size hole in deck.
  
 +
Note: See EPG 751.10.3 Bridge Deck Drainage – Slab Drain for slab drain spacing.
  
<center>[[Image:751.40 concrete wearing surface-typical elevation of exist curb outlet showing limits of epoxy seal.gif]]</center>
 
  
 +
{|border="0" align="center" style="text-align:center"
  
<center>'''TYPICAL ELEVATION OF EXISTING CURB<br/>OUTLET SHOWING LIMITS OF EPOXY SEAL'''<br/>(Wearing surface not shown for clarity)</center>
+
|[[image:751.40.5.2 typical.jpg|center|275px]]
 +
|[[image:751.40.5.2 section.jpg|center|250px]]
 +
|-
 +
|'''TYPICAL PART PLAN'''||'''SECTION SHOWING BRACKET ASSEMBLY'''
 +
|}
  
  
  
'''SLAB EDGE REPAIR'''
+
<center>[[Image:751.40_Slab_Drain_Details_(Misc._Details_-_Round_Drains)_Typical_Part_Plan_of_Drain.gif]]</center>
  
  
If slab edge repair is specified on the Design Layout when the barrier curb is not removed or when full depth repair is not a pay item, the following detail shall be provided.
+
<center>'''TYPICAL PART PLAN OF DRAIN'''</center>
  
  
<center>[[Image:751.40_Concrete_Wearing_Surface_Slab_Edge_Repair_(Concrete_Edge_Repair)_no_1.gif]]</center>
+
<center>Note:  See [[751.50 Standard Detailing Notes|EPG 751.50 Standard Detailing Notes]] for appropriate notes.</center>
  
  
<center>'''CONCRETE EDGE REPAIR'''</center>
+
===751.40.5.3 Structure with Wearing Surface Raising Slab Drains or Scuppers - Details===
  
 +
'''FOR STRUCTURE WITH WEARING SURFACE'''<br/>'''RAISING SLAB DRAINS'''
  
If the barrier curb is removed when full depth repair and slab edge repair are pay items, the following detail shall be provided.
 
  
 +
<center>[[Image:751.40_Slab_Drain_Details_(Raising_Standard_Slab_Drains)_Part_Section_of_Drain.gif]]</center>
  
<center>[[Image:751.40_Concrete_Wearing_Surface_Slab_Edge_Repair_(Concrete_Edge_Repair)_no_2.gif]]</center>
 
  
 +
<center>'''PART SECTION OF DRAIN'''</center>
  
<center>'''CONCRETE EDGE REPAIR'''</center>
 
  
  
(*) If the dimension excceds 4", the repair extending to the edge of slab will be paid for as Full Depth Repair.
+
<center>[[Image:751.40_Slab_Drain_Details_(Raising_Standard_Slab_Drains)_Part_Plan_of_Existing_Drain.gif]]</center>
  
===751.40.3.2 Longitudinal Joint Details===
 
  
'''REPLACEMENT OF EXISTING EXPANSION DEVICE'''
+
<center>'''PART PLAN OF EXISTING DRAIN'''</center>
  
'''MEDIAN BARRIER CURB'''
+
<center>Note:<br/>Outside dimensions of drain extension are 7-1/4" x 3-1/4", and drain extension shall be galvanized in accordance with ASTM A123.</center>
  
  
 +
'''FOR STRUCTURE WITH WEARING SURFACE'''<br/>'''RAISING SCUPPERS'''
  
<center>[[Image:751.40_Longitudinal_Joint_Details_Median_Barrier_Curb_Section.gif]]</center>
 
  
 +
<center>[[Image:751.40_Slab_Drain_Details_(Details_for_Raising_Scuppers)_Typ_Section_thru_Scupper.gif]]</center>
  
<CENTER>'''SECTION THRU DOUBLE FACED MEDIAN BARRIER CURB'''</CENTER>
 
  
  
 +
<center>'''TYPICAL SECTION THRU SCUPPER'''</center>
  
  
<center>[[Image:751.40_Longitudinal_Joint_Details_Median_Barrier_Curb_Section_Detail_A.gif]]</center>
 
  
 +
<center>[[Image:751.40_Slab_Drain_Details_(Details_for_Raising_Scuppers)_Plan_of_Grate_Support_and_Scupper_Extension.gif]]</center>
  
<CENTER>'''DETAIL "A"'''</CENTER>
 
  
 +
<center>'''PLAN OF GRATE SUPPORT'''<BR/>'''AND'''<BR/>'''PLAN OF SCUPPER EXTENSION'''
  
  
{|border="0" cellpadding="3"
+
'''*''' Plate thicknesses should match those of existing scupper and existing grate.</center>
  
|(1)||May be cast vertical and saw cut to slant.
+
===751.40.5.4 Cored Slab Drains===
|-
+
Cored slab drains may be installed in areas where the existing drainage is a concern, but the deck is not in need of replacement. Typically, 4-inch diameter drains are installed vertically to avoid the deck reinforcing steel which is typically spaced at 5-inch centers. If necessary, larger diameter drains or angled drains may be used with approval of the SPM or SLE.
|valign="top"|(*)||Latex Concrete Wearing Surface = 1-3/4".<br/>Low Slump Concrete Wearing Surface = 2-1/4".
+
 
 +
{| border="1" class="wikitable" style="margin: 0 auto; text-align: center"
 +
|+
 +
| style="background:#BEBEBE" | '''[https://www.modot.org/bridge-standard-drawings Bridge Standard Drawings]'''
 
|-
 
|-
|valign="top"|(**)||Cut minimum 1/2" support notch (rought finish).  Remove any existing compression seal.
+
| Rehabilitation, Surfacing & Widening - RHB/Cored Slab Drain for Existing Bridge Deck [RHB18]
 
|}
 
|}
 +
 +
==751.40.6 Closure Pour==
  
  
==751.40.4 Curb Treatments==
+
Note:
  
===751.40.4.1 Replacement of Brush Curb with Safety Barrier Curb===
+
For closure pour on solid slab or voided slab bridges, use expansive concrete.
  
'''NON-INTEGRAL END BENTS'''
+
Release the forms before the closure pour is placed.
  
  
{|border="0" cellpadding="3" align="center" style="text-align:center"
 
  
|[[Image:751.40_Replacement_of_Brush_Curb_(Non-Integral_End_Bents)_Section_thru_Wing_Existing_Brush_Curb.gif]]
+
<center>[[Image:751.40_Closure_Pour_-_Part_Section_Thru_Roadway.gif]]</center>
|[[Image:751.40_Replacement_of_Brush_Curb_(Non-Integral_End_Bents)_Section_thru_Wing_Proposed_SBC.gif]]
 
|-
 
|'''EXISTING BRUSH CURB'''||'''PROPOSED SAFETY BARRIER CURB'''
 
|-
 
|&nbsp;
 
|-
 
|colspan="2"|'''SECTIONS THRU WING'''
 
|}
 
  
  
::::::::{|border="0"
+
<center>'''PART SECTION THRU ROADWAY'''</center>
  
|Note:||Remove existing Brush Curb above lower Const. Joint.
 
|-
 
|&nbsp;||For details not shown, see Section 3.30 of this manual.
 
|}
 
  
 +
==751.40.7 Design and Posting Considerations==
  
  
{|border="0" cellpadding="3" align="center" style="text-align:center"
+
Existing structures to redecked and/or widened should be evaluated to determine if the superstructure is considered to be structurally adequate. The structural adequacy check should be determined based on load ratings using the Load Factor Method. Strengthening of the superstructure will not be required if the minimum posting values shown below meet or exceed legal load requirements. In addition, there may be cases where the existing bridge posting is acceptable based on the bridge specific site conditions such as AADT, amount of truck traffic, overweight permit route, etc.
 +
 
 +
 +
{|border="0"
  
|[[Image:751.40_Replacement_of_Brush_Curb_(Non-Integral_End_Bents)_Section_thru_Slab_Existing_Brush_Curb.gif]]
+
|1)||H20 (one lane with Impact) [Posting Rating] ≥ 23 tons
|[[Image:751.40_Replacement_of_Brush_Curb_(Non-Integral_End_Bents)_Section_thru_Slab_Proposed_SBC.gif]]
 
 
|-
 
|-
|'''EXISTING BRUSH CURB'''||'''PROPOSED SAFETY BARRIER CURB'''
+
|2)||3S2 (one lane with impact) [Posting Rating] ≥ 40 tons
|-
 
|&nbsp;
 
|-
 
|colspan="2"|'''SECTIONS THRU SLAB'''
 
 
|}
 
|}
  
  
 +
Posting Rating = 86% of Load Factor Operating Rating (Refer to figures below for H20, 3S2 and MO5 criteria).
  
'''INTEGRAL END BENTS'''
+
If a structure is located within a commercial zone, then the following additional posting condition must be investigated:
  
 +
{|border="0"
  
{|border="0" cellpadding="3" align="center" style="text-align:center"
+
|3)||M05 (two lane with impact) [Operating Rating] ≥ 70 Tons (posting limit)
 
 
|[[Image:751.40_Replacement_of_Brush_Curb_(Integral_End_Bents)_Section_thru_Wing_Existing_Brush_Curb.gif]]
 
|[[Image:751.40_Replacement_of_Brush_Curb_(Integral_End_Bents)_Section_thru_Wing_Proposed_SBC.gif]]
 
|-
 
|'''EXISTING BRUSH CURB'''||'''PROPOSED SAFETY BARRIER CURB'''
 
|-
 
|&nbsp;
 
|-
 
|colspan="2"|'''SECTIONS THRU WING'''
 
 
|}
 
|}
  
 +
Any other overstresses or inadequacies (slab, substructure, etc.) shall be reported to the Structural Project Manager.
  
::::::::{|border="0"
+
Deck thickness for redecks shall be determined such that Posting will not be required or the existing posting is not lowered, and it is generally not less than original deck thickness.
  
|Note:||Remove existing Brush Curb above lower Const. Joint.
+
Deck thickness for widenings shall be existing thickness unless thicker slab does not create overall deck stiffening irregularities.
|}
 
  
 +
See Structural Project Manager if AASHTO minimum deck thickness can not be used on redecks and widenings.
  
  
{|border="0" cellpadding="3" align="center" style="text-align:center"
+
Future Wearing Surface (FWS) Loadings for widenings with concrete wearing surfaces - In addition to weight of wearing surface:
  
|[[Image:751.40_Replacement_of_Brush_Curb_(Integral_End_Bents)_Section_thru_Slab_Existing_Brush_Curb.gif]]
+
:Add FWS of 35 psf to the design of new girders if existing girders are sufficient for the 35 psf FWS
|[[Image:751.40_Replacement_of_Brush_Curb_(Integral_End_Bents)_Section_thru_Slab_Proposed_SBC.gif]]
+
|-
+
:Lower FWS loading to 15 psf if existing girders are not sufficient for FWS loading of 35 psf
|'''EXISTING BRUSH CURB'''||'''PROPOSED SAFETY BARRIER CURB'''
+
|-
+
:If existing girders are not sufficient for any FWS then lower FWS to FWS = 0.
|&nbsp;
+
|-
+
:The existing ratings should be reviewed to determine what wearing surface loads were used.  When necessary, the rating should be evaluated for acceptability of the proposed changes in the wearing surface loads and geometry.  Preliminary ratings that are based on estimated geometry shall be revised when the updated, final geometry is known.
|colspan="2"|'''SECTIONS THRU SLAB'''
 
|}
 
  
===751.40.4.2 Replacement of Existing Curb Using Anchor Systems===
 
  
'''SAFETY BARRIER CURB ON SLAB'''
 
  
 +
<center>[[Image:751.40_Posting_Rating_(H20_Legal_Truck).gif]]</center>
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_(Safety_Barrier_Curb_on_Slab)_Section_Thru_Curb.gif]]</center>
 
  
 +
<center>[[Image:751.40_Posting_Rating_(3S2_Truck).gif]]</center>
  
<center>'''SECTION THRU CURB'''</center>
 
  
 +
<center>[[Image:751.40_Posting_Rating_(MO5_Truck).gif]]</center>
  
 +
== 751.40.8 Design Information when using AASHTO Standard Specifications for Highway Bridges 17th Edition ==
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_(Safety_Barrier_Curb_on_Slab)_Section_Thru_Curb_Optional_Anchoring_System.gif]]</center>
 
  
 +
=== 751.40.8.1 Loadings ===
  
<center>'''SECTION THRU CURB'''<br/>'''(OPTIONAL ANCHORING SYSTEM)'''</center>
 
  
  
<center>Note:  See Section 4.0 for appropriate notes.</center>
+
==== 751.40.8.1.1 Live Load ====
  
 +
Structures shall be designed to carry the dead load, live load, impact (or dynamic effect of the live load), wind load and other forces, when they are applicable.
  
 +
Members shall be designed with reference to service loads and allowable stresses as provided in AASHTO (17th edition) Service Load Design Method (Allowable Stress Design) or with reference to factored load and factored strength as provided in AASHTO Strength Design Method (Load Factor Design). Load groups represent various combination of loads and forces to which a structure may be subjected. Group loading combinations for Service Load Design and Load Factor Design are given by AASHTO (17th edition) 3.22.1 and AASHTO (17th edition) Table 3.22.1A.
  
'''SAFETY BARRIER CURB ON WING'''
+
The live load shall consist of the applied moving load of vehicles and pedestrians. The design live load to be used in the design of bridges for the state system will be as stated on the Bridge Memorandum.
 +
*The design truck: HS20-44 or HS20-44 Modified
 +
*The design tandem (Military)
 +
*The design lane loading
  
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_(Safety_Barrier_Curb_on_Wing)_Section_Thru_Curb.gif]]</center>
+
'''Criteria'''
 +
#All widened or retrofitted bridges on the National Highway System and in commercial zones may be designed for HS20-44 Modified loading. All remaining bridges will be designed for HS20-44 loading.
 +
#The Design Tandem loading is to be checked on national highway system or when Alternate Military loading appears on the Bridge Memorandum.
 +
#Carrying members of each structure shall be investigated for the appropriate loading.
 +
#*Main carrying members include:
 +
#**Steel or Concrete stringers or girders.
 +
#**Longitudinally reinforced concrete slabs supported on transverse floor beams or substructure units (includes hollow slabs).
 +
#**Transversely reinforced concrete slabs supported by main carrying members parallel to traffic and over 8'-0" center to center. Use the formulas for moment in AASHTO Article 3.24.3.1 Case A.
 +
#**Steel grid floors when the main elements of the grid extend in a direction parallel to traffic, or with main elements transverse to traffic on supports more than 8'-0" apart.
 +
#**Timber floors and orthotropic steel decks.
 +
#The reduction in live load for calculating substructure members is based on AASHTO 3.12.1. See Live Load Distribution in the Load Distribution Section.
 +
 
  
 +
'''HS20-44 Truck Loading'''
  
<center>'''SECTION THRU CURB(*)'''</center>
+
The HS20-44 truck is defined below as one 8 kip axle load and two 32 kip axle loads spaced as shown.
 +
 
 +
<center>[[Image:751.40 loadings-hs20-44 truck loading(side).gif]]</center>
  
  
 +
Varies = Variable spacing 14’ to 30’ inclusive. Spacing to be used is that which produces the maximum stresses.
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_(Safety_Barrier_Curb_on_Wing)_Section_Thru_Curb_Optional_Anchoring_System.gif]]</center>
 
  
 +
<center>[[Image:751.40 loadings-hs20-44 truck loading(back).gif]]</center>
  
<center>'''SECTION THRU CURB(*)'''<br/>'''(OPTIONAL ANCHORING SYSTEM)</center>
+
<center>'''HS20-44 Design Truck'''</center>
  
  
Note:  See Section 4.0 for appropriate notes.  For details not shown, see Section 3.30 of this manual.
+
(*) In the design of timber floors and orthotropic steel decks (excluding transverse beams) for H-20 Loading, one axle load of 24 kips or two axle loads of 16 kip each, spaced 4 feet apart may be used, whichever produces the greater stress, instead of the 32 kip axle load shown.
  
 +
(**) For slab design, the center line of wheels shall be assumed to be one foot from face of cur
  
  
'''REPLACEMENT OF EXISTING CURB AT END OF WING USING ANCHOR SYSTEMS'''
+
'''HS20-44 Modified Truck Loading'''
  
'''INTEGRAL END BENTS'''
+
The HS20-44 Modified truck is defined below as one 10 kip axle load and
 +
two 40 kip axle loads spaced as shown. This is the same as HS20-44 truck modified by a factor of 1.25.
  
 +
<center>[[Image:751.40 loadings-hs20-44 modified truck loading(side).gif]]</center>
  
{|border="0" align="center" style="text-align:center"
 
  
|
+
Varies = Variable spacing 14’ to 30’ inclusive. Spacing to be used is that which produces the maximum stresses.
{|border="0" width="250" style="text-align:left"
 
  
|valign="top"|(*)||Extend existing horizontal bars<br/>2'-3" into new concrete.
 
|-
 
|valign="top"|(**)||Fit bar to follow transition face of curb.
 
|-
 
|valign="top"|Note:||For details of Guard Rail Attachment, see Sec. 3.30
 
|}
 
|rowspan="2"|[[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Integral_End_Bents)_Part_Elevation.gif]]
 
|-
 
|[[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Integral_End_Bents)_Anchor_Systems_at_Section_CC.gif]]
 
|-
 
|'''ANCHOR SYSTEMS AT SECTION C-C'''||'''PART ELEVATION'''
 
|}
 
  
 +
<center>[[Image:751.40 loadings-hs20-44 modified truck loading(back).gif]]</center>
  
 +
<center>'''HS20-44 Modified Design Truck'''</center>
  
{|border="0" align="center" style="text-align:center"
 
  
 +
(*) For slab design, the center line of wheels shall be assumed to be one foot from face of curb.
  
|[[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Integral_End_Bents)_Section_AA.gif]]
 
|[[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Integral_End_Bents)_Section_BB.gif]]
 
|[[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Integral_End_Bents)_Section_CC.gif]]
 
|-
 
|'''SECTION A-A'''||'''SECTION B-B'''||'''SECTION C-C'''
 
|-
 
|&nbsp;||&nbsp;||(Horizontal bars are not shown for clarity)
 
|}
 
  
 +
'''Design Tandem Loading'''
  
 +
The Design Tandem Loading is a two axle load each of 24 kips. These axles are spaced at 4'-0" centers. The transverse spacing of wheels shall be taken as 6'-0".
  
'''REPLACEMENT OF EXISTING CURB AT END OF WING USING ANCHOR SYSTEMS'''
+
<center>[[Image:751.40 loadings-design tandem loading(plan view).gif]]</center>
  
'''NON-INTEGRAL END BENTS'''
+
<center>'''Design Tandem Loading - Plan View'''</center>
  
  
{|border="0" align="center" style="text-align:center"
 
  
|
+
'''Design Lane Loading'''
{|border="0" width="250" style="text-align:left"
 
  
|valign="top"|(*)||Extend existing horizontal bars<br/>2'-3" into new concrete.
+
*For HS20-44 Truck, the design lane load shall consist of a load 640 lbs per linear foot, uniformly distributed in the longitudinal direction with a single concentrated load (or two concentrated loads in case of continuous spans for determination of maximum negative moment), so placed on the span as to produce maximum stress. The concentrated load and uniform load shall be considered as uniformly distributed over a 10'-0" width on a line normal to the center line of the lane.
|-
+
*For HS20-44 Modified Truck, use the HS20-44 truck modified by a factor of 1.25.
|valign="top"|(**)||Fit bar to follow transition face of curb.
 
|-
 
|valign="top"|Note:||For details of Guard Rail Attachment, see Sec. 3.30
 
|}
 
|rowspan="2"|[[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Non-Integral_End_Bents)_Part_Elevation.gif]]
 
|-
 
|[[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Non-Integral_End_Bents)_Anchor_Systems_at_Section_CC.gif]]
 
|-
 
|'''ANCHOR SYSTEMS AT SECTION C-C'''||'''PART ELEVATION'''
 
|}
 
  
  
 +
<center>[[Image:751.40 loadings-design lane loading.gif]]</center>
  
{|border="0" align="center" style="text-align:center"
+
<center>'''Design Lane Loading'''</center>
  
 +
*For the design of continuous structures, an additional concentrated load is placed in another span to create the maximum effect. For positive moments, only one concentrated load is used, combined with as many spans loaded uniformly as are required to produce the maximum moment.
  
|[[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Non-Integral_End_Bents)_Section_AA.gif]]
 
|[[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Non-Integral_End_Bents)_Section_BB.gif]]
 
|[[Image:751.40_Replacement_of_Existing_Curb_at_End_of_Wing_(Non-Integral_End_Bents)_Section_CC.gif]]
 
|-
 
|'''SECTION A-A'''||'''SECTION B-B'''||'''SECTION C-C'''
 
|-
 
|&nbsp;||&nbsp;||(Horizontal bars are not shown for clarity)
 
|}
 
  
===751.40.4.3 Replacement of Existing Curb with Thrie Beam Rail===
+
'''Standard Roadway Width'''
  
 +
:26'-0"  (up to 2 traffic lanes)
 +
:28'-0"  (up to 2 traffic lanes)
 +
:30'-0"  (up to 3 traffic lanes)
 +
:32'-0"  (up to 3 traffic lanes)
 +
:36'-0"  (up to 3 traffic lanes)
 +
:38'-0"  (up to 3 traffic lanes)
 +
:40'-0"  (up to 4 traffic lanes)
 +
:44'-0"  (up to 4 traffic lanes)
  
'''SYSTEM 2'''
+
==== 751.40.8.1.2 Impact ====
  
'''TYPICAL CONNECTION'''
+
Highway live loads shall be increased by a factor given by the following formula:
  
 +
<math>\, I = \frac {50}{L + 125}</math> &nbsp; <math>\,L </math> in feet
  
System 2:  Applicable for rehabs only with slab depths 22" or greater.  These are typically voided slabs. Connection design load is 1.5 times plastic moment capacity (Mp) of W6 x 20 Post.
+
For continuous spans, <math>\, L</math> to be used in this equation for negative moments is the average of two adjacent spans at an intermediate bent or the length of the end span at an end bent. For positive moments, <math>\, L</math> is the span length from center to center of support for the span under consideration.
  
 +
Impact is never to be more than 30 percent. It is intended that impact be included as part of the loads transferred from superstructure to substructure but not in loads transferred to footings or parts of substructure that are below the ground line.  The design of neoprene bearing pads also does not include impact in the design loads.
  
 +
==== 751.40.8.1.3 Collision Force ====
  
{|border="0" cellpadding="5" align="center"
+
Collision forces shall be applied to the barrier or railing in the design of the cantilever slab.  A force of 10 kips is to be applied at the top of the standard barrier or railing. This force is distributed through the barrier or railing to the slab.
  
|rowspan="2"|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_2)_Part_Section.gif]]
+
==== 751.40.8.1.4 Centrifugal Force ====
|valign="top"|'''Blockout-to-Post Conn.'''
 
Centerline 2 Holes 13/16"Ø in W6 x 20 Post flange and W6 x 15 Blockout flange
 
  
Centerline 2 Hex head bolt 5/8"Ø with two washers and hex nut in W6 x 20 Post flange
+
Structures on curves shall be designed for a horizontal radial force equal to the following percentage of the live load in all the lanes, without impact.
  
'''Thrie Beam-to-Blockout Conn.'''
+
<math>\, C = \frac {6.68 S^2}{R}</math>
  
Centerline 13/16" x 2-1/2" Vertical slotted hole in W6 x 15 Blockout flange (*)
+
Where:
Centerline 5/8"Ø Carriage bolt with one flat washer and hex nut
+
{|
 +
|<math>\, C</math>||= the centrifugal force in percent of the live load
 +
|-
 +
|<math>\, S</math>||= the design speed in miles per hour
 
|-
 
|-
|valign="top"|(*) Required on one side of web only, but may be provided on both sides of web at the contrator's option.
+
|<math>\, R</math>||= the radius of the curve in feet
 +
|}
 +
 
 +
This force shall be applied at 6 feet above the centerline of the roadway with one design truck being placed in each lane in a position to create the maximum effect. Lane loads shall not be used in calculating centrifugal forces.
  
(**) Use 10" from top of original slab (before any future wearing surface).  For 20" voided slabs reduce to 8", see Structural Project Manager. <!--column 1 occupied by cell[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_2)_Part_Section.gif]]-->
+
The effects of superelevation shall be taken into account.
|-
 
|valign="top"|<center>'''PART SECTION AT RAIL POST'''</center>
 
|rowspan="2"|(1) 2 Resin Anchor Systems that shall have a minimum ultimate pullout strength (each) of 72 kip in concrete with f'c = 4,000 psi to include:
 
2 Drilled holes 1-1/8"Ø (min.) in slab or as recommended by manufacturer<br/>2 Holes 1-1/4"Ø in post plate<br/>2 Threaded rod 1"Ø A449 H.S. snug tight 12" embedment in slab.<br/>2 Hardened locking washers 2-1/2"Ø
 
  
(2) 2 Resin Anchor Systems that shall have a minimum ultimate pullout strength (each) of 20.4 kip in concrete with f'c = 4,000 psi to include:
+
==== 751.40.8.1.5 Lateral Earth Pressure ====
2 Drilled holes 7/8"Ø (min.) in slab or as recommended by manufacturer<br/>2 Holes 1"Ø in post and post plate<br/>2 Threaded rod 3/4"Ø A449 H.S. snug tight 8" embedment in slab.<br/>2 Hardened locking washers
+
 
|}
+
Structures which retain fills shall be designed for active earth pressures as
  
{|border="0" align="center" style="text-align:center"
+
<math>\, P_a = 0.5 (\gamma K_a) H^2</math>
  
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_2)_Section_AA.gif]]
+
Where:
|width="25pt"|&nbsp;
+
{|
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_2)_Detail_B.gif]]
+
|<math>\, P_a</math>||colspan="2"|= active earth pressure per length (lb/ft)
 +
|-
 +
|<math>\, \gamma</math>||colspan="2"|= unit weight of the back fill soil = 120 lb/ft³
 +
|-
 +
|<math>\, K_a</math>||colspan="2"|= coefficient of active earth pressure as given by Rankine’s formula
 
|-
 
|-
|'''SECTION A-A'''||&nbsp;||'''DETAIL "B"'''
+
|<math>\, \gamma K_a</math>||= <math>\, p_a</math>||= equivalent fluid pressure (lb/ft³)(*)
 +
|-
 +
|<math>\, H</math>||colspan="2"|= height of the back fill soil (ft)
 
|}
 
|}
  
  
<center>Note:  Design weight of (12 gage) Thrie Beam Bridge Rail = 35#/lin. ft.</center>
+
'''Rankine's Formula'''
  
 +
The coefficient of active earth pressure <math>\, K_a</math> is:
  
'''DETAILS OF POST PLATE'''
+
<math>\, K_a = (cos \alpha) \Bigg( \frac {cos \alpha - \sqrt{cos^2 \alpha - cos^2 \phi}}{cos \alpha + \sqrt{cos^2 \alpha - cos^2 \phi}} \Bigg)</math>
  
 +
Where:
 +
{|
 +
|<math>\, \phi</math>||= angle of internal friction of the backfill soil (*)
 +
|-
 +
|<math>\, \alpha</math>|| = the angle of incline of the backfill
 +
|}
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_2)_Part_Elevation_1.gif]]</center>
+
If the backfill surface is level, angle a is zero and <math>\, K_a</math> is:
  
 +
<math>\, K_a = \frac {1 - sin \phi}{1 + sin \phi}</math>
  
<center>'''PART ELEVATION'''</center>
+
(*) Use the internal friction angle indicated on the Bridge Memorandum. However, if the friction angle is not determined, use the minimum equivalent fluid pressure value, <math>\, p_a</math> , of 45 lb/ft³ for bridges and retaining walls. For box culverts use a maximum of 60 lb/ft³ and a minimum of 30 lb/ft³ for fluid pressure.
  
  
 +
'''Live Load Surcharge'''
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_2)_Part_Elevation_2.gif]]</center>
+
An additional earth pressure shall be applied to all structures which have live loads within a distance of half the structure height. This additional force shall be equal to adding 2'-0" of fill to that presently being retained by the structure.
  
 +
==== 751.40.8.1.6 Longitudinal Forces (Braking Forces) ====
  
<center>'''PART ELEVATION'''</center>
+
A longitudinal force of 5% of the live load shall be applied to the structure. This load shall be 5% of the lane load plus the concentrated load for moment applied to all lanes and adjusted by the lane reduction factor. Apply this force at 6 feet above the top of slab and to be transmitted to the substructure through the superstructure.
  
 +
==== 751.40.8.1.7 Wind Load ====
  
 +
Wind loads shall be applied to the structure regardless of length.
  
'''DETAILS OF POST'''
+
The pressure generated by wind load is:
  
 +
<math>\, P = K V^2</math>
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_2)_Details_of_Post.gif]]</center>
+
Where:
 +
{|
 +
|<math>\, P</math>||= wind pressure in pounds per square foot
 +
|-
 +
|<math>\, V</math>||= design wind velocity = 100 miles per hour
 +
|-
 +
|<math>\, K</math>||= 0.004 for wind load
 +
|}
  
 +
Basic wind load (pressure) = 0.004 x (100)² = 40 lb/ft²
  
<center>'''DETAILS OF POST'''</center>
 
  
 +
'''Wind Load for Superstructure Design'''
  
{|border="0" align="center" style="text-align:center"
+
'''Transverse'''
  
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_2)_Section_CC.gif]]
+
A wind load of the following intensity shall be applied horizontally at right angles to the longitudinal axis of the structure.
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_2)_Section_DD.gif]]
+
*Trusses and Arches = 75 pounds per square foot  = <math>\, W_t</math>
|-
+
*Girders and Beams = 50 pounds per square foot (*) = <math>\, W_t</math>  (for plate girder lateral bracing check only)
|'''SECTION C-C'''||'''SECTION D-D'''
+
*The total force shall not be less than 300 pounds per linear foot in the plane of windward chord and 150 pounds per linear foot in the plane of the leeward chord on truss spans, and not less than 300 pounds per linear foot on girder spans.
|}
 
  
  
 +
'''Wind Load for Substructure Design'''
  
 +
Forces transmitted to the substructure by the superstructure and forces applied directly to the substructure by wind load shall be as follows:
  
  
'''SYSTEM 3'''
+
'''Forces from Superstructure: Wind on Superstructure'''
  
'''TYPICAL CONNECTION'''
+
'''Transverse'''
  
 +
A wind load of the following intensity shall be applied horizontally at right angles to the longitudinal axis of the structure.
 +
*Trusses and Arches = 75 pounds per square foot  = <math>\, W_t</math>
 +
*Girders and Beams  = 50 pounds per square foot (*) = <math>\, W_t</math>
  
System 3:  Applicable for rehab and widenings with slab depths between 8-1/2" and 19" inclusive.  Connection design load is 1.5 times plastic moment capacity (mp) of W6 x 20 Post.  Vertical clearance must be checked due to obtruding lower connection.
 
  
 +
''(*)  Use Wt = 60 lbs/ft²  for design wind force on girders and beams If the column height on a structure is greater than 50 feet, where the height is the average column length from ground line to bottom of beam.''
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_3)_Part_Section.gif]]</center>
+
The transverse wind force for a bent will be:
  
 +
<math>\, P = L \times H \times W_t</math>
  
<center>'''PART SECTION AT RAIL POST'''</center>
+
Where:
 
+
{|
 
+
|valign="top"|<math>\, L</math>||= length in feet = the average of two adjacent spans for intermediate bents and half of the length of the end span for end bents.
{|border="0" align="center" style="text-align:center"
+
|-
 
+
|valign="top"|<math>\, H</math>||= the total height of the girders, slab, barrier or raling and any superelevation of the roadway, in feet
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_3)_Section_AA.gif]]
 
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_3)_Detail_B.gif]]
 
 
|-
 
|-
|'''SECTION A-A'''||'''DETAIL "B"'''
+
|valign="top"|<math>\, W_t</math>|| =  wind force per unit area in pounds per square foot
 
|}
 
|}
  
 +
This transverse wind force will be applied at the top of the beam cap for the design of the substructure.
  
<center>Note: Design weight of (12 gage) Thrie Beam Bridge Rail = 35#/lin. ft.</center>
 
  
 +
'''Longitudinal (**)'''
  
'''DETAILS OF BENT PLATE'''
+
The standard wind force in the longitudinal direction shall be applied as a percentage of the transverse loading. Use approximately 25%.
  
 +
:{|
 +
|Truss and Arch Structures||<math>\, W_I</math>||= 75 x 0.25 = approximately 20 lbs/ft²
 +
|-
 +
|Girder Structures||<math>\, W_I</math>||= 50 x 0.25 = approximately 12 lbs/ft²
 +
|}
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_3)_Top_View.gif]]</center>
+
The total longitudinal wind force <math>\, P</math> will be:
  
 +
<math>\, P = L \times H \times W_I</math>
  
<center>'''TOP VIEW'''</center>
+
Where:
 +
{|
 +
|<math>\, L</math>||= the overall bridge length in feet
 +
|-
 +
|valign="top"|<math>\, H</math>||= the total height of the girders, slab, barrier or railing and anysuperelevation of the roadway, in feet
 +
|-
 +
|<math>\, W_I</math>||= wind force per unit area in pounds per square foot
 +
|}
  
 +
This longitudinal force is distributed to the bents based on their stiffness. (**)
  
 +
The longitudinal wind force for the bent will be applied at the top of the beam cap for the design of the substructure.
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_3)_.5_in_Plate.gif]]</center>
 
  
 +
'''Forces from Superstructure:  Wind on Live Load'''
  
<center>'''1/2" BENT PLATE'''</center>
+
A force of 100 pounds per linear foot of the structure shall be applied transversely to the structure along with a force of 40 pounds per linear foot longitudinally. These forces are assumed to act 6 feet above the top of slab.
 +
The transverse force is applied at the bents based on the length of the adjacent spans affecting them. The longitudinal force is distributed to the bents based on their stiffness. (**)
  
 +
(**) See [[751.2 Loads#751.2.4.6 Longitudinal Wind Force Distribution|EPG 751.2.4.6 Longitudinal Wind Force Distribution]].
  
'''DETAILS OF POST'''
 
  
 +
'''Forces Applied Directly to the Substructure'''
 +
 +
The transverse and longitudinal forces to be applied directly to the substructure elements shall be calculated from an assumed basic wind force of 40 lbs/ft². This wind force per unit area shall be multiplied by the exposed area of each substructure member in elevation (use front view for longitudinal force and side view for transversely force, respectively). These forces are acting at the center of gravity of the exposed portion of the member.
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_3)_Details_of_Post.gif]]</center>
+
A shape factor of 0.7 shall be used in applying wind forces to round substructure members.
  
 +
When unusual conditions of terrain or the special nature of a structure indicates, a procedure other than the Standard Specification may be used subject to approval of the Structural Project Manager.
  
<center>'''DETAILS OF POST'''</center>
+
==== 751.40.8.1.8 Temperature Forces ====
  
 +
Temperature stresses or movement need to be checked on all structures regardless of length. Generation of longitudinal temperature forces is based on stiffness of the substructure. (*)
  
{|border="0" align="center" style="text-align:center"
+
'''Coefficients'''
  
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_3)_Post_Stiffener.gif]]
+
:{|
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_3)_Post_Plate_Washer.gif]]
+
|Steel:||Thermal - 0.0000065 ft/ft/°F
 +
|-
 +
|Concrete:||Thermal - 0.0000060 ft/ft/°F
 +
|-
 +
| &nbsp;||Shrinkage  - 0.0002 ft/ft (***)
 
|-
 
|-
|'''POST STIFFENER'''||'''POST PLATE WASHER'''
+
| &nbsp;||Friction  - 0.65 for concrete on concrete
 
|}
 
|}
  
  
 +
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 +
|+'''Temperature Range From 60° F (**)'''
 +
|width="100pt"|&nbsp;||width="50pt"|Rise||width="50pt"|Fall||width="50pt"|Range
 +
|-
 +
|Steel Structures||60°F||80°F||140°F
 +
|-
 +
|Concrete Structures||30°F||40°F||70°F
 +
|}
  
'''SYSTEM 4'''
 
  
'''TYPICAL CONNECTION'''
+
(*) See [[751.2 Loads#751.2.4.7 Longitudinal Temperature Force Distribution|EPG 751.2.4.7 Longitudinal Temperature Force Distribution]].
  
 +
(**) Temperature Range for expansion bearing design and expansion devices design see [[751.11 Bearings|EPG 751.11 Bearings]] and [[751.13 Expansion Devices|EPG 751.13 Expansion Devices]], respectively.
  
System 4: Applicable for rehabs on Deck Girder, Box Girder and similar structures.
+
(***) When calculating substructure forces of concrete slab bridges, the forces caused by the shrinkage of the superstructure should be included with forces due to temperature drop. This force can be ignored for most other types of bridges.
  
 +
==== 751.40.8.1.9 Sidewalk Loading ====
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_4)_Part_Section.gif]]</center>
+
Sidewalk floors and their immediate support members shall be designed for a '''live load''' of 85 pounds per square foot of sidewalk area.  Girders, trusses, and other members shall be design for the following sidewalk live load:
  
 +
:{|
 +
|width="150pt"|Spans 0 to 25 feet||width="100pt"|85 lbs/ft²
 +
|-
 +
|Spans 26 to 100 feet||60 lbs/ft²
 +
|-
 +
|Spans over 100 feet||use the following formula
 +
|}
  
<center>'''PART SECTION AT RAIL POST'''</center>
+
<math>\, P = \Bigg( 30 + \frac {3000}{L} \Bigg) \Bigg( \frac {55-W}{50} \Bigg)</math>
  
 
+
Where:
{|border="0" align="center"
+
{|
 
+
|<math>\, P</math>||= live load per square foot, max. 60 lbs/ft²
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_4)_Optional_Tie_Connection.gif]]
+
|-
|Notes:
+
|<math>\, L</math>||= loaded length of sidewalk in feet
(*) CANTILEVER MAY VARY.<BR/>IF SLAB CANTILEVER LENGTH EXCEEDS 6:, CONSIDERATION SHALL BE GIVEN TO: (WITH THE RESULT THAT ANCHORAGE INTO SLAB LIES IN THE CANTILEVER PART OF SLAB)
 
 
 
(1) Anchorage into cantilever portion of slab provided original slab thickness allows for min. embedment and 1" cover (check negative moment in cantilever).
 
 
 
(2) Extending bent plate (within reason).
 
 
 
(3) Alternating method of attachment, i.e. System 1 or System 3 types and variations thereof, Consult Structural Project Manager.
 
 
|-
 
|-
|align="center"|'''OPTIONAL TIE CONNECTION'''
+
|<math>\, W</math>||= width of sidewalk in feet
 
|}
 
|}
  
 +
When sidewalk live loads are applied along with live load and impact, if the structure is to be designed by service loads, the allowable stress in the outside beam or stringer may be increased by 25 percent as long as the member is at least as strong as if it were not designed for the additional sidewalk load using the initial allowable stress. When the combination of sidewalk live load and traffic live load plus impact governs the design under the load factor method, use a b factor of 1.25 instead of 1.67.
  
'''SYSTEM 4 AND OPTIONAL SYSTEM 4'''
+
Unless a more exact analysis can be performed, distribution of sidewalk live loads to the supporting stringers shall be considered as applied 75 percent to the exterior stringer and 25 percent to the next stringer.
  
'''DETAILS OF BENT PLATE'''
+
==== 751.40.8.1.10 Other Loads ====
  
When a latex, a low slump or a silica fume concrete overlay is used, add the following detailis:
+
'''Stream Pressure'''
  
 +
Stream flow pressure shall be considered only in extreme cases. The affect of flowing water on piers shall not be considered except in cases of extreme high water and when the load applied to substructure elements is greater than that which is applied by wind on substructure forces at low water elevations.
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_4)_Part_Section_Thru_Plate.gif]]</center>
+
The pressure generated by stream flow is:
  
 +
<math>\, P = KV^2</math>
  
<center>'''PART SECTION THRU PLATE'''</center>
+
Where:
 +
{|
 +
|<math>\, P</math>||= stream pressure in pounds per square foot
 +
|-
 +
|<math>\, V</math>||= design velocity of water in feet per second
 +
|-
 +
|<math>\, K</math>||= shape constant for the surface the water is in contact with.
 +
|-
 +
|<math>\, K</math>||= 1.4 for square-ended piers
 +
|-
 +
|<math>\, K</math>||= 0.7 for circular piers
 +
|-
 +
|<math>\, K</math>||= 0.5 for angle-ended piers where the angle is 30 degrees or less
 +
|}
  
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_4)_Plan_of_Bent_Plate.gif]]</center>
+
'''Ice Forces'''
  
 +
Ice forces on piers shall be applied if they are indicated on the Bridge Memorandum.
  
<center>'''PLAN OF BENT PLATE'''</center>
 
  
 +
'''Buoyancy'''
  
<center>Note: Bar supports shall be galvanized Beam Bolsters.</center>
+
Buoyancy shall be considered when its effects are appreciable.
  
  
 +
'''Fatigue in Structural Steel'''
  
'''DETAILS OF POST'''
+
Steel structures subjected to continuous reversal of loads are to be designed for fatigue loading.
  
  
 +
'''Prestressing'''
  
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_4)_Details_of_Post.gif]]</center>
+
See [[751.22 P/S Concrete I Girders|EPG 751.22 P/S Concrete I Girders]].
  
  
<center>'''DETAILS OF POST'''</center>
+
'''Other Loads'''
  
 +
Other loads may need to be applied if they are indicated on the Bridge Memorandum. Otherwise see Structural Project Manager before applying any additional loads.
  
{|border="0" align="center" style="text-align:center"
+
==== 751.40.8.1.11 Group Loads ====
  
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_4)_Post_Stiffener.gif]]
+
'''Group Loading (Service Load Design)'''
|[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(System_4)_Post_Plate_Washer.gif]]
 
|-
 
|'''POST STIFFENER'''||'''POST PLATE WASHER'''
 
|}
 
  
 +
Group loading combinations are:
  
 
+
:{|
'''OPTIONAL SYSTEM 4'''
+
|GP I SL||width="350pt"| <math>\, = D+L+I</math> ||100%
 
 
'''TYPICAL CONNECTION'''
 
 
 
 
 
Optional system 4: Applicable for rehabs on Deck Girder and Box Girder with large cantilevers.
 
 
 
 
 
<center>[[Image:751.40_Replacement_of_Existing_Curb_with_Thrie_Beam_Rail_(Optional_System_4)_Part_Section.gif]]</center>
 
 
 
 
 
<center>'''PART SECTION AT RAIL POST'''</center>
 
 
 
 
 
{|border="0"
 
 
 
|(1)||'''Tie-to-Deck Girder Conn.
 
 
|-
 
|-
|&nbsp;||Centerline 2 Resin Anchor Systems to include:
+
|GP II SL||width="350pt"| <math>\, = D+W</math> ||125%
 
|-
 
|-
|&nbsp;||Centerline 2 Drilled holes 7/8"Ø (min.) or as recommended by manufacturer in girder
+
|GP III SL||width="350pt"| <math>\, = D+L+I+0.3W+WL+LF</math> ||125%
 
|-
 
|-
|&nbsp;||Centerline 2 Holes 1"Ø in 6" x 6" x 3/8" plate
+
|GP IV SL||width="350pt"| <math>\, = D+L+I+T</math> ||125%
 
|-
 
|-
|&nbsp;||Centerline 2 Threaded rod 3/4"Ø A449 H.S., snug tight, 5" embedment in girder
+
|GP V SL||width="350pt"| <math>\, = D+W+T</math> ||140%
 
|-
 
|-
|&nbsp;||Centerline 2 Hardened locking washers
+
|GP VI SL||width="350pt"| <math>\, = D+L+I+0.3W+WL+LF+T</math> ||140%
 +
|}
 +
 
 +
Where:
 +
{|
 +
|<math>\, D</math>||= dead load
 +
|-
 +
|<math>\, L</math>||= live load
 
|-
 
|-
|&nbsp;
+
|<math>\, I</math>||= live load impact
 +
|-
 +
|<math>\, W</math>||= wind load on structure
 +
|-
 +
|<math>\, WL</math>||= wind load on live load
 +
|-
 +
|<math>\, T</math>||= temperature force
 
|-
 
|-
|(2)||'''Bent Plate-to-Deck Conn.'''
+
|<math>\, LF</math>||= longitudinal force from live load
 +
|}
 +
 
 +
 
 +
 
 +
'''Group Loading (Load Factor Design)'''
 +
 
 +
Group loading combinations are:
 +
 
 +
:{|
 +
|GP I LF||<math>\, = 1.3[\beta_d D+1.67 (L+I)]</math>
 
|-
 
|-
|&nbsp;||Centerline 3 Bolts 1"Ø A325 H.S. snug tight, with hardened washers
+
|GP II LF||<math>\, = 1.3[\beta_d D+W]</math>
 
|-
 
|-
|&nbsp;||Centerline 3 Drilled holes 1-1/8"Ø (min.) in old concrete or as recommended by manufacturer
+
|GP III LF||<math>\, = 1.3[\beta_d D+L+I+0.3W+WL+LF]</math>
 
|-
 
|-
|&nbsp;||Centerline 3 Holes 1-1/4"Ø in bent plate and 9" x 16" x 3/8" plate
+
|GP IV LF||<math>\, = 1.3[\beta_d D+L+I+T]</math>
 
|-
 
|-
|&nbsp;
+
|GP V LF||<math>\, = 1.25[\beta_d D+W+T]</math>
 
|-
 
|-
|(3)||'''Post-to-Bent Plate Conn.'''
+
|GP VI LF||<math>\, = 1.25[\beta_d D+L+I +0.3W+WL+LF+T]</math>
 +
|}
 +
 
 +
Where:
 +
{|
 +
|<math>\, D</math>||= dead load
 
|-
 
|-
|&nbsp;||Centerline 2 Bolts 1"Ø A325 H.S. with hardened washers
+
|<math>\, L</math>||= live load
 
|-
 
|-
|&nbsp;||Centerline 2 Vertical slotted holes 1-1/16" x 1-1/2" in post flanges
+
|<math>\, I</math>||= live load impact
 
|-
 
|-
|&nbsp;||Centerline 2 Holes 1-1/16"Ø in bent plate and post plate washer
+
|<math>\, W</math>||= wind load on structure
 
|-
 
|-
|&nbsp;
+
|<math>\, WL</math>||= wind load on live load
 
|-
 
|-
|(4)||'''Post-to-Tie Conn.'''
+
|<math>\, T</math>||= temperature force
 
|-
 
|-
|&nbsp;||Centerline 2 Bolts 3/4"Ø A325 H.S. with hardened washers
+
|<math>\, LF</math>||= longitudinal force from live load
 
|-
 
|-
|&nbsp;||Centerline 2 Holes 15/16"Ø in post flange and 6" x 6" x 3/8" plate
+
|<math>\, \beta_d</math>||= coefficient, see AASHTO Table 3.22.1A
 
|}
 
|}
  
  
==751.40.5 Drainage==
+
Other group loadings in AASHTO Table 3.22.1A shall be used when they apply.
  
===751.40.5.1 Slab Drain Details===
+
=== 751.40.8.2 Distribution of Loads ===
  
'''FOR STRUCTURES WITH OVERLAYS'''<br/>'''(GIRDER DEPTH LESS THAN 48")'''
 
  
 +
==== 751.40.8.2.1 Distribution of Dead Load ====
  
<center>[[Image:751.40_Slab_Drain_Details_(Girder_Depth_Less_than_48_in.)_Part_Elev_of_Slab_at_Drain.gif]]</center>
+
'''Composite Steel or Prestressed Concrete Structures'''
  
 +
The dead load applied to the girders through the slab shall be:
  
<center>'''PART ELEVATION OF SLAB AT DRAIN'''</center>
 
  
 +
'''Dead Load 1'''
  
 +
Non-composite dead loads should be distributed to girders (stringers) on the basis of continuous spans over simple supports.
  
<center>[[Image:751.40_Slab_Drain_Details_(Girder_Depth_Less_than_48_in.)_Elev_of_Drain.gif]]</center>
+
'''Dead Load 2'''
  
 +
Composite loads shall be distributed equally to all girders. The following are all Dead Load 2 loads:
 +
:Barrier or railing
 +
:Future wearing surface on slab
 +
:Sidewalks
 +
:Fences
 +
:Protective coatings and waterproofing on slab
  
<center>'''ELEVATION OF DRAIN'''</center>
 
  
{|border="0" align="center"
+
'''Concrete Slab Bridges'''
  
|(*)||Deck thickness minus 1/8" minus the depth of the scarification.
+
Distribute entire dead load across full width of slab.
|-
 
|(**)||Do not include the depth of the scarification.
 
|}
 
  
&nbsp;
+
For longitudinal design, heavier portions of the slab may be considered as concentrated load for entry into the "Continuous Structure Analysis" computer program.
&nbsp;
 
&nbsp;
 
  
 +
For transverse bent design, consider the dead load reaction at the bent to be a uniform load across entire length of the transverse beam.
  
 +
==== 751.40.8.2.2 Distribution of Live Load ====
  
 +
Live loading to be distributed shall be the appropriate loading shown on the Bridge Memorandum.
 +
Applying Live Load to Structure
  
<center>[[Image:751.40_Slab_Drain_Details_(Girder_Depth_Less_than_48_in.)_Plan_of_Drain.gif]]</center>
 
  
 +
'''Superstructure'''
  
<center>'''PLAN OF DRAIN'''</center>
+
For application of live load to superstructure, the lane width is considered 12 feet. Each design vehicle has wheel lines which are 6 feet apart and adjacent design    vehicles must be separated by 4 feet. 
  
  
 +
'''Substructure'''
  
'''FOR STRUCTURES WITH OVERLAYS'''<br/>'''(GIRDER DEPTH 48" AND OVER)'''
+
To produce the maximum stresses in the main carrying members of substructure elements, multiple lanes are to be loaded simultaneously. The lane width is 12 feet. Partial lanes are not to be considered. Due to the improbability of coincident maximum loading, a reduction factor is applied to the number of lanes. This reduction however, is not applied in determining the distribution of loads to the stringers.
  
  
{|border="0" cellpadding="5" align="center" style="text-align:center"
+
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 
+
|+'''Distribution of Live Load to Beams and Girders'''
|rowspan="3"|[[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Part_Elevation_of_Slab_at_Drain.gif]]
+
!width="150pt"|Number of Lanes||width="150pt"|Percent
|[[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Elev_of_Drain.gif]]
 
 
|-
 
|-
|'''ELEVATION OF DRAIN'''<!--cell a occupied by [[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Part_Elevation_of_Slab_at_Drain.gif]]-->
+
|one or two lanes||100
 
|-
 
|-
|[[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Plan_of_Drain.gif]]<!--cell a occupied by [[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Part_Elevation_of_Slab_at_Drain.gif]]-->
+
|three lanes||90
 
|-
 
|-
|'''PART ELEVATION OF SLAB AT DRAIN'''||'''PLAN OF DRAIN'''
+
|four lanes or more||75
 
|}
 
|}
  
  
{|border="0"
+
'''Moment Distribution'''
  
|valign="top"|(*)||If dimension is less than 1", drains shall be placed parallel to roadway.  Otherwise, place drains transverse to roadway.
+
Moments due to live loads shall not be distributed longitudinally. Lateral distribution shall be determined from AASHTO Table 3.23.1 for interior stringers. Outside stringers distribute live load assuming the flooring to act as a simple span, except in the case of a span with a concrete floor supported by four or more stringers, then AASHTO 3.23.2.3.1.5 shall be applied. In no case shall an exterior stringer have less carrying capacity than an interior stringer.
|-
 
|valign="top"|(**)||Do not include the depth of the scarification.
 
|-
 
|valign="top"|(***)||Deck thickness minus 1/8" minus the depth of the scarification.
 
|}
 
  
  
{|border="0" align="center" style="text-align:center"
+
'''Shear Distribution'''
  
|colspan="2"|[[Image:751.40_Slab_Drain_Details_(Girder_Depth_48_in._and_over)_Part_Plans_Showing_Bracket_Assembly.gif]]
+
As with live load moment, the reactions to the live load are not to be distributed longitudinally. Lateral distribution of live load shall be that produced by assuming the flooring to act as simply supported. Wheel lines shall be spaced on accordance with AASHTO 3.7.6 and shall be placed in a fashion which provides the most contribution to the girder under investigation, regardless of lane configuration. The shear distribution factor at bents shall be used to design bearings and bearing stiffeners.
|-
 
|'''DRAIN TRANSVERSE TO ROADWAY'''||'''DRAIN PARALLEL TO ROADWAY'''
 
|-
 
|&nbsp;
 
|-
 
|colspan="2"|'''PART PLANS SHOWING BRACKET ASSEMBLY'''
 
|}
 
  
  
'''FOR STRUCTURES WITH OVERLAYS'''<BR/>'''(CONTINUOUS CONCRETE STRUCTURES)'''
+
'''Deflection Distribution'''
  
 +
Deflection due to live loads shall not be distributed longitudinally. Lateral distribution shall be determined by averaging the moment distribution factor and the number of wheel lines divided by the number of girder lines for all girders. The number of wheel lines shall be based on 12 foot lanes. The reduction in load intensity (AASHTO Article 3.12.1) shall not be applied.
  
<center>[[Image:751.40_Slab_Drain_Details_(Continuous_Concrete_Structures)_Part_Section_Near_Drain.gif]]</center>
+
Deflection Distribution Factor = &nbsp; <math>\, \cfrac {\big\{ \frac{2n}{N} \big\} + MDF}{2}</math>
  
 +
Where:
 +
{|
 +
|<math>\, n</math>||= number of whole 12 foot lanes on the roadway
 +
|-
 +
|<math>\, N</math>||= number of girder lines;
 +
|-
 +
|<math>\, MDF</math>||= Moment Distribution Factor.
 +
|}
  
<center>'''PART SECTION NEAR DRAIN'''</center>
 
  
 +
Example: 38'-0" Roadway (Interior Girder), &nbsp; <math>\, n=3</math>, &nbsp; <math>\, N=5</math>, &nbsp; <math>\, MDF=1.576</math>
  
 +
Deflection Distribution Factor = &nbsp; <math>\, \cfrac {\big\{ \frac{2 \times 3lanes}{5 girders} \big\} + 1.576}{2} = 1.388</math>
  
<center>[[Image:751.40 Slab Drain Details (Continuous Concrete Structures) Elevation of Drain.gif]]</center>
 
  
 +
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 +
|+'''Live Load Distribution Factors for Standard Roadway Widths'''
 +
!rowspan="2" width="75pt" |Roadway<br/>Width||rowspan="2" width="75pt"|Number<br/>Girders||rowspan="2" width="75pt"|Girder<br/>Spacing||colspan="3"|Exterior Girder||colspan="3"|Interior Girder||rowspan="2"|(1)
 +
|-
 +
!Mom.||Shear||Defl.||Mom.||Shear||Defl.
 +
|-
 +
|26’-0”||4||7’-6”||1.277||1.133||1.139||1.364||1.667||1.182||1.071
 +
|-
 +
|28’-0”||4||8’-2”||1.352||1.204||1.176||1.485||1.776||1.243||1.167
 +
|-
 +
|30’-0”||4||8’-8”||1.405||1.308||1.453||1.576||1.846||1.538||1.238
 +
|-
 +
|32’-0”||4||9’-2”||1.457||1.400||1.479||1.667||1.909||1.584||1.310
 +
|-
 +
|36’-0”||5||8’-2”||1.352||1.184||1.276||1.485||1.776||1.343||1.167
 +
|-
 +
|38’-0”||5||8’-8”||1.405||1.231||1.303||1.576||1.846||1.388||1.238
 +
|-
 +
|40’-0”||5||9’-0”||1.440||1.333||1.520||1.636||1.889||1.618||1.286
 +
|-
 +
|44’-0”||5||9’-9”||1.515||1.487||1.558||1.773||1.974||1.687||1.393
 +
|}
 +
<center> '''(1)''' Use when checking interior girder moment cyclical loading Case I Fatigue for one lane loading.</center>
  
<center>'''ELEVATION OF DRAIN'''</center>
 
  
 +
'''Distribution of Live Load to Substructure'''
  
 +
For substructure design the live load wheel lines shall be positioned on the slab to produce maximum moments and shears in the substructure. The wheel lines shall be distributed to the stringers on the basis of simple spans between stringers. The number of wheel lines used for substructure design shall be based on 12 foot lanes and shall not exceed the number of lanes times two with the appropriate percentage reduction for multiple lanes where applicable.
  
<center>[[Image:751.40_Slab_Drain_Details_(Continuous_Concrete_Structures)_Plan_of_Drain.gif]]</center>
+
In computing these stresses generated by the lane loading, each 12 foot lane shall be considered a unit. Fractional units shall not be considered.
  
  
<center>'''PLAN OF DRAIN'''</center>
+
'''Distribution of Loads to Slabs'''
  
 +
For simple spans, the span length shall be the distance center to center of supports but need not be greater than the clear distance plus the thickness of the slab. Slabs for girder and floor beam structures should be designed as supported on four sides.
  
{|border="0" align="center"
+
For continuous spans on steel stringers or on thin flanged prestressed beams (top flange width to thickness ratios > 4.0), the span length shall be the distance between edges of top flanges plus one quarter of each top flange width. When the top flange width to thickness  is < 4.0 the span distance shall be the clear span between edges of the top flanges.
  
|(*)||Deck thickness minus 1/8" minus the depth of the scarification.
+
When designing the slab for live load, the wheel line shall be placed 1 foot from the face of the barrier or railing if it produces a greater moment.
|-
 
|(**)||Do not include the depth of scarification.
 
|}
 
  
  
 +
'''Bending Moments in Slab on Girders'''
  
'''FOR STRUCTURES WITH OVERLAYS'''<BR/>'''(VARIABLE DEPTH GIRDERS)'''
+
The load distributed to the stringers shall be:
  
 +
<math>\, \Bigg( \frac {S + 2}{32} \Bigg) </math> &nbsp; P20 or P25 = Moment in foot-pounds per-foot  width of slab.
  
<center>[[Image:751.40_Slab_Drain_Details_(Variable_Depth_Girders)_Part_Elevation_of_Slab_at_Drain.gif]]</center>
+
Where:
 
+
{|
 
+
|<math>\, S</math>||= effective span length between girders in feet
<center>'''PART ELEVATION OF SLAB AT DRAIN'''</center>
+
|-
 +
|P20 or P25||= wheel line load for HS20 or HS20 Modified design Truck in kips.
 +
|}
  
 +
For slabs continuous over 3 or more supports, a continuity factor of 0.8 shall be applied.
  
Note:  For variable depth girders with drains in deeper section, let the deeper section control and use throughout the structure.
 
  
 +
'''Main Reinforcement Parallel to Traffic'''
  
 +
This distribution may be applied to special structure types when its use is indicated.
  
<center>[[Image:751.40_Slab_Drain_Details_(Variable_Depth_Girders)_Typ_Section_Straight_Drain.gif]]</center>
 
  
 +
'''Distribution of Live Load to Concrete Slab Bridges'''
  
<center>'''TYPICAL SECTION STRAIGHT DRAIN'''</center>
+
Live load for transverse beam, column and pile cap design shall be applied as concentrated loads of one wheel line. The number of wheel lines used shall not exceed the number of lanes x 2 with the appropriate reduction where applicable.
  
 +
For slab longitudinal reinforcement design, use live load moment distribution factor of 1/E for a one-foot strip slab with the appropriate percentage reduction.
  
 +
<math>\, E = 4' + 0.06S, E (max.) = 7'</math>
  
'''FOR STRUCTURES WITH OVERLAY'''<BR/>'''MISCELLANEOUS DETAILS - ROUND DRAINS'''
+
Where:
 
+
{|
 
+
|<math>\, E</math>||= Width of slab in feet over which a wheel is distributed
<center>Note:  See Section 3.30 for slab drain spacing.</center>
 
 
 
 
 
{|border="0" align="center" style="text-align:center"
 
 
 
|[[Image:751.40_Slab_Drain_Details_(Misc._Details_-_Round_Drains)_Typ_Part_Plan.gif]]
 
|[[Image:751.40_Slab_Drain_Details_(Misc._Details_-_Round_Drains)_Part_Section_Showing_Bracket_Assembly.gif]]
 
 
|-
 
|-
|'''TYPICAL PART PLAN'''||'''PART SECTION SHOWING BRACKET ASSEMBLY'''
+
|<math>\, S</math>||= Effective span length in feet.
 
|}
 
|}
  
 +
For slab deflection, use the following deflection factor for a one-foot strip slab without applying percentage reduction.
  
 +
Deflection Factor = (Total number of wheel line) / (width of the slab)
  
<center>[[Image:751.40_Slab_Drain_Details_(Misc._Details_-_Round_Drains)_Typical_Part_Plan_of_Drain.gif]]</center>
+
==== 751.40.8.2.3 Frictional Resistance ====
  
 +
The frictional resistance varies with different surfaces making contact. In the design of bearings, this resistance will alter how the longitudinal forces are distributed. The following table lists commonly encountered materials and their coefficients. These coefficients may be used to calculate the frictional resistance at each bent.
  
<center>'''TYPICAL PART PLAN OF DRAIN'''</center>
+
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 +
|-
 +
!colspan="4"|Frictional Resistance of Expansion Bearings
 +
|-
 +
!colspan="2"|Bearing Type||Coef.||General Data
 +
|-
 +
!colspan="2"|Type C Bearing
 +
|0.14
 +
|rowspan=10| Coef. of sliding friction<br/>steel to steel = 0.14
  
  
<center>Note:  See Section 4 for appropriate notes.</center>
 
  
 +
Coef. for pin and rocker<br/>type  bearing =
  
 +
<math>\, \frac {0.14 (Radius\ of\ pin)}{Radius\ of\ Rocker}</math>
  
'''FOR STRUCTURES WITH OVERLAYS'''<br/>'''RAISING STANDARD SLAB DRAINS'''
 
  
  
<center>[[Image:751.40_Slab_Drain_Details_(Raising_Standard_Slab_Drains)_Part_Section_of_Drain.gif]]</center>
+
Frictional Force = <br/>Reaction x Coef.
 
+
|-
 
+
!colspan="2"|6” Diameter Roller
<center>'''PART SECTION OF DRAIN'''</center>
+
|0.01
 
+
|-
 
+
!colspan="2"|Type D Bearing|| &nbsp;
 
+
|-
<center>[[Image:751.40_Slab_Drain_Details_(Raising_Standard_Slab_Drains)_Part_Plan_of_Existing_Drain.gif]]</center>
+
!Pin Diameter||Rocker Radius|| &nbsp;
 +
|-
 +
|2”||6.5”||0.0216
 +
|-
 +
|2”||7”||0.0200
 +
|-
 +
|2”||7.5”||0.0187
 +
|-
 +
|2”||8”||0.0175
 +
|-
 +
|2”||10.5”||0.0133
 +
|-
 +
!colspan="2"|PTFE Bearing
 +
|0.0600
 +
|}
  
  
<center>'''PART PLAN OF EXISTING DRAIN'''</center>
+
The design of a bent with one of the above expansion bearings will be based on the maximum amount of load the bearing can resist by static friction. When this static friction is overcome, the longitudinal forces are redistributed to the other bents.
  
 +
The maximum static frictional force at a bent is equal to the sum of the forces in each of the bearings. The vertical reaction used to calculate this maximum static frictional force shall be Dead Loads only  for all loading cases. Since the maximum longitudinal load that can be experienced by any of the above bearings is the maximum static frictional force, the effects of longitudinal wind and temperature can not be cumulative if their sum is greater than this maximum static frictional force.
  
Note:<br/>Outside dimensions of drain extension are 7-1/4" x 3-1/4", and drain extension shall be galvanized in accordance with ASTM A123.
+
Two conditions for the bents of the bridge are to be evaluated.
 +
#Consider the expansion bents to be fixed and the longitudinal loads distributed to all of the bents.
 +
#When the longitudinal loads at the expansion bearings are greater than the static frictional force, then the longitudinal force of the expansion bearings is equal to the dynamic frictional force. It is conservative to assume the dynamic frictional force to be zero causing all longitudinal loads to be distributed to the remaining bents.
  
 +
=== 751.40.8.3 Unit Stresses ===
  
'''FOR STRUCTURES WITH OVERLAYS'''<br/>'''DETAILS FOR RAISING SCUPPERS'''
 
  
 +
==== 751.40.8.3.1 Fatigue in Structural Steel ====
  
<center>[[Image:751.40_Slab_Drain_Details_(Details_for_Raising_Scuppers)_Typ_Section_thru_Scupper.gif]]</center>
+
Steel structures subjected to continuous reversal of loads are to be designed for fatigue loading.
  
 +
AADTT, annual average daily truck traffic (one direction), shall be indicated on the Bridge Memorandum. Based on AADTT, the fatigue case and corresponding stress cycles can be obtained from ''AASHTO Table 10.3.2A''.
  
<center>'''TYPICAL SECTION THRU SCUPPER'''</center>
+
When Case I fatigue is considered, it is necessary to check fatigue due to truck loading for both the 2,000,000 and over 2,000,000 stress cycles. For the over 2,000,000 stress cycles, the moment distribution factor for all stringers or girders (for fatigue stresses only) will be based on '''one''' lane loaded. For truck loading 2,000,000 cycles and lane loading 500,000 cycles, use the moment distribution factor based on two or more traffic lanes (same as for design moment).
  
 +
The number of cycles to be used in the fatigue design is dependent on the case number and type of load producing maximum stress as indicated in AASHTO Table 10.3.2A.
 +
The allowable fatigue stress range based on the fatigue stress cycles can be obtained from ''AASHTO Table 10.3.1A''.
  
 +
The type of live load used to determine the number of cycles will be the type of loading used to determine the maximum stress at the point under consideration.
  
<center>[[Image:751.40_Slab_Drain_Details_(Details_for_Raising_Scuppers)_Plan_of_Grate_Support_and_Scupper_Extension.gif]]</center>
+
In continuous beams, the maximum stresses may be produced by the truck loading at some points, but by lane loading at other points. However, if the lane loading governs, then the longitudinal members should also be checked for truck loading.
  
 +
Only live loading and impact stresses need to be considered when designing for fatigue.
  
<center>'''PLAN OF GRATE SUPPORT'''<BR/>'''AND'''<BR/>'''PLAN OF SCUPPER EXTENSION'''</center>
+
Fatigue criteria applies only when the stress range is one of tension to tension or reversal. The fatigue criteria does not apply to the stress range from compression to compression.
  
 +
All fracture critical structures, those which consist of only one or two main carrying members, trusses or single box girders, shall be considered as Non-redundant structures. Use the appropriate table which accompanies these structures.
  
(*) Plate thicknesses should match those of existing scupper and existing grate.
+
==== 751.40.8.3.2 Reinforced Concrete ====
  
 +
'''Allowable Stresses of Reinforcing Steel'''
  
==751.40.6 Closure Pour==
+
Tensile stress in reinforcement at service loads, <math>\, f_s</math>:
  
 +
{|
 +
!colspan="2" align="left"|Concrete
 +
|-
 +
|width="250pt"|Reinforcing Steel (Grade 40)||<math>\, f_s</math>||= 20,000 psi
 +
|-
 +
|width="250pt"|Reinforcing Steel (Grade 60)||<math>\, f_s</math>||= 24,000 psi
 +
|}
  
Note:
+
For compression stress in beams, see ''AASHTO Article 8.15.3.5''.
  
For closure pour on solid slab or voided slab bridges, use expansive concrete.
+
For compression stress in columns, see ''AASHTO Article 8.15.4''.
  
Release the forms before the closure pour is placed.
+
For fatigue stress limit, see ''AASHTO Article 8.16.8.3''.
  
 +
'''Fatigue in Reinforcing Steel'''
  
 +
For flexural members designed with reference to load factors and strengths by Strength Design Method, stresses at service load shall be limited to satisfy the requirements for fatigue.  Reinforcement should be checked for fatigue at all locations of peak service load stress ranges and at bar cut-off locations except for concrete deck slab in multi-girder applications.
  
<center>[[Image:751.40_Closure_Pour_-_Part_Section_Thru_Roadway.gif]]</center>
 
  
 +
'''Allowable Stress Range:''' <math>\, fr_{allow}</math>
  
<center>'''PART SECTION THRU ROADWAY'''</center>
+
The allowable stress range is found using the equation listed below and the minimum stresses from dead load, live load, and impact based on service loads.
  
 +
The term minimum stress level fmin for this formula indicates the algebraic minimum stress level: tension stress with a positive sign and compression stress with a negative sign.
  
==751.40.7 Design and Posting Considerations==
+
<math>\, fr_{allow} = 21 - 0.33 f_{min} + 8(r/h)</math>
 +
 
 +
Where:
 +
{|
 +
|<math>\, fr_{allow}</math>||= allowable stress range (ksi)
 +
|-
 +
|<math>\, f_{min}</math>||= algebraic minimum stress level ksi):
 +
|-
 +
| &nbsp;||positive if  tension, negative if compression.
 +
|-
 +
|valign="top"|<math>\, r/h</math>||= ratio of base radius to height of rolled-on transverse deformation; if the actual value is not know, 0.3 may be used.
 +
|-
 +
|<math>fr_{allow}</math>||= <math>\, 23.4 - 0.33 f_{min}</math> &nbsp; &nbsp; when <math>\, r/h
 +
= 0.3</math>
 +
|}
 +
 
 +
Fatigue research has shown that increasing minimum tensile stress results in a decrease in fatigue strength for a tension to tension stresses case.  The fatigue strength increases with a bigger compressive stress in a tension to compression stresses case.
  
  
Existing structures to redecked and/or widened should be evaluated to determine if the superstructure is considered to be structurally adequate. The structural adequacy check should be determined based on load ratings using the Load Factor Method. Strengthening of the superstructure will not be required if the minimum posting values shown below meet or exceed legal load requirements. In addition, there may be cases where the existing bridge posting is acceptable based on the bridge specific site conditions such as AADT, amount of truck traffic, overweight permit route, etc.
+
'''Actual Stress Range:''' <math>\, fr_{act}</math>
  
+
The actual stress range, <math>\, fr_{act}</math>, is found using dead load, live load, and impact from service loads.
{|border="0"
 
  
|1)||H20 (one lane with Impact) [Posting Rating] ≥ 23 tons
+
{|
 +
|<math>\, fr_{act}</math>||colspan="2"|= <math>\, f_{GT} - f_{LT}</math>
 +
|-
 +
|<math>\, f_{GT}</math>||colspan="2"|= greatest tension stress level (ksi), always positive.
 +
|-
 +
| &nbsp;||colspan="2"|(Not necessary to check compression to compression for fatigue.)
 +
|-
 +
|<math>\, f_{LT}</math>||colspan="2"|= algebraic least stress level  (ksi):
 +
|-
 +
| &nbsp;||<math>\, f_{LT}</math>||= positive if  the least stress is tension
 +
|-
 +
| &nbsp;|| &nbsp;||'''(tension to tension stresses)'''
 +
|-
 +
| &nbsp;||<math>\, f_LT</math>||= negative if  the least stress is compression
 
|-
 
|-
|2)||3S2 (one lane with impact) [Posting Rating] ≥ 40 tons
+
| &nbsp;|| &nbsp;||(tension to compression stresses)
 
|}
 
|}
  
  
Posting Rating = 86% of Load Factor Operating Rating (Refer to figures below for H20, 3S2 and MO5 criteria).
+
'''Tension and Compression Stress Computation'''
 +
 
 +
Tension and compression stress are determined by using the following formulae for double reinforced concrete rectangular beams.
  
If a structure is located within a commercial zone, then the following additional posting condition must be investigated:
+
<math>\, f_s</math> = tensile stress in reinforcement at service loads (ksi)
  
{|border="0"
+
:Tensile stress &nbsp; <math>\, f_s = \frac {M}{A_s j d}</math>
  
|3)||M05 (two lane with impact) [Operating Rating] ≥ 70 Tons (posting limit)
+
<math>\, f'_s</math> = compressive stress in reinforcement at service loads (ksi)
|}
 
  
Any other overstresses or inadequacies (slab, substructure, etc.) shall be reported to the Structural Project Manager.
+
:Compressive stress &nbsp; <math>\, f'_s = \frac {M}{A_s j d} \Bigg( \cfrac {k - \frac {d^1}{d}} {1 - k} \Bigg)</math>
  
Deck thickness for redecks shall be determined such that Posting will not be required or the existing posting is not lowered, and it is generally not less than original deck thickness.
+
Where:
  
Deck thickness for widenings shall be existing thickness unless thicker slab does not create overall deck stiffening irregularities.
+
<math>\, j = \cfrac {k^2 \Big( 1 - \frac {k}{c} \Big) + 2 \rho'n \Big( k - \frac {d'}{d} \Big) \Big( 1 - \frac {d'}{d} \Big)}{k^2 + 2 \rho'n \Big( k - \frac {d'}{d} \Big)}</math> &nbsp; &nbsp; &nbsp;'''Eq. 2.2-1'''
  
See Structural Project Manager if AASHTO minimum deck thickness can not be used on redecks and widenings.
 
  
 +
<math>\, k = \sqrt{2n \Bigg( \rho + \rho' \Bigg( \frac{d'}{d}\Bigg) \Bigg) + n^2 \big( \rho + \rho' \big)^2 - n \big( \rho + \rho' \big)}</math> &nbsp; &nbsp; &nbsp;'''Eq. 2.2-2'''
  
Future Wearing Surface (FWS) Loadings for widenings with concrete overlays - In addition to weight of overlay:
 
  
:Add FWS of 35 psf to the design of new girders if existing girders are sufficient for the 35 psf FWS
+
{|
+
|<math>\, \rho</math>||= tension reinforcement ratio, &nbsp; <math>\, \rho = \frac{A_s}{bd}</math>
:Lower FWS loading to 15 psf if existing girders are not sufficient for FWS loading of 35 psf
+
|-
+
|<math>\, \rho'</math>||= compression reinforcement ratio, &nbsp; <math>\, \rho' = \frac{A'_s}{bd}</math>
:If existing girders are not sufficient for any FWS then lower FWS to FWS = 0.
+
|-
+
|<math>\, A_s</math>||= area of tension reinforcement (sq. inch)
:The existing ratings should be reviewed to determine what wearing surface loads were used.  When necessary, the rating should be evaluated for acceptability of the proposed changes in the wearing surface loads and geometry.  Preliminary ratings that are based on estimated geometry shall be revised when the updated, final geometry is known.
+
|-
 +
|<math>\, A'_s</math>||= area of compression reinforcement (sq. inch)
 +
|-
 +
|<math>\, b</math>||= width of beam (inch)
 +
|-
 +
|<math>\, d</math>||= distance from extreme compression fiber to centroid of tension reinforcement (inch)
 +
|-
 +
|<math>\, d'</math>||= distance from extreme compression fiber to centroid of compression reinforcement (inch)
 +
|-
 +
|<math>\, jd</math>||= distance from tensile steel to resultant compression (inch)
 +
|-
 +
|<math>\, kd</math>||= distance from neutral plane to compression surface (inch)
 +
|-
 +
|<math>\, n</math>||= ratio of modulus of elasticity of steel to that of concrete
 +
|}
  
 +
=== 751.40.8.4 Standard Details ===
  
  
<center>[[Image:751.40_Posting_Rating_(H20_Legal_Truck).gif]]</center>
+
==== 751.40.8.4.1 Welding Details ====
  
 +
All welding shall be detailed in accordance with ANSI / AASHTO / AWS D1.5, Bridge Welding Code.
  
<center>[[Image:751.40_Posting_Rating_(3S2_Truck).gif]]</center>
+
For ASTM A709, Grade 36 steel  (Service Load Design <math>\, F_u</math> = 58,000 psi) the allowable shear stress in fillet welds (<math>\, F_V</math>) is:
  
 +
<math>\, F_V = 0.27 F_u</math>
  
<center>[[Image:751.40_Posting_Rating_(MO5_Truck).gif]]</center>
+
Where:
 +
{|
 +
|<math>\, F_V</math>||= allowable basic shear stress
 +
|-
 +
|<math>\, F_u</math>||= tensile strength of the electrode classification but not greater than the tensile strength of the connected part
 +
|}
  
== 751.40.8 Design Information when using AASHTO Standard Specifications for Highway Bridges 17th Edition ==
 
  
 +
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 +
|+'''Allowable Shear Loads for Fillet Welds (*)'''
 +
|'''Size of Fillet Weld'''<br/>(Inch)||'''Allowable Shear Loads per Length'''<br/>(Pound per lineal inch)
 +
|-
 +
|1/8”||1,380
 +
|-
 +
|3/16”||2,075
 +
|-
 +
|1/4"||2,770
 +
|-
 +
|5/16”||3,460
 +
|-
 +
|3/8”||4,150
 +
|-
 +
|1/2"||5,535
 +
|-
 +
|5/8”||6,920
 +
|-
 +
|3/4"||8,300
 +
|-
 +
|7/8”||9,690
 +
|-
 +
|1”||11,070
 +
|}
  
=== 751.40.8.1 Loadings ===
 
 
 
 
==== 751.40.8.1.1 Live Load ====
 
 
Structures shall be designed to carry the dead load, live load, impact (or dynamic effect of the live load), wind load and other forces, when they are applicable.
 
 
Members shall be designed with reference to service loads and allowable stresses as provided in AASHTO (17th edition) Service Load Design Method (Allowable Stress Design) or with reference to factored load and factored strength as provided in AASHTO Strength Design Method (Load Factor Design). Load groups represent various combination of loads and forces to which a structure may be subjected. Group loading combinations for Service Load Design and Load Factor Design are given by AASHTO (17th edition) 3.22.1 and AASHTO (17th edition) Table 3.22.1A.
 
  
The live load shall consist of the applied moving load of vehicles and pedestrians. The design live load to be used in the design of bridges for the state system will be as stated on the Design Layout.
+
(*) Allowable Shear Load  = <math>\, (0.27)(58000 psi)(0.707xSize of Weld)(L)</math>
*The design truck: HS20-44 or HS20-44 Modified
 
*The design tandem (Military)
 
*The design lane loading
 
  
 +
Where:
 +
{|
 +
|align="right"| <math>\, L</math>||= Effective Length, in inch
 +
|-
 +
|align="right"| <math>\, (0.707xSize of Weld)</math>||= Effective Throat, in inch
 +
|-
 +
|align="right"| <math>\, (0.707xSize of Weld)(L)</math>||= Effective weld area in sq. inch
 +
|}
  
'''Criteria'''
+
==== 751.40.8.4.2 Development and splicing of Reinforcement ====
#All widened or retrofitted bridges on the National Highway System and in commercial zones may be designed for HS20-44 Modified loading. All remaining bridges will be designed for HS20-44 loading.
 
#The Design Tandem loading is to be checked on national highway system or when Alternate Military loading appears on the Design Layout.
 
#Carrying members of each structure shall be investigated for the appropriate loading.
 
#*Main carrying members include:
 
#**Steel or Concrete stringers or girders.
 
#**Longitudinally reinforced concrete slabs supported on transverse floor beams or substructure units (includes hollow slabs).
 
#**Transversely reinforced concrete slabs supported by main carrying members parallel to traffic and over 8'-0" center to center. Use the formulas for moment in AASHTO Article 3.24.3.1 Case A.
 
#**Steel grid floors when the main elements of the grid extend in a direction parallel to traffic, or with main elements transverse to traffic on supports more than 8'-0" apart.
 
#**Timber floors and orthotropic steel decks.
 
#The reduction in live load for calculating substructure members is based on AASHTO 3.12.1. See Live Load Distribution in the Load Distribution Section.
 
  
 +
===== 751.40.8.4.2.1 General =====
  
'''HS20-44 Truck Loading'''
+
'''Development of Tension Reinforcement'''
  
The HS20-44 truck is defined below as one 8 kip axle load and two 32 kip axle loads spaced as shown.
+
Development lengths for tension reinforcement shall be calculated in accordance with AASHTO Article 8.25. Development length modification factors described in AASHTO Articles 8.25.3.2 and 8.25.3.3 shall only be used in situations where development length without these factors is difficult to attain. All other modification factors shown shall be used.
  
<center>[[Image:751.40 loadings-hs20-44 truck loading(side).gif]]</center>
+
Development lengths for tension reinforcement have been tabulated on the following pages and include the modification factors except those described above.
  
  
Varies = Variable spacing 14’ to 30’ inclusive. Spacing to be used is that which produces the maximum stresses.
+
'''Lap Splices of Tension Reinforcement'''
  
 +
Lap splices of reinforcement in tension shall be calculated in accordance with AASHTO Article 8.32.1 and 8.32.3. Class C splices are preferred when possible, however it is permissible to use Class A or B when physical space is limited. The designer shall satisfy AASHTO Table 8.32.3.2 when using Class A or B splices. It should be noted that As required is based on the stress encountered at the splice location, which is not necessarily the maximum stress used to design the reinforcement.
  
<center>[[Image:751.40 loadings-hs20-44 truck loading(back).gif]]</center>
+
Temperature and shrinkage reinforcement is assumed to fully develop the specified yield stresses. Therefore the development length shall not be reduced by (<math>\, A_s</math> required)/(<math>\, A_s</math> supplied).
  
<center>'''HS20-44 Design Truck'''</center>
+
Splice lengths for tension reinforcement have been tabulated on the following pages and include the development length modifications as described above.
  
  
(*) In the design of timber floors and orthotropic steel decks (excluding transverse beams) for H-20 Loading, one axle load of 24 kips or two axle loads of 16 kip each, spaced 4 feet apart may be used, whichever produces the greater stress, instead of the 32 kip axle load shown.
+
'''Development of Tension Hooks'''
  
(**) For slab design, the center line of wheels shall be assumed to be one foot from face of cur
+
Development of tension hooks shall be calculated in accordance with AASHTO Article 8.29. Hook length modification factors described in Articles 8.29.3.3 and 8.29.3.4 shall only be used in situations where hook length without these factors is difficult to attain. All other modification factors shown shall be used.
  
 +
Development lengths of tension hooks have been tabulated on the following pages and include the modification factors except those described above.
  
'''HS20-44 Modified Truck Loading'''
 
  
The HS20-44 Modified truck is defined below as one 10 kip axle load and
+
'''Development of Compression Reinforcement'''
two 40 kip axle loads spaced as shown. This is the same as HS20-44 truck modified by a factor of 1.25.
 
  
<center>[[Image:751.40 loadings-hs20-44 modified truck loading(side).gif]]</center>
+
Development lengths for compression reinforcement shall be calculated in accordance with AASHTO Article 8.26. Development length modification factors described in AASHTO Articles 8.26.2.1 and 8.26.2.2 shall only be used in situations where development length without these factors is difficult to attain. All other modification factors shown shall be used.
  
 +
Development lengths for compression reinforcement have been tabulated on the following pages and include the modification factors except those described above.
  
Varies = Variable spacing 14’ to 30’ inclusive. Spacing to be used is that which produces the maximum stresses.
 
  
 +
'''Lap Splices of Compression Reinforcement'''
  
<center>[[Image:751.40 loadings-hs20-44 modified truck loading(back).gif]]</center>
+
Lap splices of reinforcement in compression shall be calculated in accordance with AASHTO Article 8.32.1 and 8.32.4.
  
<center>'''HS20-44 Modified Design Truck'''</center>
+
Splice lengths for compression reinforcement have been tabulated on the following pages.
  
  
(*) For slab design, the center line of wheels shall be assumed to be one foot from face of curb.
+
'''Mechanical Bar Splices'''
  
 +
Mechanical bar splices may be used in situations where it is not possible or feasible to use lap splices. Mechanical bar splices shall meet the criteria of AASHTO Article 8.32.2. Refer to the manufacturers literature for more information on the design of mechanical bar splices.
  
'''Design Tandem Loading'''
+
===== 751.40.8.4.2.2 Development and Tension Lap Splice Lengths - Top Bars  (<math>\, F_y</math> = 60 ksi) =====
  
The Design Tandem Loading is a two axle load each of 24 kips. These axles are spaced at 4'-0" centers. The transverse spacing of wheels shall be taken as 6'-0".
 
  
<center>[[Image:751.40 loadings-design tandem loading(plan view).gif]]</center>
+
<center>[[Image:751.40 reinforcement- Development and Tension Lap Splice Lengths - Top Bars (Fy = 60 ksi).gif]]</center>
  
<center>'''Design Tandem Loading - Plan View'''</center>
 
  
 +
Top reinforcement is placed so that more than 12” of concrete is cast below the reinforcement.
  
 +
Class A splice =1.0 <math>\, L_d</math>, Class B splice =1.3 <math>\, L_d</math>, Class C splice =1.7 <math>\, L_d</math>
  
'''Design Lane Loading'''
+
Use development and tension lap splices of <math>\, f'_c</math> = 4 ksi for concrete strengths greater than 4 ksi.
  
*For HS20-44 Truck, the design lane load shall consist of a load 640 lbs per linear foot, uniformly distributed in the longitudinal direction with a single concentrated load (or two concentrated loads in case of continuous spans for determination of maximum negative moment), so placed on the span as to produce maximum stress. The concentrated load and uniform load shall be considered as uniformly distributed over a 10'-0" width on a line normal to the center line of the lane.
+
===== 751.40.8.4.2.3 Development and Tension Lap Splice Lengths - Other Than Top Bars (<math>\, F_y</math> = 60 ksi) =====
*For HS20-44 Modified Truck, use the HS20-44 truck modified by a factor of 1.25.
 
  
  
<center>[[Image:751.40 loadings-design lane loading.gif]]</center>
+
<center>[[Image:751.40 reinforcement- Development and Tension Lap Splice Lengths - Other Than Top Bars (Fy = 60 ksi).gif]]</center>
  
<center>'''Design Lane Loading'''</center>
 
  
*For the design of continuous structures, an additional concentrated load is placed in another span to create the maximum effect. For positive moments, only one concentrated load is used, combined with as many spans loaded uniformly as are required to produce the maximum moment.
+
Class A splice =1.0 <math>\, L_d</math>, Class B splice =1.3 <math>\, L_d</math>, Class C splice =1.7 <math>\, L_d</math>
  
 +
Use development and tension lap splices of <math>\, f'_c</math> = 4 ksi for concrete strengths greater than 4 ksi.
  
'''Standard Roadway Width'''
+
===== 751.40.8.4.2.4 Development and Lap Splice Lengths - Bars in Compression (<math>\, F_y</math> = 60 ksi) =====
  
:26'-0"  (up to 2 traffic lanes)
 
:28'-0"  (up to 2 traffic lanes)
 
:30'-0"  (up to 3 traffic lanes)
 
:32'-0"  (up to 3 traffic lanes)
 
:36'-0"  (up to 3 traffic lanes)
 
:38'-0"  (up to 3 traffic lanes)
 
:40'-0"  (up to 4 traffic lanes)
 
:44'-0"  (up to 4 traffic lanes)
 
  
==== 751.40.8.1.2 Impact ====
+
<center>[[Image:751.40 reinforcement- Development and Lap Splice Lengths - Bars in Compression (Fy = 60 ksi).gif]]</center>
  
Highway live loads shall be increased by a factor given by the following formula:
 
  
<math>\, I = \frac {50}{L + 125}</math> &nbsp; <math>\,L </math> in feet
+
Development length for spirals, <math>\, L_d</math>, <math>\, _{spiral}</math>, should be used if reinforcement is enclosed in a spiral of not less than 1/4” diameter and no more than 4” pitch. See AASHTO 8.26 for special conditions.
  
For continuous spans, <math>\, L</math> to be used in this equation for negative moments is the average of two adjacent spans at an intermediate bent or the length of the end span at an end bent. For positive moments, <math>\, L</math> is the span length from center to center of support for the span under consideration.
+
All values are for splices with the same size bars. For different size bars, see AASHTO 8.32.4.
  
Impact is never to be more than 30 percent. It is intended that impact be included as part of the loads transferred from superstructure to substructure but not in loads transferred to footings or parts of substructure that are below the ground line.  The design of neoprene bearing pads also does not include impact in the design loads.
+
(*) Lap splices for #14 and #18 bars are not permitted except as column to footing dowels.
  
==== 751.40.8.1.3 Collision Force ====
+
===== 751.40.8.4.2.5 Development of Standard Hooks in Tension, Ldh  (<math>\, F_y</math> = 60 ksi) =====
  
Collision forces shall be applied to the barrier curb in the design of the cantilever slab.  A force of 10 kips is to be applied at the top of the standard barrier curb. This force is distributed through the barrier curb to the slab.
+
The development length, <math>\, L_{dh}</math>, is measured from the critical section to the outside edge of hook. The tabulated values are valid for both epoxy and uncoated hooks.
  
==== 751.40.8.1.4 Centrifugal Force ====
 
  
Structures on curves shall be designed for a horizontal radial force equal to the following percentage of the live load in all the lanes, without impact.
+
<center>[[Image:751.40 reinforcement- Development of Standard Hooks in Tension, Ldh (Fy = 60 ksi).gif]]</center>
  
<math>\, C = \frac {6.68 S^2}{R}</math>
 
  
Where:
+
'''Case A''' - For #11 bar and smaller, side cover (normal to plane of hook) less than 2 1/2 inches and for a 90 degree hook with cover on the hook extension less than 2 inches.
{|
 
|<math>\, C</math>||= the centrifugal force in percent of the live load
 
|-
 
|<math>\, S</math>||= the design speed in miles per hour
 
|-
 
|<math>\, R</math>||= the radius of the curve in feet
 
|}
 
  
This force shall be applied at 6 feet above the centerline of the roadway with one design truck being placed in each lane in a position to create the maximum effect. Lane loads shall not be used in calculating centrifugal forces.
+
'''Case B''' - For #11 bar and smaller, side cover (normal to plane of hook) greater than 2 1/2 inches and for a 90-dgree hook with cover on the hook extension 2 inches or greater.
  
The effects of superelevation shall be taken into account.
+
(*) See Structural Project Manager before using #14 or #18 hook.
  
==== 751.40.8.1.5 Lateral Earth Pressure ====
+
{| border="0" cellpadding="3" cellspacing="1" align="center" style="text-aling:center"
  
Structures which retain fills shall be designed for active earth pressures as
+
| rowspan="4"|[[Image:751.40 reinforcement-DETAIL NEAR FREE EDGE OR CONSTRUCTION JOINT.gif]]
 
+
| rowspan="4" width="40px"|&nbsp;
<math>\, P_a = 0.5 (\gamma K_a) H^2</math>
+
|[[Image:751.40 reinforcement- HOOKED-BAR DETAILS FOR DEVELOPMENT OF STANDARD HOOKS.gif]]
 
 
Where:
 
{|
 
|<math>\, P_a</math>||colspan="2"|= active earth pressure per length (lb/ft)
 
 
|-
 
|-
|<math>\, \gamma</math>||colspan="2"|= unit weight of the back fill soil = 120 lb/ft³
+
|(1) = <math>\,4d_b</math> (#3 thru #8)
 
|-
 
|-
|<math>\, K_a</math>||colspan="2"|= coefficient of active earth pressure as given by Rankine’s formula
+
|(1) = <math>\,5d_b</math> (#9, #10 and #11)
 
|-
 
|-
|<math>\, \gamma K_a</math>||= <math>\, p_a</math>||= equivalent fluid pressure (lb/ft³)(*)
+
|(1) = <math>\,6d_b</math> (#14 and #18)
 
|-
 
|-
|<math>\, H</math>||colspan="2"|= height of the back fill soil (ft)
+
!DETAILS NEAR FREE EDGE<br/>OR CONSTRUCTION JOINT||&nbsp;||HOOKED-BAR DETAILS FOR<br/>DEVELOPMENT OF STANDARD HOOKS
 
|}
 
|}
  
 +
===== 751.40.8.4.2.6 Development of Uncoated Grade 40 Deformed Bars in Tension, <math>\, L_d</math> (AASHTO 8.25) =====
  
'''Rankine's Formula'''
 
  
The coefficient of active earth pressure <math>\, K_a</math> is:
+
{|border="1" style="text-align:center;" cellpadding="5" align="center" cellspacing="0"
 
+
|+'''Bars spaced laterally less than 6 inches on center or less than 3 inches concrete cover in direction of the spacing'''
<math>\, K_a = (cos \alpha) \Bigg( \frac {cos \alpha - \sqrt{cos^2 \alpha - cos^2 \phi}}{cos \alpha + \sqrt{cos^2 \alpha - cos^2 \phi}} \Bigg)</math>
+
!rowspan="2" width="50pt"|Bar||colspan="2"| <math>\, f'_c</math> = 3 ksi||colspan="2"|<math>\, f'_c</math> = 4 ksi||colspan="2"|<math>\, f'_c</math> = 5 ksi
 
+
|-
Where:
+
|width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar||width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar||width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar
{|
+
|-
|<math>\, \phi</math>||= angle of internal friction of the backfill soil (*)
+
|#3||12||12||12||12||12||12
 +
|-
 +
|#4||12||12||12||12||12||12
 
|-
 
|-
|<math>\, \alpha</math>|| = the angle of incline of the backfill
+
|#5||12||14||12||14||12||14
|}
+
|-
 
+
|#6||13||19||12||17||12||17
If the backfill surface is level, angle a is zero and <math>\, K_a</math> is:
+
|-
 
+
|#7||18||25||16||22||14||20
<math>\, K_a = \frac {1 - sin \phi}{1 + sin \phi}</math>
+
|-
 
+
|#8||23||33||20||28||18||25
(*) Use the internal friction angle indicated on the Design Layout. However, if the friction angle is not determined, use the minimum equivalent fluid pressure value, <math>\, p_a</math> , of 45 lb/ft³ for bridges and retaining walls. For box culverts use a maximum of 60 lb/ft³ and a minimum of 30 lb/ft³ for fluid pressure.
+
|-
 
+
|#9||30||41||26||36||23||32
 
+
|-
'''Live Load Surcharge'''
+
|#10||38||52||33||45||29||41
 
+
|-
An additional earth pressure shall be applied to all structures which have live loads within a distance of half the structure height. This additional force shall be equal to adding 2'-0" of fill to that presently being retained by the structure.
+
|#11||46||64||40||56||36||50
 
 
==== 751.40.8.1.6 Longitudinal Forces (Braking Forces) ====
 
 
 
A longitudinal force of 5% of the live load shall be applied to the structure. This load shall be 5% of the lane load plus the concentrated load for moment applied to all lanes and adjusted by the lane reduction factor. Apply this force at 6 feet above the top of slab and to be transmitted to the substructure through the superstructure.
 
 
 
==== 751.40.8.1.7 Wind Load ====
 
 
 
Wind loads shall be applied to the structure regardless of length.
 
 
 
The pressure generated by wind load is:
 
 
 
<math>\, P = K V^2</math>
 
 
 
Where:
 
{|
 
|<math>\, P</math>||= wind pressure in pounds per square foot
 
 
|-
 
|-
|<math>\, V</math>||= design wind velocity = 100 miles per hour
+
|#14||63||87||54||76||49||68
 
|-
 
|-
|<math>\, K</math>||= 0.004 for wind load
+
|#18||81||113||70||98||63||88
 
|}
 
|}
  
Basic wind load (pressure) = 0.004 x (100)² = 40 lb/ft²
 
  
 
+
{|border="1" style="text-align:center;" cellpadding="5" align="center" cellspacing="0"
'''Wind Load for Superstructure Design'''
+
|+'''Bars spaced laterally 6 inches or more on center and at least 3 inches concrete cover in direction of the spacing'''
 
+
!rowspan="2" width="50pt"|Bar||colspan="2"| <math>\, f'_c</math> = 3 ksi||colspan="2"|<math>\, f'_c</math> = 4 ksi||colspan="2"|<math>\, f'_c</math> = 5 ksi
'''Transverse'''
+
|-
 
+
|width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar||width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar||width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar
A wind load of the following intensity shall be applied horizontally at right angles to the longitudinal axis of the structure.
+
|-
*Trusses and Arches = 75 pounds per square foot  = <math>\, W_t</math>  
+
|#3||12||12||12||12||12||12
*Girders and Beams = 50 pounds per square foot (*) = <math>\, W_t</math> (for plate girder lateral bracing check only)
+
|-
*The total force shall not be less than 300 pounds per linear foot in the plane of windward chord and 150 pounds per linear foot in the plane of the leeward chord on truss spans, and not less than 300 pounds per linear foot on girder spans.
+
|#4||12||12||12||12||12||12
 
+
|-
 
+
|#5||12||12||12||12||12||12
'''Wind Load for Substructure Design'''
+
|-
 
+
|#6||12||15||12||14||12||14
Forces transmitted to the substructure by the superstructure and forces applied directly to the substructure by wind load shall be as follows:
+
|-
 
+
|#7||15||20||13||18||12||16
 
+
|-
'''Forces from Superstructure: Wind on Superstructure'''
+
|#8||19||26||16||23||15||20
 
+
|-
'''Transverse'''
+
|#9||24||33||21||29||19||26
 
+
|-
A wind load of the following intensity shall be applied horizontally at right angles to the longitudinal axis of the structure.
+
|#10||30||42||26||36||23||33
*Trusses and Arches = 75 pounds per square foot  = <math>\, W_t</math>  
+
|-
*Girders and Beams  = 50 pounds per square foot (*) = <math>\, W_t</math>
+
|#11||37||52||32||45||29||40
 
 
 
 
''(*)  Use Wt = 60 lbs/ft²  for design wind force on girders and beams If the column height on a structure is greater than 50 feet, where the height is the average column length from ground line to bottom of beam.''
 
 
 
The transverse wind force for a bent will be:
 
 
 
<math>\, P = L \times H \times W_t</math>
 
 
 
Where:
 
{|
 
|valign="top"|<math>\, L</math>||= length in feet = the average of two adjacent spans for intermediate bents and half of the length of the end span for end bents.
 
 
|-
 
|-
|valign="top"|<math>\, H</math>||= the total height of the girders, slab, barrier curb and any superelevation of the roadway, in feet
+
|#14||50||70||44||61||39||54
 
|-
 
|-
|valign="top"|<math>\, W_t</math>|| =  wind force per unit area in pounds per square foot
+
|#18||65||90||56||78||50||70
 
|}
 
|}
  
This transverse wind force will be applied at the top of the beam cap for the design of the substructure.
+
===== 751.40.8.4.2.7 Minimum lap length for uncoated Grade 40 tension lap splices, <math>\, L_{lap}</math> (AASHTO 8.32) =====
  
 
+
{|border="1" style="text-align:center;" cellpadding="5" align="center" cellspacing="0"
'''Longitudinal (**)'''
+
|+'''Bars spaced less than 6 inches laterally on center and at least 3 inches concrete cover in direction of the spacing'''
 
+
!rowspan="2"| &nbsp;||colspan="9"|Other than Top Bars||colspan="9"|Top Bars
The standard wind force in the longitudinal direction shall be applied as a percentage of the transverse loading. Use approximately 25%.
 
 
 
:{|
 
|Truss and Arch Structures||<math>\, W_I</math>||= 75 x 0.25 = approximately 20 lbs/ft²
 
 
|-
 
|-
|Girder Structures||<math>\, W_I</math>||= 50 x 0.25 = approximately 12 lbs/ft²
+
|colspan="3"|<math>\, f'_c</math> = 3 ksi||colspan="3"|<math>\, f'_c</math> = 4 ksi||colspan="3"|<math>\, f'_c</math> = 5 ksi||colspan="3"|<math>\, f'_c</math> = 3 ksi||colspan="3"|<math>\, f'_c</math> = 4 ksi||colspan="3"|<math>\, f'_c</math> = 5 ksi
|}
+
|-
 
+
|Bar||A||B||C||A||B||C||A||B||C||A||B||C||A||B||C||A||B||C
The total longitudinal wind force <math>\, P</math> will be:
+
|-
 +
|#3||12||12||12||12||12||12||12||12||12||12||16||21||12||16||21||12||16||21
 +
|-
 +
|#4||12||12||14||12||12||14||12||12||14||12||16||21||12||16||21||12||16||21
 +
|-
 +
|#5||12||13||17||12||13||17||12||13||17||14||19||24||14||19||24||14||19||24
 +
|-
 +
|#6||13||17||22||12||16||21||12||16||21||19||24||31||17||22||29||17||22||29
 +
|-
 +
|#7||18||23||30||16||20||26||14||19||24||25||32||42||22||28||37||20||26||34
 +
|-
 +
|#8||23||30||40||20||26||34||18||24||31||33||42||55||28||37||48||25||33||43
 +
|-
 +
|#9||30||38||50||26||33||43||23||30||39||41||54||70||36||47||61||32||42||54
 +
|-
 +
|#10||38||49||63||33||42||55||29||38||49||52||68||89||45||59||77||41||53||69
 +
|-
 +
|#11||46||60||78||40||52||68||36||46||61||64||84||109||56||72||95||50||65||85
 +
|}
 +
 
  
<math>\, P = L \times H \times W_I</math>
 
  
Where:
+
{|border="1" style="text-align:center;" cellpadding="5" align="center" cellspacing="0"
{|
+
|+'''Bars spaced 6 inches or more laterally on center and at least 3 inches concrete cover in direction of the spacing'''
|<math>\, L</math>||= the overall bridge length in feet
+
!rowspan="2"| &nbsp;||colspan="9"|Other than Top Bars||colspan="9"|Top Bars
 +
|-
 +
|colspan="3"|<math>\, f'_c</math> = 3 ksi||colspan="3"|<math>\, f'_c</math> = 4 ksi||colspan="3"|<math>\, f'_c</math> = 5 ksi||colspan="3"|<math>\, f'_c</math> = 3 ksi||colspan="3"|<math>\, f'_c</math> = 4 ksi||colspan="3"|<math>\, f'_c</math> = 5 ksi
 +
|-
 +
|Bar||A||B||C||A||B||C||A||B||C||A||B||C||A||B||C||A||B||C
 +
|-
 +
|#3||12||12||12||12||12||12||12||12||12||12||16||21||12||16||21||12||16||21
 +
|-
 +
|#4||12||12||12||12||12||12||12||12||12||12||16||21||12||16||21||12||16||21
 +
|-
 +
|#5||12||12||14||12||12||14||12||12||14||12||16||21||12||16||21||12||16||21
 +
|-
 +
|#6||12||14||18||12||13||17||12||13||17||15||19||25||14||18||23||14||18||23
 +
|-
 +
|#7||15||19||24||13||16||21||12||15||20||20||26||34||18||23||29||16||21||27
 +
|-
 +
|#8||19||24||32||16||21||28||15||19||25||26||34||44||23||29||38||20||26||34
 +
|-
 +
|#9||24||31||40||21||27||35||19||24||31||33||43||56||29||37||49||26||33||44
 
|-
 
|-
|valign="top"|<math>\, H</math>||= the total height of the girders, slab, barrier curb and anysuperelevation of the roadway, in feet
+
|#10||30||39||51||26||34||44||23||30||39||42||54||71||36||47||62||33||42||55
 
|-
 
|-
|<math>\, W_I</math>||= wind force per unit area in pounds per square foot
+
|#11||37||48||63||32||42||54||29||37||49||52||67||87||45||58||76||40||52||68
 
|}
 
|}
  
This longitudinal force is distributed to the bents based on their stiffness. (**)
+
==== 751.40.8.4.3 Miscellaneous ====
  
The longitudinal wind force for the bent will be applied at the top of the beam cap for the design of the substructure.
+
'''Negative Moment Steel over Intermediate Supports'''
  
 +
Dimension negative moment steel over intermediate supports as shown.
  
'''Forces from Superstructure: Wind on Live Load'''
+
<center>[[Image:751.40 reinforcement-Negative Moment Steel over Intermediate Supports.gif]]</center>
  
A force of 100 pounds per linear foot of the structure shall be applied transversely to the structure along with a force of 40 pounds per linear foot longitudinally. These forces are assumed to act 6 feet above the top of slab.  
+
{|
The transverse force is applied at the bents based on the length of the adjacent spans affecting them. The longitudinal force is distributed to the bents based on their stiffness. (**)
+
!colspan="2" align="left"|Prestressed Structures:
 +
|-
 +
|(1)||Bar length by design.
 +
|-
 +
|(2)||Reinforcement placed between longitudinal temperature reinforcing in top.
 +
|}
 +
:{|
 +
|Bar size:||#5 bars at 7-1/2" cts. (Min.)
 +
|-
 +
| &nbsp;||#8 bars at 5" cts. (Max.)
 +
|}
  
(**) See Longitudinal Distribution of Wind Loads in Distribution of Loads Section.
+
{|
 +
!colspan="2" align="left"|Steel Structures:
 +
|-
 +
|valign="top"|(1)||Extend into positive moment region beyond "Anchor" Stud shear connectors at least '''40 x bar diameter x 1.5''' (Epoxy Coated Factor)(*) as shown below.  (AASHTO 10.38.4.4 & AASHTO 8.25.2.3)
 +
|-
 +
|(2)||Use #6 bars at 5" cts. between longitudinal temperature reinforcing in top.
 +
|}
  
 +
<center>[[Image:751.40 reinforcement-elevation of girder showning negative moment steel.gif]]</center>
  
'''Forces Applied Directly to the Substructure'''
+
{|
 +
|(*)||40 x bar diameter x 1.5 = 40 x 0.75" x 1.5 = 45” for #6 epoxy coated bar.
 +
|}
  
The transverse and longitudinal forces to be applied directly to the substructure elements shall be calculated from an assumed basic wind force of 40 lbs/ft². This wind force per unit area shall be multiplied by the exposed area of each substructure member in elevation (use front view for longitudinal force and side view for transversely force, respectively). These forces are acting at the center of gravity of the exposed portion of the member.  
+
=== 751.40.8.5 General Superstructure ===
  
A shape factor of 0.7 shall be used in applying wind forces to round substructure members.
 
  
When unusual conditions of terrain or the special nature of a structure indicates, a procedure other than the Standard Specification may be used subject to approval of the Structural Project Manager.
+
==== 751.40.8.5.1 Concrete Slabs ====
  
==== 751.40.8.1.8 Temperature Forces ====
 
  
Temperature stresses or movement need to be checked on all structures regardless of length. Generation of longitudinal temperature forces is based on stiffness of the substructure. (*)
+
===== 751.40.8.5.1.1 Design Criteria =====
  
'''Coefficients'''
+
'''Slabs on Girders'''
  
 +
'''Stresses:'''
 
:{|
 
:{|
|Steel:||Thermal - 0.0000065 ft/ft/°F
+
|<math>\, f_c</math>||= 1,600 psi
 
|-
 
|-
|Concrete:||Thermal - 0.0000060 ft/ft/°F
+
|<math>\, f'_c</math>||= 4,000 psi
 
|-
 
|-
| &nbsp;||Shrinkage  - 0.0002 ft/ft (***)
+
|<math>\, n</math>||= 8
 
|-
 
|-
| &nbsp;||Friction  - 0.65 for concrete on concrete
+
|<math>\, f_y</math>||= 60,000 psi
 
|}
 
|}
  
  
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
'''Moments Over Interior Support''' (Use for positive moment reinf. also) (Sec. 1.5 E40A)
|+'''Temperature Range From 60° F (**)'''
+
 
|width="100pt"|&nbsp;||width="50pt"|Rise||width="50pt"|Fall||width="50pt"|Range
+
{|
 +
|Dead Load =|| <math>\, -0.107wS^2</math> ||(Continuous over 5 supports)
 
|-
 
|-
|Steel Structures||60°F||80°F||140°F
+
|Dead Load =|| <math>\, -0.100wS^2</math> ||(Continuous over 4 supports)
 +
|}
 +
{|
 +
|Live Load =|| <math>\, (S + 2) \frac {P}{32}</math> ||width="20pt"| &nbsp;||Continuity Factor||= 0.8
 
|-
 
|-
|Concrete Structures||30°F||40°F||70°F
+
| &nbsp; || &nbsp; || &nbsp; ||align="right"|Impact Factor||= 1.3
|}
+
|-
 +
| &nbsp; || &nbsp; || &nbsp; ||align="right"|P||= 16 Kips for HS20
 +
|-
 +
| &nbsp; || &nbsp; || &nbsp; ||align="right"|P||= 20 Kips for HS20 Modified
 +
|-
 +
|colspan="5"| &nbsp;
 +
|-
 +
|Design Load:||colspan="4"| &nbsp; <math>\, M_u = 1.3 (M_{DL} + 1.67 M_{LL+I})</math>
 +
|}
  
 +
<div id="Cantilever Moment"></div>
  
(*) See Longitudinal Distribution of Temperature Forces in Distribution of Loads Section.
+
'''Cantilever Moment'''
  
(**) Temperature Range for expansion bearing design and expansion devices design see Bearing Section, Expansion Devices Section, respectively.
+
Dead Load = Moment due to slab, F.W.S. and S.B.C.
  
(***) When calculating substructure forces of concrete slab bridges, the forces caused by the shrinkage of the superstructure should be included with forces due to temperature drop. This force can be  ignored for most other types of bridges.
+
Live Load:
  
==== 751.40.8.1.9 Sidewalk Loading ====
+
Wheel Load = &nbsp; <math>\, M_{LL=I} = \frac {Px}{E}</math>
  
Sidewalk floors and their immediate support members shall be designed for a '''live load''' of 85 pounds per square foot of sidewalk area.  Girders, trusses, and other members shall be design for the following sidewalk live load:
+
Where:
 
+
{|
:{|
+
|<math>\, P</math>||= Wheel load (apply impact factor)
|width="150pt"|Spans 0 to 25 feet||width="100pt"|85 lbs/ft²
 
 
|-
 
|-
|Spans 26 to 100 feet||60 lbs/ft²
+
|<math>\, x</math>||= Distance from load to support (ft.)
 
|-
 
|-
|Spans over 100 feet||use the following formula
+
|<math>\, E</math>||= <math>\, 0.8x + 3.75</math>
 
|}
 
|}
  
<math>\, P = \Bigg( 30 + \frac {3000}{L} \Bigg) \Bigg( \frac {55-W}{50} \Bigg)</math>
+
 
 +
Collision Load = &nbsp; <math>M_{COLL} = \frac {Py}{E}</math>
  
 
Where:
 
Where:
 
{|
 
{|
|<math>\, P</math>||= live load per square foot, max. 60 lbs/ft²
+
|<math>\, P</math>||= 10 kips (Collision force)
 
|-
 
|-
|<math>\, L</math>||= loaded length of sidewalk in feet
+
|<math>\, y</math>||= Moment arm (Curb ht.+ 1/2 Slab th.)
 
|-
 
|-
|<math>\, W</math>||= width of sidewalk in feet
+
|<math>\, E</math>||= <math>\, 0.8x + 5.0</math>
 
|}
 
|}
  
When sidewalk live loads are applied along with live load and impact, if the structure is to be designed by service loads, the allowable stress in the outside beam or stringer may be increased by 25 percent as long as the member is at least as strong as if it were not designed for the additional sidewalk load using the initial allowable stress. When the combination of sidewalk live load and traffic live load plus impact governs the design under the load factor method, use a b factor of 1.25 instead of 1.67.
 
  
Unless a more exact analysis can be performed, distribution of sidewalk live loads to the supporting stringers shall be considered as applied 75 percent to the exterior stringer and 25 percent to the next stringer.
+
Where:
 +
{|
 +
|<math>\, x</math>||= Distance from center of gravity of barrier to support
 +
|}
  
==== 751.40.8.1.10 Other Loads ====
 
  
'''Stream Pressure'''
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
Stream flow pressure shall be considered only in extreme cases. The affect of flowing water on piers shall not be considered except in cases of extreme high water and when the load applied to substructure elements is greater than that which is applied by wind on substructure forces at low water elevations.
 
 
 
The pressure generated by stream flow is:
 
 
 
<math>\, P = KV^2</math>
 
 
 
Where:
 
{|
 
|<math>\, P</math>||= stream pressure in pounds per square foot
 
 
|-
 
|-
|<math>\, V</math>||= design velocity of water in feet per second
+
|width="250pt" align="left"|The "support" is assumed at the  1/4  point of the minimum flange.
 +
|rowspan="4"|[[Image:751.40.8.5.1.1 slab cantilever.jpg|275px]]
 
|-
 
|-
|<math>\, K</math>||= shape constant for the surface the water is in contact with.
+
|width="250pt" align="left"|Wheel loads and collision loads shall not be applied simultaneously.
 
|-
 
|-
|<math>\, K</math>||= 1.4 for square-ended piers
+
|width="250pt" align="left"|Use the greater of the two for the Design Load.
 
|-
 
|-
|<math>\, K</math>||= 0.7 for circular piers
+
|width="250pt" align="left"|Design Load:<br./><math>\, M_u = 1.3 (M_{DL} + 1.67 M_{LL+I})</math>
 
|-
 
|-
|<math>\, K</math>||= 0.5 for angle-ended piers where the angle is 30 degrees or less
+
!&nbsp;||Slab Cantilever Section
 
|}
 
|}
  
 +
Design of top reinforcement is based on maximum moment over supports or cantilever moment. Flexural reinforcement shall meet the criteria of AASHTO Art. 8.16.3.
 +
 +
When designing for bottom transverse reinforcement, a 1" wearing surface is removed from the effective depth.
 +
 +
Prestressed panels replace the bottom transverse reinforcement.
 +
 +
Prestressed panels are assumed to carry DL1 stresses. Therefore, the negative moment due to DL1 at interior supports may be neglected.
 +
 +
The maximum P/S panel width (clear span + 6") for HS20 Modified is 9'-6".  (Based on 10'-0" girder spacing and 10" flanges) The maximum P/S panel width (clear span + 6") for HS20 is 9'-11".
  
'''Ice Forces'''
 
  
Ice forces on piers shall be applied if they are indicated on the Design Layout.
+
'''Distribution of Flexural Reinforcement'''
  
 +
Allowable Stress: &nbsp; <math>\, f_s = \frac {Z}{(d_c \times A)^{1/3}} \le 0.6 f_y</math>
  
'''Buoyancy'''
+
Where:
 
+
{|
Buoyancy shall be considered when its effects are appreciable.
+
|<math>\, Z</math>||= 130 k/in.
 
 
 
 
'''Fatigue in Structural Steel'''
 
 
 
Steel structures subjected to continuous reversal of loads are to be designed for fatigue loading.
 
 
 
 
 
'''Prestressing'''
 
 
 
See [[751.22 P/S Concrete I Girders|EPG 751.22 P/S Concrete I Girders]].
 
 
 
 
 
'''Other Loads'''
 
 
 
Other loads may need to be applied if they are indicated on the Design Layout. Otherwise see Structural Project Manager before applying any additional loads.
 
 
 
==== 751.40.8.1.11 Group Loads ====
 
 
 
'''Group Loading (Service Load Design)'''
 
 
 
Group loading combinations are:
 
 
 
:{|
 
|GP I SL||width="350pt"| <math>\, = D+L+I</math> ||100%
 
 
|-
 
|-
|GP II SL||width="350pt"| <math>\, = D+W</math> ||125%
+
|valign="top"|<math>\, d_c</math>||= Dist. from extreme tension fiber to center of closest bar (concrete cover shalll not be taken greater than 2")
 
|-
 
|-
|GP III SL||width="350pt"| <math>\, = D+L+I+0.3W+WL+LF</math> ||125%
+
|<math>\, A</math>||= Effective tension area of concrete
 
|-
 
|-
|GP IV SL||width="350pt"| <math>\, = D+L+I+T</math> ||125%
+
| &nbsp;||= <math>\, 2d_c s</math>
 
|-
 
|-
|GP V SL||width="350pt"| <math>\, = D+W+T</math> ||140%
+
|<math>\, s</math>||= Bar spacing ctr. to ctr.
|-
 
|GP VI SL||width="350pt"| <math>\, = D+L+I+0.3W+WL+LF+T</math> ||140%
 
 
|}
 
|}
 +
 +
 +
Actual Stress: &nbsp; <math>\, f_s = \frac {M_W}{A_S \times j \times d}</math>
  
 
Where:
 
Where:
 
{|
 
{|
|<math>\, D</math>||= dead load
+
|<math>\, M_W</math>||= Service load moment
 
|-
 
|-
|<math>\, L</math>||= live load
+
|<math>\, A_S</math>||= Area of steel
 +
|-
 +
|<math>\, j</math>||= <math>\, 1 - k/3</math>
 
|-
 
|-
|<math>\, I</math>||= live load impact
+
|<math>\, k</math>||= <math>\, \sqrt {2n\rho + (n \rho)^2 - n \rho}</math>
 
|-
 
|-
|<math>\, W</math>||= wind load on structure
+
|<math>\, n</math>||= <math>\, E_S/E_C</math>
 
|-
 
|-
|<math>\, WL</math>||= wind load on live load
+
|<math>\, \rho</math>||= <math>\, A_S /(b \times d)</math>
 
|-
 
|-
|<math>\, T</math>||= temperature force
+
|<math>\, b</math>||= Effective width
 
|-
 
|-
|<math>\, LF</math>||= longitudinal force from live load
+
|<math>\, d</math>||= Effective depth
 
|}
 
|}
  
 +
Distribution of flexural reinforcement does not need to be checked in
 +
concrete considered unexposed to weather.
 +
 +
 +
'''Longitudinal distribution reinforcement:'''
 +
 +
Top of slab - use #5 bars at 15" cts. for temperature distribution.
 +
 +
Bottom of slab - by design.
 +
  
 +
'''Negative moment reinforcement over supports:'''
 +
 +
Steel structures - add. #6 bars at 5" between #5 bars.
  
'''Group Loading (Load Factor Design)'''
+
P/S girder structures - by design.
 +
 +
Additional reinforcement over supports shall be a minimum of #5 bars and a maximum of #8 bars at 5" ctrs.  When necessary, replace the #5 temperature reinforcement with a larger bar to satisfy negative moment reinforcement requirement, but keep all bars within two bar sizes.
 +
 +
Note:  See details of negative moment reinforcement.
  
Group loading combinations are:
 
  
:{|
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
|GP I LF||<math>\, = 1.3[\beta_d D+1.67 (L+I)]</math>
 
 
|-
 
|-
|GP II LF||<math>\, = 1.3[\beta_d D+W]</math>
+
|colspan="2"|[[Image:751.40 general superstructure-sections thru slab showing negative moment reinforcement.gif]]
 
|-
 
|-
|GP III LF||<math>\, = 1.3[\beta_d D+L+I+0.3W+WL+LF]</math>
+
!width="50%"|CIP Slab||width="50%"|P\S Panel Slab
 +
|}
 +
 
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|-
|GP IV LF||<math>\, = 1.3[\beta_d D+L+I+T]</math>
+
|valign="top" align="right"|[[Image:751.40 circled 1.gif]]||align="left" width="400pt" |3" Cl. preferred min., 2 3/4" Cl. preferred min. for P/S panels to accommodate #8 bars over supports and 2 1/2" Cl. absolute min. by AASHTO 8.22.1.
|-
 
|GP V LF||<math>\, = 1.25[\beta_d D+W+T]</math>
 
|-
 
|GP VI LF||<math>\, = 1.25[\beta_d D+L+I +0.3W+WL+LF+T]</math>
 
 
|}
 
|}
  
Where:
+
Method of measurement:
{|
+
 
|<math>\, D</math>||= dead load
+
The area of the concrete slab shall be measured and computed to the nearest square yard.  This area shall be measured transversely from out to out of slab and longitudinally from end to end of bridge slab.
|-
 
|<math>\, L</math>||= live load
 
|-
 
|<math>\, I</math>||= live load impact
 
|-
 
|<math>\, W</math>||= wind load on structure
 
|-
 
|<math>\, WL</math>||= wind load on live load
 
|-
 
|<math>\, T</math>||= temperature force
 
|-
 
|<math>\, LF</math>||= longitudinal force from live load
 
|-
 
|<math>\, \beta_d</math>||= coefficient, see AASHTO Table 3.22.1A
 
|}
 
  
  
Other group loadings in AASHTO Table 3.22.1A shall be used when they apply.
+
'''Precast Prestressed Panels'''
  
=== 751.40.8.2 Distribution of Loads ===
+
3" Precast prestressed concrete panels with 5-1/2" minimum cast-in-place concrete will be the standard slab used on all girder superstructures except curved steel structures.
  
 +
Concrete for prestressed panels shall be Class A1 with <math>\, f'{c}</math> = 6,000 psi, <math>\, f'_{ci}</math> = 3,500 psi.  Prestressing tendons shall be uncoated, low-relaxation, seven-wire(7) strands for prestressed concrete conforming to AASHTO M203 Grade 270, with nominal diameter of strand = 3/8" and area = 0.085 sq.in., minimum ultimate strength = 22.95 kips (270 ksi), and strand spacing = 4.5 inches.
  
==== 751.40.8.2.1 Distribution of Dead Load ====
+
Panels shall be set on joint filler or polystyrene bedding material. Filler thickness shall be a Min. of 3/4" and a Max. of 2". Standard filler width is 1 1/2" except at splice plates where 3/4" Min. is allowed to clear splice bolts.  Joint filler thickness may be reduced to a minimum of 1/4" over splice plates on steel structures.  For prestressed girder structures, joint filler thickness may be varied within these limits to offset girder camber or at the contractor's option a uniform 3/4" (Min.) thickness may be used throughout.  The same thickness shall be used under any one edge of any panel and the maximum change in thickness between adjacent panels shall be 1/4 inch for steel spans and 1/2 inch for concrete spans.
  
'''Composite Steel or Prestressed Concrete Structures'''
+
Standard roadway cross sections and slab reinforcement for HS20 and HS20 Modified live loads are shown in this section. Reinforcement shown is for a cast-in-place slab or a P/S panel slab with the bottom layer of reinforcement between girders being replaced by the panels. Cantilever reinforcement details for P/S panel slab are shown in this section.
  
The dead load applied to the girders through the slab shall be:
+
:Maximum panel width (clear span + 6") = 9'-6" for HS20 Modified.
 +
:Maximum panel width (clear span + 6") = 9'-11" for HS20.
  
 +
When a barrier or railing is permanently required on the structure, other than at the edge of slab, precast prestressed panels will not be allowed in the bay underneath the barrier or railing.  Prestressed panels are not allowed for use as simply supported for live loads, i.e. staging, where only two supports may be provided for live loads.
  
'''Dead Load 1'''
 
  
Non-composite dead loads should be distributed to girders (stringers) on the basis of continuous spans over simple supports.  
+
'''S.I.P.'''
  
'''Dead Load 2'''
+
Stay-in-place corrugated metal forms with cast-in-place concrete may be used on horizontally curved steel structures with the approval of the Structural Project Manager.
  
Composite loads shall be distributed equally to all girders. The following are all Dead Load 2 loads:
+
The standard slab reinforcements shown in this section for HS20 live load were designed using S.I.P. Dead Loads.  If design is for HS20 Modified, the standard slab reinforcement needs to be checked for S.I.P. forms.
:Barrier curb
 
:Future wearing surface on slab
 
:Sidewalks
 
:Fences
 
:Protective coatings and waterproofing on slab
 
  
 +
The bottom transverse reinforcement shall maintain a 1" clear distance from the top of forms.
  
'''Concrete Slab Bridges'''
 
  
Distribute entire dead load across full width of slab.
+
'''C.I.P.'''
  
For longitudinal design, heavier portions of the slab may be considered as concentrated load for entry into the "Continuous Structure Analysis" computer program.
+
8 1/2" cast-in-place concrete slab with conventional forming may be used at the contractor's option, on all girder structures.  Conventional forming shall also be used between girders with stage construction joints.
  
For transverse bent design, consider the dead load reaction at the bent to be a uniform load across entire length of the transverse beam.
 
  
==== 751.40.8.2.2 Distribution of Live Load ====
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|+'''Details of Precast Prestressed Panels Prestressed Structure:'''
 +
|colspan="1"|[[Image:751.40 general superstructure-panels - square ends - prestressed structures.gif]]
 +
|[[Image:751.40 general superstructure-panels - skewed ends - prestressed structures.gif]]
 +
|-
 +
!colspan="1"|Panels-Squared Ends
 +
!Panels-Skewed Ends
 +
|-
 +
!colspan="3"|PLAN OF PRECAST PRESTRESSED PANELS PLACEMENT
 +
|}
  
Live loading to be distributed shall be the appropriate loading shown on the Design Layout.
+
{|border="0" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
Applying Live Load to Structure
 
  
 
+
|valign="top"|(1)
'''Superstructure'''
+
|align="left"|End panels shall be dimensioned 1" min. to 1-1/2"<br/>max. from the inside face of diaphragm.
 
+
|rowspan="3" colspan="2"|[[Image:751.40 general superstructure-panels - section thru const joint.gif]]
For application of live load to superstructure, the lane width is considered 12 feet. Each design vehicle has wheel lines which are 6 feet apart and adjacent design    vehicles must be separated by 4 feet.
+
|-
 
+
|valign="top"|(2)
 
+
|align="left"|S-Bars shown are bottom steel in slab between<br/>panels and used with squared end panels only.
'''Substructure'''
+
|-
 
+
|valign="top"|(3)
To produce the maximum stresses in the main carrying members of substructure elements, multiple lanes are to be loaded simultaneously. The lane width is 12 feet. Partial lanes are not to be considered. Due to the improbability of coincident maximum loading, a reduction factor is applied to the number of lanes. This reduction however, is not applied in determining the distribution of loads to the stringers.
+
|align="left"|Extend S-Bars 18 inches beyond the front<br/>face of end bents only.
 
+
|-
 
+
|colspan="2" rowspan="2"|[[Image:751.40 general superstructure-panels - section a-a.gif]]
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
!colspan="2"|Section Thru Const. Joint
|+'''Distribution of Live Load to Beams and Girders'''
+
|-
!width="150pt"|Number of Lanes||width="150pt"|Percent
+
|valign="top"|(*)
 +
|align="left" valign="top"|Adjust the permissible construction joint to a clearance of 6<br/>inches minimum from the joints of the panels.
 +
 +
Note: All reinforcement other than prestressing strands shall<br/>be epoxy coated.
 +
|-
 +
!colspan="2"|Section A-A
 +
|colspan="2" rowspan="5"|[[Image:751.40 general superstructure-panels - section thru cantilever.gif]]
 +
|-
 +
|valign="top"|(**)
 +
|align="left" valign="top"|3/4" Min. thru 2" max. thickness and 1 1/2" width of<br/>preformed fiber expansion joint material or Sec 1057<br/>or polystyrene bedding material Sec 1073.
 +
|-
 +
|colspan="2"| &nbsp;
 
|-
 
|-
|one or two lanes||100
+
|colspan="2"| &nbsp;
 
|-
 
|-
|three lanes||90
+
|colspan="2"| &nbsp;
 
|-
 
|-
|four lanes or more||75
+
|colspan="2"| &nbsp;
 +
!colspan="2"|Section Thru Cantilever
 
|}
 
|}
  
  
'''Moment Distribution'''
 
  
Moments due to live loads shall not be distributed longitudinally. Lateral distribution shall be determined from AASHTO Table 3.23.1 for interior stringers. Outside stringers distribute live load assuming the flooring to act as a simple span, except in the case of a span with a concrete floor supported by four or more stringers, then AASHTO 3.23.2.3.1.5 shall be applied. In no case shall an exterior stringer have less carrying capacity than an interior stringer.
+
{|border="0" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
 
+
|+'''Details of Precast Prestressed Panels Steel Structure:'''
 
+
|colspan="2"|[[Image:751.40 general superstructure-panels - square ends - end bent - steel structure.gif|250px]]
'''Shear Distribution'''
+
|[[Image:751.40 general superstructure-panels - square ends - int end bent - steel structure.gif|250px]]
 
+
|[[Image:751.40 general superstructure-panels - square ends - int bent - steel structure.gif|250px]]
As with live load moment, the reactions to the live load are not to be distributed longitudinally. Lateral distribution of live load shall be that produced by assuming the flooring to act as simply supported. Wheel lines shall be spaced on accordance with AASHTO 3.7.6 and shall be placed in a fashion which provides the most contribution to the girder under investigation, regardless of lane configuration. The shear distribution factor at bents shall be used to design bearings and bearing stiffeners.
+
|-
 
+
!colspan="2"|End Bent
 
+
!End Bent (Integral)
'''Deflection Distribution'''
+
!Int. Bent (Exp. Gap)
 
 
Deflection due to live loads shall not be distributed longitudinally. Lateral distribution shall be determined by averaging the moment distribution factor and the number of wheel lines divided by the number of girder lines for all girders. The number of wheel lines shall be based on 12 foot lanes. The reduction in load intensity (AASHTO Article 3.12.1) shall not be applied.
 
 
 
Deflection Distribution Factor = &nbsp; <math>\, \cfrac {\big\{ \frac{2n}{N} \big\} + MDF}{2}</math>
 
 
 
Where:
 
{|
 
|<math>\, n</math>||= number of whole 12 foot lanes on the roadway
 
 
|-
 
|-
|<math>\, N</math>||= number of girder lines;
+
!colspan="4"|Panels-Squared Ends
 
|-
 
|-
|<math>\, MDF</math>||= Moment Distribution Factor.
+
|colspan="2"|[[Image:751.40 general superstructure-panels - skewed ends - int bent exp gap - steel structure.gif]]
|}
+
|[[Image:751.40 general superstructure-panels - skewed ends - end bent - steel structure.gif]]
 
+
|[[Image:751.40 general superstructure-panels - skewed ends - int end bent - steel structure.gif]]
 
 
Example: 38'-0" Roadway (Interior Girder), &nbsp; <math>\, n=3</math>, &nbsp; <math>\, N=5</math>, &nbsp; <math>\, MDF=1.576</math>
 
 
 
Deflection Distribution Factor = &nbsp; <math>\, \cfrac {\big\{ \frac{2 \times 3lanes}{5 girders} \big\} + 1.576}{2} = 1.388</math>
 
 
 
 
 
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 
|+'''Live Load Distribution Factors for Standard Roadway Widths'''
 
!rowspan="2" width="75pt" |Roadway<br/>Width||rowspan="2" width="75pt"|Number<br/>Girders||rowspan="2" width="75pt"|Girder<br/>Spacing||colspan="3"|Exterior Girder||colspan="3"|Interior Girder||rowspan="2"|(1)
 
 
|-
 
|-
!Mom.||Shear||Defl.||Mom.||Shear||Defl.
+
!colspan="2"|Int. Bent (Exp. Gap)
 +
!End Bent
 +
!End Bent (Integral)
 
|-
 
|-
|26’-0”||4||7’-6”||1.277||1.133||1.139||1.364||1.667||1.182||1.071
+
!colspan="4"|Panels-Skewed Ends
 
|-
 
|-
|28’-0”||4||8’-2”||1.352||1.204||1.176||1.485||1.776||1.243||1.167
+
!colspan="4"|PLAN OF PRECAST PRESTRESSED PANELS PLACEMENT
 
|-
 
|-
|30’-0”||4||8’-8”||1.405||1.308||1.453||1.576||1.846||1.538||1.238
+
|valign="top"|(1)
 +
|align="left"|End panels shall be dimensioned 1" min. to 1 1/2" max. from the inside face of diaphragm.
 +
|colspan="2" rowspan="2"|[[Image:751.40 general superstructure-panels - section a-a steel structure.gif]]
 
|-
 
|-
|32’-0”||4||9’-2”||1.457||1.400||1.479||1.667||1.909||1.584||1.310
+
|valign="top"|(2)
 +
|align="left"|S-Bars shown are bottom steel in slab between panels and used with squared end panels only.
 
|-
 
|-
|36’-0”||5||8’-2”||1.352||1.184||1.276||1.485||1.776||1.343||1.167
+
|valign="top"|(3)
 +
|align="left"|Extend S-bars 18 inches beyond the front face of end bents only.
 +
|colspan="2"|'''Section A-A'''<br/>(*)  Over splice plates, 3/4" Min. thickness allowed.
 
|-
 
|-
|38’-0”||5||8’-8”||1.405||1.231||1.303||1.576||1.846||1.388||1.238
+
|valign="top"|(5)
 +
|align="left" valign="top"|S-Bars shown are used with skewed end panels, or square end panels of square structures only. The #5-S Bars will extend the width of slab (30" lap if necessary) or to within 3" of expansion device assemblies.
 +
|colspan="2" rowspan="3"|[[Image:751.40 general superstructure-panels - section b-b steel structure.gif]]
 
|-
 
|-
|40’-0”||5||9’-0”||1.440||1.333||1.520||1.636||1.889||1.618||1.286
+
|valign="top"|Note:
 +
|align="left"|All reinforcement other than prestressing strands shall be epoxy coated.
 
|-
 
|-
|44’-0”||5||9’-9”||1.515||1.487||1.558||1.773||1.974||1.687||1.393
+
| &nbsp;
|}
+
| &nbsp;
<center> '''(1)''' Use when checking interior girder moment cyclical loading Case I Fatigue for one lane loading.</center>
+
|-
 
+
| &nbsp;
 
+
| &nbsp;
'''Distribution of Live Load to Substructure'''
+
|colspan="2"|'''Part Section B-B'''
 
+
|-
For substructure design the live load wheel lines shall be positioned on the slab to produce maximum moments and shears in the substructure. The wheel lines shall be distributed to the stringers on the basis of simple spans between stringers. The number of wheel lines used for substructure design shall be based on 12 foot lanes and shall not exceed the number of lanes times two with the appropriate percentage reduction for multiple lanes where applicable.
+
|colspan="4"|[[Image:751.40 general superstructure-panels - section thru cantilever steel structure.gif]]
 
 
In computing these stresses generated by the lane loading, each 12 foot lane shall be considered a unit. Fractional units shall not be considered.
 
 
 
 
 
'''Distribution of Loads to Slabs'''
 
 
 
For simple spans, the span length shall be the distance center to center of supports but need not be greater than the clear distance plus the thickness of the slab. Slabs for girder and floor beam structures should be designed as supported on four sides.
 
 
 
For continuous spans on steel stringers or on thin flanged prestressed beams (top flange width to thickness ratios > 4.0), the span length shall be the distance between edges of top flanges plus one quarter of each top flange width. When the top flange width to thickness  is < 4.0 the span distance shall be the clear span between edges of the top flanges
 
 
 
When designing the slab for live load, the wheel line shall be placed 1 foot from the face of the barrier curb if it produces a greater moment.
 
 
 
 
 
'''Bending Moments in Slab on Girders'''
 
 
 
The load distributed to the stringers shall be:
 
 
 
<math>\, \Bigg( \frac {S + 2}{32} \Bigg) </math> &nbsp; P20 or P25 = Moment in foot-pounds per-foot  width of slab.
 
 
 
Where:
 
{|
 
|<math>\, S</math>||= effective span length between girders in feet
 
 
|-
 
|-
|P20 or P25||= wheel line load for HS20 or HS20 Modified design Truck in kips.
+
|colspan="4"|'''Section Thru Cantilever'''
 
|}
 
|}
  
For slabs continuous over 3 or more supports, a continuity factor of 0.8 shall be applied.
 
  
 
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
'''Main Reinforcement Parallel to Traffic'''
+
|+'''Details of Precast Prestressed Panels for all Structures:'''
 
+
|colspan="2"|[[Image:751.40 general superstructure-panels - plan of precast prestressed panel.gif]]
This distribution may be applied to special structure types when its use is indicated.
+
|colspan="2"|[[Image:751.40 general superstructure-panels - plan of precast prestressed panel (skewed end-option).gif]]
 
 
 
 
'''Distribution of Live Load to Concrete Slab Bridges'''
 
 
 
Live load for transverse beam, column and pile cap design shall be applied as concentrated loads of one wheel line. The number of wheel lines used shall not exceed the number of lanes x 2 with the appropriate reduction where applicable.
 
 
 
For slab longitudinal reinforcement design, use live load moment distribution factor of 1/E for a one-foot strip slab with the appropriate percentage reduction.
 
 
 
<math>\, E = 4' + 0.06S, E (max.) = 7'</math>
 
 
 
Where:
 
{|
 
|<math>\, E</math>||= Width of slab in feet over which a wheel is distributed
 
 
|-
 
|-
|<math>\, S</math>||= Effective span length in feet.
+
!colspan="2" valign="top"|Plan of Precast Prestressed Panel
|}
+
!colspan="2" valign="top"|Plan of Precast Prestressed Panel<br/>(Skewed End-Optional)
 
+
|-
For slab deflection, use the following deflection factor for a one-foot strip slab without applying percentage reduction.
+
|(*)
 
+
|align="left"|= 3" (Typ.) for steel girder structures
Deflection Factor = (Total number of wheel line) / (width of the slab)
+
!colspan="2" rowspan="3"|[[Image:751.40 general superstructure-panels - detail a (precast panels).gif]]
 
+
|-
==== 751.40.8.2.3 Frictional Resistance ====
+
|(*)
 
+
|align="left"|= 3" (Typ.) for P/S girder structures
The frictional resistance varies with different surfaces making contact. In the design of bearings, this resistance will alter how the longitudinal forces are distributed. The following table lists commonly encountered materials and their coefficients. These coefficients may be used to calculate the frictional resistance at each bent.
+
|-
 
+
|(**)
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
|align="left"|Use #3-P3 bars if panel is skewed <math>\,45^\circ</math> or greater.
 
|-
 
|-
!colspan="4"|Frictional Resistance of Expansion Bearings
+
|colspan="2" rowspan="2"|[[Image:751.40 general superstructure-panels - section b-b (precast panels).gif]]
 +
!colspan="2"|Detail "A"
 
|-
 
|-
!colspan="2"|Bearing Type||Coef.||General Data
+
|valign="top"|Note:
 +
|align="left" valign="top"|Area of Strand = Astra = 0.085 sq. in./strand<br/>Initial prestressing stress = fsi = (0.75)(270 ksi) = 202.5 ksi<br/>Initial prestressing force = Astra x fsi<br/>= (0.085 sq. in./strand)(202.5 ksi) = 17.2 kips/strand
 
|-
 
|-
!colspan="2"|Type C Bearing
+
!colspan="2"|Section B-B
|0.14
+
|}
|rowspan=10| Coef. of sliding friction<br/>steel to steel = 0.14
 
  
 +
===== 751.40.8.5.1.2 Details of Concrete Slabs for Structures =====
  
 
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
Coef. for pin and rocker<br/>type  bearing =  
 
 
 
<math>\, \frac {0.14 (Radius\ of\ pin)}{Radius\ of\ Rocker}</math>
 
 
 
 
 
 
 
Frictional Force = <br/>Reaction x Coef.
 
 
|-
 
|-
!colspan="2"|6” Diameter Roller
+
|[[Image:751.40 general superstructure-HS20 (26ft0in ROADWAY - 4 GIRDER).gif]]
|0.01
 
 
|-
 
|-
!colspan="2"|Type D Bearing|| &nbsp;
+
!colspan="2"|HS20 (26'-0" ROADWAY - 4 GIRDER)
 
|-
 
|-
!Pin Diameter||Rocker Radius|| &nbsp;
+
|colspan="2"| &nbsp;
 
|-
 
|-
|2”||6.5”||0.0216
+
|[[Image:751.40 general superstructure-HS20 modified (26ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
|-
|2”||7”||0.0200
+
!colspan="2"|HS20 Modified (26'-0" ROADWAY - 4 GIRDER)
 
|-
 
|-
|2”||7.5”||0.0187
+
|colspan="2"| &nbsp;
 
|-
 
|-
|2”||8”||0.0175
+
|[[Image:751.40 general superstructure-HS20 (28ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
|-
|2”||10.5”||0.0133
+
!colspan="2"|HS20 (28'-0" ROADWAY - 4 GIRDER)
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-HS20 modified (28ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
|-
!colspan="2"|PTFE Bearing
+
!colspan="2"|HS20 Modified (28'-0" ROADWAY - 4 GIRDER)
|0.0600
 
|}
 
 
 
 
 
The design of a bent with one of the above expansion bearings will be based on the maximum amount of load the bearing can resist by static friction. When this static friction is overcome, the longitudinal forces are redistributed to the other bents.
 
 
 
The maximum static frictional force at a bent is equal to the sum of the forces in each of the bearings. The vertical reaction used to calculate this maximum static frictional force shall be Dead Loads only  for all loading cases. Since the maximum longitudinal load that can be experienced by any of the above bearings is the maximum static frictional force, the effects of longitudinal wind and temperature can not be cumulative if their sum is greater than this maximum static frictional force.
 
 
 
Two conditions for the bents of the bridge are to be evaluated.
 
#Consider the expansion bents to be fixed and the longitudinal loads distributed to all of the bents.
 
#When the longitudinal loads at the expansion bearings are greater than the static frictional force, then the longitudinal force of the expansion bearings is equal to the dynamic frictional force. It is conservative to assume the dynamic frictional force to be zero causing all longitudinal loads to be distributed to the remaining bents.
 
 
 
=== 751.40.8.3 Unit Stresses ===
 
 
 
 
 
==== 751.40.8.3.1 Fatigue in Structural Steel ====
 
 
 
Steel structures subjected to continuous reversal of loads are to be designed for fatigue loading.
 
 
 
AADTT, Average Daily Truck Traffic (one direction), shall be indicated on the Design Layout. Based on AADTT, the fatigue case and corresponding stress cycles can be obtained from ''AASHTO Table 10.3.2A''.
 
 
 
When Case I fatigue is considered, it is necessary to check fatigue due to truck loading for both the 2,000,000 and over 2,000,000 stress cycles. For the over 2,000,000 stress cycles, the moment distribution factor for all stringers or girders (for fatigue stresses only) will be based on '''one''' lane loaded. For truck loading 2,000,000 cycles and lane loading 500,000 cycles, use the moment distribution factor based on two or more traffic lanes (same as for design moment).
 
 
 
The number of cycles to be used in the fatigue design is dependent on the case number and type of load producing maximum stress as indicated in AASHTO Table 10.3.2A.
 
The allowable fatigue stress range based on the fatigue stress cycles can be obtained from ''AASHTO Table 10.3.1A''.
 
 
 
The type of live load used to determine the number of cycles will be the type of loading used to determine the maximum stress at the point under consideration.
 
 
 
In continuous beams, the maximum stresses may be produced by the truck loading at some points, but by lane loading at other points. However, if the lane loading governs, then the longitudinal members should also be checked for truck loading.
 
 
 
Only live loading and impact stresses need to be considered when designing for fatigue.
 
 
 
Fatigue criteria applies only when the stress range is one of tension to tension or reversal. The fatigue criteria does not apply to the stress range from compression to compression.
 
 
 
All fracture critical structures, those which consist of only one or two main carrying members, trusses or single box girders, shall be considered as Non-redundant structures. Use the appropriate table which accompanies these structures.
 
 
 
==== 751.40.8.3.2 Reinforced Concrete ====
 
 
 
'''Allowable Stresses of Reinforcing Steel'''
 
 
 
Tensile stress in reinforcement at service loads, <math>\, f_s</math>:
 
 
 
{|
 
!colspan="2" align="left"|Concrete
 
 
|-
 
|-
|width="250pt"|Reinforcing Steel (Grade 40)||<math>\, f_s</math>||= 20,000 psi
+
|colspan="2"| &nbsp;
 
|-
 
|-
|width="250pt"|Reinforcing Steel (Grade 60)||<math>\, f_s</math>||= 24,000 psi
+
|[[Image:751.40 general superstructure-HS20 (30ft0in ROADWAY - 4 GIRDER).gif]]
|}
+
|-
 
+
!colspan="2"|HS20 (30'-0" ROADWAY - 4 GIRDER)
For compression stress in beams, see ''AASHTO Article 8.15.3.5''.
 
 
 
For compression stress in columns, see ''AASHTO Article 8.15.4''.
 
 
 
For fatigue stress limit, see ''AASHTO Article 8.16.8.3''.
 
 
 
'''Fatigue in Reinforcing Steel'''
 
 
 
For flexural members designed with reference to load factors and strengths by Strength Design Method, stresses at service load shall be limited to satisfy the requirements for fatigue.  Reinforcement should be checked for fatigue at all locations of peak service load stress ranges and at bar cut-off locations except for concrete deck slab in multi-girder applications.
 
 
 
 
 
'''Allowable Stress Range:''' <math>\, fr_{allow}</math>
 
 
 
The allowable stress range is found using the equation listed below and the minimum stresses from dead load, live load, and impact based on service loads.
 
 
 
The term minimum stress level fmin for this formula indicates the algebraic minimum stress level: tension stress with a positive sign and compression stress with a negative sign.
 
 
 
<math>\, fr_{allow} = 21 - 0.33 f_{min} + 8(r/h)</math>
 
 
 
Where:
 
{|
 
|<math>\, fr_{allow}</math>||= allowable stress range (ksi)
 
 
|-
 
|-
|<math>\, f_{min}</math>||= algebraic minimum stress level ksi):
+
|colspan="2"| &nbsp;
 
|-
 
|-
| &nbsp;||positive if  tension, negative if compression.  
+
|[[Image:751.40 general superstructure-HS20 modified (30ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
|-
|valign="top"|<math>\, r/h</math>||= ratio of base radius to height of rolled-on transverse deformation; if the actual value is not know, 0.3 may be used.
+
!colspan="2"|HS20 Modified (30'-0" ROADWAY - 4 GIRDER)
 
|-
 
|-
|<math>fr_{allow}</math>||= <math>\, 23.4 - 0.33 f_{min}</math> &nbsp; &nbsp; when <math>\, r/h
+
|colspan="2"| &nbsp;
= 0.3</math>
 
|}
 
 
 
Fatigue research has shown that increasing minimum tensile stress results in a decrease in fatigue strength for a tension to tension stresses case.  The fatigue strength increases with a bigger compressive stress in a tension to compression stresses case.
 
 
 
 
 
'''Actual Stress Range:''' <math>\, fr_{act}</math>
 
 
 
The actual stress range, <math>\, fr_{act}</math>, is found using dead load, live load, and impact from service loads.
 
 
 
{|
 
|<math>\, fr_{act}</math>||colspan="2"|= <math>\, f_{GT} - f_{LT}</math>
 
 
|-
 
|-
|<math>\, f_{GT}</math>||colspan="2"|= greatest tension stress level (ksi), always positive.
+
|[[Image:751.40 general superstructure-HS20 (32ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
|-
| &nbsp;||colspan="2"|(Not necessary to check compression to compression for fatigue.)
+
!colspan="2"|HS20 (32'-0" ROADWAY - 4 GIRDER)
 
|-
 
|-
|<math>\, f_{LT}</math>||colspan="2"|= algebraic least stress level  (ksi):
+
|colspan="2"| &nbsp;
 
|-
 
|-
| &nbsp;||<math>\, f_{LT}</math>||= positive if  the least stress is tension
+
|[[Image:751.40 general superstructure-HS20 modified (32ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
|-
| &nbsp;|| &nbsp;||'''(tension to tension stresses)'''
+
!colspan="2"|HS20 Modified (32'-0" ROADWAY - 4 GIRDER)
 
|-
 
|-
| &nbsp;||<math>\, f_LT</math>||= negative if  the least stress is compression
+
|colspan="2"| &nbsp;
 
|-
 
|-
| &nbsp;|| &nbsp;||(tension to compression stresses)
+
|[[Image:751.40 general superstructure-HS20 (36ft0in ROADWAY - 5 GIRDER).gif]]
|}
 
 
 
 
 
'''Tension and Compression Stress Computation'''
 
 
 
Tension and compression stress are determined by using the following formulae for double reinforced concrete rectangular beams.
 
 
 
<math>\, f_s</math> = tensile stress in reinforcement at service loads (ksi)
 
 
 
:Tensile stress &nbsp; <math>\, f_s = \frac {M}{A_s j d}</math>
 
 
 
<math>\, f'_s</math> = compressive stress in reinforcement at service loads (ksi)
 
 
 
:Compressive stress &nbsp; <math>\, f'_s = \frac {M}{A_s j d} \Bigg( \cfrac {k - \frac {d^1}{d}} {1 - k} \Bigg)</math>
 
 
 
Where:
 
 
 
<math>\, j = \cfrac {k^2 \Big( 1 - \frac {k}{c} \Big) + 2 \rho'n \Big( k - \frac {d'}{d} \Big) \Big( 1 - \frac {d'}{d} \Big)}{k^2 + 2 \rho'n \Big( k - \frac {d'}{d} \Big)}</math> &nbsp; &nbsp; &nbsp;'''Eq. 2.2-1'''
 
 
 
 
 
<math>\, k = \sqrt{2n \Bigg( \rho + \rho' \Bigg( \frac{d'}{d}\Bigg) \Bigg) + n^2 \big( \rho + \rho' \big)^2 - n \big( \rho + \rho' \big)}</math> &nbsp; &nbsp; &nbsp;'''Eq. 2.2-2'''
 
 
 
 
 
{|
 
|<math>\, \rho</math>||= tension reinforcement ratio, &nbsp; <math>\, \rho = \frac{A_s}{bd}</math>
 
 
|-
 
|-
|<math>\, \rho'</math>||= compression reinforcement ratio, &nbsp; <math>\, \rho' = \frac{A'_s}{bd}</math>
+
!colspan="2"|HS20 (36'-0" ROADWAY - 5 GIRDER)
 
|-
 
|-
|<math>\, A_s</math>||= area of tension reinforcement (sq. inch)
+
|colspan="2"| &nbsp;
 
|-
 
|-
|<math>\, A'_s</math>||= area of compression reinforcement (sq. inch)
+
|[[Image:751.40 general superstructure-HS20 modified (36ft0in ROADWAY - 5 GIRDER).gif]]
 
|-
 
|-
|<math>\, b</math>||= width of beam (inch)
+
!colspan="2"|HS20 Modified (36'-0" ROADWAY - 5 GIRDER)
 
|-
 
|-
|<math>\, d</math>||= distance from extreme compression fiber to centroid of tension reinforcement (inch)
+
|colspan="2"| &nbsp;
 
|-
 
|-
|<math>\, d'</math>||= distance from extreme compression fiber to centroid of compression reinforcement (inch)
+
|[[Image:751.40 general superstructure-HS20 (38ft0in ROADWAY - 5 GIRDER)(unsymmetrical).gif]]
 
|-
 
|-
|<math>\, jd</math>||= distance from tensile steel to resultant compression (inch)
+
!colspan="2"|HS20 (38'-0" ROADWAY - 5 GIRDER)(Unsymmetrical)
 
|-
 
|-
|<math>\, kd</math>||= distance from neutral plane to compression surface (inch)
+
|colspan="2"| &nbsp;
 
|-
 
|-
|<math>\, n</math>||= ratio of modulus of elasticity of steel to that of concrete
+
|[[Image:751.40 general superstructure-HS20 modified (38ft0in ROADWAY - 5 GIRDER)(unsymmetrical).gif]]
|}
 
 
 
=== 751.40.8.4 Standard Details ===
 
 
 
 
 
==== 751.40.8.4.1 Welding Details ====
 
 
 
All welding shall be detailed in accordance with ANSI / AASHTO / AWS D1.5, Bridge Welding Code.
 
 
 
For ASTM A709, Grade 36 steel  (Service Load Design <math>\, F_u</math>  = 58,000 psi) the allowable shear stress in fillet welds ( <math>\, F_V</math> ) is:
 
 
 
<math>\, F_V = 0.27 F_u</math>
 
 
 
Where:
 
{|
 
|<math>\, F_V</math>||= allowable basic shear stress
 
 
|-
 
|-
|<math>\, F_u</math>||= tensile strength of the electrode classification but not greater than the tensile strength of the connected part
+
!colspan="2"|HS20 Modified (38'-0" ROADWAY - 5 GIRDER)(Unsymmetrical)
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-HS20 (40ft0in ROADWAY - 5 GIRDER).gif]]
 +
|-
 +
!colspan="2"|HS20 (40'-0" ROADWAY - 5 GIRDER)
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-HS20 modified (40ft0in ROADWAY - 5 GIRDER).gif]]
 +
|-
 +
!colspan="2"|HS20 Modified (40'-0" ROADWAY - 5 GIRDER)
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-HS20 (44ft0in ROADWAY - 5 GIRDER).gif]]
 +
|-
 +
!colspan="2"|HS20 (36'-0" ROADWAY - 5 GIRDER)
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-HS20 modified (44ft0in ROADWAY - 5 GIRDER).gif]]
 +
|-
 +
!colspan="2"|HS20 Modified (36'-0" ROADWAY - 5 GIRDER)
 +
|-
 +
|colspan="2"| &nbsp;
 
|}
 
|}
  
 +
==== 751.40.8.5.2 Timber Floor ====
  
 
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 
{|border="1" style="text-align:center;" cellpadding="5" align="center"
|+'''Allowable Shear Loads for Fillet Welds (*)'''
 
|'''Size of Fillet Weld'''<br/>(Inch)||'''Allowable Shear Loads per Length'''<br/>(Pound per lineal inch)
 
 
|-
 
|-
|1/8”||1,380
+
!colspan="3"|Maximum stringer spacing as determined by strength of timber floor
 +
|-
 +
!colspan="3"|Stress = 1,200 lbs. per square inch
 
|-
 
|-
|3/16”||2,075
+
!width="200pt"| &nbsp;||width="200pt"|H-10||width="200pt"|H-15
 
|-
 
|-
|1/4"||2,770
+
|(*) 3" x 12" Plank||18" + 1/2 Flange Width||16" + 1/2 Flange Width
 
|-
 
|-
|5/16”||3,460
+
|4" Laminated Floor||2'-11" + 1/2 Flange Width||2'-3" + 1/2 Flange Width
 
|-
 
|-
|3/8”||4,150
+
|6" Laminated Floor||6'-0" + 1/2 Flange Width||4'-4" + 1/2 Flange Width
 
|-
 
|-
|1/2"||5,535
+
!colspan="3"|Stress = 1,600 lbs. per square inch
 
|-
 
|-
|5/8”||6,920
+
! &nbsp; ||H-10||H-15
 
|-
 
|-
|3/4"||8,300
+
|3" x 12" Plank||23" + 1/2 Flange Width||21" + 1/2 Flange Width
 
|-
 
|-
|7/8”||9,690
+
|4" Laminated Floor||3'-9" + 1/2 Flange Width||2'-11 1/2" + 1/2 Flange Width
 
|-
 
|-
|1”||11,070
+
|6" Laminated Floor||7'-10 3/4" + 1/2 Flange Width||5'-9" + 1/2 Flange Width
 
|}
 
|}
 +
<center>(*) 3" x 12" Plank without treads.</center>
  
 +
==== 751.40.8.5.3 Steel Grid Bridge Flooring ====
  
(*) Allowable Shear Load = <math>\, (0.27)(58000 psi)(0.707xSize of Weld)(L)</math>
+
In general, the 5" depth (concrete filled to half depth) steel grid bridge flooring shall be specified.  Bar spacing may vary as necessary to meet minimum section modulus requirements.  Main member spacing shall not exceed  10" and cross bar spacing shall not exceed 4".  At present, the manufacturers of the following types have provided data to show they are acceptable:
 
+
Where:
+
:Greulich 5" Standard
{|
+
:Foster 5" Standard
|align="right"| <math>\, L</math>||= Effective Length, in inch
+
   
 +
The section properties <math>\, (n = 8)</math> and maximum span for HS20 loading have been computed for these types and are as follows:
 +
 
 +
 
 +
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 +
|-
 +
|rowspan="3" width="75pt"|Company
 +
|rowspan="3"|(For Design<br/>Purpose only)<br/>Weight (PSF)<br/>(Steel & Conc.)
 +
|rowspan="3"|Main bar<br/>Spacing
 +
|rowspan="3"|Cross bar<br/>Spacing
 +
|colspan="3"|Moment of Inertia<br/><math>\, (in^4/Ft.)</math>
 +
|-
 +
|colspan="2"|Mid Span
 +
||Over-Support
 +
|-
 +
|Conc.||Steel||Steel
 
|-
 
|-
|align="right"| <math>\, (0.707xSize of Weld)</math>||= Effective Throat, in inch
+
|Greulich||width="100pt"|48.0||width="50pt"|7 1/2"||width="50pt"|3 3/4"||width="50pt"|99.41||width="50pt"|12.43||width="50pt"|9.03
 
|-
 
|-
|align="right"| <math>\, (0.707xSize of Weld)(L)</math>||= Effective weld area in sq. inch
+
|Foster||48.0||8"||4"||128.1||16.01||12.25
 
|}
 
|}
  
==== 751.40.8.4.2 Development and splicing of Reinforcement ====
 
  
===== 751.40.8.4.2.1 General =====
+
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 +
|-
 +
|rowspan="3" width="75pt"|Company
 +
|colspan="4"|Section Modulus <math>\, (in^2/ft.)</math>
 +
|colspan="4"|Maximum Span (*)
 +
|-
 +
|colspan="2"|Mid-Span
 +
|colspan="2"|Over-Support
 +
|colspan="2"|Simple Span
 +
|colspan="2"|Continuous Spans
 +
|-
 +
|width="50pt"|Conc.<br/>(Top)
 +
|width="50pt"|Steel<br/>(Bott.)
 +
|width="50pt"|Steel<br/>(Top)
 +
|width="50pt"|Steel<br/>(Bott.)
 +
|width="50pt"|ASTM<br/>A709<br/>Gr. 36
 +
|width="50pt"|ASTM<br/>A709<br/>Gr. 50W
 +
|width="50pt"|ASTM<br/>A709<br/>Gr. 36
 +
|width="50pt"|ASTM<br/>A709<br/>Gr. 50W
 +
|-
 +
|Greulich||59.5||3.53||3.90||3.14||4'-4"||5'-10"||5'-10"||7'-1"
 +
|-
 +
|Foster||72.5||4.68||5.25||4.30||5'-9"||7'-5"||7'-2"||9'-4"
 +
|}
  
'''Development of Tension Reinforcement'''
 
  
Development lengths for tension reinforcement shall be calculated in accordance with AASHTO Article 8.25. Development length modification factors described in AASHTO Articles 8.25.3.2 and 8.25.3.3 shall only be used in situations where development length without these factors is difficult to attain. All other modification factors shown shall be used.
+
The cross-section DETAILS used in computing the section properties are shown on the sketches on the following sheets. Maximum span determination included an allowance for a 35#/sq.ft. future
 
+
wearing surface and assumed a wheel load to be distributed, normal to the main bars, over a width of 4'-0".
Development lengths for tension reinforcement have been tabulated on the following pages and include the modification factors except those described above.
+
 +
(Place the following note on the Bridge Plans with the Steel Grid Details.
 +
 +
Note: The steel grid deck shall be electrically grounded.
  
 +
(*) For main beams of grid either parallel or perpendicular to traffic.
  
'''Lap Splices of Tension Reinforcement'''
 
  
Lap splices of reinforcement in tension shall be calculated in accordance with AASHTO Article 8.32.1 and 8.32.3. Class C splices are preferred when possible, however it is permissible to use Class A or B when physical space is limited. The designer shall satisfy AASHTO Table 8.32.3.2 when using Class A or B splices. It should be noted that As required is based on the stress encountered at the splice location, which is not necessarily the maximum stress used to design the reinforcement.
+
<center>[[Image:751.40 general superstructure-greulich 5in standard.gif]]</center>
  
Temperature and shrinkage reinforcement is assumed to fully develop the specified yield stresses. Therefore the development length shall not be reduced by (<math>\, A_s</math> required)/(<math>\, A_s</math> supplied).
+
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 +
|-
 +
|&nbsp;||Composite Section||Steel Section Only (net)
 +
|-
 +
|y||1.671"||2.317"
 +
|}
  
Splice lengths for tension reinforcement have been tabulated on the following pages and include the development length modifications as described above.
 
  
 +
<center>'''Greulich 5" Standard'''</center>
  
'''Development of Tension Hooks'''
+
{|border="0" style="text-align:center;" cellpadding="2" align="center"
 +
|-
 +
|Note:||Dimensions obtained form Greulich plans.
 +
|}
  
Development of tension hooks shall be calculated in accordance with AASHTO Article 8.29. Hook length modification factors described in Articles 8.29.3.3 and 8.29.3.4 shall only be used in situations where hook length without these factors is difficult to attain. All other modification factors shown shall be used.
 
  
Development lengths of tension hooks have been tabulated on the following pages and include the modification factors except those described above.
+
<center>[[Image:751.40 general superstructure-foster 5in standard.gif]]</center>
  
 +
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 +
|-
 +
|&nbsp;||Composite Section||Steel Section Only (net)
 +
|-
 +
|y||1.766"||2.338"
 +
|}
  
'''Development of Compression Reinforcement'''
 
 
Development lengths for compression reinforcement shall be calculated in accordance with AASHTO Article 8.26. Development length modification factors described in AASHTO Articles 8.26.2.1 and 8.26.2.2 shall only be used in situations where development length without these factors is difficult to attain. All other modification factors shown shall be used.
 
  
Development lengths for compression reinforcement have been tabulated on the following pages and include the modification factors except those described above.
+
<center>'''Foster 5" Standard'''</center>
  
 +
{|border="0" style="text-align:center;" cellpadding="2" align="center"
 +
|-
 +
|Note:||Dimensions obtained form Foster Catalog.
 +
|}
  
'''Lap Splices of Compression Reinforcement'''
+
==== 751.40.8.5.4 Longitudinal Diagrams ====
  
Lap splices of reinforcement in compression shall be calculated in accordance with AASHTO Article 8.32.1 and 8.32.4.
 
  
Splice lengths for compression reinforcement have been tabulated on the following pages.
+
===== 751.40.8.5.4.1 Hinged Beam Connections =====
  
 +
The diagrams of various joints in steel structures are intended to be guides primarily for the determination of horizontal longitudinal dimensions for the plan view on the first sheet of plans.
 +
 +
These diagrams are not to be detailed on the design plans.  However, the arrangement of the joints should be useful in detailing the longitudinal diagram for structural steel, particularly for bridges on grades and vertical curves.
 +
 +
Longitudinal dimensions for the plan of structural steel and for the plan of slab shall be horizontal from centerline bearing to centerline bearing.
 +
 +
For proper correlation of details when developing plans for widening or redecking bridges, match the method of dimensioning on the new plans with the method used on the originals.
  
'''Mechanical Bar Splices'''
 
  
Mechanical bar splices may be used in situations where it is not possible or feasible to use lap splices. Mechanical bar splices shall meet the criteria of AASHTO Article 8.32.2. Refer to the manufacturers literature for more information on the design of mechanical bar splices.
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
+
|+'''Hinged Beam Connections'''
===== 751.40.8.4.2.2 Development and Tension Lap Splice Lengths - Top Bars  (<math>\, F_y</math> = 60 ksi) =====
+
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves1.gif]]
 +
|-
 +
!Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves
 +
|-
 +
|&nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Flat Grade.gif]]
 +
|-
 +
!Geometrics for Hinged Beam Connections for Bridges on Flat Grade
 +
|-
 +
|&nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Straight, Plus Grades.gif]]
 +
|-
 +
!Geometrics for Hinged Beam Connections for Bridges on Straight, Plus Grades
 +
|-
 +
|&nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves.gif]]
 +
|-
 +
!Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves
 +
|-
 +
|&nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves2.gif]]
 +
|-
 +
!Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves
 +
|-
 +
|&nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Symmetrical Vertical Curves.gif]]
 +
|-
 +
!Geometrics for Hinged Beam Connections for Bridges on Symmetrical Vertical Curves
 +
|-
 +
|&nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves1.gif]]
 +
|-
 +
!Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves
 +
|}
  
  
<center>[[Image:751.40 reinforcement- Development and Tension Lap Splice Lengths - Top Bars (Fy = 60 ksi).gif]]</center>
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|+'''Hanger Beam Connections'''
 +
|[[Image:751.40 general superstructure-Geometrics for Hanger Beam Connections for Bridges on Crown Vertical Curves.gif]]
 +
|-
 +
!Geometrics for Hanger Beam Connections for Bridges on Crown Vertical Curves
 +
|-
 +
|&nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-Geometrics for Hanger Beam Connections for Bridges on Sag Vertical Curves.gif]]
 +
|-
 +
!Geometrics for Hanger Beam Connections for Bridges on Sag Vertical Curves
 +
|}
  
  
Top reinforcement is placed so that more than 12” of concrete is cast below the reinforcement.
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
+
|+'''Pin Plate Connections'''
Class A splice =1.0 <math>\, L_d</math>, Class B splice =1.3 <math>\, L_d</math>, Class C splice =1.7 <math>\, L_d</math>
+
|[[Image:751.40 general superstructure-Geometrics for Pin Plate Connections for Bridges on Crown Vertical Curves.gif]]
 
+
|-
Use development and tension lap splices of <math>\, f'_c</math> = 4 ksi for concrete strengths greater than 4 ksi.
+
!Geometrics for Pin Plate Connections for Bridges on Crown Vertical Curves
 +
|-
 +
|&nbsp;
 +
|-
 +
|[[Image:751.40 general superstructure-Geometrics for Pin Plate Connections for Bridges on Sag Vertical Curves.gif]]
 +
|-
 +
!Geometrics for Pin Plate Connections for Bridges on Sag Vertical Curves
 +
|}
  
===== 751.40.8.4.2.3 Development and Tension Lap Splice Lengths - Other Than Top Bars (<math>\, F_y</math> = 60 ksi) =====
+
===== 751.40.8.5.4.2 Longitudinal Sections =====
  
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|+'''Expansion Device at End Bent'''
 +
|Colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-expansion device at end bent(not on grade).gif]]
 +
|-
 +
!Bearing Stiffener||Connection Plate
 +
|-
 +
!colspan="2"|Structures Not on Grade (Typical)
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
|colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-expansion device at end bent(on grade).gif]]
 +
|-
 +
!Colspan="2"|Structures on Grade (Typical)
 +
|}
  
<center>[[Image:751.40 reinforcement- Development and Tension Lap Splice Lengths - Other Than Top Bars (Fy = 60 ksi).gif]]</center>
+
{|border="0" cellpadding="5" cellspacing="1" align="center"
 +
|-
 +
|align="right" valign="top"|(*)||width="400pt"|Parallel to Girder.  All other dimensions shown are normal to backwall.
 +
|-
 +
|align="right" valign="top"|(**)||width="400pt"|See [[751.13 Expansion Devices|EPG 751.13 Expansion Devices]] for dimension of overhang from end of stringer or girder to face of plate, edge of concrete or face of vertical leg of angle.
 +
|}
  
  
Class A splice =1.0 <math>\, L_d</math>, Class B splice =1.3 <math>\, L_d</math>, Class C splice =1.7 <math>\, L_d</math>
 
  
Use development and tension lap splices of <math>\, f'_c</math> = 4 ksi for concrete strengths greater than 4 ksi.
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|+'''No Expansion Device at End Bent'''
 +
|Colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-no expansion device at end bent(not on grade) 1.gif]]
 +
|-
 +
!Bearing Stiffener||Connection Plate
 +
|-
 +
!colspan="2"|Structures Not on Grade (Typical)
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
|colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-no expansion device at end bent(on grade) 1.gif]]
 +
|-
 +
!Colspan="2"|Structures on Grade (Typical)
 +
|}
  
===== 751.40.8.4.2.4 Development and Lap Splice Lengths - Bars in Compression (<math>\, F_y</math> = 60 ksi) =====
+
{|border="0" cellpadding="5" cellspacing="1" align="center"
 +
|-
 +
|align="right" valign="top"|(*)||width="400pt"|Parallel to Girder. All other dimensions shown are normal to backwall.
 +
|-
 +
|align="right" valign="top"|(**)||width="400pt"|18" min. (Use same dimension as the expansion device end on 3-span continuous, if it is not more than 2" greater.)
 +
|-
 +
|align="right" valign="top"|(***)||width="400pt"|3" min. for type C, D and E bearing, and 2" min. for an elastomeric bearing.
 +
|}
  
  
<center>[[Image:751.40 reinforcement- Development and Lap Splice Lengths - Bars in Compression (Fy = 60 ksi).gif]]</center>
 
  
  
Development length for spirals, <math>\, L_d</math>, <math>\, _{spiral}</math>, should be used if reinforcement is enclosed in a spiral of not less than 1/4” diameter and no more than 4” pitch. See AASHTO 8.26 for special conditions.
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|+'''Intermediate Bent'''
 +
|width="300pt"|[[Image:751.40 general superstructure-longitudinal sections-intermediate bent-no expansion device.gif]]
 +
|width="300pt"|[[Image:751.40 general superstructure-longitudinal sections-intermediate bent-expansion device.gif]]
 +
|-
 +
!No Expansion Device||Expansion Device
 +
|}
  
All values are for splices with the same size bars. For different size bars, see AASHTO 8.32.4.
+
{|border="0" cellpadding="5" cellspacing="1" align="center"
 
+
|-
(*) Lap splices for #14 and #18 bars are not permitted except as column to footing dowels.
+
|align="right" valign="top"|[[Image:751.40 circled 1.gif]]||width="400pt"|1/2" minimum overhang from end of stringer to face of plate, edge of concrete or face of vertical leg of angle.
 +
|-
 +
|align="right" valign="top"|[[Image:751.40 circled 2.gif]]||width="400pt"|Gap as required for a particular type of expansion device.
 +
|-
 +
|align="right" valign="top"|[[Image:751.40 circled 3.gif]]||width="400pt"|Expansion device gap plus 1 1/2" minimum (taken parallel to centerline stringer).
 +
|-
 +
|align="right" valign="top"|(*)||width="400pt"|Parallel to Girder.  All other dimensions shown are normal to centerline Bent.
 +
|-
 +
|colspan="2" align=left" valign-"top"|Blockout shown is for Elastomeric Expansion Joint Seal.  Check<br/>Bridge Memorandum for type of device for a particular structure.
 +
|}
  
===== 751.40.8.4.2.5 Development of Standard Hooks in Tension, Ldh  (<math>\, F_y</math> = 60 ksi) =====
 
  
The development length, <math>\, L_{dh}</math>, is measured from the critical section to the outside edge of hook. The tabulated values are valid for both epoxy and uncoated hooks.
 
  
  
<center>[[Image:751.40 reinforcement- Development of Standard Hooks in Tension, Ldh (Fy = 60 ksi).gif]]</center>
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
+
|+'''Expansion Device at Any Bent'''
 
+
|[[Image:751.40 general superstructure-longitudinal sections-expansion device at any bent-end(no grade).gif]]
'''Case A''' - For #11 bar and smaller, side cover (normal to plane of hook) less than 2 1/2 inches and for a 90 degree hook with cover on the hook extension less than 2 inches.
+
|[[Image:751.40 general superstructure-longitudinal sections-expansion device at any bent-int(no grade).gif]]
 
 
'''Case B''' - For #11 bar and smaller, side cover (normal to plane of hook) greater than 2 1/2 inches and for a 90-dgree hook with cover on the hook extension 2 inches or greater.
 
 
 
(*) See Structural Project Manager before using #14 or #18 hook.
 
 
 
{| border="0" cellpadding="3" cellspacing="1" align="center" style="text-aling:center"
 
 
 
| rowspan="4"|[[Image:751.40 reinforcement-DETAIL NEAR FREE EDGE OR CONSTRUCTION JOINT.gif]]
 
| rowspan="4" width="40px"|&nbsp;
 
|[[Image:751.40 reinforcement- HOOKED-BAR DETAILS FOR DEVELOPMENT OF STANDARD HOOKS.gif]]
 
 
|-
 
|-
|(1) = <math>\,4d_b</math> (#3 thru #8)
+
!colspan="2"|Structures Not on Grade (Typical)
 
|-
 
|-
|(1) = <math>\,5d_b</math> (#9, #10 and #11)
+
|colspan="2"| &nbsp;
 
|-
 
|-
|(1) = <math>\,6d_b</math> (#14 and #18)
+
|colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-expansion device at any bent-end(on grade).gif]]
 
|-
 
|-
!DETAILS NEAR FREE EDGE <br\>OR CONSTRUCTION JOINT||&nbsp;||HOOKED-BAR DETAILS FOR<br\>DEVELOPMENT OF STANDARD HOOKS
+
!colspan="2"|Structures On Grade (Typical)
 
|}
 
|}
  
===== 751.40.8.4.2.6 Development of uncoated Grade 40 deformed bars in tension, <math>\, L_d</math> (AASHTO 8.25) =====
 
  
  
{|border="1" style="text-align:center;" cellpadding="5" align="center" cellspacing="0"
+
 
|+'''Bars spaced laterally less than 6 inches on center or less than 3 inches concrete cover in direction of the spacing'''
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
!rowspan="2" width="50pt"|Bar||colspan="2"|<math>\, f'_c</math> = 3 ksi||colspan="2"|<math>\, f'_c</math> = 4 ksi||colspan="2"|<math>\, f'_c</math> = 5 ksi
+
|+'''Point on Rotation of Bearings'''
 +
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-type c bearing.gif]]
 +
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-type c bearing grade 4% and greater.gif]]
 
|-
 
|-
|width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar||width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar||width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar
+
!valign="top" width="300pt"|Type "C" Bearing||width="300pt"|Type "C" Bearing<br/>(Grade 4% and Greater)
 
|-
 
|-
|#3||12||12||12||12||12||12
+
|colspan="2"| &nbsp;
 
|-
 
|-
|#4||12||12||12||12||12||12
+
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-type d bearing.gif]]
 +
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-type e bearing.gif]]
 
|-
 
|-
|#5||12||14||12||14||12||14
+
!width="300pt"|Type "D" Bearing||width="300pt"|Type "E" Bearing
 
|-
 
|-
|#6||13||19||12||17||12||17
+
|colspan="2"| &nbsp;
 
|-
 
|-
|#7||18||25||16||22||14||20
+
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-flat plate bearing.gif]]
 +
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-prestressed structure bearing pad.gif]]
 
|-
 
|-
|#8||23||33||20||28||18||25
+
!width="300pt"|Flat Plate Bearing<br/>(For Grade 2% and Greater)||width="300pt"|Prestressed Structure<br/>Bearing Pad
 
|-
 
|-
|#9||30||41||26||36||23||32
+
|colspan="2"| &nbsp;
 
|-
 
|-
|#10||38||52||33||45||29||41
+
|colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-steel structure bearing pad.gif]]
 
|-
 
|-
|#11||46||64||40||56||36||50
+
!colspan="2"|Steel Structure<br/>Bearing Pad
|-
 
|#14||63||87||54||76||49||68
 
|-
 
|#18||81||113||70||98||63||88
 
 
|}
 
|}
  
  
{|border="1" style="text-align:center;" cellpadding="5" align="center" cellspacing="0"
+
 
|+'''Bars spaced laterally 6 inches or more on center and at least 3 inches concrete cover in direction of the spacing'''
+
 
!rowspan="2" width="50pt"|Bar||colspan="2"|<math>\, f'_c</math> = 3 ksi||colspan="2"|<math>\, f'_c</math> = 4 ksi||colspan="2"|<math>\, f'_c</math> = 5 ksi
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|+'''Blocking Diagram'''
 +
|[[Image:751.40 general superstructure-longitudinal sections-blocking diagram.gif]]
 
|-
 
|-
|width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar||width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar||width="75pt"|<math>\, L_d</math>||width="75pt"|<math>\, L_d</math> Top bar
+
!Elevation of Longitudinal Steel Diagram
 +
|}
 +
 
 +
{|border="0" cellpadding="5" cellspacing="1" align="center"
 
|-
 
|-
|#3||12||12||12||12||12||12
+
|align="right" valign="top"|Note:||width="400pt"|The typical elevation shown above should be detailed on the plans for all steel structures that are on vertical curve grades.
 
|-
 
|-
|#4||12||12||12||12||12||12
+
|align="right" valign="top"|(1)||width="400pt"|Longitudinal dimensions are horizontal from centerline Brg. to centerline Brg.
 
|-
 
|-
|#5||12||12||12||12||12||12
+
|align="right" valign="top"|(*)||width="400pt"|Horizontal dimensions.
 
|-
 
|-
|#6||12||15||12||14||12||14
+
!colspan="2"|BLOCKING DIAGRAM SHOULD NOT BE USED FOR CAMBERED GIRDERS.
 +
|}
 +
 
 +
==== 751.40.8.5.5 Miscellaneous Bearing Connections ====
 +
 
 +
 
 +
===== 751.40.8.5.5.1 Typical Details of “Hinged Connection" =====
 +
 
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|-
|#7||15||20||13||18||12||16
+
|colspan="3"|[[Image:751.40 general superstructure-misc details-section showing hinged beam conn1.gif]]
 
|-
 
|-
|#8||19||26||16||23||15||20
+
!colspan="3"|Section Showing Hinged Beam Connection
 
|-
 
|-
|#9||24||33||21||29||19||26
+
|colspan="3"| &nbsp;
 
|-
 
|-
|#10||30||42||26||36||23||33
+
|rowspan="2"|[[Image:751.40 general superstructure-misc details-detail of web at radius transition.gif]]
 +
|valign="bottom"|[[Image:751.40 general superstructure-misc details-plan of brg plate.gif]]
 +
|rowspan="2"|[[Image:751.40 general superstructure-misc details-typ welding details for stiffeners.gif]]
 
|-
 
|-
|#11||37||52||32||45||29||40
+
!valign="top"|Plan of Brg. Plate
 
|-
 
|-
|#14||50||70||44||61||39||54
+
!Detail of Web at<br/>Radius Transition|| &nbsp;||Typical Welding Details<br/>for Stiff. Plates
 
|-
 
|-
|#18||65||90||56||78||50||70
+
|colspan="3"| &nbsp;
|}
 
 
 
===== 751.40.8.4.2.7 Minimum lap length for uncoated Grade 40 tension lap splices, <math>\, L_{lap}</math> (AASHTO 8.32) =====
 
 
 
{|border="1" style="text-align:center;" cellpadding="5" align="center" cellspacing="0"
 
|+'''Bars spaced less than 6 inches laterally on center and at least 3 inches concrete cover in direction of the spacing'''
 
!rowspan="2"| &nbsp;||colspan="9"|Other than Top Bars||colspan="9"|Top Bars
 
 
|-
 
|-
|colspan="3"|<math>\, f'_c</math> = 3 ksi||colspan="3"|<math>\, f'_c</math> = 4 ksi||colspan="3"|<math>\, f'_c</math> = 5 ksi||colspan="3"|<math>\, f'_c</math> = 3 ksi||colspan="3"|<math>\, f'_c</math> = 4 ksi||colspan="3"|<math>\, f'_c</math> = 5 ksi
+
|[[Image:751.40 general superstructure-misc details-section c-c.gif]]
 +
| colspan="2" rowspan="2" |
 +
{|border="0" cellpadding="3" cellspacing="1" align="center"
 
|-
 
|-
|Bar||A||B||C||A||B||C||A||B||C||A||B||C||A||B||C||A||B||C
+
|valign="top" align="right"|"D"||align="left" width="375pt" |Gap as required for expansion (3" Min.)
 
|-
 
|-
|#3||12||12||12||12||12||12||12||12||12||12||16||21||12||16||21||12||16||21
+
|valign="top" align="right"|"J"||align="left" width="375pt" |5" for bearing with 3" web thickness. Use 6" for all others.
 
|-
 
|-
|#4||12||12||14||12||12||14||12||12||14||12||16||21||12||16||21||12||16||21
+
|valign="top" align="right"|[[Image:751.40 circled 1.gif]]||align="left" width="375pt" |Dimension to be 1/3 brg. length (Typ.)
 
|-
 
|-
|#5||12||13||17||12||13||17||12||13||17||14||19||24||14||19||24||14||19||24
+
|valign="top" align="right"|(*)||align="left" width="375pt" |To be used unless greater depth is required by design.
 
|-
 
|-
|#6||13||17||22||12||16||21||12||16||21||19||24||31||17||22||29||17||22||29
+
|valign="top" align="right"|(**)||align="left" width="375pt" |See [[751.13 Expansion Devices|EPG 751.13 Expansion Devices]]
 
|-
 
|-
|#7||18||23||30||16||20||26||14||19||24||25||32||42||22||28||37||20||26||34
+
|valign="top" align="right"|Note:||align="left" width="375pt" |Web thickness and size of fillet weld connecting bearing stiffener plate to web as required by design.
 
|-
 
|-
|#8||23||30||40||20||26||34||18||24||31||33||42||55||28||37||48||25||33||43
+
|valign="top" align="right"| &nbsp;||align="left" width="375pt" |Plans for bridges on a grade or vertical curve shall have the conn. detailed in relation to the slope of the girders and stringers.
 +
|}
 
|-
 
|-
|#9||30||38||50||26||33||43||23||30||39||41||54||70||36||47||61||32||42||54
+
!Section C-C
|-
 
|#10||38||49||63||33||42||55||29||38||49||52||68||89||45||59||77||41||53||69
 
|-
 
|#11||46||60||78||40||52||68||36||46||61||64||84||109||56||72||95||50||65||85
 
 
|}
 
|}
  
  
  
{|border="1" style="text-align:center;" cellpadding="5" align="center" cellspacing="0"
+
 
|+'''Bars spaced 6 inches or more laterally on center and at least 3 inches concrete cover in direction of the spacing'''
+
 
!rowspan="2"| &nbsp;||colspan="9"|Other than Top Bars||colspan="9"|Top Bars
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|-
|colspan="3"|<math>\, f'_c</math> = 3 ksi||colspan="3"|<math>\, f'_c</math> = 4 ksi||colspan="3"|<math>\, f'_c</math> = 5 ksi||colspan="3"|<math>\, f'_c</math> = 3 ksi||colspan="3"|<math>\, f'_c</math> = 4 ksi||colspan="3"|<math>\, f'_c</math> = 5 ksi
+
|colspan="4"|[[Image:751.40 general superstructure-misc details-section showing hinged beam conn2.gif]]
 
|-
 
|-
|Bar||A||B||C||A||B||C||A||B||C||A||B||C||A||B||C||A||B||C
+
!colspan="4"|Section Showing Hinged Beam Connection
 
|-
 
|-
|#3||12||12||12||12||12||12||12||12||12||12||16||21||12||16||21||12||16||21
+
|colspan="4"| &nbsp;
 
|-
 
|-
|#4||12||12||12||12||12||12||12||12||12||12||16||21||12||16||21||12||16||21
+
|colspan="4"|[[Image:751.40 general superstructure-misc details-sections d-d & e-e.gif]]
 
|-
 
|-
|#5||12||12||14||12||12||14||12||12||14||12||16||21||12||16||21||12||16||21
+
!width="15%"| &nbsp;||Section D-D||Section E-E||width="18%"| &nbsp;
 
|-
 
|-
|#6||12||14||18||12||13||17||12||13||17||15||19||25||14||18||23||14||18||23
+
|colspan="4"| &nbsp;
 +
|-
 +
|colspan="4"|[[Image:751.40 general superstructure-misc details-typical welding details for stiffeners.gif]]
 +
|-
 +
!colspan="4"|Typical Welding Details<br/>for Stiff. Plates
 +
|}
 +
 
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|valign="top" align="right"|(*)||align="left"|See below for dimension "G".
 
|-
 
|-
|#7||15||19||24||13||16||21||12||15||20||20||26||34||18||23||29||16||21||27
+
|valign="top" align="right"|(**)||align="left"|See [[751.13 Expansion Devices|EPG 751.13 Expansion Devices]]
 
|-
 
|-
|#8||19||24||32||16||21||28||15||19||25||26||34||44||23||29||38||20||26||34
+
|valign="top" align="right"|"F"||align="left"|= Gap as required for expansion (3" Min.).
 
|-
 
|-
|#9||24||31||40||21||27||35||19||24||31||33||43||56||29||37||49||26||33||44
+
|valign="top" align="right"|"H"||align="left"|= 10 3/4" Min. (12" preferred.)
 
|-
 
|-
|#10||30||39||51||26||34||44||23||30||39||42||54||71||36||47||62||33||42||55
+
|valign="top" align="right"|"J"||align="left"|= 5" for bearing with 3" web thickness. Use 6" for all others.
 
|-
 
|-
|#11||37||48||63||32||42||54||29||37||49||52||67||87||45||58||76||40||52||68
+
|colspan="2"|All dimensions shown are minimum, increase, as necessary.
 
|}
 
|}
  
==== 751.40.8.4.3 Miscellaneous ====
 
  
'''Negative Moment Steel over Intermediate Supports'''
+
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 
+
|+'''Allowable Dead Load Reactions for Various Depths of "G"'''
Dimension negative moment steel over intermediate supports as shown.
+
!width="75pt"|Web<br/>Thickness
 
+
!width="75pt"|Depth<br/>"G"
<center>[[Image:751.40 reinforcement-Negative Moment Steel over Intermediate Supports.gif]]</center>
+
!width="150pt"|(*) Allowable<br/>Dead Load<br/>Reactions, Kips<br/>(At 150% Overstress)
 
+
|rowspan="9"| &nbsp;
{|
+
!width="75pt"|Web<br/>Thickness
!colspan="2" align="left"|Prestressed Structures:
+
!width="75pt"|Depth<br/>"G"
 +
!width="150pt"|(*) Allowable<br/>Dead Load<br/>Reactions, Kips<br/>(At 150% Overstress)
 +
|-
 +
|5/16"||8"||45.0||7/16"||8"||63.0
 
|-
 
|-
|(1)||Bar length by design.
+
|5/16"||9"||50.6||7/16"||9"||70.8
 
|-
 
|-
|(2)||Reinforcement placed between longitudinal temperature reinforcing in top.
+
|5/16"||10"||56.2||7/16"||10"||78.7
|}
 
:{|
 
|Bar size:||#5 bars at 7-1/2" cts. (Min.)
 
 
|-
 
|-
| &nbsp;||#8 bars at 5" cts. (Max.)
+
|5/16"||11"||61.8||7/16"||11"||86.6
|}
 
 
 
{|
 
!colspan="2" align="left"|Steel Structures:
 
 
|-
 
|-
|valign="top"|(1)||Extend into positive moment region beyond "Anchor" Stud shear connectors at least '''40 x bar diameter x 1.5''' (Epoxy Coated Factor)(*) as shown below.  (AASHTO 10.38.4.4 & AASHTO 8.25.2.3)
+
|5/16"||12"||67.5||7/16"||12"||94.5
 
|-
 
|-
|(2)||Use #6 bars at 5" cts. between longitudinal temperature reinforcing in top.
+
|5/16"||13"||73.1||7/16"||13"||102.3
 +
|-
 +
|5/16"||14"||78.8||7/16"||14"||110.2
 +
|-
 +
|5/16"||15"||84.3||7/16"||15"||118.1
 
|}
 
|}
  
<center>[[Image:751.40 reinforcement-elevation of girder showning negative moment steel.gif]]</center>
 
  
{|
+
{|border="1" style="text-align:center;" cellpadding="5" align="center"
|(*)||40 x bar diameter x 1.5 = 40 x 0.75" x 1.5 = 45” for #6 epoxy coated bar.
+
|-
 +
|width="75pt"|3/8"
 +
|width="75pt"|8"
 +
|width="150pt"|54.0
 +
|rowspan="8"| &nbsp;
 +
|width="75pt"|1/2"
 +
|width="75pt"|8"
 +
|width="150pt"|72.0
 +
|-
 +
|3/8"||9"||60.7||1/2"||9"||81.0
 +
|-
 +
|3/8"||10"||67.5||1/2"||10"||90.0
 +
|-
 +
|3/8"||11"||74.2||1/2"||11"||99.0
 +
|-
 +
|3/8"||12"||81.0||1/2"||12"||108.0
 +
|-
 +
|3/8"||13"||87.7||1/2"||13"||117.0
 +
|-
 +
|3/8"||14"||94.5||1/2"||14"||126.0
 +
|-
 +
|3/8"||15"||101.2||1/2"||15"||135.0
 
|}
 
|}
 +
<center>(*) No (Live load + impact) excluded.</center>
  
=== 751.40.8.5 General Superstructure ===
 
  
  
==== 751.40.8.5.1 Concrete Slabs ====
 
  
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|+'''Typical Details of "Hinged" Connection"'''
 +
|[[Image:751.40 general superstructure-misc details-section showing hinged beam conn3.gif]]
 +
|-
 +
!Section Showing Hinged Beam Connection
 +
|}
  
===== 751.40.8.5.1.1 Design Criteria =====
 
  
'''Slabs on Girders'''
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
'''Stresses:'''
 
:{|
 
|<math>\, f_c</math>||= 1,600 psi
 
 
|-
 
|-
|<math>\, f'_c</math>||= 4,000 psi
+
|colspan="2"|[[Image:751.40 general superstructure-misc details-section thru plate girders.gif]]
 
|-
 
|-
|<math>\, n</math>||= 8
+
!valign="top"|Plate Girder 42" Thru 46"<br/>Also 48" and Over
|-
+
!valign="top"|Plate Girder 36" Thru 40"
|<math>\, f_y</math>||= 60,000 psi
 
 
|}
 
|}
  
  
'''Moments Over Interior Support''' (Use for positive moment reinf. also) (Sec. 1.5 E40A)
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
{|
 
|Dead Load =|| <math>\, -0.107wS^2</math> ||(Continuous over 5 supports)
 
 
|-
 
|-
|Dead Load =|| <math>\, -0.100wS^2</math> ||(Continuous over 4 supports)
+
|[[Image:751.40 general superstructure-misc details-detail a.gif]]
 +
|[[Image:751.40 general superstructure-misc details-detail b.gif]]
 +
|-
 +
!Detail "A"||Detail "B"
 
|}
 
|}
{|
+
 
|Live Load =|| <math>\, (S + 2) \frac {P}{32}</math> ||width="20pt"| &nbsp;||Continuity Factor||= 0.8
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|-
| &nbsp; || &nbsp; || &nbsp; ||align="right"|Impact Factor||= 1.3
+
|valign="top" align="right"|Note:||align="left" width="400pt"|Modify standard end diaphragm connections as shown above, if clearance problems exist between bearing plate and end diaphragm connection bolts.
|-
 
| &nbsp; || &nbsp; || &nbsp; ||align="right"|P||= 16 Kips for HS20
 
|-
 
| &nbsp; || &nbsp; || &nbsp; ||align="right"|P||= 20 Kips for HS20 Modified
 
|-
 
|colspan="5"| &nbsp;
 
|-
 
|Design Load:||colspan="4"| &nbsp; <math>\, M_u = 1.3 (M_{DL} + 1.67 M_{LL+I})</math>
 
 
|}
 
|}
  
  
'''Cantilever Moment'''
+
=== 751.40.8.6 Composite Design ===
 +
====751.40.8.6.1 General ====
  
Dead Load = Moment due to slab, F.W.S. and S.B.C.
+
'''GENERAL'''
  
Live Load:
+
This portion of the article pertains to structures composed of steel girders with concrete
 +
slab connected by shear connectors. The stresses of composite girders and slab shall be computed based on the composite cross-section properties and shall be consistent with the
 +
properties of the various materials used. The regions subjected to positive moment are considered as composite and the regions subjected to negative moment are considered as non-composite. For the initial girder design, composite/non-composite regions can be approximately assumed as:
 +
<center>
  
Wheel Load = &nbsp; <math>\, M_{LL=I} = \frac {Px}{E}</math>
+
[[Image:751.40 Widen and Repair Design Assumptions- Initial Girder Design.gif|650px]]
 +
</center>
  
Where:
 
{|
 
|<math>\, P</math>||= Wheel load (apply impact factor)
 
|-
 
|<math>\, x</math>||= Dist. from load to support (ft.)
 
|-
 
|<math>\, E</math>||= <math>\, 0.8x + 3.75</math>
 
|}
 
  
 +
'''SECTION PROPERTIES'''
  
Collision Load = &nbsp; <math>M_{COLL} = \frac {Py}{E}</math>
+
Cross-section properties of the composite section shall include concrete
 +
slab and steel section.
  
Where:
+
Cross-section properties of the non-composite section shall include steel
{|
+
section only.
|<math>\, P</math>||= 10 kips (Collision force)
 
|-
 
|<math>\, y</math>||= Moment arm (Curb ht.+ 1/2 Slab th.)
 
|-
 
|<math>\, E</math>||= <math>\, 0.8x + 5.0</math>
 
|}
 
  
 +
Use composite property for positive moment section.
  
Where:
+
Use non-composite property for negative moment section. The effect of reinforcing steel in the section is not considered.
{|
 
|<math>\, x</math>||= Dist. from C.G. of S.B.C. to support
 
|}
 
  
 +
The ratio of modulus of elasticity of steel to that of concrete, n, shall be assumed to be eight. The effect of creep shall be considered in the design of composite girders which have dead loads acting on the composite section. In such structures, n=24 shall be used.
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|width="250pt" align="left"|The "support" is assumed at the  1/4  pt. of the minimum flange.
 
|rowspan="4"|[[Image:751.40 general superstructure-slab cantilever section.gif]]
 
|-
 
|width="250pt" align="left"|Wheel loads and collision loads shall not be applied simultaneously.
 
|-
 
|width="250pt" align="left"|Use the greater of the two for the Design Load.
 
|-
 
|width="250pt" align="left"|Design Laod:<br./><math>\, M_u = 1.3 (M_{DL} + 1.67 M_{LL+I})</math>
 
|-
 
!&nbsp;||Slab Cantilever Section
 
|}
 
  
Design of top reinf. is based on maximum moment over supports or cantilever moment. Flexural reinforcement shall meet the criteria of AASHTO Art. 8.16.3.
 
 
When designing for bottom transverse reinforcement, a 1" wearing surface is removed from the effective depth.
 
 
Prestressed panels replace the bottom transverse reinforcement.
 
 
Prestressed panels are assumed to carry DL1 stresses. Therefore, the negative moment due to DL1 at interior supports may be neglected.
 
 
The maximum P/S panel width (clear span + 6") for HS20 Modified is 9'-6".  (Based on 10'-0" girder spacing and 10" flanges) The maximum P/S panel width (clear span + 6") for HS20 is 9'-11".
 
  
 +
'''DESIGN UNIT STRESSES''' (also see [[751.50 Standard Detailing Notes#A1. Design Specifications, Loadings & Unit Stresses and Standard Plans|note A1.1 in EPG 751.50 Standard Detailing Notes]])
  
'''Distributioon of Flexural Reinforcement'''
+
'''Reinforcement Concrete'''
  
Allowable Stress: &nbsp; <math>\, f_s = \frac {Z}{(d_c \times A)^{1/3}} \le 0.6 f_y</math>
+
{|style="text-align:left"
 
 
Where:
 
{|
 
|<math>\, Z</math>||= 130 k/in.
 
 
|-
 
|-
|valign="top"|<math>\, d_c</math>||= Dist. from extreme tension fiber to center of closest bar (concrete cover shalll not be taken greater than 2")
+
|width="250"|Reinforcing Steel (Grade 60)||width="150"|<math>\, f_s</math> = 24,000 psi||width="150"|<math>\, f_y</math> = 60,000 psi
 
|-
 
|-
|<math>\, A</math>||= Effective tension area of concrete
+
|Class B-2 Concrete (Substructure)||  <math>\, f_c</math> = 1,600 psi||     <math>\, f'_c</math> = 4,000 psi
|-
 
| &nbsp;||= <math>\, 2d_c s</math>
 
 
|-
 
|-
|<math>\, s</math>||= Bar spacing ctr. to ctr.
 
 
|}
 
|}
 +
'''Structural Steel'''
  
 
Actual Stress: &nbsp; <math>\, f_s = \frac {M_W}{A_S \times j \times d}</math>
 
 
Where:
 
 
{|
 
{|
|<math>\, M_W</math>||= Service load moment
 
 
|-
 
|-
|<math>\, A_S</math>||= Area of steel
+
|width="300"|Structural Carbon Steel (ASTM A709 Grade 36)||width="150"|<math>\, f_s</math> = 20,000 psi||width="150"|<math>\, f_y</math> = 36,000 psi
 
|-
 
|-
|<math>\, j</math>||= <math>\, 1 - k/3</math>
+
|Structural Steel (ASTM A709 Grade 50)||<math>\, f_s</math> = 27,000 psi||<math>\, f_y</math> = 50,000 psi
 
|-
 
|-
|<math>\, k</math>||= <math>\, \sqrt {2n\rho + (n \rho)^2 - n \rho}</math>
+
|Structural Steel (ASTM A709 Grade 50W)||<math>\, f_s</math> = 27,000 psi||<math>\, f_y</math> = 50,000 psi
|-
 
|<math>\, n</math>||= <math>\, E_S/E_C</math>
 
|-
 
|<math>\, \rho</math>||= <math>\, A_S /(b \times d)</math>
 
|-
 
|<math>\, b</math>||= Effective width
 
 
|-
 
|-
|<math>\, d</math>||= Effective depth
 
 
|}
 
|}
  
Distribution of flexural reinforcement does not need to be checked in
+
==== 751.40.8.6.2 Design ====
concrete considered unexposed to weather.
+
===== 751.40.8.6.2.1 Shear Connector Design =====
 
  
'''Longitudinal distribution reinforcement:'''
+
The shear connectors shall be designed for fatigue and checked for ultimate strength (AASHTO Article 10.38.5.1).
+
 
Top of slab - use #5 bars at 15" cts. for temperature distribution.
+
<u>Step 1:</u>
  
Bottom of slab - by design.
+
Compute Vr, the range of shear in kips, from the structural analysis, due to live loads and impact, for entire span.   
   
 
  
'''Negative moment reinforcement over supports:'''
+
At any section, the range of shear shall be taken as the difference in the minimum and maximum shear envelopes (excluding dead loads).
 
Steel structures - add. #6 bars at 5" between #5 bars.
 
  
P/S girder structures - by design.
 
 
Additional reinforcement over supports shall be a minimum of #5 bars and a maximum of #8 bars at 5" ctrs.  When necessary, replace the #5 temperature reinforcement with a larger bar to satisfy negative moment reinforcement requirement, but keep all bars within two bar sizes.
 
 
Note:  See details of negative moment reinforcement.
 
  
 +
<u>Step 2:</u>
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
Use the average Vr per span, for the section of the span that is assumed to act compositely (from end of span to point of contraflexure for end spans, or from point of contraflexure to point of contraflexure for int. spans).
|-
 
|colspan="2"|[[Image:751.40 general superstructure-sections thru slab showing negative moment reinforcement.gif]]
 
|-
 
!width="50%"|CIP Slab||width="50%"|P\S Panel Slab
 
|}
 
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|valign="top" align="right"|[[Image:751.40 circled 1.gif]]||align="left" width="400pt" |3" Cl. preferred min., 2 3/4" Cl. preferred min. for P/S panels to accommodate #8 bars over supports and 2 1/2" Cl. absolute min. by AASHTO 8.22.1.
 
|}
 
  
Method of measurement:
+
<u>Step 3:</u>
  
The area of the concrete slab shall be measured and computed to the nearest square yard.  This area shall be measured transversely from out to out of slab and longitudinally from end to end of bridge slab.
+
Using the average Vr from step 2, compute the range of horizontal shear load per linear inch, Sr in kips per inch, at the junction of the slab and stringer from the following equation:
  
 +
<math>\,  \ Sr = \frac{VrQ}{I}</math> 
  
'''Precast Prestressed Panels'''
+
(AASHTO Article 10.38.5.1.1 Eq. 10-58)
  
3" Precast prestressed concrete panels with 5-1/2" minimum cast-in-place concrete will be the standard slab used on all girder superstructures except curved steel structures.
 
  
Concrete for prestressed panels shall be Class A1 with <math>\, f'{c}</math> = 6,000 psi, <math>\, f'_{ci}</math> = 3,500 psi.  Prestressing tendons shall be uncoated, low-relaxation, seven-wire(7) strands for prestressed concrete conforming to AASHTO M203 Grade 270, with nominal diameter of strand = 3/8" and area = 0.085 sq.in., minimum ultimate strength = 22.95 kips (270 ksi), and strand spacing = 4.5 inches.
+
where:
  
Panels shall be set on joint filler or polystyrene bedding material. Filler thickness shall be a Min. of 3/4" and a Max. of 2".  Standard filler width is 1 1/2" except at splice plates where 3/4" Min. is allowed to clear splice bolts.  Joint filler thickness may be reduced to a minimum of 1/4" over splice plates on steel structures.  For prestressed girder structures, joint filler thickness may be varied within these limits to offset girder camber or at the contractor's option a uniform 3/4" (Min.) thickness may be used throughout.  The same thickness shall be used under any one edge of any panel and the maximum change in thickness between adjacent panels shall be 1/4".
+
<math>\, Q </math> = static moment of the transformed compressive concrete area about the neutral axis of the composite section, in cubic inches (*);
  
Standard roadway cross sections and slab reinforcement for HS20 and HS20 Modified live loads are shown in this section. Reinforcement shown is for a cast-in-place slab or a P/S panel slab with the bottom layer of reinforcement between girders being replaced by the panels. Cantilever reinforcement details for P/S panel slab are shown in this section.
+
<math>\,  I </math> = moment of inertia of the transformed composite girder in positive moment regions in inches to the fourth power (*).
  
:Maximum panel width (clear span + 6") = 9'-6" for HS20 Modified.
+
(*) In the formula, the compressive concrete area is transformed into an equivalent area of steel by dividing the effective concrete flange width by the modular ratio n=8.
:Maximum panel width (clear span + 6") = 9'-11" for HS20.
 
  
When a safety barrier curb or median barrier curb is permanently required on the structure, other than at the edge of slab, precast prestressed panels will not be allowed in the bay underneath the curb.  P/S panels are not allowed for use as simply supported for live loads, i.e. staging, where only two supports may be provided for live loads.
 
  
 +
<u>Step 4:</u>
  
'''S.I.P.'''
+
Compute the allowable range of horizontal shear, Zr, in pounds on an individual connector, welded stud, by use of the following formula:
  
Stay-in-place corrugated metal forms with cast-in-place concrete may be used on horizontally curved steel structures with the approval of the Structural Project Manager.
+
<math>\,  Zr = \alpha \ d^2 </math>
  
The standard slab reinforcements shown in this section for HS20 live load were designed using S.I.P. Dead Loads.  If design is for HS20 Modified, the standard slab reinforcement needs to be checked for S.I.P. forms.
+
where:
  
The bottom transverse reinforcement shall maintain a 1" clear distance from the top of forms.
+
<math>\,  \frac{H}{d} \ge 4</math>
  
  
'''C.I.P.'''
 
  
8 1/2" cast-in-place concrete slab with conventional forming may be used at the contractor's option, on all girder structures.  Conventional forming shall also be used between girders with stage construction joints.
+
<math>\,  H </math> =height of stud in inches;
  
 +
<math>\,  d </math> =diameter of stud in inches;
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
<math>\,  \alpha </math> =13,000 for 100,000 cycles
|+'''Details of Precast Prestressed Panels Prestressed Structure:'''
+
 
|colspan="1"|[[Image:751.40 general superstructure-panels - square ends - prestressed structures.gif]]
+
:10,600 for 500,000 cycles
|[[Image:751.40 general superstructure-panels - skewed ends - prestressed structures.gif]]
+
 
|-
+
:7,850 for 2,000,000 cycles
!colspan="1"|Panels-Squared Ends
+
 
!Panels-Skewed Ends
+
:5,500 for over 2,000,000 cycles.
|-
 
!colspan="3"|PLAN OF PRECAST PRESTRESSED PANELS PLACEMENT
 
|}
 
  
{|border="0" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
 
  
|valign="top"|(1)
+
<u>Step 5:</u>
|align="left"|End panels shall be dimensioned 1" min. to 1-1/2"<br/>max. from the inside face of diaphragm.
 
|rowspan="3" colspan="2"|[[Image:751.40 general superstructure-panels - section thru const joint.gif]]
 
|-
 
|valign="top"|(2)
 
|align="left"|S-Bars shown are bottom steel in slab between<br/>panels and used with squared end panels only.
 
|-
 
|valign="top"|(3)
 
|align="left"|Extend S-Bars 18 inches beyond the front<br/>face of end bents only.
 
|-
 
|colspan="2" rowspan="2"|[[Image:751.40 general superstructure-panels - section a-a.gif]]
 
!colspan="2"|Section Thru Const. Joint
 
|-
 
|valign="top"|(*)
 
|align="left" valign="top"|Adjust the permissible construction joint to a clearance of 6<br/>inches minimum from the joints of the panels.
 
 
Note: All reinforcement other than prestressing strands shall<br/>be epoxy coated.
 
|-
 
!colspan="2"|Section A-A
 
|colspan="2" rowspan="5"|[[Image:751.40 general superstructure-panels - section thru cantilever.gif]]
 
|-
 
|valign="top"|(**)
 
|align="left" valign="top"|3/4" Min. thru 2" max. thickness and 1 1/2" width of<br/>preformed fiber expansion joint material or Sec 1057<br/>or polystyrene bedding material Sec 1073.
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|colspan="2"| &nbsp;
 
!colspan="2"|Section Thru Cantilever
 
|}
 
  
 +
Compute the number of additional connectors required at point of contraflexure, N , from the following formula:
  
 +
Pitch = <math>\, \frac{\sum Z_r}{S_r}</math>
  
{|border="0" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
+
Where:
|+'''Details of Precast Prestressed Panels Steel Structure:'''
+
Pitch = required pitch, in inches;
|colspan="2"|[[Image:751.40 general superstructure-panels - square ends - end bent - steel structure.gif|250px]]
+
 
|[[Image:751.40 general superstructure-panels - square ends - int end bent - steel structure.gif|250px]]
+
<math>\, \sum Z_r</math> = the resistance of all connectors at one (1) transverse girder cross-section as a shear connector unit.
|[[Image:751.40 general superstructure-panels - square ends - int bent - steel structure.gif|250px]]
+
 
|-
+
Note:
!colspan="2"|End Bent
 
!End Bent (Integral)
 
!Int. Bent (Exp. Gap)
 
|-
 
!colspan="4"|Panels-Squared Ends
 
|-
 
|colspan="2"|[[Image:751.40 general superstructure-panels - skewed ends - int bent exp gap - steel structure.gif]]
 
|[[Image:751.40 general superstructure-panels - skewed ends - end bent - steel structure.gif]]
 
|[[Image:751.40 general superstructure-panels - skewed ends - int end bent - steel structure.gif]]
 
|-
 
!colspan="2"|Int. Bent (Exp. Gap)
 
!End Bent
 
!End Bent (Integral)
 
|-
 
!colspan="4"|Panels-Skewed Ends
 
|-
 
!colspan="4"|PLAN OF PRECAST PRESTRESSED PANELS PLACEMENT
 
|-
 
|valign="top"|(1)
 
|align="left"|End panels shall be dimensioned 1" min. to 1 1/2" max. from the inside face of diaphragm.
 
|colspan="2" rowspan="2"|[[Image:751.40 general superstructure-panels - section a-a steel structure.gif]]
 
|-
 
|valign="top"|(2)
 
|align="left"|S-Bars shown are bottom steel in slab between panels and used with squared end panels only.
 
|-
 
|valign="top"|(3)
 
|align="left"|Extend S-bars 18 inches beyond the front face of end bents only.
 
|colspan="2"|'''Section A-A'''<br/>(*) Over splice plates, 3/4" Min. thickness allowed.
 
|-
 
|valign="top"|(5)
 
|align="left" valign="top"|S-Bars shown are used with skewed end panels, or square end panels of square structures only. The #5-S Bars will extend the width of slab (30" lap if necessary) or to within 3" of expansion device assemblies.
 
|colspan="2" rowspan="3"|[[Image:751.40 general superstructure-panels - section b-b steel structure.gif]]
 
|-
 
|valign="top"|Note:
 
|align="left"|All reinforcement other than prestressing strands shall be epoxy coated.
 
|-
 
| &nbsp;
 
| &nbsp;
 
|-
 
| &nbsp;
 
| &nbsp;
 
|colspan="2"|'''Part Section B-B'''
 
|-
 
|colspan="4"|[[Image:751.40 general superstructure-panels - section thru cantilever steel structure.gif]]
 
|-
 
|colspan="4"|'''Section Thru Cantilever'''
 
|}
 
  
 +
The pitch is to be constant and spaced in the composite section (round to the nearest inch).
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
<u>Step 6:</u>
|+'''Details of Precast Prestressed Panels for all Structures:'''
+
 
|colspan="2"|[[Image:751.40 general superstructure-panels - plan of precast prestressed panel.gif]]
+
Compute the required pitch of the shear connector units, pitch by the following formula:
|colspan="2"|[[Image:751.40 general superstructure-panels - plan of precast prestressed panel (skewed end-option).gif]]
+
 
|-
+
<math>\, N_c = \frac{{A_r}^2 f_r}{Z_r}</math>
!colspan="2" valign="top"|Plan of Precast Prestressed Panel
+
 
!colspan="2" valign="top"|Plan of Precast Prestressed Panel<br/>(Skewed End-Optional)
+
 
|-
+
(AASHTO Article 10.38.5.1.1 Eq. 10-69)
|(*)
+
 
|align="left"|= 3" (Typ.) for steel girder structures
+
where:
!colspan="2" rowspan="3"|[[Image:751.40 general superstructure-panels - detail a (precast panels).gif]]
+
 
|-
+
<math>\, N_c</math> = number of additional connectors required at the point of contraflexure;
|(*)
+
 
|align="left"|= 3" (Typ.) for P/S girder structures
+
<math>\,  {A_r}^s </math> = total area of longitudinal slab reinforcing steel for each girder over interior support;
|-
+
 
|(**)
+
<math>\,  f_r</math> = range of stress due to live load plus impact, in the slab reinforcement over the support (in lieu of more accurate computations, f may be taken as equal to 10,000 psi);
|align="left"|Use #3-P3 bars if panel is skewed <math>\,45^\circ</math> or greater.
+
 
|-
+
<math>\,  Z_r</math> = the allowable range of horizontal shear on an individual connector.
|colspan="2" rowspan="2"|[[Image:751.40 general superstructure-panels - section b-b (precast panels).gif]]
 
!colspan="2"|Detail "A"
 
|-
 
|valign="top"|Note:
 
|align="left" valign="top"|Area of Strand = Astra = 0.085 sq. in./strand<br/>Initial prestressing stress = fsi = (0.75)(270 ksi) = 202.5 ksi<br/>Initial prestressing force = Astra x fsi<br/>= (0.085 sq. in./strand)(202.5 ksi) = 17.2 kips/strand
 
|-
 
!colspan="2"|Section B-B
 
|}
 
  
===== 751.40.8.5.1.2 Details of Concrete Slabs for Structures =====
 
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|[[Image:751.40 general superstructure-HS20 (26ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 (26'-0" ROADWAY - 4 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 modified (26ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 Modified (26'-0" ROADWAY - 4 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 (28ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 (28'-0" ROADWAY - 4 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 modified (28ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 Modified (28'-0" ROADWAY - 4 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 (30ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 (30'-0" ROADWAY - 4 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 modified (30ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 Modified (30'-0" ROADWAY - 4 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 (32ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 (32'-0" ROADWAY - 4 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 modified (32ft0in ROADWAY - 4 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 Modified (32'-0" ROADWAY - 4 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 (36ft0in ROADWAY - 5 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 (36'-0" ROADWAY - 5 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 modified (36ft0in ROADWAY - 5 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 Modified (36'-0" ROADWAY - 5 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 (38ft0in ROADWAY - 5 GIRDER)(unsymmetrical).gif]]
 
|-
 
!colspan="2"|HS20 (38'-0" ROADWAY - 5 GIRDER)(Unsymmetrical)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 modified (38ft0in ROADWAY - 5 GIRDER)(unsymmetrical).gif]]
 
|-
 
!colspan="2"|HS20 Modified (38'-0" ROADWAY - 5 GIRDER)(Unsymmetrical)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 (40ft0in ROADWAY - 5 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 (40'-0" ROADWAY - 5 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 modified (40ft0in ROADWAY - 5 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 Modified (40'-0" ROADWAY - 5 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 (44ft0in ROADWAY - 5 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 (36'-0" ROADWAY - 5 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-HS20 modified (44ft0in ROADWAY - 5 GIRDER).gif]]
 
|-
 
!colspan="2"|HS20 Modified (36'-0" ROADWAY - 5 GIRDER)
 
|-
 
|colspan="2"| &nbsp;
 
|}
 
  
==== 751.40.8.5.2 Timber Floor ====
+
This number of additional connectors, N , shall be placed adjacent to the point of dead load contraflexure within a distance equal to 1/3 of the effective slab width, if it is possible. If it is impossible, use minimum pitch of 6".
 +
 
 +
 
 +
<u>Step 7: Check connectors for ultimate strength</u>
 +
 
 +
The number of connectors provided for fatigue must be checked to ensure that adequate connectors are provided for ultimate strength. 
 +
 
 +
To check for ultimate strength, proceed as follows:
 +
 
 +
(1) Compute the force in the slab (P), which is defined as: at the point of maximum positive moment, the force in the slab is taken as the smaller value of the following two formulae:
 +
 
 +
 
 +
<math>\, P_1 = A_s F_y</math>  (AASHTO Article 10.38.5.1.2 Eq. 10-62)
 +
 
 +
or
 +
 
 +
<math>\, P_2 = 0.85 f'_{c}b{t_s}</math>  (AASHTO Article 10.38.5.1.2 Eq. 10-63)
 +
 
 +
 
 +
Where:
 +
 
 +
<math>\, A_s</math> = total area of the steel section including cover plates (if used);
 +
 
 +
<math>\, F_y</math> = specified minimum yield point of the steel being used;
 +
 
 +
<math>\, f'_c</math> = compressive strength of concrete at age of 28 days;
 +
 
 +
<math>\, b</math> = effective flange width given in AASHTO Article 10.38.3;
 +
 
 +
<math>\, t_s</math> = thickness of concrete slab.
 +
 
 +
 
 +
Note:
  
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
If it becomes impractical to place the number of shear connectors required by ultimate strength in the specified distance (structures with span ratios greater than 1.5); base the number and spacing of shear connectors on the fatigue analysis only.
|-
 
!colspan="3"|Maximum stringer spacing as determined by strength of timber floor
 
|-
 
!colspan="3"|Stress = 1,200 lbs. per square inch
 
|-
 
!width="200pt"| &nbsp;||width="200pt"|H-10||width="200pt"|H-15
 
|-
 
|(*) 3" x 12" Plank||18" + 1/2 Flange Width||16" + 1/2 Flange Width
 
|-
 
|4" Laminated Floor||2'-11" + 1/2 Flange Width||2'-3" + 1/2 Flange Width
 
|-
 
|6" Laminated Floor||6'-0" + 1/2 Flange Width||4'-4" + 1/2 Flange Width
 
|-
 
!colspan="3"|Stress = 1,600 lbs. per square inch
 
|-
 
! &nbsp; ||H-10||H-15
 
|-
 
|3" x 12" Plank||23" + 1/2 Flange Width||21" + 1/2 Flange Width
 
|-
 
|4" Laminated Floor||3'-9" + 1/2 Flange Width||2'-11 1/2" + 1/2 Flange Width
 
|-
 
|6" Laminated Floor||7'-10 3/4" + 1/2 Flange Width||5'-9" + 1/2 Flange Width
 
|}
 
<center>(*) 3" x 12" Plank without treads.</center>
 
  
==== 751.40.8.5.3 Steel Grid Bridge Flooring ====
+
Increase the haunch by 1/2"± more than what is required to make one size shear connector work for C.I.P. or S.I.P. option.
  
In general, the 5" depth (concrete filled to half depth) steel grid bridge flooring shall be specified. Bar spacing may vary as necessary to meet minimum section modulus requirements. Main member spacing shall not exceed  10" and cross bar spacing shall not exceed 4". At present, the manufacturers of the following types have provided data to show they are acceptable:
+
===== 751.40.8.6.2.2 Shear Connector Spacing =====
 
:Greulich 5" Standard
 
:Foster 5" Standard
 
 
The section properties <math>\, (n = 8)</math> and maximum span for HS20 loading have been computed for these types and are as follows:
 
  
 +
If it becomes impractical to place the number of shear connectors required by ultimate strength in the specified distance (structures with span ratios greater than 1.5); base the number and spacing of shear connectors on the fatigue analysis only.
  
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
For a typical 3-spans bridge, the shear connector units can be approximately
|-
+
arranged as below:
|rowspan="3" width="75pt"|Company
 
|rowspan="3"|(For Design<br/>Purpose only)<br/>Weight (PSF)<br/>(Steel & Conc.)
 
|rowspan="3"|Main bar<br/>Spacing
 
|rowspan="3"|Cross bar<br/>Spacing
 
|colspan="3"|Moment of Inertia<br/><math>\, (in^4/Ft.)</math>
 
|-
 
|colspan="2"|Mid Span
 
||Over-Support
 
|-
 
|Conc.||Steel||Steel
 
|-
 
|Greulich||width="100pt"|48.0||width="50pt"|7 1/2"||width="50pt"|3 3/4"||width="50pt"|99.41||width="50pt"|12.43||width="50pt"|9.03
 
|-
 
|Foster||48.0||8"||4"||128.1||16.01||12.25
 
|}
 
  
 +
[[Image:751.40 Widen and Repair Design Assumptions- Shear Connectors Spacing 2 2 1.gif]]
  
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
==== 751.40.8.6.3 Details ====
|-
+
=====751.40.8.6.3.1 Shear Connector Details =====
|rowspan="3" width="75pt"|Company
 
|colspan="4"|Section Modulus <math>\, (in^2/ft.)</math>
 
|colspan="4"|Maximum Span (*)
 
|-
 
|colspan="2"|Mid-Span
 
|colspan="2"|Over-Support
 
|colspan="2"|Simple Span
 
|colspan="2"|Continuous Spans
 
|-
 
|width="50pt"|Conc.<br/>(Top)
 
|width="50pt"|Steel<br/>(Bott.)
 
|width="50pt"|Steel<br/>(Top)
 
|width="50pt"|Steel<br/>(Bott.)
 
|width="50pt"|ASTM<br/>A709<br/>Gr. 36
 
|width="50pt"|ASTM<br/>A709<br/>Gr. 50W
 
|width="50pt"|ASTM<br/>A709<br/>Gr. 36
 
|width="50pt"|ASTM<br/>A709<br/>Gr. 50W
 
|-
 
|Greulich||59.5||3.53||3.90||3.14||4'-4"||5'-10"||5'-10"||7'-1"
 
|-
 
|Foster||72.5||4.68||5.25||4.30||5'-9"||7'-5"||7'-2"||9'-4"
 
|}
 
  
 +
Use precast prestressed panels on all tangent steel structures.  Evaluate the viability of the use of P/S panels on curved structures on a case by case basis and use or include as an option to a CIP slab where deemed appropriate.
  
The cross-section DETAILS used in computing the section properties are shown on the sketches on the following sheets.  Maximum span determination included an allowance for a 35#/sq.ft. future
+
Whenever panels are used, the minimum top flange width shall be 12" for Plate Girders and 10" for Wide Flange Beams.
wearing surface and assumed a wheel load to be distributed, normal to the main bars, over a width of 4'-0".
 
 
(Place the following note on the Bridge Plans with the Steel Grid Details.
 
 
Note: The steel grid deck shall be electrically grounded.
 
  
(*) For main beams of grid either parallel or perpendicular to traffic.
+
Steel girders shall be cambered when using P/S Panels. Minimum joint filler thickness is 3/4", except over splice plates, in which case use 1/4" minimum. Maximum joint filler thickness is 2".
  
 +
Shear connectors shall have a minimum height equal to the top of panel.
  
<center>[[Image:751.40 general superstructure-greulich 5in standard.gif]]</center>
+
Shear connectors shall be spaced by units and shear connectors in each unit shall be placed along <math>\, C_{\!\!\!\!L}</math> of girder. On wide flange widths, two lines of connectors may be used if spacings and clearances allow.
  
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
Additional shear connectors, Nc, at point of contraflexure may be placed in units normal to <math>\, C_{\!\!\!\!L}</math> girder as space allows or in a single row along <math>\, C_{\!\!\!\!L}</math> girder as shown below:
|-
 
|&nbsp;||Composite Section||Seel Section Only (net)
 
|-
 
|y||1.671"||2.317"
 
|}
 
  
 +
<center>
 +
[[Image:751.40 Widen and Repair Design Assumptions- PCP on Steel Shear Connector.gif]]
 +
</center>
  
<center>'''Greulich 5" Standard'''</center>
+
P/S strands shall extend 3" minimum and 6" maximum past edge of precast prestressed panel and not closer than 1" to the adjacent panels.
  
{|border="0" style="text-align:center;" cellpadding="2" align="center"
+
Panel end at splices shall be notched to avoid bolt heads as shown below:
|-
+
<center>
|Note:||Dimensions obtained form Greulich plans.
+
[[Image:751.40 Widen and Repair Design Assumptions- PCP on Steel Shear Connector- B.gif]]
|}
+
</center>
  
 +
[[Image:751.40 circled 1.gif]] 3/4" min. wide bearing edge for panel at splice, typ. (*)
  
<center>[[Image:751.40 general superstructure-foster 5in standard.gif]]</center>
+
[[Image:751.40 circled 2.gif]] 1-1/4" min. (Typ.)
  
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
[[Image:751.40 circled 3.gif]] 4 x (Stud diameter) preferred minimum, may be reduced if necessary for a more economical design; 2-1/4" absolute minimum.
 +
 
 +
 
 +
(*) In order to meet [[Image:751.40 circled 1.gif]] and [[Image:751.40 circled 2.gif]] above, it is necessary to have an edge bolt distance of 2" or greater for splice plate. For unusual cases, which would require field splices for flange widths 14" or 15" for P/S precast panel option, it will be necessary to change the top flange width to either 13" or 16" of equal area to maintain the 3/4" minimum panel bearing edge on the splice plates.
 +
 
 +
Minimum joint filler thickness is 3/4" except over splice plates in which case use 1/4" minimum. When joint filler is less than 1/2" thick over splice plate, make the width of joint filler at splice the same width as panel on splice (maximum 1-1/2" wide).
 +
 
 +
Maximum difference in top of flange thickness should be checked so that joint filler thickness does not exceed 2".
 +
 
 +
===== 751.40.8.6.3.2 Deflection =====
 +
 
 +
Allowable Live Load Deflection
 +
 
 +
{|
 +
|-
 +
|1.||Composite Design:||Defl.||= 1/1000 of span;
 
|-
 
|-
|&nbsp;||Composite Section||Seel Section Only (net)
+
|2.||Non-composite Design:||Defl.||= 1/800 of span
 
|-
 
|-
|y||1.766"||2.338"
 
 
|}
 
|}
  
  
<center>'''Foster 5" Standard'''</center>
+
:Where:
 +
 
 +
:Defl. = allowable deflection due to service live load plus impact.
 +
 
 +
 
 +
Dead Load Deflection
 +
Compute at 1/4 point for bridge with spans less than 75’, at 1/10 points for spans 75’ and over.
  
{|border="0" style="text-align:center;" cellpadding="2" align="center"
+
=== 751.40.8.7 Wide Flange Beam Spans ===
|-
 
|Note:||Dimensions obtained form Foster Catalog.
 
|}
 
  
==== 751.40.8.5.4 Longitudinal Diagrams ====
 
  
 +
==== 751.40.8.7.1 Design ====
  
===== 751.40.8.5.4.1 Hinged Beam Connections =====
 
  
The diagrams of various joints in steel structures are intended to be guides primarily for the determination of horizontal longitudinal dimensions for the plan view on the first sheet of plans.
+
===== 751.40.8.7.1.1 Design Data =====
 
These diagrams are not to be detailed on the design plans. However, the arrangement of the joints should be useful in detailing the longitudinal diagram for structural steel, particularly for bridges on grades and vertical curves.
 
 
Longitudinal dimensions for the plan of structural steel and for the plan of slab shall be horizontal from centerline bearing to centerline bearing.
 
 
For proper correlation of details when developing plans for widening or redecking bridges, match the method of dimensioning on the new plans with the method used on the originals.
 
  
 +
'''Slabs'''
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
{|
|+'''Hinged Beam Connections'''
+
|width="150pt"|Reinforcing Steel||<math>\, f_y</math>||= 60,000 psi
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves1.gif]]
 
 
|-
 
|-
!Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves
+
|width="150pt"|Concrete||<math>\, f_c</math>||= 1,600 psi|| &nbsp;||<math>\, f'_c</math>||= 4,000 psi
 
|-
 
|-
|&nbsp;
+
| &nbsp;||<math>\, n</math>||= 8
|-
+
|}
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Flat Grade.gif]]
+
 
|-
+
 
!Geometrics for Hinged Beam Connections for Bridges on Flat Grade
+
'''Simple Design Span'''
|-
+
 
|&nbsp;
+
Design Span = Center to Center of Bearings.
|-
+
 
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Straight, Plus Grades.gif]]
+
 
|-
+
'''Dead Load'''
!Geometrics for Hinged Beam Connections for Bridges on Straight, Plus Grades
+
 
|-
+
 
|&nbsp;
+
'''Live Load Distribution Factors'''
|-
+
 
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves.gif]]
+
See [[#751.40.8.2.2 Distribution of Live Load|EPG 751.40.8.2.2 Distribution of Live Load]]
|-
+
 
!Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves
 
|-
 
|&nbsp;
 
|-
 
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves2.gif]]
 
|-
 
!Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves
 
|-
 
|&nbsp;
 
|-
 
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Symmetrical Vertical Curves.gif]]
 
|-
 
!Geometrics for Hinged Beam Connections for Bridges on Symmetrical Vertical Curves
 
|-
 
|&nbsp;
 
|-
 
|[[Image:751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves1.gif]]
 
|-
 
!Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves
 
|}
 
  
 +
'''Live Load Deflection Allowable'''
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
{|
|+'''Hanger Beam Connections'''
+
|width="150pt"|Composite||<math>\, \frac {L}{1000}</math>
|[[Image:751.40 general superstructure-Geometrics for Hanger Beam Connections for Bridges on Crown Vertical Curves.gif]]
 
 
|-
 
|-
!Geometrics for Hanger Beam Connections for Bridges on Crown Vertical Curves
+
|width="150pt"|Non-Composite||<math>\, \frac {L}{800}</math>
|-
 
|&nbsp;
 
|-
 
|[[Image:751.40 general superstructure-Geometrics for Hanger Beam Connections for Bridges on Sag Vertical Curves.gif]]
 
|-
 
!Geometrics for Hanger Beam Connections for Bridges on Sag Vertical Curves
 
 
|}
 
|}
  
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
'''Live Load Reaction'''
|+'''Pin Plate Connections'''
+
 
|[[Image:751.40 general superstructure-Geometrics for Pin Plate Connections for Bridges on Crown Vertical Curves.gif]]
+
Live Load <math>\, (LL) /</math> Wheel Line <math>\, (WL)</math> is the Live Load Reaction per Wheel Line, no distribution, no impact; Maximim Live Load <math>\, (LL) +</math> Impact <math>\, (I)</math> is the Live Load Reaction x Distribution Factor = Impact.
 +
 
 +
 
 +
<center>[[Image:751.40 wf bm spans-truck loading.gif|500px]]</center>
 +
 
 +
<center>'''Truck Loading'''</center>
 +
 
 +
<center>(Governs thru 33' simple spans for H20 and all simple spans for HS20)</center>
 +
 
 +
 
 +
<center>[[Image:751.40 wf bm spans-lane loading1.gif|500px]]</center>
 +
 
 +
<center>'''Lane Loading'''</center>
 +
 
 +
<center>(Governs for simple soabs 35' and over for H20)</center>
 +
 
 +
 
 +
 
 +
'''Typical Continuous Steel Structures - Integral End Bents:'''
 +
 
 +
<center>[[Image:751.40 wf bm spans-structure length.gif|600px]]</center>
 +
 
 +
<center>(*) Maximum length for End Bent to end Bent - 500 feet.</center>
 +
 
 +
===== 751.40.8.7.1.2 Stringer Design =====
 +
 
 +
'''Stresses:'''
 +
 
 +
{|
 
|-
 
|-
!Geometrics for Pin Plate Connections for Bridges on Crown Vertical Curves
+
|width="50pt"|Steel:||colspan="2"|AASHTO - Article 10.2, 10.32
 
|-
 
|-
|&nbsp;
+
| &nbsp;||width="100pt"|ASTM A709 Grade 36||width="125pt"|<math>\, f_y</math> = 36,000 psi ||width="125pt"|( <math>\, f_s</math> = 20,000 psi)
 
|-
 
|-
|[[Image:751.40 general superstructure-Geometrics for Pin Plate Connections for Bridges on Sag Vertical Curves.gif]]
+
| &nbsp;||width="100pt"|ASTM A709 Grade 50 & Grade 50W||width="125pt"|<math>\, f_y</math> = 50,000 psi ||width="125pt"|( <math>\, f_s</math> = 27,000 psi)
|-
 
!Geometrics for Pin Plate Connections for Bridges on Sag Vertical Curves
 
 
|}
 
|}
  
===== 751.40.8.5.4.2 Longitudinal Sections =====
 
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
{|
|+'''Expansion Device at End Bent'''
 
|Colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-expansion device at end bent(not on grade).gif]]
 
 
|-
 
|-
!Bearing Stiffener||Connection Plate
+
|width="175pt"|Superstructure Concrete:||<math>\, f_c</math>||= 1,600 psi
 
|-
 
|-
!colspan="2"|Structures Not on Grade (Typical)
+
|width="175pt"| &nbsp;||<math>\, f'_c</math>||= 4,000 psi
 
|-
 
|-
|colspan="2"| &nbsp;
+
|width="175pt"| &nbsp;||<math>\, n</math>||= 8
|-
 
|colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-expansion device at end bent(on grade).gif]]
 
|-
 
!Colspan="2"|Structures on Grade (Typical)
 
 
|}
 
|}
  
{|border="0" cellpadding="5" cellspacing="1" align="center"
+
 
 +
{|
 
|-
 
|-
|align="right" valign="top"|(*)||width="400pt"|Parallel to Girder.  All other dimensions shown are normal to backwall.
+
|width="125pt"|Reinforcing Steel:||<math>\, f_y</math>||= 60,000 psi
|-
 
|align="right" valign="top"|(**)||width="400pt"|See [[751.13 Expansion Devices|EPG 751.13 Expansion Devices]] for dimension of overhang from end of stringer or girder to face of plate, edge of concrete or face of vertical leg of angle.
 
 
|}
 
|}
  
  
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
'''Physical Properties of Spans'''
|+'''No Expansion Device at End Bent'''
+
 
|Colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-no expansion device at end bent(not on grade) 1.gif]]
+
:Composite Design - See [[#751.40.8.6 Composite Design|Widening and Repair - Composite Design]].
|-
+
 
!Bearing Stiffener||Connection Plate
+
:Non-Composite Design - Use "Constant I" analysis.
|-
+
 
!colspan="2"|Structures Not on Grade (Typical)
+
When the neutral axis of a composite section falls in the concrete fange, the section shall be designed as Non-Composite (21" Wide Flange is the smallest beam generaly made conposite).
|-
+
 
|colspan="2"| &nbsp;
+
 
|-
+
'''Deflection'''
|colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-no expansion device at end bent(on grade) 1.gif]]
 
|-
 
!Colspan="2"|Structures on Grade (Typical)
 
|}
 
  
{|border="0" cellpadding="5" cellspacing="1" align="center"
+
:{|
 +
|width="150pt"|Live Load Deflection:||width="300pt"|AASHTO - Article 10.6
 
|-
 
|-
|align="right" valign="top"|(*)||width="400pt"|Parallel to Girder.  All other dimensions shown are normal to backwall.
+
| &nbsp;||width="300pt"|Composite - Allowable Deflection L/1000
 
|-
 
|-
|align="right" valign="top"|(**)||width="400pt"|18" min. (Use same dimension as the expansion device end on 3-span continuous, if it is not more than 2" greater.)
+
| &nbsp;||width="300pt"|Non-Composite - Allowable Deflection l/800
 
|-
 
|-
|align="right" valign="top"|(***)||width="400pt"|3" min. for type C, D and E bearing, and 2" min. for an elastomeric bearing.
+
|valign="top"|Dead Load Deflection:||width="300pt"|Compute at 1/4 points for bridges with spans less than 75', at 1/10 points for spans 75' and over. Give percentage of deflection due to weight of structural steel.
 
|}
 
|}
  
  
  
 +
'''Fatigue Stress'''
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
AASHTO - Article 10.3 Case I, Case II or Case III (as specified on Bridge Memorandum generally within the following limitations).
|+'''Intermediate Bent'''
 
|width="300pt"|[[Image:751.40 general superstructure-longitudinal sections-intermediate bent-no expansion device.gif]]
 
|width="300pt"|[[Image:751.40 general superstructure-longitudinal sections-intermediate bent-expansion device.gif]]
 
|-
 
!No Expansion Device||Expansion Device
 
|}
 
  
{|border="0" cellpadding="5" cellspacing="1" align="center"
+
:{|
 +
|align="right" valign="top"|Case I:||width="500pt"|Bridges with the '''TRUCK''' traffic count of 2500 or more vehicles per day (one direction).
 
|-
 
|-
|align="right" valign="top"|[[Image:751.40 circled 1.gif]]||width="400pt"|1/2" minimum overhang from end of stringer to face of plate, edge of concrete or face of vertical leg of angle.
+
|align="right" valign="top"|Case II:||width="500pt"|Bridges with traffic count of 750 or more vehicles per day, and less than 2500 '''TRUCK''' traffic count (one direction) per day.
 
|-
 
|-
|align="right" valign="top"|[[Image:751.40 circled 2.gif]]||width="400pt"|Gap as required for a particular type of expansion device.
+
|align="right" valign="top"|Case III:||width="500pt"|Bridges with traffic count of less than 750 vehicles per day, except when Live Loading is H20 or greater.
 
|-
 
|-
|align="right" valign="top"|[[Image:751.40 circled 3.gif]]||width="400pt"|Expansion device gap plus 1 1/2" minimum (taken parallel to centerline stringer).
+
|align="right" valing="top"|No Fatigue:||width="500pt"|Bridges with traffic of less than 75 vehicles per day.
|-
 
|align="right" valign="top"|(*)||width="400pt"|Parallel to Girder.  All other dimensions shown are normal to centerline Bent.
 
|-
 
|colspan="2" align=left" valign-"top"|Blockout shown is for Elastomeric Expansion Joint Seal.  Check<br/>Design Layout for type of device for a particular structure.
 
 
|}
 
|}
  
  
 +
'''Economic Comparison'''
  
 +
When comparing cost of low-alloy steels (A-572, Gr.-50, and A-588) to the cost of A-36 steel, the low-alloy steels shall be figured a t 3 1/2 cents for A-572, Gr.-50 and 5 1/4 cents for A-588 per pound more than A-36 steel. Cost comparisions will be based on current average bid prices that may be obtained from the CHIEF DESIGNER, for comparable bridges.
 +
 +
No overstressed will be permitted in the design.
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|+'''Expansion Device at Any Bent'''
 
|[[Image:751.40 general superstructure-longitudinal sections-expansion device at any bent-end(no grade).gif]]
 
|[[Image:751.40 general superstructure-longitudinal sections-expansion device at any bent-int(no grade).gif]]
 
|-
 
!colspan="2"|Structures Not on Grade (Typical)
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-expansion device at any bent-end(on grade).gif]]
 
|-
 
!colspan="2"|Structures On Grade (Typical)
 
|}
 
  
 +
'''Total Capacity of Exterior Griders''' (Dead Load and Live Load)
  
 +
In no case shall an exterior stringer have less carrying capacity than an interior stringer.
  
 +
===== 751.40.8.7.1.3 Flange Plate Lengths =====
  
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
|+'''Point on Rotation of Bearings'''
 
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-type c bearing.gif]]
 
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-type c bearing grade 4% and greater.gif]]
 
 
|-
 
|-
!valign="top" width="300pt"|Type "C" Bearing||width="300pt"|Type "C" Bearing<br/>(Grade 4% and Greater)
+
|colspan="2"|[[Image:751.40 wf bm spans-flange plates-details of flange plates at int bents1.gif]]
 
|-
 
|-
|colspan="2"| &nbsp;
+
!width="50%"|Top Flange||width="50%"|Bottom Flange
 
|-
 
|-
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-type d bearing.gif]]
+
!colspan="2"|Details of Flange Plates at Intermediate Bents
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-type e bearing.gif]]
 
|-
 
!width="300pt"|Type "D" Bearing||width="300pt"|Type "E" Bearing
 
 
|-
 
|-
 
|colspan="2"| &nbsp;
 
|colspan="2"| &nbsp;
 
|-
 
|-
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-flat plate bearing.gif]]
+
|colspan="2"|[[Image:751.40 wf bm spans-flange plates-details of flange plates at int bents2.gif]]
|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-prestressed structure bearing pad.gif]]
 
 
|-
 
|-
!width="300pt"|Flat Plate Bearing<br/>(For Grade 2% and Greater)||width="300pt"|Prestressed Structure<br/>Bearing Pad
+
!colspan="2"|Details of Flange Plates at Intermediate Bents<br/>(Top and Bottom Flanges)
|-
 
|colspan="2"| &nbsp;
 
|-
 
|colspan="2"|[[Image:751.40 general superstructure-longitudinal sections-point of rotation of bearings-steel structure bearing pad.gif]]
 
|-
 
!colspan="2"|Steel Structure<br/>Bearing Pad
 
 
|}
 
|}
  
 +
Allowable flange plate sizes are as shown with the section properties. Different plate sizes may be used on adjacent stringers.
  
 +
Lengths to be shown on the bridge plans are those required as follows:
 +
:Lengths each side of the bearing shall be the larger of:
 +
#Theoretical End + Terminal Distance (***) or
 +
#Point where the stress range (tension or reversal) in the beam flange is equal to or less than allowable fatigue stess range (Cat. E or E') or where the beam flange is in compression, whichever is smaller.
 +
#*Use Cat. E when the flange is less than or equal to 0.8 inch thick.
 +
#*Use Cat. E' when the flange is greater than 0.8 inch thick.
  
 +
(***) Where the theoretical end = the point where the flange stress without cover plate less than or equal to base allowable stress.  Terminal distance = 1 1/2 times nominal cover plate width.
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
The total length of the cover plate greater than or equal to (2D + 3'-0"). Where "D" = Depth of beam in feet.
|+'''Blocking Diagram'''
 
|[[Image:751.40 general superstructure-longitudinal sections-blocking diagram.gif]]
 
|-
 
!Elevation of Longitudinal Steel Diagram
 
|}
 
  
{|border="0" cellpadding="5" cellspacing="1" align="center"
+
When required lengths of plates vary by 12" or less on adjacent stringers or on each side of the centerline stiffener plate, use greater length for all such positions.
 +
 
 +
Plate lengths taken form the computer programs should be rouned up to at least the nearest 6".
 +
 
 +
 
 +
===751.40.8.8 Welded Plate Girders===
 +
 
 +
====751.40.8.8.1 Design====
 +
 
 +
=====751.40.8.8.1.1 Design Assumptions & Procedures=====
 +
 
 +
'''Design Unit Stresses'''
 +
 
 +
{|
 +
|Reinforcement Concrete
 +
|-
 +
|width="300pt"|Reinforcing Steel (Grade 60)||width="110pt"| <math>\, f_s</math> = 24,000 psi,|| <math>\, f_y</math> = 60,000 psi
 
|-
 
|-
|align="right" valign="top"|Note:||width="400pt"|The typical elevation shown above should be detailed on the plans for all steel structures that are on vertical curve grades.
+
|Class B2 Concrete (Superstructure)||width="110pt"| <math>\, f_c</math> = 1,600 psi,|| <math>\, f'_c</math> = 4,000 psi
 +
|}
 +
 
 +
 
 +
 
 +
{|
 +
|Structural Steel:
 
|-
 
|-
|align="right" valign="top"|(1)||width="400pt"|Longitudinal dimensions are horizontal from centerline Brg. to centerline Brg.
+
|width="300pt"|Structural Carbon Steel (ASTM A709 Grade 36)||width="110pt"| <math>\, f_s</math> = 20,000 psi,||  <math>\, f_y</math> = 36,000 psi
 
|-
 
|-
|align="right" valign="top"|(*)||width="400pt"|Horizontal dimensions.
+
|Structural Steel (ASTM A709 Grade 50)||width="110pt"| <math>\, f_s</math> = 27,000 psi,||  <math>\, f_y</math> = 50,000 psi
 
|-
 
|-
!colspan="2"|BLOCKING DIAGRAM SHOULD NOT BE USED FOR CAMBERED GIRDERS.
+
|Structural Steel (ASTM A709 Grade 50W)||width="110pt"| <math>\, f_s</math> = 27,000 psi,||  <math>\, f_y</math> = 50,000 psi
 
|}
 
|}
  
==== 751.40.8.5.5 Miscellaneous Bearing Connections ====
+
 
 +
'''Design Procedure:'''
 +
 
 +
Moments and shears by "Variable '''I'''" analysis:
 +
::use computer program.
 +
 
 +
Trial sections from "Preliminary analysis":
 +
::Combination of web depth, flanges and length of plates used shall be the most economical section available with depths compatible with vertical clearance requirements. Web depths in 6" increments are preferred, however other increments may be used when required by the Bridge Memorandum. (See Structural Project Manager)
 +
 
  
  
===== 751.40.8.5.5.1 Typical Details of “Hinged Connection" =====
+
'''Flanges:'''
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
Minimum flange dimensions = 3/4" x 12" (*).
|-
+
 
|colspan="3"|[[Image:751.40 general superstructure-misc details-section showing hinged beam conn1.gif]]
+
Increments:
|-
+
 
!colspan="3"|Section Showing Hinged Beam Connection
+
:Thickness 1/8"
|-
 
|colspan="3"| &nbsp;
 
|-
 
|rowspan="2"|[[Image:751.40 general superstructure-misc details-detail of web at radius transition.gif]]
 
|valign="bottom"|[[Image:751.40 general superstructure-misc details-plan of brg plate.gif]]
 
|rowspan="2"|[[Image:751.40 general superstructure-misc details-typ welding details for stiffeners.gif]]
 
|-
 
!valign="top"|Plan of Brg. Plate
 
|-
 
!Detail of Web at<br/>Radius Transition|| &nbsp;||Typical Welding Details<br/>for Stiff. Plates
 
|-
 
|colspan="3"| &nbsp;
 
|-
 
|[[Image:751.40 general superstructure-misc details-section c-c.gif]]
 
| colspan="2" rowspan="2" |
 
{|border="0" cellpadding="3" cellspacing="1" align="center"
 
|-
 
|valign="top" align="right"|"D"||align="left" width="375pt" |Gap as required for expansion (3" Min.)
 
|-
 
|valign="top" align="right"|"J"||align="left" width="375pt" |5" for bearing with 3" web thickness. Use 6" for all others.
 
|-
 
|valign="top" align="right"|[[Image:751.40 circled 1.gif]]||align="left" width="375pt" |Dimension to be 1/3 brg. length (Typ.)
 
|-
 
|valign="top" align="right"|(*)||align="left" width="375pt" |To be used unless greater depth is required by design.
 
|-
 
|valign="top" align="right"|(**)||align="left" width="375pt" |See [[751.13 Expansion Devices|EPG 751.13 Expansion Devices]]
 
|-
 
|valign="top" align="right"|Note:||align="left" width="375pt" |Web thickness and size of fillet weld connecting bearing stiffener plate to web as required by design.
 
|-
 
|valign="top" align="right"| &nbsp;||align="left" width="375pt" |Plans for bridges on a grade or vertical curve shall have the conn. detailed in relation to the slope of the girders and stringers.
 
|}
 
|-
 
!Section C-C
 
|}
 
  
 +
:Width 1"
  
 +
Maximum flange dimensions:
  
 +
:Reference AASHTO - Table 10.32.1A)
  
 +
:maximum thickness = 4"
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
Note:
|-
+
It is preferred office practice to maintain the same flange thickness at as many locations as practical. This can be accomplished by varying the flange width.
|colspan="4"|[[Image:751.40 general superstructure-misc details-section showing hinged beam conn2.gif]]
 
|-
 
!colspan="4"|Section Showing Hinged Beam Connection
 
|-
 
|colspan="4"| &nbsp;
 
|-
 
|colspan="4"|[[Image:751.40 general superstructure-misc details-sections d-d & e-e.gif]]
 
|-
 
!width="15%"| &nbsp;||Section D-D||Section E-E||width="18%"| &nbsp;
 
|-
 
|colspan="4"| &nbsp;
 
|-
 
|colspan="4"|[[Image:751.40 general superstructure-misc details-typical welding details for stiffeners.gif]]
 
|-
 
!colspan="4"|Typical Welding Details<br/>for Stiff. Plates
 
|}
 
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
(*) For shipping and erection purposes, minimum width of both compression and tension flanges shall not be less than L/85 where L is the shipping length of the girder. This limitation is for
|-
+
preventing out-of-plane distortion of the girder.
|valign="top" align="right"|(*)||align="left"|See below for dimension "G".
+
 
|-
+
 
|valign="top" align="right"|(**)||align="left"|See [[751.13 Expansion Devices|EPG 751.13 Expansion Devices]]
+
 
 +
'''Webs:'''
 +
 
 +
Web dimensions:
 +
 
 +
:(Reference AASHTO - Article 10.34 & 10.48)
 +
 
 +
:ASTM A709 Grade 36 = 3/8" minimum thickness for curved girders and for continuous straight girders.
 +
 
 +
:ASTM A709 Grade 50W = 3/8" minimum thickness.
 +
 
 +
:AASHTO - Article 10.3 Case I, Case II or Case III.
 +
 
 +
:Case I
 +
 
 +
::Bridges with the truck traffic count of 2500 or more vehicles per day. (One direction)
 +
 
 +
:Case II
 +
 
 +
::Bridges with traffic count of 750 or more vehicles per day, and less than 2500 truck traffic count (One direction) per day.
 +
 
 +
:Case III
 +
 
 +
::Bridges with traffic count of less than 750 vehicles per day, except when live loading is H20 or greater.
 +
 
 +
:No Fatigue:
 +
 
 +
::Bridges with traffic count of less than 75 vehicles per day.
 +
 
 +
 
 +
'''Total Capacity of Exterior Girders:'''
 +
 
 +
'''(Dead Load and Live Load)'''
 +
 
 +
:In no case shall an exterior girder have less carrying capacity than an interior girder.
 +
 
 +
'''Horizontal Curved Girders Design Procedures (*)'''
 +
 
 +
Curved plate girders are to be designed using load factor design criteria. The 1980 AASHTO Guide Specifications for Horizontally Curved Highway Bridges as revised by Interim Specifications for Bridges 1981, 1982, 1984, 1985 and 1986 is to be applied with the USS Highway Structure Design Handbook (\) V-Load method to be used as a working example.
 +
 
 +
The following procedure may be followed to determine the required cross-section for any system of curved girders with skews less than 46°.
 +
 
 +
1. Determine the primary moments by the same procedures as for a system of straight girders, using the developed lengths of the curved girders.
 +
 
 +
<div id="2. From primary moments, compute shear loads"></div>
 +
 
 +
2. From primary moments, compute shear loads, <math>\, V</math>, using the formula:
 +
<center>
 +
{|
 
|-
 
|-
|valign="top" align="right"|"F"||align="left"|= Gap as required for expansion (3" Min.).
+
|width= "300"|<math>\, V = \frac{\sum M}{Coeff. * K}</math>||style="text-align:left"|<math>\, V</math> = Shear loads.<br>M = Primary moments.
 
|-
 
|-
|valign="top" align="right"|"H"||align="left"|= 10 3/4" Min. (12" preferred.)
+
|<math>\, K = \frac{RD}{d}</math>||style="text-align:left"|<math>\, R</math> = Radius of curvature (outside girder).<br><math>\, D</math> = Radial distance between inside and outside girders.<br><math>\, d</math> = Distance between diaphragms measured along axis of outside girder.
 
|-
 
|-
|valign="top" align="right"|"J"||align="left"|= 5" for bearing with 3" web thickness. Use 6" for all others.
 
|-
 
|colspan="2"|All dimensions shown are minimum, increase, as necessary.
 
 
|}
 
|}
 +
 +
</center>
 +
The following coefficients may be applied to '''"'''<math>\, K</math>'''"''' for the various multiple-girder systems with equal spacing between girders.
  
  
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
<center>
|+'''Allowable Dead Load Reactions for Various Depths of "G"'''
+
{|border="1" cellspacing="1" cellpadding="1"
!width="75pt"|Web<br/>Thickness
+
|-
!width="75pt"|Depth<br/>"G"
+
|width="100"|SYSTEM||width="100"|COEFFICIENT<br>FRACTION||width="100"|COEFFICIENT<br>DECIMAL
!width="150pt"|(*) Allowable<br/>Dead Load<br/>Reactions, Kips<br/>(At 150% Overstress)
+
|-
|rowspan="9"| &nbsp;
+
|2 girders ||1|| 1.00
!width="75pt"|Web<br/>Thickness
+
|-
!width="75pt"|Depth<br/>"G"
+
|3 girders ||1||1.00
!width="150pt"|(*) Allowable<br/>Dead Load<br/>Reactions, Kips<br/>(At 150% Overstress)
 
 
|-
 
|-
|5/16"||8"||45.0||7/16"||8"||63.0
+
|4 girders ||10/9||1.11
 
|-
 
|-
|5/16"||9"||50.6||7/16"||9"||70.8
+
|5 girders ||5/4||1.25
 
|-
 
|-
|5/16"||10"||56.2||7/16"||10"||78.7
+
|6 girders ||7/5||1.40
 
|-
 
|-
|5/16"||11"||61.8||7/16"||11"||86.6
+
|7 girders || 14/9||1.56
 
|-
 
|-
|5/16"||12"||67.5||7/16"||12"||94.5
+
|8 girders ||12/7|| 1.72
 
|-
 
|-
|5/16"||13"||73.1||7/16"||13"||102.3
+
|9 girders ||15/8  || 1.88
 
|-
 
|-
|5/16"||14"||78.8||7/16"||14"||110.2
+
|10 girders ||165/81  || 2.04
 
|-
 
|-
|5/16"||15"||84.3||7/16"||15"||118.1
 
 
|}
 
|}
 +
</center>
 +
 +
3. Compute <math>\, V-Load</math> moments
  
  
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
*  Reference:  USS "Highway Structures Design Handbook" 1965 Edition.  (Updated 1986 Volume II Section 6) developed by Richardson, Gordon and Associates in cooperation with Dr. John Scalzi is to be used as a working example.
 +
 
 +
 
 +
4. Compute lateral bending moments using the approximate formula:
 +
 
 +
{|
 
|-
 
|-
|width="75pt"|3/8"
+
|width="150"|<math>\, M_L = \frac{Hd}{10} = \frac{Md^2}{10Rh}</math>||width="150"|&nbsp;||<math>\, ML </math> = Lateral bending moment
|width="75pt"|8"
 
|width="150pt"|54.0
 
|rowspan="8"| &nbsp;
 
|width="75pt"|1/2"
 
|width="75pt"|8"
 
|width="150pt"|72.0
 
 
|-
 
|-
|3/8"||9"||60.7||1/2"||9"||81.0
+
|&nbsp;||&nbsp;||<math>\, H </math> = The <math>\, H</math> values are approximately equal to the reactions at the supports.
 
|-
 
|-
|3/8"||10"||67.5||1/2"||10"||90.0
+
|&nbsp;||&nbsp;||<math>\, h </math> = Depth of girder between centers of gravity of flanges.
 
|-
 
|-
|3/8"||11"||74.2||1/2"||11"||99.0
+
|&nbsp;||&nbsp;||<math>\, M </math> = Primary moment + Secondary moment.
 
|-
 
|-
|3/8"||12"||81.0||1/2"||12"||108.0
 
|-
 
|3/8"||13"||87.7||1/2"||13"||117.0
 
|-
 
|3/8"||14"||94.5||1/2"||14"||126.0
 
|-
 
|3/8"||15"||101.2||1/2"||15"||135.0
 
 
|}
 
|}
<center>(*) No (Live load + impact) excluded.</center>
 
  
 +
<center>
 +
[[Image:751.40 Widen and Repair Design Assumptions- Horizontally Curved Girders Design Procedure.gif]]
 +
</center>
  
 +
5. Determine cross-section required to provide for vertical and lateral forces computed under Items 1 to 4 inclusive.  As with any statically indeterminate system it is necessary to make an initial assumption of the required cross-sections and to repeat the calculations one or more times to obtain reasonable agreement between the assumed and required sections.
  
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
6. The non-compact section requirement that <math>\, F_y > (f_b + f_w)</math> is to be applied to all sections with the tension flange <math>\, F_y > (f_b + f_w)</math> and the compression flange as <math>\, F_y (1-3 \lambda^2) > (f_b + f_w)</math> to ensure conservative design.
|+'''Typical Details of "Hinged" Connection"'''
 
|[[Image:751.40 general superstructure-misc details-section showing hinged beam conn3.gif]]
 
|-
 
!Section Showing Hinged Beam Connection
 
|}
 
  
 +
In computing <math>\, \lambda</math>, use <math> \ell</math> to be actual diaphragm spacing for compression and tension stresses.
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
The value of <math>\, f_w</math> is to be selected as plus or minus in the equations for <math>\, P_w</math> to give the worst possible case.
|-
 
|colspan="2"|[[Image:751.40 general superstructure-misc details-section thru plate girders.gif]]
 
|-
 
!valign="top"|Plate Girder 42" Thru 46"<br/>Also 48" and Over
 
!valign="top"|Plate Girder 36" Thru 40"
 
|}
 
  
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
'''Design and Detail Guides'''
|-
 
|[[Image:751.40 general superstructure-misc details-detail a.gif]]
 
|[[Image:751.40 general superstructure-misc details-detail b.gif]]
 
|-
 
!Detail "A"||Detail "B"
 
|}
 
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
1. Economic Arrangement of Spans and Depth-to-Spans Ratios
|-
 
|valign="top" align="right"|Note:||align="left" width="400pt"|Modify standard end diaphragm connections as shown above, if clearance problems exist between bearing plate and end diaphragm connection bolts.
 
|}
 
  
 +
Where there is flexibility in span arrangement, the same guides that apply to economic arrangement of straight girders are equally applicable to curved girders.  Similarly the rules used to establish depth-to-span ratios for straight girders usually will apply to curved girders.
  
=== 751.40.8.6 Composite Design ===
 
====751.40.8.6.1 General ====
 
  
'''GENERAL'''
+
2. Spacing of Girders
  
This portion of the article pertains to structures composed of steel girders with concrete
+
Spacing depends on the arrangements of diaphragms and bracing.  In general, however, it will be found that the most economical arrangement for straight girders will accord very well with the best arrangement for a system of curved girders. The effect of curvature increases in proportion to the square of the span length and decreases in proportion to the radius of curvature and the spacing of girders.
slab connected by shear connectors. The stresses of composite girders and slab shall be computed based on the composite cross-section properties and shall be consistent with the
 
properties of the various materials used. The regions subjected to positive moment are considered as composite and the regions subjected to negative moment are considered as non-composite. For the initial girder design, composite/non-composite regions can be approximately assumed as:
 
<center>
 
  
[[Image:751.40 Widen and Repair Design Assumptions- Initial Girder Design.gif|650px]]
 
</center>
 
  
 +
3. Arrangement and Spacing of Diaphragms
  
'''SECTION PROPERTIES'''
+
The diaphragms shall be placed radially, with a maximum spacing of 15'-0".  In order to minimize lateral bending of the girder flanges, the flanges should be as wide as practical.
  
Cross-section properties of the composite section shall include concrete
 
slab and steel section.
 
  
Cross-section properties of the non-composite section shall include steel
+
Sway frame bracing is selected for curved girder system, by same methods as for straight girders.
section only.
 
  
Use composite property for positive moment section.
 
  
Use non-composite property for negative moment section. The effect of reinforcing steel in the section is not considered.
+
4. Effect of Lateral Bracing
  
The ratio of modulus of elasticity of steel to that of concrete, n, shall be assumed to be eight. The effect of creep shall be considered in the design of composite girders which have dead loads acting on the composite section. In such structures, n=24 shall be used.
+
made in a similar manner as for straight bridges. If lateral Provision for lateral loading on curved girders may be bracing is used in a system of curved girders, the forces resulting
 +
from the radial components of flange stress may be carried partially or entirely by the bracing system; when both diaphragms and lateral bracing are used, radial reaction components may be divided between the two systems.
  
  
 +
5. Approximate Estimate of Curvature
  
'''DESIGN UNIT STRESSES''' (also see note A1.1 in Section 4)
+
The following formula may be used in making preliminary approximations of the effect of curvature:
  
'''Reinforcement Concrete'''
+
{|
 
 
{|style="text-align:left"
 
 
|-
 
|-
|width="250"|Reinforcing Steel (Grade 60)||width="150"|<math>\, f_s</math> = 24,000 psi||width="150"|<math>\, f_y</math> = 60,000 psi
+
|width="400"|<math>\, P = 10.5 \times \frac{(1+r)(L')^2}{R_2D}</math>||Note: For "r" refer to paragraph No. 7
 
|-
 
|-
|Class B-2 Concrete (Substructure)||  <math>\, f_c</math> = 1,600 psi||     <math>\, f'_c</math> = 4,000 psi
+
|<math>\, r = \frac{(R_1)^2}{(R_2)^2} \times \bigg( \frac {Inside \ girder \ loading)}{Outside \ girder \ loading} \bigg)</math>||(*)
 
|-
 
|-
 
|}
 
|}
'''Structural Steel'''
+
 
  
 
{|
 
{|
 
|-
 
|-
|width="300"|Structural Carbon Steel (ASTM A709 Grade 36)||width="150"|<math>\, f_s</math> = 20,000 psi||width="150"|<math>\, f_y</math> = 36,000 psi
+
|(*)||May be omiteed if supports are on radial lines.
 +
|-
 +
|<math>\, P </math>||% increase in positive moment due to effect of curvature.
 +
|-
 +
|<math>\, R_2</math>||Radius of inside girder.
 +
|-
 +
|<math>\, R_1</math>||Radius of outside girder.
 
|-
 
|-
|Structural Steel (ASTM A709 Grade 50)||<math>\, f_s</math> = 27,000 psi||<math>\, f_y</math> = 50,000 psi
+
|<math>\, L'</math>||Distance between points of contraflexure in any pisitive moment area.
 
|-
 
|-
|Structural Steel (ASTM A709 Grade 50W)||<math>\, f_s</math> = 27,000 psi||<math>\, f_y</math> = 50,000 psi
+
|<math>\, D </math>||Spacing between inside and outside girders.
 
|-
 
|-
 
|}
 
|}
  
==== 751.40.8.6.2 Design ====
 
===== 751.40.8.6.2.1 Shear Connector Design =====
 
  
The shear connectors shall be designed for fatigue and checked for ultimate strength (AASHTO Article 10.38.5.1).
+
In the above form, the formula applies to a two-girder system, but it may be modified by reference to the table of coefficients for multiple-girder systems shown in [[#2. From primary moments, compute shear loads|Item #2. From primary moments, compute shear loads]].
  
<u>Step 1:</u>
+
The formula applies particularly to positive moment, but for preliminary approximation it may be assumed that the curvature effect on negative moments will be about the same.
  
Compute Vr, the range of shear in kips, from the structural analysis, due to live loads and impact, for entire span. 
 
  
At any section, the range of shear shall be taken as the difference in the minimum and maximum shear envelopes (excluding dead loads).
+
6. Design of Diaphragms and Connections
  
 +
Where the degree of curvature is equal to or under 1&deg; - 30' and when spans are equal to or under 75'-0" in length, the diaphragm and connections shall be the same as for Bridges with straight girders.  Where the degree of curvature is over 1&deg;- 30' to 3&deg; or with a span length of more than 75'-0", the diaphragm must be attached to the tension flange.  Where the degree of curvature is over 3&deg;, a special design will be required for connection of intermediate diaphragms to flanges.
  
<u>Step 2:</u>
+
The maximum allowable diaphragm spacing is 15'-0", regardless of the amount of curvature, or span lengths.
  
Use the average Vr per span, for the section of the span that is assumed to act compositely (from end of span to point of contraflexure for end spans, or from point of contraflexure to point of contraflexure for int. spans).
 
  
 +
The following applies to those bridges where the special design is to be considered:
  
<u>Step 3:</u>
 
  
Using the average Vr from step 2, compute the range of horizontal shear load per linear inch, Sr in kips per inch, at the junction of the slab and stringer from the following equation:
+
Since diaphragm moments due to effect of curvature are a function of the radial component of flange stress, they are directly proportional to the vertical bending moment in the girders.
  
<math>\,  \ Sr = \frac{VrQ}{I}</math> 
 
  
(AASHTO Article 10.38.5.1.1 Eq. 10-58)
+
For exterior girders the moment in the diaphragm equals <math>\, M \times d/R</math>, in which <math>\, M</math> = vertical bending moment in girder for any particular condition of loading; <math>\, d</math> = diaphragm spacing; <math>\, R</math> = Radius of curvature of girder.
  
  
where:
+
For negative moment over the support, the <math>\, M</math> value used in this equation should be the average moment between a point at the support and a point at the first adjacent diaphragm. 
  
<math>\,  Q </math> = static moment of the transformed compressive concrete area about the neutral axis of the composite section, in cubic inches (*);
 
  
<math>\,  I </math> = moment of inertia of the transformed composite girder in positive moment regions in inches to the fourth power (*).
+
Diaphragm connections may be made directly to the flanges of the girders or through stiffeners, provided details are arranged to adequately transfer radial components of flange stress into the diaphragms.
  
(*) In the formula, the compressive concrete area is transformed into an equivalent area of steel by dividing the effective concrete flange width by the modula ration n=8.
 
  
 +
7. Supports positioned other than on radial lines.
  
<u>Step 4:</u>
+
If field conditions permit, the most orderly arrangement for curved girders will be attained by placing the supports on radial lines.
  
Compute the allowable range of horizontal shear, Zr, in pounds on an individual connector, welded stud, by use of the following formula:
 
  
<math>\, Zr = \alpha \ d^2 </math>
+
It may be necessary to treat each line of girders independently, first finding the direct loading moments and then correcting for curvature by applying the separate <math>\, V-loads</math>.
  
where:
 
  
<math>\,  \frac{H}{d} \ge 4</math>
+
8. Transverse stiffeners
  
  
 +
The maximum transverse stiffener spacing for curved plate girders is <math>\, D</math>, the web height.
  
<math>\,  H </math> =height of stud in inches;
 
  
<math>\,  d </math> =diameter of stud in inches;
+
Transverse stiffeners should be placed along the girder length only as far as required by design.
  
<math>\, \alpha </math> =13,000 for 100,000 cycles
+
The maximum spacing of the first transverse stiffener at the simple support end of a curved plate girder is <math>\, D/2</math>.
  
:10,600 for 500,000 cycles
 
  
:7,850 for 2,000,000 cycles
+
Reference:  
 +
:AASHTO - Article 10.5
 +
:Limit radius of heat curved girders according to AASHTO Article 10.15.
  
:5,500 for over 2,000,000 cycles.
+
Where the distance between field splices of curved girders exceeds that given by the following formula, a special note shall be placed on the plans.
  
 +
{|
 +
|-
 +
|<math>\, L</math> =||<math>\, \sqrt{\frac{0.667 \ x \ f_s \ x \ SM}{W}}</math>||(*)
 +
|-
 +
|<math>\, L</math> =||Allowable distance between field splices, in feet.
 +
|-
 +
|<math>\, f_s</math> =||Allowable fs of flange steel, in psi. e.g. use 20,000 psi for Grade 36 steel.
 +
|-
 +
|<math>\, W</math> =||Weight of girder (flanges and web), in pounds per foot.
 +
|-
 +
|<math>\, SM</math> =||Section Modulus of girder about x-x axis as shown, in inches cubed.
 +
|-
 +
|}
  
<u>Step 5:</u>
 
  
Compute the number of additional connectors required at point of contraflexure, N , from the following formula:
+
[[Image:751.40 Design Assumptions- Heat Curved Girders- Section Modulus.gif]]
  
Pitch = <math>\, \frac{\sum Z_r}{S_r}</math>
 
  
Where:
+
Note:
Pitch = required pitch, in inches;
 
  
<math>\, \sum Z_r</math> = the resistance of all connectors at one (1) transverse girder cross-section as a shear connector unit.
+
If flanges are of different sizes, use smaller Section Modulus.
  
Note:
+
See Structural Project Manager for allowable overstress.
  
The pitch is to be constant and spaced in the composite section (round to the nearest inch).
 
  
<u>Step 6:</u>
+
<u>(*) Derivation</u>
  
Compute the required pitch of the shear connector units, pitch by the following formula:
+
:Positive moment at centerline, <math>\, Mom. = \frac{WL^2}{8} \times 12</math>
  
<math>\, N_c = \frac{{A_r}^2 f_r}{Z_r}</math>
+
:<math>\, fs = \frac{Mom.}{SM}</math>
  
 +
:Substitute mom. in fs equation.
  
(AASHTO Article 10.38.5.1.1 Eq. 10-69)
+
::<math>\, fs = \frac{WL^2 \times 12}{8 \times SM}</math>
  
where:
+
:solve for L
  
<math>\, N_c</math> = number of additional connectors required at the point of contraflexure;
+
::<math>\, L = \sqrt{\frac{8 f_s \times SM}{12W}}</math>
  
<math>\,  {A_r}^s </math> = total area of longitudinal slab reinforcing steel for each girder over interior support;
+
<center>
 +
'''Design Example'''
  
<math>\,  f_r</math> = range of stress due to live load plus impact, in the slab reinforcement over the support (in lieu of more accurate computations, f may be taken as equal to 10,000 psi);
+
'''ASTM A709 Grade 36 Steel'''
  
<math>\,  Z_r</math> = the allowable range of horizontal shear on an individual connector.
+
[[Image:751.40 Design Assumptions- Heat Curved Girders- Design Example Plan View.gif]]
  
 +
</center>
  
 +
{|
 +
|-
 +
|width="400"|&nbsp;||width="400"|[[Image:751.40 Design Assumptions- Heat Curved Girders- Design Example Section 2.gif]]
 +
|-
 +
|[[Image:751.40 Design Assumptions- Heat Curved Girders- Design Example Section A-A.gif]]||
 +
{|border="1" cellpadding="1" cellspacing="1" style="text-align:center"
 +
|-
 +
|Shape||<math>\, I_{xx}</math>
 +
|-
 +
|PL 13" x 3/4"||<math>\, \frac{0.75 \times (13)^3}{12} = 137.31</math>
 +
|-
 +
|PL 70" x 3/8"||<math>\, \frac{70 \times (0.375)^3}{12} = 0.31</math>
 +
|-
 +
|PL 12" x 3/4"||<math>\, \frac{0.75 \times (12)^3}{12} = 108.00</math>
 +
|-
 +
|<math> Total \ I_{xx}</math>||align="right"|<math> = 245.62 \ In.^4</math>
 +
|-
 +
|}
 +
|-
 +
|SECTION A-A ||rowspan="1"|<math>\, SM_A = I/C = 245.62/6.5 = 37.79 In.^3</math>
 +
|-
 +
|&nbsp;||rowspan="1"|<math>\, SM_B = I/C = 245.62/6 = 40.94 In.^3</math>
 +
|-
 +
{|border="1" cellpadding="1" cellspacing="1"
 +
|-
 +
|Weight per Foot of Girder
 +
|-
 +
|PL 12" x 3/4" = 30.6 lbs./ft.
 +
|-
 +
|PL 70" x 3/8" = 89.3 lbs./ft.
 +
|-
 +
|PL 13" x 3/4" = 33.2 lbs./ft.
 +
|-
 +
|Total =  153.1 lbs./ft.
 +
|-
 +
|}
 +
||&nbsp;
 +
|-
 +
|<u>From Formula:</u>||&nbsp;
 +
|-
 +
|colspan="2" style="text-align:center"|<math>\, L = \sqrt{\frac{0.667 \times fs \times SM}{W}} = \sqrt{\frac{0.667 \times 20,000 \times 37.79}{153.1}} = 57.38'</math>  (Use 57.5')
 +
|-
 +
|}
  
This number of additional connectors, N , shall be placed adjacent to the point of dead load contraflexure within a distance equal to 1/3 of the effective slab width, if it is possible. If it is impossible, use minimum pitch of 6".
 
  
 +
<center>57'-6" < 60'-0".  Therefore, Special Note required.</center>
  
<u>Step 7: Check connectors for ultimate strength</u>
+
Special Note:
  
The number of connectors provided for fatigue must be checked to ensure that adequate connectors are provided for ultimate strength.
+
Heat curving of girders <u>(Identify)</u> (*) will not be allowed shile in the horizontal position.
  
To check for ultimate strength, proceed as follows:
+
(*)Complete underlined portion as required.
  
(1) Compute the force in the slab (P), which is defined as: at the point of maximum positive moment, the force in the slab is taken as the smaller value of the following two formulae:
 
  
  
<math>\, P_1 = A_s F_y</math>  (AASHTO Article 10.38.5.1.2 Eq. 10-63)
+
Maximum Plate Lengths:
 +
:80 feet. See Structural Project Manager for use of longer lengths up to 85' for ASTM A709 Grade 50 or ASTM A709 Grade 50W and 100' for ASTM A709 Grade 36.
 +
 +
Minimum Plate Lengths:
 +
:10 feet. Shop flange splices should be eliminated and extra plate material used when :economy indicates and span lengths permit.
  
or
+
Preliminary Analysis:
 +
:(1) Compute moments from influence lines on basis of "Constant I" analysis and apply the following percentage increase or decrease to non-composite dead load moments. 
  
<math>\, P_2 = 0.85 f'_{cbt_s}  P</math> = (AASHTO Article 10.38.5.1.2 Eq. 10-62)
+
References may be used in lieu of the above.
  
 +
<center>
 +
[[Image:751.40 Design Assumptions- Preliminary Analysis-Moments Diagram.gif]]
 +
</center>
  
Where:
+
{|style="text-align:center"
 +
|-
 +
|width="500"|<math>\, n</math> = 1.2 to 1.5||width="90"|<math>\, n</math> = 1.2 to 1.5
 +
|-
 +
|
 +
{|border="1" cellspacing="1" cellpadding="1"
 +
|-
 +
|<math>\, +M_1</math>||-5%
 +
|-
 +
|<math>\, -M_2</math>||+15%
 +
|-
 +
|<math>\, +M_3</math>||-15%
 +
|-
 +
|}
 +
||
 +
{|border="1" cellspacing="1" cellpadding="1"
 +
|-
 +
|<math>\, +M_1</math>||-5%
 +
|-
 +
|<math>\, -M_2</math>||+15%
 +
|-
 +
|<math>\, +M_3</math>||-15%
 +
|-
 +
|<math>\, -M_4</math>||+15%
 +
|-
 +
|}
 +
|-
 +
|}
  
<math>\, A_s</math> = total area of the steel section including cover plates (if used);
+
(2) Determine trial sections and plot a rough moment curve to determine location of flange plate cutoffs, if any.
  
<math>\, F_y</math> = specified minimum yield point of the steel being used;
+
(3) Complete analysis by using computer programs to obtain actual moments and stresses.
  
<math>\, f'_c</math> = compressive strength of concrete at age of 28 days;
+
<center>
 +
'''Design Stress investigation for Positive Moment Area of Plate Girder Structure'''
 +
</center>
  
<math>\, b</math> = effective flange width given in AASHTO Article 10.38.3;
+
The design stresses are to be checked at the top of flange (steel) and the top of concrete slab in the composible area of Plate Girder Structures to ensure that they are within the allowable stresses.
 +
<center>
  
<math>\, t_s</math> = thickness of concrete slab.
+
[[Image:751.40 Design Assumptions- Design Stress Investigation- Plate Girder.gif]]
  
 +
SECTION A-A   
  
Note:
 
  
If it becomes impractical to place the number of shear connectors required by ultimate strength in the specified distance (structures with span ratios greater than 1.5); base the number and spacing of shear connectors on the fatigue analysis only.
+
'''Structure Length'''
  
Increase the haunch by 1/2"± more than what is required to make one size shear connector work for C.I.P. or S.I.P. option.
 
  
===== 751.40.8.6.2.2 Shear Connector Spacing =====
+
Typical Continuous Steel Structures- Integral End Bents:
  
If it becomes impractical to place the number of shear connectors required by ultimate strength in the specified distance (structures with span ratios greater than 1.5); base the number and spacing of shear connectors on the fatigue analysis only.
 
  
For a typical 3-spans bridge, the shear connector units can be approximately
 
arranged as below:
 
  
[[Image:751.40 Widen and Repair Design Assumptions- Shear Connectors Spacing 2 2 1.gif]]
+
[[Image:751.40 Design Assumptions- Structure Length- Maximum Length for Continuous Steel.gif]]
  
==== 751.40.8.6.3 Details ====
+
</center>
=====751.40.8.6.3.1 Shear Connector Details =====
 
  
Use precast prestressed panels on all tangent steel structures.  Evaluate the viability of the use of P/S panels on curved structures on a case by case basis and use or include as an option to a CIP slab where deemed appropriate.
 
  
Whenever panels are used, the minimum top flange width shall be 12" for Plate Girders and 10" for Wide Flange Beams.
+
'''Estimated Girder Depth'''
 +
''Based on Three Spans With Ratio N = 1.3±''
  
Steel girders shall be cambered when using P/S Panels. Minimum joint filler thickness is 3/4", except over splice plates, in which case use 1/4" minimum. Maximum joint filler thickness is 2".
+
<center>
  
Shear connectors shall have a minimum height equal to the top of panel.
+
Continuous Plate Girders HS20 Loading Load Factor
 +
<br>(ASTM A709 Grade 50 or ASTM A709 Grade 50W)
  
Shear connectors shall be spaced by units and shear connectors in each unit shall be placed along <math>\, C_{\!\!\!\!L}</math> of girder. On wide flange widths, two lines of connectors may be used if spacings and clearances allow.
+
{|border="1" cellpadding="1" cellspacing="1" style="text-align:center"
 +
|-
 +
|Initial Estimate<br>(Feet) ||Girder Depths (*)<br>(Inches)|| Structure Depth (**)<br>(Feet)
 +
|-
 +
|85 to 104||42||4.50
 +
|-
 +
|105 to 124||48||5.00
 +
|-
 +
|125 to 134||54||5.50
 +
|-
 +
|135 to 144||60||6.00
 +
|-
 +
|145 to 159||66||6.50
 +
|-
 +
|160 to 174||72||7.00
 +
|-
 +
|175 to 184||78||7.50
 +
|-
 +
|185 to 194||84||8.00
 +
|-
 +
|195 to 204||90||8.50
 +
|-
 +
|}
 +
</center>
  
Additional shear connectors, Nc, at point of contraflexure may be placed in units normal to <math>\, C_{\!\!\!\!L}</math> girder as space allows or in a single row along <math>\, C_{\!\!\!\!L}</math> girder as shown below:
 
  
<center>
+
Trial steel plate girder depths use program BR109 to check designs and deflections. Web depths may be adjusted by two inch increments.
[[Image:751.40 Widen and Repair Design Assumptions- PCP on Steel Shear Connector.gif]]
 
</center>
 
  
P/S strands shall extend 3" minimum and 6" maximum past edge of precast prestressed panel and not closer than 1" to the adjacent panels.
+
(*) Bethlehem steel economic study (N = 1.3±). Bethlehem steel provided an economic study of multiple steel girder depths. The study indicated that cheaper designs are obtained by reducing the plate girder depths and reducing the number of stiffeners. The recommended initial estimates above are based on these designs.
  
Panel end at splices shall be notched to avoid bolt heads as shown below:
 
<center>
 
[[Image:751.40 Widen and Repair Design Assumptions- PCP on Steel Shear Connector- B.gif]]
 
</center>
 
  
[[Image:751.40 circled 1.gif]] 3/4" min. wide bearing edge for panel at splice, typ. (*)
+
(**) Structure depth includes slab and haunch.
 +
 
 +
A general rule of thumb is to determine the minimum web thickness without stiffeners; then, use a web thickness of one-sixteenth inch less. Match MoDOT requirements for web increments of one-sixteenth inch only.
  
[[Image:751.40 circled 2.gif]] 1-1/4" min. (Typ.)
 
  
[[Image:751.40 circled 3.gif]] 4 x (Stud diameter) preferred minimum, may be reduced if necessary for a more economical design; 2-1/4" absolute minimum.
+
If two-span structures are used, a deeper web is required. A good estimate is to use six inches additional depth than the above tables for two-span structures.
  
 +
====751.40.8.8.2 Details====
  
(*) In order to meet [[Image:751.40 circled 1.gif]] and [[Image:751.40 circled 2.gif]] above, it is necessary to have an edge bolt distance of 2" or greater for splice plate. For unusual cases, which would require field splices for flange widths 14" or 15" for P/S precast panel option, it will be necessary to change the top flange width to either 13" or 16" of equal area to maintain the 3/4" minimum panel bearing edge on the splice plates.
+
=====751.40.8.8.2.1 Field Flange Splice – Bolted=====
 +
 
 +
'''General'''
  
Minimum joint filler thickness is 3/4" except over splice plates in which case use 1/4" minimum. When joint filler is less than 1/2" thick over splice plate, make the width of joint filler at splice the same width as panel on splice (maximum 1-1/2" wide).
+
Splices shall be designed using the Service Load Design Method and in accordance with AASHTO Articles 10.18, 10.24 and 10.32 except as noted.
  
Maximum difference in top of flange thickness should be checked so that joint filler thickness does not exceed 2".
+
Splices shall be designed to develop 100% of the flange strength by the flange splice plate strength.  When the flange section or steel grade changes at a splice, the smaller flange strength shall be used to design the splice. Splice plates shall then match the lower grade used in the flanges.
  
===== 751.40.8.6.3.2 Deflection =====
 
  
Allowable Live Load Deflection
+
'''Minimum Yield Strength <math>\, (Fy)</math> and Minimum Tensile Strength <math>\, (Fu)</math>'''
  
 
{|
 
{|
 
|-
 
|-
|1.||Composite Design:||Defl.||= 1/1000 of span;
+
|width="200"|ASTM A709 Grade 36||width="100"|<math>\, F_y</math>  = 36 ksi||<math>\, F_u</math> = 58 ksi
 +
|-
 +
|ASTM A709 Grade 50||<math>\, F_y</math>  = 50 ksi||<math>\, F_u</math> = 65 ksi
 
|-
 
|-
|2.||Non-composite Design:||Defl.||= 1/800 of span
+
|ASTM A709 Grade 50W||<math>\, F_y</math>  = 50 ksi||<math>\, F_u</math> = 70 ksi
 
|-
 
|-
 
|}
 
|}
  
  
:Where:
+
'''Allowable Steel Stresses <math>\, (F_t)</math>'''
  
:Defl. = allowable deflection due to service live load plus impact.
+
Allowable stresses are determined by AASHTO Table 10.32.1A.
  
 
+
{|
Dead Load Deflection
+
|-
Compute at 1/4 point for bridge with spans less than 75’, at 1/10 points for spans 75’ and over.
+
|width="200"|Allowable tensile stress||<math>\, F_t = 0.55 \times F_y</math>
 
+
|-
=== 751.40.8.7 Wide Flange Beam Spans ===
+
|}
  
 
==== 751.40.8.7.1 Design ====
 
 
 
===== 751.40.8.7.1.1 Design Data =====
 
 
'''Slabs'''
 
  
 
{|
 
{|
|width="150pt"|Reinforcing Steel||<math>\, f_y</math>||= 60,000 psi
 
 
|-
 
|-
|width="150pt"|Concrete||<math>\, f_c</math>||= 1,600 psi|| &nbsp;||<math>\, f'_c</math>||= 4,000 psi
+
|width="200"|ASTM A709|| Grade 36||<math>\, F_t</math> = 20 ksi
 +
|-
 +
|width="200"|ASTM A709|| Grade 50|| <math>\, F_t</math> = 27 ksi
 +
|-
 +
|width="200"|ASTM A709|| Grade 50W||<math>\, F_t</math>  = 27 ksi
 
|-
 
|-
| &nbsp;||<math>\, n</math>||= 8
 
 
|}
 
|}
  
  
'''Simple Design Span'''
+
'''Allowable Bolt Stresses '''
  
Design Span = Center to Center of Bearings.
+
Splices shall be designed as slip critical connections with Class B surface preparation and oversized holes.  Although standard holes are used in the fabrication of flange splices, designing the splices for oversize holes allows for some fabrication and erection tolerances.  All splice bolts shall be 7/8" diameter ASTM F3125 Grade A325.  
  
 +
AASHTO Table 10.32.3C specifies <math>\, F_s</math> = 19 ksi for a class B slip-critical connection.  Tables shown in this article are based on 19 ksi that should also be used to design splices not listed in the table. 
  
'''Dead Load'''
 
  
 +
Although slip-critical connections are theoretically not subject to shear and bearing, they must be capable of resisting these stresses in the event of an overload that causes slip to occur. The allowable shear stress per bolt <math>\, (Fv)</math> for bearing is 19 ksi with the threads included and <math>\, 1.25 \times 19 = 23.75</math> ksi for threads not included.
  
'''Live Load Distribution Factors'''
 
  
See [[751.40 Widening and Repair #751.40.8.2.2 Distribution of Live Load|EPG 751.40.8.2.2 Distribution of Live Load]]
+
'''Flange Strength'''
 +
 
 +
The flange strength shall be determined by multiplying the allowable stress of the flange by the area of the flange. The area of the flange shall be taken as the gross area of the flange, except that if more than 15 percent of each flange area is removed, that amount removed in excess of 15 percent shall be deducted from the gross area. Bolt holes are considered to be 1" diameter for the purpose of determining flange area.  
 +
 
  
 +
'''Splice Plate Strength'''
  
'''Live Load Deflection Allowable'''
+
The splice plate strength shall be determined by multiplying the allowable stress of the splice plates by the area of the splice plates.  The area of the splice plates shall be taken as the gross area of the splice plates, except that if more than 15 percent of the splice plate area is removed, that amount in excess of 15 percent shall be deducted from the gross area.
  
{|
 
|width="150pt"|Composite||<math>\, \frac {L}{1000}</math>
 
|-
 
|width="150pt"|Non-Composite||<math>\, \frac {L}{800}</math>
 
|}
 
  
 +
'''Two Row Splices'''
  
'''Live Load Reaction'''
+
Splices with two rows of bolts are used with flanges 12 to 13 inches wide. The inner and outer plates may either be the same length or the inner plate may be shorter. This is the case if the end bolts in the splice are only needed to be in single shear. All other bolts will be in double shear. (See Figure 3.42.2.2-1)
  
Live Load <math>\, (LL) /</math> Wheel Line <math>\, (WL)</math> is the Live Load Reaction per Wheel Line, no distribution, no impact; Maximim Live Load <math>\, (LL) +</math> Impact <math>\, (I)</math> is the Live Load Reaction x Distribution Factor = Impact.
+
<center>
 +
[[Image:751.40 Widen and Repair- Field Flange Splice- Bolted.gif]]
  
 +
'''<u>Figure 3.42.2.2-1</u>'''
 +
</center>
  
<center>[[Image:751.40 wf bm spans-truck loading.gif|500px]]</center>
 
  
<center>'''Truck Loading'''</center>
+
'''Four Row Splices'''
  
<center>(Governs thru 33' simple spans for H20 and all simple spans for HS20)</center>
+
When the width of the flange being spliced is 14 inches or greater, four longitudinal rows of bolts are used. Three variations of the end bolts positioning may be used.  In each of these variations, the last two bolts shall be located in the outer rows closest to the edge of the splice plate.
 +
<center>
  
 +
[[Image:751.40 Widen and Repair- Field Flange Splice- Bolted Four Row Splice.gif]]
  
<center>[[Image:751.40 wf bm spans-lane loading1.gif|500px]]</center>
+
'''<u>Figure 3.42.2.2-2</u>'''
 +
</center>
  
<center>'''Lane Loading'''</center>
 
  
<center>(Governs for simple soabs 35' and over for H20)</center>
+
'''Flange Width Transitions'''
  
 +
When the width of the flanges being spliced differs by more than 2", the larger flange shall be beveled as shown in Figure 3.42.2.2-3
  
 +
<center>
 +
[[Image:751.40 Widen and Repair- Field Flange Splice- Bolted- Flange Width Transition.gif]]
  
'''Typical Continuous Steel Structures - Integral End Bents:'''
 
  
<center>[[Image:751.40 wf bm spans-structure length.gif|600px]]</center>
+
'''<u>Figure 3.42.2.2-3</u>'''
 +
</center>
  
<center>(*) Maximum length for End Bent to end Bent - 500 feet.</center>
 
  
===== 751.40.8.7.1.2 Stringer Design =====
 
  
'''Stresses:'''
+
'''Weight of Splice'''
  
{|
+
When calculating the weight of splice, the following simplified weights shall be used.
|-
 
|width="50pt"|Steel:||colspan="2"|AASHTO - Article 10.2, 10.32
 
|-
 
| &nbsp;||width="100pt"|ASTM A709 Grade 36||width="125pt"|<math>\, f_y</math> = 36,000 psi ||width="125pt"|( <math>\, f_s</math> = 20,000 psi)
 
|-
 
| &nbsp;||width="100pt"|ASTM A709 Grade 50 & Grade 50W||width="125pt"|<math>\, f_y</math> = 50,000 psi ||width="125pt"|( <math>\, f_s</math> = 27,000 psi)
 
|}
 
  
 +
Weight of High-Strength bolts (diameter 7/8") = 0.95 lbs/bolt
  
{|
+
Unit weight of Structural Steel = 490 lbs/ft<sup>3</sup>
|-
 
|width="175pt"|Superstructure Concrete:||<math>\, f_c</math>||= 1,600 psi
 
|-
 
|width="175pt"| &nbsp;||<math>\, f'_c</math>||= 4,000 psi
 
|-
 
|width="175pt"| &nbsp;||<math>\, n</math>||= 8
 
|}
 
  
 +
=====751.40.8.8.2.2 Field Web Splice – Bolted=====
  
{|
+
'''General'''
|-
 
|width="125pt"|Reinforcing Steel:||<math>\, f_y</math>||= 60,000 psi
 
|}
 
  
 +
Splices shall be designed using the Service Load Design Method and in accordance with AASHTO Articles 10.18, 10.24 and 10.32 except as noted.
  
 +
The web splice consists of 2-Plates:
 +
::Thickness = 5/16" minimum.
 +
::Width = 12-1/2" (18-1/2" if 3 rows of bolts are required).
  
'''Physical Properties of Spans'''
+
When the web section or steel grade changes at a splice, the smaller web strength should be used to design the splice. 
  
:Composite Design - See [[751.40 Widening and Repair #751.40.8.6 Composite Design|Widening and Repair - Composite Design]].
 
  
:Non-Composite Design - Use "Constant I" analysis.
+
'''Minimum Yield Strength <math>\, (F_y)</math> and Minimum Tensile Strength <math>\, (F_u)</math>'''
  
When the neutral axis of a composite section falls in the concrete fange, the section shall be designed as Non-Composite (21" Wide Flange is the smallest beam generaly made conposite).
+
{|
 
+
|-
 
+
|width="200"|ASTM A709 Grade 36||width="100"|<math>\, F_y</math>  = 36 ksi||<math>\, F_u</math> = 58 ksi
'''Deflection'''
 
 
 
:{|
 
|width="150pt"|Live Load Deflection:||width="300pt"|AASHTO - Article 10.6
 
 
|-
 
|-
| &nbsp;||width="300pt"|Composite - Allowable Deflection L/1000
+
|ASTM A709 Grade 50||<math>\, F_y</math>  = 50 ksi||<math>\, F_u</math> = 65 ksi
 
|-
 
|-
| &nbsp;||width="300pt"|Non-Composite - Allowable Deflection l/800
+
|ASTM A709 Grade 50W||<math>\, F_y</math>  = 50 ksi||<math>\, F_u</math> = 70 ksi
 
|-
 
|-
|valign="top"|Dead Load Deflection:||width="300pt"|Compute at 1/4 points for bridges with spans less than 75', at 1/10 points for spans 75' and over. Give percentage of deflection due to weight of structural steel.
 
 
|}
 
|}
  
  
 +
'''Allowable Steel Stresses <math>\, (F_b, F_w)</math>'''
  
'''Fatigue Stress'''
+
Allowable stresses are determined by AASHTO Table 10.32.1A.
  
AASHTO - Article 10.3 Case I, Case II or Case III (as specified on design layout generally within the following limitations).
+
{|
 
 
:{|
 
|align="right" valign="top"|Case I:||width="500pt"|Bridges with the '''TRUCK''' traffic count of 2500 or more vehicles per day (one direction).
 
 
|-
 
|-
|align="right" valign="top"|Case II:||width="500pt"|Bridges with traffic count of 750 or more vehicles per day, and less than 2500 '''TRUCK''' traffic count (one direction) per day.
+
|width="200"|Allowable bending stress||<math>\, F_b = 0.55 \times F_y</math>
 
|-
 
|-
|align="right" valign="top"|Case III:||width="500pt"|Bridges with traffic count of less than 750 vehicles per day, except when Live Loading is H20 or greater.
+
|Allowable shear stress||<math>\, F_v = 0.33 \times F_y</math>
 
|-
 
|-
|align="right" valing="top"|No Fatigue:||width="500pt"|Bridges with traffic of less than 75 vehicles per day.
 
 
|}
 
|}
  
  
'''Economic Comparison'''
+
{|
 +
|-
 +
|width="200"|ASTM A709 Grade 36||width="100"|<math>\, F_b</math>  = 20 ksi||<math>\, F_v</math> = 12 ksi
 +
|-
 +
|width="200"|ASTM A709 Grade 50||<math>\, F_b</math>  = 27 ksi||<math>\, F_v</math> = 17 ksi
 +
|-
 +
|width="200"|ASTM A709 Grade 50W||<math>\, F_b</math>  = 27 ksi||<math>\, F_v</math> = 17 ksi
 +
|-
 +
|}
  
When comparing cost of low-alloy steels (A-572, Gr.-50, and A-588) to the cost of A-36 steel, the low-alloy steels shall be figured a t 3 1/2 cents for A-572, Gr.-50 and 5 1/4 cents for A-588 per pound more than A-36 steel. Cost comparisions will be based on current average bid prices that may be obtained from the CHIEF DESIGNER, for comparable bridges.
 
  
No overstressed will be permitted in the design.
+
'''Allowable Bolt Stresses '''
  
 +
Although standard holes are used in the fabrication of web splices, designing the splices for oversize holes allows for some fabrication and erection tolerances.  Web splices required to resist shear between their connected parts are designated as slip-critical connections.  Shear connections subjected to stress reversal, or where slippage would be undesirable, shall be slip-critical connections.  Potential slip of joints should be investigated at intermediate load stages especially those joints located in composite regions.  The resultant force shall be less than the allowable bolt shear force. All splice bolts shall be ASTM F3125 Grade A325 7/8" diameter High Strength Bolts. 
  
'''Total Capacity of Exterior Griders''' (Dead Load and Live Load)
+
<math>\, F_v</math> = 19 ksi
 +
 
 +
 
 +
'''Bolt Arrangement'''
  
In no case shall an exterior stringer have less carrying capacity than an interior stringer.
+
The minimum distance from the center of any fastener in a standard hole to a sheared or thermally cut edge shall be 1-1/2 inches for 7/8" diameter fasteners.  The minimum distance between centers of fasteners in standard holes shall be three times the diameter of the fastener, but shall not be less than 3 inches for 7/8" diameter fasteners.  
  
===== 751.40.8.7.1.3 Flange Plate Lengths =====
 
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
'''Splice Plate Strength'''
|-
 
|colspan="2"|[[Image:751.40 wf bm spans-flange plates-details of flange plates at int bents1.gif]]
 
|-
 
!width="50%"|Top Flange||width="50%"|Bottom Flange
 
|-
 
!colspan="2"|Details of Flange Plates at Intermediate Bents
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|colspan="2"|[[Image:751.40 wf bm spans-flange plates-details of flange plates at int bents2.gif]]
 
|-
 
!colspan="2"|Details of Flange Plates at Intermediate Bents<br/>(Top and Bottom Flanges)
 
|}
 
  
Allowable flange plate sizes are as shown with the section properties. Different plate sizes may be used on adjacent stringers.
+
The strength of the splice plates shall be determined by multiplying the allowable stress of the splice plates by the net area of all splice plates.  The splice plates net area shall be taken as the gross area of the splice plates minus the bolt holes. Bolt holes are considered to be 1 inch diameter for the purpose of determining splice plate net area.  Web splices are designed to develop 75% of net section of the web.
  
Lengths to be shown on the bridge plans are those required as follows:
 
:Lengths each side of the bearing shall be the larger of:
 
#Theoretical End + Terminal Distance (***) or
 
#Point where the stress range (tension or reversal) in the beam flange is equal to or less than allowable fatigue stess range (Cat. E or E') or where the beam flange is in compression, whichever is smaller.
 
#*Use Cat. E when the flange is less than or equal to 0.8 inch thick.
 
#*Use Cat. E' when the flange is greater than 0.8 inch thick.
 
  
(***) Where the theoretical end = the point where the flange stress without cover plate less than or equal to base allowable stress.  Terminal distance = 1 1/2 times nominal cover plate width.
+
'''Web Strength'''
  
The total length of the cover plate greater than or equal to (2D + 3'-0"). Where "D" = Depth of beam in feet.
+
The strength of the web should be determined from the allowable web stress at the "top of web" to account for hybrid sections. Otherwise, the allowable web stress is based on a linear distribution of stress from outside face of flange to "top of web".
  
When required lengths of plates vary by 12" or less on adjacent stringers or on each side of the centerline stiffener plate, use greater length for all such positions.
 
  
Plate lengths taken form the computer programs should be rouned up to at least the nearest 6".
+
'''Weight of Splice'''
  
 +
When calculating the weight of splice, the following simplified weights shall be used.
  
===751.40.8.8 Welded Plate Girders===
+
Weight of High-Strength bolts (diameter 7/8") = 0.95 lbs/bolt
  
====751.40.8.8.1 Design====
+
Unit weight of Structural Steel = 490 lbs/ft<sup>3</sup>
  
=====751.40.8.8.1.1 Design Assumptions & Procedures=====
+
===751.40.8.9 Continuous Concrete Slab Bridges===
  
'''Design Unit Stresses'''
+
====751.40.8.9.1 Slabs====
  
{|
+
=====751.40.8.9.1.1 Design Assumptions=====
|Reinforcement Concrete
 
|-
 
|width="300pt"|Reinforcing Steel (Grade 60)||width="110pt"| <math>\, f_s</math> = 24,000 psi,|| <math>\, f_y</math> = 60,000 psi
 
|-
 
|Class B2 Concrete (Superstructure)||width="110pt"| <math>\, f_c</math> = 1,600 psi,||  <math>\, f'_c</math> = 4,000 psi
 
|}
 
  
  
 +
{|border="0" cellpadding="0"
  
{|
+
|width="65"|Stresses -||FC||=||width="150"|1600 psi||N||=||width="50"|8||(Slab, Integral Column)
|Structural Steel:
 
 
|-
 
|-
|width="300pt"|Structural Carbon Steel (ASTM A709 Grade 36)||width="110pt"| <math>\, f_s</math> = 20,000 psi,||   <math>\, f_y</math> = 36,000 psi
+
|&nbsp;||FC|||=||1200 psi||N||=||10||(Open Bent, Footing)
 
|-
 
|-
|Structural Steel (ASTM A709 Grade 50)||width="110pt"| <math>\, f_s</math> = 27,000 psi,||   <math>\, f_y</math> = 50,000 psi
+
|&nbsp;||FY||=||colspan="5"|60,000 psi reinforcing steel
|-
 
|Structural Steel (ASTM A709 Grade 50W)||width="110pt"| <math>\, f_s</math> = 27,000 psi,||  <math>\, f_y</math> = 50,000 psi
 
 
|}
 
|}
  
 +
Use "Variable I" analysis for all structures except solid slabs without drop panels.<br/>Use "Constant I" analysis for solid slabs without drop panels.
  
'''Design Procedure:'''
 
  
Moments and shears by "Variable '''I'''" analysis:
 
::use computer program.
 
  
Trial sections from "Preliminary analysis":
+
<center>[[Image:751.40_Slabs_Design_Assumptions_Diagram.gif]]</center>
::Combination of web depth, flanges and length of plates used shall be the most economical section available with depths compatible with vertical clearance requirements. Web depths in 6" increments are preferred, however other increments may be used when required by the Design Layout. (See Structural Project Manager)
 
  
  
 +
{|border="0"
  
'''Flanges:'''
+
|"L"||=||Design Span
 +
|-
 +
|"H"||=||Design Height
 +
|-
 +
|valign="top"|"I"||valign="top"|=||Gross moment of inertia of the full cross-section (Slab minus voids - integral wearing surface not included) ("I1", "IA", etc. suggested I's to be considered.)
 +
|-
 +
|"S"||=||The effective span length for the use in determining minimum slab thickness under load factor design (AASHTO 8.9).
 +
|}
  
Minimum flange dimensions = 3/4" x 12" (*).
+
Use the same column diameter and spacing for all Intermediate Bents.<br/>Use the same slab thickness for all spans.
  
Increments:
 
  
:Thickness 1/8"
+
{|border="1" cellpadding="5" align="center" style="text-align:center"
  
:Width 1"
+
|colspan="5"|'''DEGREE OF RESTRAINT - LONGITUDINAL'''
 +
|-
 +
|&nbsp;||Column Type||Footing Type||Top Column||Bottom Column
 +
|-
 +
|rowspan="2"|'''INT. BENTS'''||Integral Column||Spread or Pile||Integral||(**)
 +
|-
 +
|Integral Column <!--column 1 occupied by cell '''INT. BENTS'''-->||Pedestal Pile||Integral||(**)
 +
|-
 +
|rowspan="3"|'''END BENTS'''||Pinned Column||any||Pinned||(**)
 +
|-
 +
|Integral Pile <!--column 1 occupied by cell '''END BENTS'''-->||&nbsp;||(*) Pinned||rowspan="3"|&nbsp;
 +
|-
 +
|Open Bent with Column<!--column 1 occupied by cell '''END BENTS'''-->||any||Simple
 +
|-
 +
|'''INT. BENTS'''||Open Bent with Pile||&nbsp;||Simple
 +
|}
  
Maximum flange dimensions:
 
  
:Reference AASHTO - Table 10.32.1A)
+
{|border="0"
  
:maximum thickness = 4"
+
|align="right" valign="top"|(*)||&nbsp;||See [[#751.40.8.9.2.5 Design Assumptions for Integral Piles|EPG 751.40.8.9.2.5 Design Assumptions for Integral Piles]].
 +
|-
 +
|align="right" valign="top"|(**)||&nbsp;||Use "Pinned" for Seismic Performance Category A and "Fixed for Seismic Performance Categories B, C & D. (See Structural Project Manager or Liaison)
 +
|}
  
Note:
+
=====751.40.8.9.1.2 Slab Design and Drop Panel=====
It is preferred office practice to maintain the same flange thickness at as many locations as practical. This can be accomplished by varying the flange width.
 
  
(*) For shipping and erection purposes, minimum width of both compression and tension flanges shall not be less than L/85 where L is the shipping length of the girder. This limitation is for
 
preventing out-of-plane distortion of the girder.
 
  
 +
The Slab Depth is based on the following limitations:
 +
 +
  
 +
{|border="0"
  
'''Webs:'''
+
|1.||&nbsp;||colspan="4"|Vertical Clearance Requirements: see the Bridge Memorandum.
 +
|-
 +
|2.||&nbsp;||colspan="4"|Allowable Depths:
 +
|-
 +
|&nbsp;||A.||colspan="3"|Positive Moments -
 +
|-
 +
|colspan="2"|&nbsp;||colspan="3"|see table of "Available Slab Depths and Void Data", in [[#751.40.8.9.1.4 Slab Cross Section and Section Properties|EPG 751.40.8.9.1.4 Slab Cross Section and Section Properties]].
 +
|-
 +
|&nbsp;||B.||colspan="3"|Slab Depth controlled by the minimum thickness formula -
 +
|-
 +
|colspan="2"|&nbsp;||colspan="3"|(Integral wearing surface is included with the total depth provided.)
 +
|-
 +
|colspan="2"|&nbsp;||colspan="3"|Continuous Spans - AASHTO 8.9 = (S + 10)/30
 +
|-
 +
|colspan="3"|&nbsp;||"S"||may be used as the clear distance between drop panels.
 +
|-
 +
|colspan="4"|&nbsp;||Bridges may have two adjacent spans averaged if S<sub>2</sub>/S<sub>1</sub> < 1.5
 +
|-
 +
|colspan="2"|&nbsp;||colspan="3"|Simple Spans - AASHTO 8.9 = 1.2 (S + 10)/30
 +
|-
 +
|&nbsp;||C.||colspan="3"|Negative Moments -
 +
|}
  
Web dimensions:
 
  
:(Reference AASHTO - Articale 10.34 & 10. 48)
+
{|border="3" cellpadding="3" cellspacing="0" style="text-align:center"
  
:ASTM A709 Grade 36 = 3/8" minimum thickness for curved girders and for continuous straight girders.
+
|&nbsp;||colspan="2"|'''DROP PANEL DEPTHS'''
 +
|-
 +
|&nbsp;||'''MIN.'''||'''MAX.'''
 +
|-
 +
|align="left"|Bents in median of dual roadway||0" or 3"||13"
 +
|-
 +
|align="left"|Other Bents||0" or 3"||9"
 +
|-
 +
|colspan="3"|'''INCREMENTS OF 1"
 +
|}
  
:ASTM A709 Grade 50W = 3/8" minimum thickness.
 
  
:AASHTO - Article 10.3 Case I, Case II or Case III.
+
{|border="3" cellpadding="3" cellspacing="0" style="text-align:center"
  
:Case I
+
|colspan="2"|&nbsp;||colspan="6"|'''APPROXIMATE DROP PANEL WIDTH (FEET)<br/>(PARALLEL TO THE CENTERLINE OF ROADWAY)'''
 +
|-
 +
|rowspan="2"|&nbsp;||rowspan="2"|Bents||colspan="6"|Drop Panel Depth
 +
|-
 +
|4"<!--column 1 occupied by cell &nbsp;--> <!--column 2 occupied by cell Bents-->||6"||7"||8"||9"||12"
 +
|-
 +
|3 Span Bridge||2 & 3||6'||6'||10'||8'||6'
 +
|-
 +
|rowspan="2"|4 Span Bridge||2 & 4||6'||6'||10'||8'||6'
 +
|-
 +
|3<!--column 1 occupied by cell 4 Span Bridge-->||8'||10'||12'||12'||12'||12'
 +
|-
 +
|colspan="8"|'''THESE WIDTHS ARE SUGGESTED ONLY AS TRIAL DIMENSIONS FOR<br/>DESIGN AND ARE NOT TO BE USED AS LIMITS FOR THE FINAL DESIGN.'''
 +
|}
  
::Bridges with the truck traffic count of 2500 or more vehicles per day. (One direction)
 
  
:Case II
 
  
::Bridges with traffic count of 750 or more vehicles per day, and less than 2500 truck traffic count (One direction) per day.
+
{|border="0"
  
:Case III
+
|3.||&nbsp;||colspan="4"|Reinforcing Steel:
 +
|-
 +
|&nbsp;||align="center" valign="top" |A.||colspan="3"|Positive Moments = Maximum #11 @ 5" cts.
 +
|-
 +
|&nbsp;||align="center" valign="top" |B.||colspan="3"|Negative Moments = Maximum #11 @ 5" cts., except #14s @ 6" cts., may be used for long spans.
 +
|-
 +
|4.||&nbsp;||colspan="4"|Live Load Deflection - AASHTO 10.6
 +
|-
 +
|&nbsp;||colspan="4"|The deflection due to service live load plus impact shall not exceed 1/800 of the span, except on bridges in urban areas used in part by pedestrains whereon the ratio preferably shall not exceed 1/1000.
 +
|}
  
::Bridges with traffic count of less than 750 vehicles per day, except when live loading is H20 or greater.
+
=====751.40.8.9.1.3 Slab Longitudinal Sections=====
  
:No Fatigue:
 
  
::Bridges with traffic count of less than 75 vehicles per day.
+
'''HOLLOW SLABS'''
  
  
'''Total Capacity of Exterior Girders:'''
+
<center>[[Image:751.40_Slabs_-_Hollow_End_Spans.gif]]</center>
  
'''(Dead Load and Live Load)'''
+
<center>'''END SPANS'''</center>
  
:In no case shall an exterior girder have less carrying capacity than an interior girder.
 
  
'''Horizontal Curved Girders Design Procedures (*)'''
+
<center>[[Image:751.40_Slabs_-_Hollow_Intermediate_Spans.gif]]</center>
  
Curved plate girders are to be designed using load factor design criteria. The 1980 AASHTO Guide Specifications for Horizontally Curved Highway Bridges as revised by Interim Specifications for Bridges 1981, 1982, 1984, 1985 and 1986 is to be applied with the USS Highway Structure Design Handbook (\) V-Load method to be used as a working example.
+
<center>'''INTERMEDIATE SPANS'''</center>
  
The following procedure may be followed to determine the required cross-section for any system of curved girders with skews less than 46°.
 
  
1. Determine the primary moments by the same procedures as for a system of straight girders, using the developed lengths of the curved girders.
+
{|border="0" align="center"
  
 
+
|width="200" rowspan="3"|[[Image:751.40_Slabs_-_Hollow_Part_Plan_Skewed_Detail.gif]]
2. From primary moments, compute shear loads, <math>\, V</math>, using the formula:
+
|(*)Increase to maintain 6" minimum on skews (see detail)
<center>
 
{|
 
 
|-
 
|-
|width= "300"|<math>\, V = \frac{\sum M}{Coeff. * K}</math>||style="text-align:left"|<math>\, V</math> = Shear loads.<br>M = Primary moments.
+
|(**) By Design (6" increments measured normal to the centerline of bent) (The minimum is equal to the column diameter + 2'-6")<!--column 1 occupied by cell [[Image:751.40_Slabs_-_Hollow_Part_Plan_Skewed_Detail.gif]]-->
|-
 
|<math>\, K = \frac{RD}{d}</math>||style="text-align:left"|<math>\, R</math> = Radius of curvature (outside girder).<br><math>\, D</math> = Radial distance between inside and outside girders.<br><math>\, d</math> = Distance between diaphragms measured along axis of outside girder.
 
 
|-
 
|-
 +
|width="400"|Note:<br/>All longitudinal dimensions shown are horizontal (Bridges on grades and vertical curves, included).<br/>For Sections A-A and B-B see [[#751.40.8.9.1.4 Slab Cross Section and Section Properties|EPG 751.40.8.9.1.4 Slab Cross Section and Section Properties]].<!--column 1 occupied by cell [[Image:751.40_Slabs_-_Hollow_Part_Plan_Skewed_Detail.gif]]-->
 
|}
 
|}
  
</center>
+
 
The following coefficients may be applied to '''"'''<math>\, K</math>'''"''' for the various multiple-girder systems with equal spacing between girders.
+
&nbsp;
 +
 
 +
 
 +
 
 +
'''SOLID SLABS'''
  
  
<center>
+
<center>[[Image:751.40_Slabs_-_Solid_End_Spans.gif]]</center>
{|border="1" cellspacing="1" cellpadding="1"
+
 
|-
+
<center>'''END SPANS'''</center>
|width="100"|SYSTEM||width="100"|COEFFICIENT<br>FRACTION||width="100"|COEFFICIENT<br>DECIMAL
 
|-
 
|2 girders ||1|| 1.00
 
|-
 
|3 girders ||1||1.00
 
|-
 
|4 girders ||10/9||1.11
 
|-
 
|5 girders ||5/4||1.25
 
|-
 
|6 girders ||7/5||1.40
 
|-
 
|7 girders || 14/9||1.56
 
|-
 
|8 girders ||12/7|| 1.72
 
|-
 
|9 girders ||15/8  ||  1.88
 
|-
 
|10 girders ||165/81  ||  2.04
 
|-
 
|}
 
</center>
 
  
3. Compute <math>\, V-Load</math> moments
 
  
  
*  Reference: USS "Highway Structures Design Handbook" 1965 Edition. (Updated 1986 Volume II Section 6) developed by Richardson, Gordon and Associates in cooperation with Dr. John Scalzi is to be used as a working example.
+
<center>[[Image:751.40_Slabs_-_Solid_Intermediate_Spans.gif]]</center>
  
 +
<center>'''INTERMEDIATE SPANS'''</center>
  
4. Compute lateral bending moments using the approximate formula:
 
  
{|
+
(*) By Design (6" increments measured normal to the centerline of Bent) (The minimum is equal to the column diameter + 2'-6")
|-
 
|width="150"|<math>\, M_L = \frac{Hd}{10} = \frac{Md^2}{10Rh}</math>||width="150"|&nbsp;||<math>\, ML </math> = Lateral bending moment
 
|-
 
|&nbsp;||&nbsp;||<math>\, H </math> = The <math>\, H</math> values are approximately equal to the reactions at the supports.
 
|-
 
|&nbsp;||&nbsp;||<math>\, h </math> = Depth of girder between centers of gravity of flanges.
 
|-
 
|&nbsp;||&nbsp;||<math>\, M </math> = Primary moment + Secondary moment.
 
|-
 
|}
 
  
<center>
 
[[Image:751.40 Widen and Repair Design Assumptions- Horizontally Curved Girders Design Procedure.gif]]
 
</center>
 
  
5. Determine cross-section required to provide for vertical and lateral forces computed under Items 1 to 4 inclusive.  As with any statically indeterminate system it is necessary to make an initial assumption of the required cross-sections and to repeat the calculations one or more times to obtain reasonable agreement between the assumed and required sections.
+
Note:<br/>All longitudinal dimensions shown are horizontal (Bridges on grades and vertical curves, included).
  
 +
=====751.40.8.9.1.4 Slab Cross Section and Section Properties=====
  
6. The non-compact section requirement that <math>\, F_y > (f_b + f_w)</math> is to be applied to all sections with the tension flange <math>\, F_y > (f_b + f_w)</math> and the compression flange as <math>\, F_y (1-3 \lambda^2) > (f_b + f_w)</math> to ensure conservative design.
 
  
In computing <math>\, \lambda</math>, use <math> \ell</math> to be actual diaphragm spacing for compression and tension stresses.
+
<center>[[Image:751.40_Slab_Cross_Section_AA_&_BB.gif]]</center>
  
The value of <math>\, f_w</math> is to be selected as plus or minus in the equations for <math>\, P_w</math> to give the worst possible case.
 
  
 +
{|border="0" style="text-align:center" align="center"
  
'''Design and Detail Guides'''
+
|width="300"|'''HALF SECTION A-A<br/>CENTER OF SPAN'''||width="300"|'''HALF SECTION B-B<br/>NEAR INTERMEDIATE BENT'''
  
1. Economic Arrangement of Spans and Depth-to-Spans Ratios
+
|}
  
Where there is flexibility in span arrangement, the same guides that apply to economic arrangement of straight girders are equally applicable to curved girders.  Similarly the rules used to establish depth-to-span ratios for straight girders usually will apply to curved girders.
 
  
 +
{|border="0" cellpadding="5" align="center" style="text-align:center"
  
2. Spacing of Girders
+
|rowspan="4" width="250" align="left"|
 
+
{|border="3" cellpadding="2" cellspacing="0" style="text-align:center"
Spacing depends on the arrangements of diaphragms and bracing.  In general, however, it will be found that the most economical arrangement for straight girders will accord very well with the best arrangement for a system of curved girders.  The effect of curvature increases in proportion to the square of the span length and decreases in proportion to the radius of curvature and the spacing of girders.
+
|colspan="5"|'''AVAILABLE SLAB DEPTHS<br/>AND VOID DATA'''
 
+
|-
 
+
|colspan="5"|Truck Loading
3. Arrangement and Spacing of Diaphragms
+
|-
 
+
|T (*)||&nbsp;||"D"||"E"||"F"
The diaphragms shall be placed radially, with a maximum spacing of 15'-0".  In order to minimize lateral bending of the girder flanges, the flanges should be as wide as practical.
+
|-
 
+
|17"||colspan="4" align="left"|and less - no voids
 
+
|-
Sway frame bracing is selected for curved girder system, by same methods as for straight girders.
+
|18"||&nbsp;||9"||15"||21"
 
+
|-
 
+
|19"||(***)||10"||16"||22"
4. Effect of Lateral Bracing
+
|-
 
+
|21"||&nbsp;||12"||18"||24"
made in a similar manner as for straight bridges.  If lateral Provision for lateral loading on curved girders may be bracing is used in a system of curved girders, the forces resulting
+
|-
from the radial components of flange stress may be carried partially or entirely by the bracing system; when both diaphragms and lateral bracing are used, radial reaction components may be divided between the two systems.
+
|23"||&nbsp;||14"||20"||26"
 
+
|-
 
+
|25"||&nbsp;||15.7"||22"||28"
5. Approximate Estimate of Curvature
 
 
 
The following formula may be used in making preliminary approximations of the effect of curvature:
 
 
 
{|
 
 
|-
 
|-
|width="400"|<math>\, P = 10.5 \times \frac{(1+r)(L')^2}{R_2D}</math>||Note: For "r" refer to paragraph No. 7
+
|26"||&nbsp;||16.7"||23"||29"
 
|-
 
|-
|<math>\, r = \frac{(R_2)^2}{(R_2)^2} \times \bigg( \frac {Inside \ girder \ loading)}{Outside \ girder \ loading} \bigg)</math>||(*)
+
|28"||&nbsp;||18.7"||25"||31"
 
|-
 
|-
|}
+
|30"||&nbsp;||20.85"||27"||33"
 
 
 
 
{|
 
 
|-
 
|-
|(*)||May be omiteed if supports are on radial lines.
+
|colspan="4"|Pedestrian Overpasses||rowspan="7"|&nbsp;
 
|-
 
|-
|<math>\,  P </math>||% increase in positive moment due to effect of curvature.
+
|T (*)||&nbsp;||"D"||"E"
 
|-
 
|-
|<math>\,  R_2</math>||Radius of inside girder.
+
|15"||colspan="3" align="left"|and less - no voids
 
|-
 
|-
|<math>\,  R_1</math>||Radius of outside girder.
+
|16"||&nbsp;||8"||14"
 
|-
 
|-
|<math>\,  L'</math>||Distance between points of contraflexure in any pisitive moment area.
+
|17"||&nbsp;||9"||15"
 
|-
 
|-
|<math>\,  D </math>||Spacing between inside and outside girders.
+
|18"||&nbsp;||10"||16"
 
|-
 
|-
 +
|20"||&nbsp;||12"||18"
 
|}
 
|}
 
+
|[[Image:751.40_Slab_Cross_Section_Thru_Void.gif]]<!--column 1 occupied by cell {|border="3" cellpadding="2" cellspacing="0" style="text-align:center"
 
+
|colspan="5"|'''AVAILABLE SLAB DEPTHS<br/>AND VOID DATA'''
In the above form, the formula applies to a two-girder system, but it may be modified by reference to the table of coefficients for multiple-girder systems shown on page 1.1-5 of this section.
 
 
 
The formula applies particularly to positive moment, but for preliminary approximation it may be assumed that the curvature effect on negative moments will be about the same.
 
 
 
 
 
6. Design of Diaphragms and Connections
 
 
 
Where the degree of curvature is equal to or under 1&deg; - 30' and when spans are equal to or under 75'-0" in length, the diaphragm and connections shall be the same as for Bridges with straight girders.  Where the degree of curvature is over 1&deg;- 30' to 3&deg; or with a span length of more than 75'-0", the diaphragm must be attached to the tension flange.  Where the degree of curvature is over 3&deg;, a special design will be required for connection of intermediate diaphragms to flanges.
 
 
 
The maximum allowable diaphragm spacing is 15'-0", regardless of the amount of curvature, or span lengths.
 
 
 
 
 
The following applies to those bridges where the special design is to be considered:
 
 
 
 
 
Since diaphragm moments due to effect of curvature are a function of the radial component of flange stress, they are directly proportional to the vertical bending moment in the girders.
 
 
 
 
 
For exterior girders the moment in the diaphragm equals <math>\, M \times d/R</math>, in which <math>\, M</math> = vertical bending moment in girder for any particular condition of loading; <math>\, d</math> = diaphragm spacing; <math>\, R</math> = Radius of curvature of girder.
 
 
 
 
 
For negative moment over the support, the <math>\, M</math> value used in this equation should be the average moment between a point at the support and a point at the first adjacent diaphragm. 
 
 
 
 
 
Diaphragm connections may be made directly to the flanges of the girders or through stiffeners, provided details are arranged to adequately transfer radial components of flange stress into the diaphragms.
 
 
 
 
 
7. Supports positioned other than on radial lines.
 
 
 
If field conditions permit, the most orderly arrangement for curved girders will be attained by placing the supports on radial lines.
 
 
 
 
 
It may be necessary to treat each line of girders independently, first finding the direct loading moments and then correcting for curvature by applying the separate <math>\, V-loads</math>.
 
 
 
 
 
8. Transverse stiffeners
 
 
 
 
 
The maximum transverse stiffener spacing for curved plate girders is <math>\, D</math>, the web height.
 
 
 
 
 
Transverse stiffeners should be placed along the girder length only as far as required by design.
 
 
 
The maximum spacing of the first transverse stiffener at the simple support end of a curved plate girder is <math>\, D/2</math>.
 
 
 
 
 
Reference:
 
:AASHTO - Article 10.5
 
:Limit radius of heat curved girders according to AASHTO Article 10.15.
 
 
 
Where the distance between field splices of curved girders exceeds that given by the following formula, a special note shall be placed on the plans.
 
 
 
{|
 
 
|-
 
|-
|<math>\, L</math> =||<math>\, \sqrt{\frac{0.667 \ x \ f_s \ x \ SM}{W}}</math>||(*)
+
|colspan="5"|Truck Loading
 
|-
 
|-
|<math>\, L</math> =||Allowable distance between field splices, in feet.
+
|T (*)||&nbsp;||"D"||"E"||"F"
 
|-
 
|-
|<math>\, f_s</math> =||Allowable fs of flange steel, in psi. e.g. use 20,000 psi for Grade 36 steel.
+
|17"||colspan="4" align="left"|and less - no voids
 
|-
 
|-
|<math>\, W</math> =||Weight of girder (flanges and web), in pounds per foot.
+
|18"||&nbsp;||9"||15"||21"
 
|-
 
|-
|<math>\, SM</math> =||Section Modulus of girder about x-x axis as shown, in inches cubed.
+
|19"||(***)||10"||16"||22"
 
|-
 
|-
|}
+
|21"||&nbsp;||12"||18"||24"
 
 
 
 
[[Image:751.40 Design Assumptions- Heat Curved Girders- Section Modulus.gif]]
 
 
 
 
 
Note:
 
 
 
If flanges are of different sizes, use smaller Section Modulus.
 
 
 
See Structural Project Manager for allowable overstress.
 
 
 
 
 
<u>(*) Derivation</u>
 
 
 
:Positive moment at centerline, <math>\, Mom. = \frac{WL^2}{8} \times 12</math>
 
 
 
:<math>\, fs = \frac{Mom.}{SM}</math>
 
 
 
:Substitute mom. in fs equation.
 
 
 
::<math>\, fs = \frac{WL^2 \times 12}{8 \times SM}</math>
 
 
 
:solve for L
 
 
 
::<math>\, L = \sqrt{\frac{8 f_s \times SM}{12W}}</math>
 
 
 
<center>
 
'''Design Example'''
 
 
 
'''ASTM A709 Grade 36 Steel'''
 
 
 
[[Image:751.40 Design Assumptions- Heat Curved Girders- Design Example Plan View.gif]]
 
 
 
</center>
 
 
 
{|
 
 
|-
 
|-
|width="400"|&nbsp;||width="400"|[[Image:751.40 Design Assumptions- Heat Curved Girders- Design Example Section 2.gif]]
+
|23"||&nbsp;||14"||20"||26"
 
|-
 
|-
|[[Image:751.40 Design Assumptions- Heat Curved Girders- Design Example Section A-A.gif]]||
+
|25"||&nbsp;||15.7"||22"||28"
{|border="1" cellpadding="1" cellspacing="1" style="text-align:center"
 
 
|-
 
|-
|Shape||<math>\, I_{xx}</math>
+
|26"||&nbsp;||16.7"||23"||29"
 
|-
 
|-
|PL 13" x 3/4"||<math>\, \frac{0.75 \times (13)^3}{12} = 137.31</math>
+
|28"||&nbsp;||18.7"||25"||31"
 
|-
 
|-
|PL 70" x 3/8"||<math>\, \frac{70 \times (0.375)^3}{12} = 0.31</math>
+
|30"||&nbsp;||20.85"||27"||33"
 
|-
 
|-
|PL 12" x 3/4"||<math>\, \frac{0.75 \times (12)^3}{12} = 108.00</math>
+
|colspan="4"|Pedestrian Overpasses
 
|-
 
|-
|<math> Total \ I_{xx}</math>||align="right"|<math> = 245.62 \ In.^4</math>
+
|T (*)||&nbsp;||"D"||"E"
 +
|-
 +
|15"||colspan="3" align="left"|and less - no voids
 +
|-
 +
|16"||&nbsp;||8"||14"
 +
|-
 +
|17"||&nbsp;||9"||15"
 +
|-
 +
|18"||&nbsp;||10"||16"
 +
|-
 +
|20"||&nbsp;||12"||18"
 +
|}-->
 +
|-
 +
|'''PART SECTION THRU VOID'''<!--column 1 occupied by cell {|border="3" cellpadding="2" cellspacing="0" style="text-align:center"
 +
|colspan="5"|'''AVAILABLE SLAB DEPTHS<br/>AND VOID DATA'''
 +
|-
 +
|colspan="5"|Truck Loading
 
|-
 
|-
|}
+
|T (*)||&nbsp;||"D"||"E"||"F"
 
|-
 
|-
|SECTION A-A ||rowspan="1"|<math>\, SM_A = I/C = 245.62/6.5 = 37.79 In.^3</math>
+
|17"||colspan="4" align="left"|and less - no voids
 
|-
 
|-
|&nbsp;||rowspan="1"|<math>\, SM_B = I/C = 245.62/6 = 40.94 In.^3</math>
+
|18"||&nbsp;||9"||15"||21"
 
|-
 
|-
{|border="1" cellpadding="1" cellspacing="1"
+
|19"||(***)||10"||16"||22"
 
|-
 
|-
|Weight per Foot of Girder
+
|21"||&nbsp;||12"||18"||24"
 
|-
 
|-
|PL 12" x 3/4" = 30.6 lbs./ft.
+
|23"||&nbsp;||14"||20"||26"
 
|-
 
|-
|PL 70" x 3/8" = 89.3 lbs./ft.
+
|25"||&nbsp;||15.7"||22"||28"
 
|-
 
|-
|PL 13" x 3/4" = 33.2 lbs./ft.
+
|26"||&nbsp;||16.7"||23"||29"
 
|-
 
|-
|Total =  153.1 lbs./ft.
+
|28"||&nbsp;||18.7"||25"||31"
 
|-
 
|-
|}
+
|30"||&nbsp;||20.85"||27"||33"
||&nbsp;
 
 
|-
 
|-
|<u>From Formula:</u>||&nbsp;
+
|colspan="4"|Pedestrian Overpasses
 
|-
 
|-
|colspan="2" style="text-align:center"|<math>\, L = \sqrt{\frac{0.667 \times fs \times SM}{W}} = \sqrt{\frac{0.667 \times 20,000 \times 37.79}{153.1}} = 57.38'</math>  (Use 57.5')
+
|T (*)||&nbsp;||"D"||"E"
 
|-
 
|-
|}
+
|15"||colspan="3" align="left"|and less - no voids
 
+
|-
 
+
|16"||&nbsp;||8"||14"
<center>57'-6" < 60'-0".  Therefore, Special Note required.</center>
+
|-
 
+
|17"||&nbsp;||9"||15"
Special Note:
+
|-
 
+
|18"||&nbsp;||10"||16"
Heat curving of girders <u>(Identify)</u> (*) will not be allowed shile in the horizontal position.
+
|-
 
+
|20"||&nbsp;||12"||18"
(*)Complete underlined portion as required.
+
|}-->
 
 
 
 
 
 
Maximum Plate Lengths:
 
:80 feet.  See Structural Project Manager for use of longer lengths up to 85' for ASTM A709 Grade 50 or ASTM A709 Grade 50W and 100' for ASTM A709 Grade 36.
 
 
Minimum Plate Lengths:
 
:10 feet.  Shop flange splices should be eliminated and extra plate material used when :economy indicates and span lengths permit.
 
 
 
Preliminary Analysis:
 
:(1) Compute moments from influence lines on basis of "Constant I" analysis and apply the following percentage increase or decrease to non-composite dead load moments. 
 
 
 
References may be used in lieu of the above.
 
 
 
<center>
 
[[Image:751.40 Design Assumptions- Preliminary Analysis-Moments Diagram.gif]]
 
</center>
 
 
 
{|style="text-align:center"
 
 
|-
 
|-
|width="500"|<math>\, n</math> = 1.2 to 1.5||width="90"|<math>\, n</math> = 1.2 to 1.5
+
|[[Image:751.40_Slab_Cross_Section_-_Detail_C.gif]]<!--column 1 occupied by cell {|border="3" cellpadding="2" cellspacing="0" style="text-align:center"
 +
|colspan="5"|'''AVAILABLE SLAB DEPTHS<br/>AND VOID DATA'''
 
|-
 
|-
|
+
|colspan="5"|Truck Loading
{|border="1" cellspacing="1" cellpadding="1"
 
 
|-
 
|-
|<math>\, +M_1</math>||-5%
+
|T (*)||&nbsp;||"D"||"E"||"F"
 
|-
 
|-
|<math>\, -M_2</math>||+15%
+
|17"||colspan="4" align="left"|and less - no voids
 
|-
 
|-
|<math>\, +M_3</math>||-15%
+
|18"||&nbsp;||9"||15"||21"
 
|-
 
|-
|}
+
|19"||(***)||10"||16"||22"
||
 
{|border="1" cellspacing="1" cellpadding="1"
 
 
|-
 
|-
|<math>\, +M_1</math>||-5%
+
|21"||&nbsp;||12"||18"||24"
 
|-
 
|-
|<math>\, -M_2</math>||+15%
+
|23"||&nbsp;||14"||20"||26"
 
|-
 
|-
|<math>\, +M_3</math>||-15%
+
|25"||&nbsp;||15.7"||22"||28"
 
|-
 
|-
|<math>\, -M_4</math>||+15%
+
|26"||&nbsp;||16.7"||23"||29"
 
|-
 
|-
|}
+
|28"||&nbsp;||18.7"||25"||31"
 
|-
 
|-
|}
+
|30"||&nbsp;||20.85"||27"||33"
 
+
|-
(2) Determine trial sections and plot a rough moment curve to determine location of flange plate cutoffs, if any.
+
|colspan="4"|Pedestrian Overpasses
 
 
(3) Complete analysis by using computer programs to obtain actual moments and stresses.
 
 
 
<center>
 
'''Design Stress investigation for Positive Moment Area of Plate Girder Structure'''
 
</center>
 
 
 
The design stresses are to be checked at the top of flange (steel) and the top of concrete slab in the composible area of Plate Girder Structures to insure that they are within the allowable stresses.
 
<center>
 
 
 
[[Image:751.40 Design Assumptions- Design Stress Investigation- Plate Girder.gif]]
 
 
 
SECTION A-A   
 
 
 
 
 
'''Structure Length'''
 
 
 
 
 
Typical Continuous Steel Structures- Integral End Bents:
 
 
 
 
 
 
 
[[Image:751.40 Design Assumptions- Structure Length- Maximum Length for Continuous Steel.gif]]
 
 
 
</center>
 
 
 
 
 
'''Estimated Girder Depth'''
 
''Based on Three Spans With Ratio N = 1.3±''
 
 
 
<center>
 
 
 
Continuous Plate Girders HS20 Loading Load Factor
 
<br>(ASTM A709 Grade 50 or ASTM A709 Grade 50W)
 
 
 
{|border="1" cellpadding="1" cellspacing="1" style="text-align:center"
 
 
|-
 
|-
|Initial Estimate<br>(Feet) ||Girder Depths (*)<br>(Inches)|| Structure Depth (**)<br>(Feet)
+
|T (*)||&nbsp;||"D"||"E"
 
|-
 
|-
|85 to 104||42||4.50
+
|15"||colspan="3" align="left"|and less - no voids
 
|-
 
|-
|105 to 124||48||5.00
+
|16"||&nbsp;||8"||14"
 
|-
 
|-
|125 to 134||54||5.50
+
|17"||&nbsp;||9"||15"
 
|-
 
|-
|135 to 144||60||6.00
+
|18"||&nbsp;||10"||16"
 
|-
 
|-
|145 to 159||66||6.50
+
|20"||&nbsp;||12"||18"
 +
|}-->
 
|-
 
|-
|160 to 174||72||7.00
+
|'''DETAIL "C"'''<!--column 1 occupied by cell {|border="3" cellpadding="2" cellspacing="0" style="text-align:center"
 +
|colspan="5"|'''AVAILABLE SLAB DEPTHS<br/>AND VOID DATA'''
 
|-
 
|-
|175 to 184||78||7.50
+
|colspan="5"|Truck Loading
 
|-
 
|-
|185 to 194||84||8.00
+
|T (*)||&nbsp;||"D"||"E"||"F"
 
|-
 
|-
|195 to 204||90||8.50
+
|17"||colspan="4" align="left"|and less - no voids
 
|-
 
|-
|}
+
|18"||&nbsp;||9"||15"||21"
</center>
+
|-
 +
|19"||(***)||10"||16"||22"
 +
|-
 +
|21"||&nbsp;||12"||18"||24"
 +
|-
 +
|23"||&nbsp;||14"||20"||26"
 +
|-
 +
|25"||&nbsp;||15.7"||22"||28"
 +
|-
 +
|26"||&nbsp;||16.7"||23"||29"
 +
|-
 +
|28"||&nbsp;||18.7"||25"||31"
 +
|-
 +
|30"||&nbsp;||20.85"||27"||33"
 +
|-
 +
|colspan="4"|Pedestrian Overpasses
 +
|-
 +
|T (*)||&nbsp;||"D"||"E"
 +
|-
 +
|15"||colspan="3" align="left"|and less - no voids
 +
|-
 +
|16"||&nbsp;||8"||14"
 +
|-
 +
|17"||&nbsp;||9"||15"
 +
|-
 +
|18"||&nbsp;||10"||16"
 +
|-
 +
|20"||&nbsp;||12"||18"
 +
|}-->
 +
|}
  
  
Trial steel plate girder depths use program BR109 to check designs and deflections. Web depths may be adjusted by two inch increments.
 
  
(*) Bethlehem steel economic study (N = 1.3±). Bethlehem steel provided an economic study of multiple steel girder depths. The study indicated that cheaper designs are obtained by reducing the plate girder depths and reducing the number of stiffeners. The recommended initial estimates above are based on these designs.
+
{|border="0"
  
 +
|colspan="2"|Notes:
 +
|-
 +
|(*)||Increase the Dimension "T" by 1/2" for #14 bars placed in the top or bottom of the slab.
 +
|-
 +
|&nbsp;||Increase the Dimension "T" by 1" for #14 bars placed in the top and bottom of the slab.
 +
|-
 +
|&nbsp;||("T" and "D" are based on 3" clearance which includes the integral wearing surface to the top of the longitudinal bar.)
 +
|-
 +
|&nbsp;
 +
|-
 +
|(**)||For Roadways with slab drains, use 10" minimum. For Roadways that require additional reinforcement for resisting moment of the edge beam 20" minimum, refer to [[#751.40.5.1 Structure with Wearing Surface Slab Drains - Details|EPG 751.40.5.1 Structure with Wearing Surface Slab Drains - Details]].
 +
|-
 +
|&nbsp;
 +
|-
 +
|(***)||Preferred minimum (Consult the Structural Project Manager prior to the use of a thinner slab.)
 +
|}
  
(**) Structure depth includes slab and haunch.
 
  
A general rule of thumb is to determine the minimum web thickness without stiffeners; then, use a web thickness of one-sixteenth inch less. Match MoDOT requirements for web increments of one-sixteenth inch only.
 
  
 +
'''Voided Slab Spans'''
  
If two-span structures are used, a deeper web is required. A good estimate is to use six inches additional depth than the above tables for two-span structures.
 
  
====751.40.8.8.2 Details====
+
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
  
=====751.40.8.8.2.1 Field Flange Splice – Bolted=====
+
|Void Dia.<br/>(in.)||Area<br/>(sq.ft.)||Area<br/>(sq.in.)||Moment<br/>of Inertia<br/>(ft.<sup>4</sup>)||Moment<br/>of Inertia<br/>(in.<sup>4</sup>)||Weight<br/>(lb./ft.)
 
 
'''General'''
 
 
 
Splices shall be designed using the Service Load Design Method and in accordance with AASHTO Articles 10.18,10.24 and 10.32 except as noted.
 
 
 
Splices shall be designed to develop 100% of the flange strength by the flange splice plate strength.  When the flange section or steel grade changes at a splice, the smaller flange strength shall be used to design the splice. Splice plates shall then match the lower grade used in the flanges.
 
 
 
 
 
'''Minimum Yield Strength <math>\, (Fy)</math> and Minimum Tensile Strength <math>\, (Fu)</math>'''
 
 
 
{|
 
 
|-
 
|-
|width="200"|ASTM A709 Grade 36||width="100"|<math>\, F_y</math>  = 36 ksi||<math>\, F_u</math> = 58 ksi
+
|8.00||0.3490||50.2656||0.0096||201.0624||52.35
 
|-
 
|-
|ASTM A709 Grade 50||<math>\, F_y</math>  = 50 ksi||<math>\, F_u</math> = 65 ksi
+
|9.00||0.4417||63.6174||0.0155||322.0630||66.26
 
|-
 
|-
|ASTM A709 Grade 50W||<math>\, F_y</math>  = 50 ksi||<math>\, F_u</math> = 70 ksi
+
|10.00||0.5454||78.5400||0.0236||490.8750||81.81
 
|-
 
|-
|}
+
|12.00||0.7854||113.0976||0.0490||1017.8784||117.81
 
 
 
 
'''Allowable Steel Stresses <math>\, (F_t)</math>'''
 
 
 
Allowable stresses are determined by AASHTO Table 10.32.1A.
 
 
 
{|
 
 
|-
 
|-
|width="200"|Allowable tensile stress||<math>\, F_t = 0.55 \times F_y</math>
+
|14.00||1.0690||153.9384||0.0909||1885.7454||160.35
 
|-
 
|-
|}
+
|15.70||1.3443||193.5932||0.1438||2982.4242||201.66
 
 
 
 
{|
 
 
|-
 
|-
|width="200"|ASTM A709|| Grade 36||<math>\, F_t</math>  = 20 ksi
+
|16.70||1.5211||219.0402||0.1841||3818.0075||228.17
 
|-
 
|-
|width="200"|ASTM A709|| Grade 50|| <math>\, F_t</math>  = 27 ksi
+
|18.70||1.9072||274.6465||0.2894||6002.5789||286.09
|-
 
|width="200"|ASTM A709|| Grade 50W||<math>\, F_t</math>  = 27 ksi
 
 
|-
 
|-
 +
|20.85||2.3710||341.4310||0.4473||9276.7336||355.65
 
|}
 
|}
  
 +
=====751.40.8.9.1.5 Slab Reinforcement=====
  
'''Allowable Bolt Stresses '''
+
&nbsp;
  
Splices shall be designed as slip critical connections with Class B surface preparation and oversized holes.  Although standard holes are used in the fabrication of flange splices, designing the splices for oversize holes allows for some fabrication and erection tolerances.  All splice bolts shall be 7/8" diameter ASTM A325 high strength bolts.
+
'''HOLLOW SLABS'''
  
  
AASHTO Table 10.32.3C specifies <math>\, F_s</math> = 19 ksi for a class B slip-critical connection.  Tables shown in this manual are based on 19 ksi that should also be used to design splices not listed in the table. 
+
<center>[[Image:751.40_Slab_Reinf_-_Positive_Moment.gif]]</center>
  
  
Although slip-critical connections are theoretically not subject to shear and bearing, they must be capable of resisting these stresses in the event of an overload that causes slip to occur. The allowable shear stress per bolt <math>\, (Fv)</math> for bearing is 19 ksi with the threads included and <math>\, 1.25 \times 19 = 23.75</math> ksi for threads not included.
+
<center>'''DETAIL "A"<br/>(POSITIVE MOMENT)'''</center>
  
  
'''Flange Strength'''
+
<center>[[Image:751.40_Slab_Reinf_-_Negative_Moment.gif]]</center>
  
The flange strength shall be determined by multiplying the allowable stress of the flange by the area of the flange.  The area of the flange shall be taken as the gross area of the flange, except that if more than 15 percent of each flange area is removed, that amount removed in excess of 15 percent shall be deducted from the gross area. Bolt holes are considered to be 1" diameter for the purpose of determining flange area.
 
  
 +
<center>'''DETAIL "B"<br/>(NEGATIVE MOMENT)'''</center>
  
'''Splice Plate Strength'''
 
  
The splice plate strength shall be determined by multiplying the allowable stress of the splice plates by the area of the splice plates.  The area of the splice plates shall be taken as the gross area of the splice plates, except that if more than 15 percent of the splice plate area is removed, that amount in excess of 15 percent shall be deducted from the gross area.
+
{|border="3" cellpadding="4" cellspacing="0" align="center" style="text-align:center"
  
 +
|Longitudinal Reinforcement<br/>(Largest Bar)||width="50"|"G"
 +
|-
 +
|#8||3-5/8"
 +
|-
 +
|#9||3-3/4"
 +
|-
 +
|#10||3-7/8"
 +
|-
 +
|#11||4"
 +
|-
 +
|#14||4-3/8"
 +
|}
  
'''Two Row Splices'''
 
 
Splices with two rows of bolts are used with flanges 12 to 13 inches wide. The inner and outer plates may either be the same length or the inner plate may be shorter. This is the case if the end bolts in the splice are only needed to be in single shear. All other bolts will be in double shear. (See Figure 3.42.2.2-1)
 
 
<center>
 
[[Image:751.40 Widen and Repair- Field Flange Splice- Bolted.gif]]
 
  
'''<u>Figure 3.42.2.2-1</u>'''
+
'''Moment Curves'''
</center>
 
  
 +
{|border="0"
  
'''Four Row Splices'''
+
|valign="top"|1.||Determine reinforcing steel from the sum of the dead loads and the live loads + impact (working stress design) or design in accordance with AASHTO Article 8.16 and 8.9 (load factor design).
 +
|-
 +
|valign="top"|2.||Determine the cut-off points for the stress bars in sets of 2 or 3.<br/>Maximum length = 60'-0", see AASHTO Article 8.24 for extension of reinforcement.
 +
|-
 +
|3.||Determine the drop panel width:
 +
|-
 +
|&nbsp;||Minimum width = Column diameter plus 2~6".<br/>Maximum width = (Parallel to the centerline of roadway) as determined by deign).
 +
|-
 +
|&nbsp;||In general, the width of the drop panel normal to centerline bent should be adjusted to 6" increments.
 +
|}
  
When the width of the flange being spliced is 14 inches or greater, four longitudinal rows of bolts are used. Three variations of the end bolts positioning may be used.  In each of these variations, the last two bolts shall be located in the outer rows closest to the edge of the splice plate.
 
<center>
 
  
[[Image:751.40 Widen and Repair- Field Flange Splice- Bolted Four Row Splice.gif]]
+
'''SOLID SLABS (BOTTOM)'''
  
'''<u>Figure 3.42.2.2-2</u>'''
+
Use AASHTO 3.24.10 Distribution Reinforcement shall be a percentage of positive moment reinforcement (% = 100/√S, with a maximum of 50%).
</center>
 
  
  
'''Flange Width Transitions'''
+
'''EDGE BEAM'''
  
When the width of the flanges being spliced differs by more than 2", the larger flange shall be beveled as shown in Figure 3.42.2.2-3
+
{|border="0"
  
<center>
+
|colspan="3"|Positive Moment:
[[Image:751.40 Widen and Repair- Field Flange Splice- Bolted- Flange Width Transition.gif]]
+
|-
 +
|colspan="3"|The bridge curb is not to be used in determining the resisting moment of the edge beam.
 +
|-
 +
|valign="top"|Dead Load:||colspan="2"|Use the same distribution as for the slab design.<br/>Use for simple spans 0.1 PS.
 +
|-
 +
|colspan="3"|Live Load + I: AASHTO Article 3.24.8
 +
|-
 +
|&nbsp;||colspan="2"|Use for negative moment on continuous spans 0.1 PS.<br/>Use for positive moment on continuous spans 0.08 PS.
 +
|-
 +
|&nbsp;||Where||P = Wheel load in pounds, see [[#Cantilever Moment|EPG 751.40.8.5.1.1 Cantilever Moment]].
 +
|-
 +
|&nbsp;||&nbsp;||S = Span in feet
 +
|}
  
  
'''<u>Figure 3.42.2.2-3</u>'''
+
<center>[[Image:751.40_Slab_Reinf_-_Edge_Beam_Detail.gif]]</center>
</center>
 
  
 +
=====751.40.8.9.1.6 Shear=====
  
  
'''Weight of Splice'''
+
'''Shear Loads'''
  
When calculating the weight of splice, the following simplified weights shall be used.
+
The shear in the Hollow Slab should be computed for all loadings H20 and over.
  
Weight of High-Strength bolts (diameter 7/8") = 0.95 lbs/bolt
 
  
Unit weight of Structural Steel = 490 lbs/ft<sup>3</sup>
+
'''Distribution of Loads'''
  
=====751.40.8.8.2.2 Field Web Splice – Bolted=====
+
Use the same distribution for the dead and live load as was used for the moment.
  
'''General'''
 
  
Splices shall be designed using the Service Load Design Method and in accordance with AASHTO Articles 10.18,10.24 and 10.32 except as noted.
+
'''Unit Shear Stress'''
  
The web splice consists of 2-Plates:
+
{|border="0"  
::Thickness = 5/16" minimum.
 
::Width = 12-1/2" (18-1/2" if 3 rows of bolts are required).
 
  
When the web section or steel grade changes at a splice, the smaller web strength should be used to design the splice. 
+
|colspan="4"|Load Factor:
 
 
 
 
'''Minimum Yield Strength <math>\, (F_y)</math> and Minimum Tensile Strength <math>\, (F_u)</math>'''
 
 
 
{|
 
 
|-
 
|-
|width="200"|ASTM A709 Grade 36||width="100"|<math>\, F_y</math>  = 36 ksi||<math>\, F_u</math> = 58 ksi
+
|&nbsp;||Shear Stress||=||<math>\, Vu = \frac{Vu}{\phi(Bd - voids~area)}</math>
 
|-
 
|-
|ASTM A709 Grade 50||<math>\, F_y</math>  = 50 ksi||<math>\, F_u</math> = 65 ksi
+
|colspan="4"|Working Stress:
 
|-
 
|-
|ASTM A709 Grade 50W||<math>\, F_y</math>  = 50 ksi||<math>\, F_u</math> = 70 ksi
+
|&nbsp;||Shear Stress||=||<math>\, v = \frac{v}{(Bd - Area~of~voids)}</math>
 
|-
 
|-
 +
|colspan="4"|Where "d" = effective depth, <math>\phi</math> = 0.85 for shear
 
|}
 
|}
  
  
'''Allowable Steel Stresses <math>\, (F_b, F_w)</math>'''
 
  
Allowable stresses are determined by AASHTO Table 10.32.1A.
+
<center>[[Image:751.40_Slab_Shear_Stress_Elevation.gif]]</center>
 +
 
 +
 
 +
 
 +
'''Allowable Shear Stress'''
 +
 
 +
{|border="0"
  
{|
+
|colspan="2"|Load Factor:
 
|-
 
|-
|width="200"|Allowable bending stress||<math>\, F_b = 0.55 \times F_y</math>
+
|width="20"|&nbsp;||<math>\, Vc = 2.0\sqrt{f'c}</math>
 
|-
 
|-
|Allowable shear stress||<math>\, F_v = 0.33 \times F_y</math>
+
|&nbsp;||Where Vc = shear strength provided by concrete
 
|-
 
|-
|}
+
|&nbsp;
 
 
 
 
{|
 
 
|-
 
|-
|width="200"|ASTM A709 Grade 36||width="100"|<math>\, F_b</math>  = 20 ksi||<math>\, F_v</math> = 12 ksi
+
|colspan="2"|Working Stress:
 
|-
 
|-
|width="200"|ASTM A709 Grade 50||<math>\, F_b</math>  = 27 ksi||<math>\, F_v</math> = 17 ksi
+
|&nbsp;||<math>\, Vc = 0.95\sqrt{f'c}</math>
 
|-
 
|-
|width="200"|ASTM A709 Grade 50W||<math>\, F_b</math>  = 27 ksi||<math>\, F_v</math> = 17 ksi
+
|&nbsp;
 
|-
 
|-
 +
|&nbsp;||Where Vc = Allowable shear stress carried by concrete
 
|}
 
|}
  
  
'''Allowable Bolt Stresses '''
+
If shear stress (load) exceeds the allowable shear use one or more of the following solutions.
  
Although standard holes are used in the fabrication of web splices, designing the splices for oversize holes allows for some fabrication and erection tolerances. Web splices required to resist shear between their connected parts are designated as slip-critical connections.  Shear connections subjected to stress reversal, or where slippage would be undesirable, shall be slip-critical connections.  Potential slip of joints should be investigated at intermediate load stages especially those joints located in composite regions.  The resultant force shall be less than the allowable bolt shear force. All splice bolts shall be A325 7/8" diameter High Strength Bolts.
+
# Eliminate some voids and replace remainder.
 
+
# Shorten alternate voids
<math>\, F_v</math> = 19 ksi
+
# Use shear reinforcing in the critical zone.
  
  
'''Bolt Arrangement'''
+
<center>[[Image:751.40_Slab_Shear_Stress_Diagram.gif]]</center>
  
The minimum distance from the center of any fastener in a standard hole to a sheared or thermally cut edge shall be 1-1/2 inches for 7/8" diameter fasteners.  The minimum distance between centers of fasteners in standard holes shall be three times the diameter of the fastener, but shall not be less than 3 inches for 7/8" diameter fasteners.   
 
  
 +
Note:<br/>Consider a voided slab the same as a regular slab as it pertains to the minimum stirrups (AASHTO - Article 8.19).<br/>i.e. The minimum stirrups are not required if the shear stress is less than allowable.
  
'''Splice Plate Strength'''
+
=====751.40.8.9.1.7 Camber Deflection=====
  
The strength of the splice plates shall be determined by multiplying the allowable stress of the splice plates by the net area of all splice plates.  The splice plates net area shall be taken as the gross area of the splice plates minus the bolt holes. Bolt holes are considered to be 1 inch diameter for the purpose of determining splice plate net area.  Web splices are designed to develop 75% of net section of the web.
 
  
 +
'''Ultimate Deflection:'''
  
'''Web Strength'''
+
Compute the "ultimate deflection" at 0.2 points of the spans for the dead loads without the 35# future wearing surface.
  
The strength of the web should be determined from the allowable web stress at the "top of web" to account for hybrid sections. Otherwise, the allowable web stress is based on a linear distribution of stress from outside face of flange to "top of web".
+
Ultimate deflection (long term) = elastic deflection x 3
  
 +
{|border="0"
  
'''Weight of Splice'''
+
|Ec (Elastic Modulus) =|| <math>\, 4 \times 10^6</math> psi (districts 1 and 4)
 +
|-
 +
|&nbsp;||<math>\, 6 \times 10^6</math> psi (remainder of districts)
 +
|}
  
When calculating the weight of splice, the following simplified weights shall be used.
+
The modulus of elasticity for the use in a continuous structure analysis computer program should be determined as follows:
  
Weight of High-Strength bolts (diameter 7/8") = 0.95 lbs/bolt
+
{|border="0"
  
Unit weight of Structural Steel = 490 lbs/ft<sup>3</sup>
+
|<math>\, \Delta_{ULT}</math>||=||<math>\, 3 \times  \Delta_{ELASTIC}</math>
 +
|-
 +
|<math>\, \Delta_{ELASTIC}</math>||=||<math>\, Coeff./E_c</math>
 +
|-
 +
|<math>\, \Delta_{ULT}</math>||=||<math>\, (Coeff./E_c \times 3 = Coeff./(E_c / 3)</math>
 +
|-
 +
|&nbsp;
 +
|-
 +
|Where:
 +
|-
 +
|<math>\, \Delta</math>||=||deflection.
 +
|-
 +
|<math>\, \Delta_{ULT}</math>||=||Ultimate deflection
 +
|-
 +
|<math>\, \Delta_{ELASTIC}</math>||=||Elastic deflection
 +
|}
  
===751.40.8.9 Continuous Concrete Slab Bridges===
 
  
====751.40.8.9.1 Slabs====
+
'''Example No. 1'''
  
=====751.40.8.9.1.1 Design Assumptions=====
+
(Assume bridge is in District 8)
  
 +
{|border="0"
  
{|border="0" cellpadding="0"
+
|<math>\, E_c</math>||=|| <math>\, 6 \times 10^6 psi</math>
 
 
|width="65"|Stresses -||FC||=||width="150"|1600 psi||N||=||width="50"|8||(Slab, Integral Column)
 
 
|-
 
|-
|&nbsp;||FC|||=||1200 psi||N||=||10||(Open Bent, Footing)
+
|<math>\, \Delta_{ULT}</math>||=||<math>\, Coeff. / (6/3) = Coeff./2</math>
|-
 
|&nbsp;||FY||=||colspan="5"|60,000 psi reinforcing steel
 
 
|}
 
|}
  
Use "Variable I" analysis for all structures except solid slabs without drop panels.<br/>Use "Constant I" analysis for solid slabs without drop panels.
+
Therefore, use 2 \times 10<sup>6</sup> psi for modulus of elasticity in the structure analysis computer program to get ultimate deflection. (*)
  
  
  
<center>[[Image:751.40_Slabs_Design_Assumptions_Diagram.gif]]</center>
+
'''Example No. 2'''
  
 +
(Assume bridge is in District 1)
  
 
{|border="0"
 
{|border="0"
  
|"L"||=||Design Span
+
|<math>\, E_c</math>||=||<math>\, 4 \times 10^6 psi</math>
 
|-
 
|-
|"H"||=||Design Height
+
|<math>\, \Delta_{ULT}</math>||=||<math>\, Coeff. / (4/3) = Coeff./1.333</math>
|-
 
|valign="top"|"I"||valign="top"|=||Gross moment of inertia of the full cross-section (Slab minus voids - integral wearing surface not included) ("I1", "IA", etc. suggested I's to be considered.)
 
|-
 
|"S"||=||The effective span length for the use in determining minimum slab thickness under load factor design (AASHTO 8.9).
 
 
|}
 
|}
  
Use the same column diameter and spacing for all Intermediate Bents.<br/>Use the same slab thickness for all spans.
+
Therefore, use <math>\, 1.333 \times 10^6</math> psi for modulus of elasticity in the structure analysis computer program to get ultimate deflection. (*)
 +
 
 +
 
 +
 
 +
(*) Gives long term deflection as output.
 +
 
 +
=====751.40.8.9.1.8 Slab Construction Joint Details=====
 +
 
  
 +
<center>[[Image:751.40_Slab_Const_Jt_Key_(Slab_Depth_17_in_or_more).gif]]</center>
  
{|border="1" cellpadding="5" align="center" style="text-align:center"
 
  
|colspan="5"|'''DEGREE OF RESTRAINT - LONGITUDINAL'''
+
<center>'''DETAILS OF SLAB CONSTRUCTION JOINT KEY<br/>(FOR SLAB DEPTHS 17" OR MORE)'''</center>
|-
 
|&nbsp;||Column Type||Footing Type||Top Column||Bottom Column
 
|-
 
|rowspan="2"|'''INT. BENTS'''||Integral Column||Spread or Pile||Integral||(**)
 
|-
 
|Integral Column <!--column 1 occupied by cell '''INT. BENTS'''-->||Pedestal Pile||Integral||(**)
 
|-
 
|rowspan="3"|'''END BENTS'''||Pinned Column||any||Pinned||(**)
 
|-
 
|Integral Pile <!--column 1 occupied by cell '''END BENTS'''-->||&nbsp;||(*) Pinned||rowspan="3"|&nbsp;
 
|-
 
|Open Bent with Column<!--column 1 occupied by cell '''END BENTS'''-->||any||Simple
 
|-
 
|'''INT. BENTS'''||Open Bent with Pile||&nbsp;||Simple
 
|}
 
  
  
{|border="0"
 
  
|align="right" valign="top"|(*)||&nbsp;||See "Integral Piles" this Manual Section.
+
<center>[[Image:751.40_Slab_Const_Jt_Key_(Slab_Depth_16.5_in_or_less).gif]]</center>
|-
 
|align="right" valign="top"|(**)||&nbsp;||Use "Pinned" for Seismic Performance Category A and "Fixed for Seismic Performance Categories B, C & D. (See Structural Project Manager or Liaison)
 
|}
 
  
=====751.40.8.9.1.2 Slab Design and Drop Panel=====
 
  
 +
<center>'''DETAILS OF SLAB CONSTRUCTION JOINT KEY<br/>(FOR SLAB DEPTHS 16½" OR LESS)'''</center>
  
The Slab Depth is based on the following limitations:
 
 
 
  
{|border="0"
 
  
|1.||&nbsp;||colspan="4"|Vertical Clearance Requirements: see the Design Layout.
+
<center>[[Image:751.40_Slab_Const_Jt_Void_Spacing.gif]]</center>
|-
 
|2.||&nbsp;||colspan="4"|Allowable Depths:
 
|-
 
|&nbsp;||A.||colspan="3"|Positive Moments -
 
|-
 
|colspan="2"|&nbsp;||colspan="3"|see table of "Available Slab Depths", of this Section.
 
|-
 
|&nbsp;||B.||colspan="3"|Slab Depth controlled by the minimum thickness formula -
 
|-
 
|colspan="2"|&nbsp;||colspan="3"|(Integral wearing surface is included with the total depth provided.)
 
|-
 
|colspan="2"|&nbsp;||colspan="3"|Continuous Spans - AASHTO 8.9 = (S + 10)/30
 
|-
 
|colspan="3"|&nbsp;||"S"||may be used as the clear distance between drop panels.
 
|-
 
|colspan="4"|&nbsp;||Bridges may have two adjacent spans averaged if S<sub>2</sub>/S<sub>1</sub> < 1.5
 
|-
 
|colspan="2"|&nbsp;||colspan="3"|Simple Spans - AASHTO 8.9 = 1.2 (S + 10)/30
 
|-
 
|&nbsp;||C.||colspan="3"|Negative Moments -
 
|}
 
  
  
{|border="3" cellpadding="3" cellspacing="0" style="text-align:center"
+
<center>'''VOID SPACING AT LONGITUDINAL CONSTRUCTION JOINT'''</center>
  
|&nbsp;||colspan="2"|'''DROP PANEL DEPTHS'''
 
|-
 
|&nbsp;||'''MIN.'''||'''MAX.'''
 
|-
 
|align="left"|Bents in median of dual roadway||0" or 3"||13"
 
|-
 
|align="left"|Other Bents||0" or 3"||9"
 
|-
 
|colspan="3"|'''INCREMENTS OF 1"
 
|}
 
  
 +
====751.40.8.9.2 End Bents====
  
{|border="3" cellpadding="3" cellspacing="0" style="text-align:center"
+
=====751.40.8.9.2.1 Pile Cap Bents=====
  
|colspan="2"|&nbsp;||colspan="6"|'''APPROXIMATE DROP PANEL WIDTH (FEET)<br/>(PARALLEL TO THE CENTERLINE OF ROADWAY)'''
+
<center>[[Image:751.40_End_Bent_(Pile_Cap_Sections).gif]]</center>
|-
 
|rowspan="2"|&nbsp;||rowspan="2"|Bents||colspan="6"|Drop Panel Depth
 
|-
 
|4"<!--column 1 occupied by cell &nbsp;--> <!--column 2 occupied by cell Bents-->||6"||7"||8"||9"||12"
 
|-
 
|3 Span Bridge||2 & 3||6'||6'||10'||8'||6'
 
|-
 
|rowspan="2"|4 Span Bridge||2 & 4||6'||6'||10'||8'||6'
 
|-
 
|3<!--column 1 occupied by cell 4 Span Bridge-->||8'||10'||12'||12'||12'||12'
 
|-
 
|colspan="8"|'''THESE WIDTHS ARE SUGGESTED ONLY AS TRIAL DIMENSIONS FOR<br/>DESIGN AND ARE NOT TO BE USED AS LIMITS FOR THE FINAL DESIGN.'''
 
|}
 
  
 +
<center>* See Bridge Memorandum for maximum slope of spill fill.</center>
  
 +
{|border="0" align="center" style="text-align:center"
  
{|border="0"
+
|width="275"|'''SECTION THRU WING'''||width="175" align="right"|'''SECTION A-A'''
  
|3.||&nbsp;||colspan="4"|Reinforcing Steel:
 
|-
 
|&nbsp;||align="center" valign="top" |A.||colspan="3"|Positive Moments = Maximum #11 @ 5" cts.
 
|-
 
|&nbsp;||align="center" valign="top" |B.||colspan="3"|Negative Moments = Maximum #11 @ 5" cts., except #14s @ 6" cts., may be used for long spans.
 
|-
 
|4.||&nbsp;||colspan="4"|Live Load Deflection - AASHTO 10.6
 
|-
 
|&nbsp;||colspan="4"|The deflection due to service live load plus impact shall not exceed 1/800 of the span, except on bridges in urban areas used in part by pedestrains whereon the ratio preferably shall not exceed 1/1000.
 
 
|}
 
|}
  
=====751.40.8.9.1.3 Slab Longitudinal Sections=====
 
  
 +
<center>[[Image:751.40_End_Bent_(Pile_Cap_Elevation).gif]]</center>
  
'''HOLLOW SLABS'''
 
  
 +
<center>'''ELEVATION'''</center>
  
<center>[[Image:751.40_Slabs_-_Hollow_End_Spans.gif]]</center>
 
  
<center>'''END SPANS'''</center>
 
  
 +
<center>[[Image:751.40_End_Bent_(Pile_Cap_Plan_(SQ)).gif]]</center>
  
<center>[[Image:751.40_Slabs_-_Hollow_Intermediate_Spans.gif]]</center>
 
  
<center>'''INTERMEDIATE SPANS'''</center>
+
<center>'''PLAN (SQUARE)'''</center>
  
  
 
{|border="0" align="center"
 
{|border="0" align="center"
  
|width="200" rowspan="3"|[[Image:751.40_Slabs_-_Hollow_Part_Plan_Skewed_Detail.gif]]
+
|width="300"|(1) Wing brace details.||[[Image:751.40_End_Bent_(Pile_Cap_Detail_B).gif]]
|(*)Increase to maintain 6" minimum on skews (see detail)
 
|-
 
|(**) By Design (6" increments measured normal to the centerline of bent) (The minimum is equal to the column diameter + 2'-6")<!--column 1 occupied by cell [[Image:751.40_Slabs_-_Hollow_Part_Plan_Skewed_Detail.gif]]-->
 
|-
 
|width="400"|Note:<br/>All longitudinal dimensions shown are horizontal (Bridges on grades and vertical curves, included).<br/>For Sections A-A and B-B see this Manual Section.<!--column 1 occupied by cell [[Image:751.40_Slabs_-_Hollow_Part_Plan_Skewed_Detail.gif]]-->
 
 
|}
 
|}
  
  
&nbsp;
+
<center>[[Image:751.40_End_Bent_(Pile_Cap_Plan_(Skewed)).gif]]</center>
 +
 
  
 +
<center>'''PLAN (SKEWED)'''</center>
  
 +
<center>(*) Use the same Dimension (centerline Curb Joint) as the opposite side when the wings are the same length.</center>
 +
 +
=====751.40.8.9.2.2 Integral Column Bents=====
 +
'''SEISMIC PERFORMANCE CATEGORY A<BR/>(PINNED COLUMN AT TOP AND BOTTOM)'''
  
'''SOLID SLABS'''
 
  
 +
<center>[[Image:751.40_End_Bent_(Integral_Column_Part_Section).gif]]</center>
  
<center>[[Image:751.40_Slabs_-_Solid_End_Spans.gif]]</center>
+
<center>'''PART SECTION'''</center>
  
<center>'''END SPANS'''</center>
 
  
 +
{|border="0" style="text-align:center" align="center"
  
 +
|rowspan="3"|[[Image:751.40_End_Bent_(Integral_Column_Pinned_Column).gif]]||[[Image:751.40_End_Bent_(Integral_Column_Section_AA).gif]]
 +
|-
 +
|'''SECTION A-A'''<!--column 1 occupied by cell [[Image:751.40_End_Bent_(Integral_Column_Pinned_Column).gif]]-->
 +
|-
 +
|[[Image:751.40_End_Bent_(Integral_Column_Section_BB).gif]]<!--column 1 occupied by cell [[Image:751.40_End_Bent_(Integral_Column_Pinned_Column).gif]]-->
 +
|-
 +
|'''PINNED COLUMN'''||'''SECTION B-B'''
 +
|}
  
<center>[[Image:751.40_Slabs_-_Solid_Intermediate_Spans.gif]]</center>
 
  
<center>'''INTERMEDIATE SPANS'''</center>
+
Note:  If the columns at an end bent have excessive moments due to shortness of the Column or length of the span, they should be detailed as "pinned" and designed for vertical reactions only.
  
  
(*) By Design (6" increments measured normal to the centerline of Bent) (The minimum is equal to the column diameter + 2'-6")
+
'''SEISMIC PERFORMANCE CATEGORIES B, C & D<BR/>(PINNED COLUMN AT TOP, FIXED COLUMN AT BOTTOM)'''
  
 +
For pinned column conditions at the top, see the above details.<br/>For fixed column conditions at the bottom and column reinforcement details.
  
Note:<br/>All longitudinal dimensions shown are horizontal (Bridges on grades and vertical curves, included).
+
Note: For details not shown, see integral pile cap details.
  
=====751.40.8.9.1.4 Slab Cross Section and Section Properties=====
+
=====751.40.8.9.2.3 Reinforcement - Pile Cap Bents=====
  
  
<center>[[Image:751.40_Slab_Cross_Section_AA_&_BB.gif]]</center>
+
<center>[[Image:751.40_Reinforcement_-_Pile_Cap_Section_1_(Slab_Depth_less_than_16_in).gif]]</center>
  
 +
::::::::::'''SECTION THRU END BENT<BR/>(Slab depth less than 16")'''
  
{|border="0" style="text-align:center" align="center"
 
  
|width="300"|'''HALF SECTION A-A<br/>CENTER OF SPAN'''||width="300"|'''HALF SECTION B-B<br/>NEAR INTERMEDIATE BENT'''
+
<center>[[Image:751.40_Reinforcement_-_Pile_Cap_Section_2_(Slab_Depth_16_in_or_more).gif]]</center>
  
|}
+
::::::::::'''SECTION THRU END BENT<BR/>(Slab depth 16" or more)'''
  
  
{|border="0" cellpadding="5" align="center" style="text-align:center"
+
(**) Development length for top bar minimum.
  
|rowspan="4" width="250" align="left"|
+
=====751.40.8.9.2.4 Reinforcement - Wing=====
{|border="3" cellpadding="2" cellspacing="0" style="text-align:center"
+
 
|colspan="5"|'''AVAILABLE SLAB DEPTHS<br/>AND VOID DATA'''
+
 
 +
<center>[[Image:751.40_Reinforcement_-_Wing_(Elevation_&_Part_Section).gif]]</center>
 +
 
 +
{|border="0" style="text-align:center" align="right"
 +
 
 +
|width="225"|'''ELEVATION OF WING'''||width="375"|'''PART SECTION THRU WING'''
 
|-
 
|-
|colspan="5"|Truck Loading
+
|align="left" colspan="2"|(*) Clip K bars as required to maintain<br/>minimum clearance at bottom of wing.
 +
|}
 +
 
 +
 
 +
&nbsp;
 +
&nbsp;
 +
 
 +
 
 +
<center>[[Image:751.40_Reinforcement_-_Wing_(Section_AA_&_Part_Section_Thru_End).gif]]</center>
 +
 
 +
{|border="0" style="text-align:center" align="right"
 +
 
 +
|width="225"|'''SECTION A-A'''<BR/>(K-bars not shown for clarity)||width="375"|'''PART SECTION THRU<BR/>END OF WING'''
 +
|}
 +
 
 +
&nbsp;
 +
 
 +
&nbsp;
 +
 
 +
Note: See _____ for <u>barrier</u> <u>railing</u> details and spacing of K-bars.
 +
 
 +
=====751.40.8.9.2.5 Design Assumptions for Integral Piles=====
 +
 
 +
 
 +
'''Seismic Performance Category A'''
 +
 
 +
Piles may be considered as "pinned" (for superstructure) at the pile cap and designed for vertical loads only unless they fall under the following general conditions in which case they should be checked for the loadings as specified for columns.
 +
 
 +
{|border="0"
 +
 
 +
|1.||Height from centerline of slab to "pin" is less than 15'.
 
|-
 
|-
|T (*)||&nbsp;||"D"||"E"||"F"
+
|&nbsp;||The location of the pinned joint is arbitratily taken as about 1/3 of the length of long piles or at a point about 10' below the natural ground line.
 
|-
 
|-
|17"||colspan="4" align="left"|and less - no voids
+
|2.||Piles having a large gross moment of inertia (cast-in-place concrete) gross I of steel BP = I x n.
 
|-
 
|-
|18"||&nbsp;||9"||15"||21"
+
|3.||The number of piles used on a fairly long structure is small.
|-
+
|}
|19"||(***)||10"||16"||22"
+
 
|-
+
 
|21"||&nbsp;||12"||18"||24"
+
 
|-
+
'''Seismic Performance Categories B, C & D'''
|23"||&nbsp;||14"||20"||26"
+
 
 +
Piles shall be checked for combined axial and bending stresses for seismic loading conditions.  For AASHTO group loads I thru VI as applicable, follow criteria noted above for seismic performance category A.
 +
 
 +
 
 +
 
 +
====751.40.8.9.3 Intermediate Bents====
 +
=====751.40.8.9.3.1 Integral Bents=====
 +
 
 +
 
 +
<center>[[Image:751.40_Intermediate_Bents_(Integral_Bents_Half_Section).gif]]</center>
 +
 
 +
 
 +
<center>'''HALF SECTION'''</center>
 +
 
 +
 
 +
(*) 25'-0" is the max. column spacing allowed.  However, the footing pressure may be the controlling factor for the column spacing.  It is suggested that a rough check be made of the footing pressure before the spacing is definitely established.
 +
 
 +
In congested areas, when it is desired to keep the number of columns to a min., larger column spacings may be desirable.  (consult the Structural Project Manager).
 +
 
 +
In general, use two 2'-6" columns for Roadways thru 44'-0" and additional 2'-6" columns for wider Roadways.
 +
 
 +
 
 +
'''SEISMIC PERFORMANCE CATEGORY A'''
 +
 
 +
 
 +
<center>[[Image:751.40_Intermediate_Bents_(Integral_Bents_Category_A_Half_Section).gif]]</center>
 +
 
 +
 
 +
<center>'''HALF SECTION'''</center>
 +
 
 +
 
 +
<center>[[Image:751.40_Intermediate_Bents_(Integral_Bents_Category_A_Part_Section_AA).gif]]</center>
 +
 
 +
 
 +
<center>'''PART SECTION A-A'''</center>
 +
 
 +
=====751.40.8.9.3.2 Integral Column Bent with Drop Panel=====
 +
 
 +
 
 +
{|border="0" align="center"
 +
 
 +
|[[Image:751.40_Intermediate_Bents_-_Integral_Column_Bents_with_Drop_Panel_(Part_Section).gif]]||valign="top"|'''<u>ATTENTION DETAILER:</u>'''<br/>When detailing Int. Bents on SPS the Section thru drop panel shall be drawn to appropriate grade.
 
|-
 
|-
|25"||&nbsp;||15.7"||22"||28"
+
|align="center"|'''PART SECTION'''
|-
+
|}
|26"||&nbsp;||16.7"||23"||29"
+
 
|-
+
 
|28"||&nbsp;||18.7"||25"||31"
+
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Column_Bents_with_Drop_Panel_(Part_Sections_AA).gif]]</center>
|-
+
 
|30"||&nbsp;||20.85"||27"||33"
+
 
|-
+
{|border="0" align="center" style="text-align:center"
|colspan="4"|Pedestrian Overpasses||rowspan="7"|&nbsp;
+
 
 +
|valign="top" width="300"|'''PART SECTION A-A<BR/>(FLAT)'''||width="300"|'''PART SECTION A-A<BR/>(GRADE OR V.C.)'''<BR/>D = Diameter of Column
 +
|}
 +
 
 +
 
 +
 
 +
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Column_Bents_with_Drop_Panel_(Part_Plans_Square_&_Skewed).gif]]</center>
 +
 
 +
 
 +
{|border="0" align="center" style="text-align:center"
 +
 
 +
|width="175"|'''PART PLAN - SQUARE'''||width="350"|'''PART PLAN - SKEWED'''
 +
|}
 +
 
 +
 
 +
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Column_Bents_with_Drop_Panel_(Section_Thru_Drop_Panel).gif]]</center>
 +
 
 +
 
 +
<center>'''SECTION THRU DROP PANEL'''</center>
 +
 
 +
 
 +
{|border="0" align="center"
 +
 
 +
|
 +
{|border="1" cellspacing="0" cellpadding="3" align="center" style="text-align:center"
 +
 
 +
|Largest<br/>Longitudinal<br/>Slab Bar||"a"
 
|-
 
|-
|T (*)||&nbsp;||"D"||"E"
+
|#8||1-13/16"
 
|-
 
|-
|15"||colspan="3" align="left"|and less - no voids
+
|#9, #10 & #11||2-1/16"
 
|-
 
|-
|16"||&nbsp;||8"||14"
+
|#14||2-9/16"
|-
 
|17"||&nbsp;||9"||15"
 
|-
 
|18"||&nbsp;||10"||16"
 
|-
 
|20"||&nbsp;||12"||18"
 
 
|}
 
|}
|[[Image:751.40_Slab_Cross_Section_Thru_Void.gif]]<!--column 1 occupied by cell {|border="3" cellpadding="2" cellspacing="0" style="text-align:center"
+
|[[Image:Symbol.gif]]||For Reference Only
|colspan="5"|'''AVAILABLE SLAB DEPTHS<br/>AND VOID DATA'''
 
 
|-
 
|-
|colspan="5"|Truck Loading
+
|&nbsp;
 
|-
 
|-
|T (*)||&nbsp;||"D"||"E"||"F"
+
|
 +
{|border="1" cellspacing="0" cellpadding="5" align="center" style="text-align:center"
 +
 
 +
|Largest<br/>Longitudinal<br/>Slab Bar||"a" (*)
 
|-
 
|-
|17"||colspan="4" align="left"|and less - no voids
+
|#8 & #9||2-5/8"
 
|-
 
|-
|18"||&nbsp;||9"||15"||21"
+
|#10 & #11||2-7/8"
 
|-
 
|-
|19"||(***)||10"||16"||22"
+
|#14||3-3/8"
|-
+
|}
|21"||&nbsp;||12"||18"||24"
+
|}
 +
 
 +
 
 +
(*) Based on 3" clearance and #6 stirrups, (includes Integral W.S.) to top longitudinal bar.
 +
 
 +
(1) Standard 90° Hook.
 +
 
 +
(2) Const. joint key D/3 x D/3 x 2", D = Diameter of Column
 +
 
 +
=====751.40.8.9.3.3 Integral Pile Cap Bents with Drop Panel=====
 +
 
 +
 
 +
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_with_Drop_Panel_(Part_Section_&_Flat).gif]]</center>
 +
 
 +
{|border="0" align="center" style="text-align:center"
 +
 
 +
|width="350"|'''PART SECTION'''||width="250"|'''PART SECTION A-A<BR/>(FLAT)'''
 +
|}
 +
 
 +
 
 +
{|border="0" align="center"
 +
 
 +
|valign="bottom"|Bottom or drop panel to be parallel to top of slab both transversely and longitudinally.||rowspan="5"|[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_with_Drop_Panel_(Part_Section_Grade_or_VC).gif]]
 
|-
 
|-
|23"||&nbsp;||14"||20"||26"
+
|(1)Horizontal except for superelevated structures.
 
|-
 
|-
|25"||&nbsp;||15.7"||22"||28"
+
|valign="top"|(2) Use 3" Min. clip on beam for skews above 35°.
 
|-
 
|-
|26"||&nbsp;||16.7"||23"||29"
+
|&nbsp;
 
|-
 
|-
|28"||&nbsp;||18.7"||25"||31"
+
|&nbsp;
 
|-
 
|-
|30"||&nbsp;||20.85"||27"||33"
+
|&nbsp;||align="center"|'''PART SECTION A-A<BR/>(GRADE OR V.C.)
|-
+
|}
|colspan="4"|Pedestrian Overpasses
+
 
|-
+
 
|T (*)||&nbsp;||"D"||"E"
+
 
|-
+
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_with_Drop_Panel_(Part_Plans_Square_&_Skewed).gif]]</center>
|15"||colspan="3" align="left"|and less - no voids
+
 
|-
+
{|border="0" align="center" style="text-align:center"
|16"||&nbsp;||8"||14"
+
 
|-
+
|width="250"|'''PART PLAN - SQUARE'''||width="250"|'''PART PLAN - SKEWED'''
|17"||&nbsp;||9"||15"
+
|}
|-
+
 
|18"||&nbsp;||10"||16"
+
 
|-
+
 
|20"||&nbsp;||12"||18"
+
'''REINFORCEMENT'''
|}-->
+
 
|-
+
 
|'''PART SECTION THRU VOID'''<!--column 1 occupied by cell {|border="3" cellpadding="2" cellspacing="0" style="text-align:center"
+
 
|colspan="5"|'''AVAILABLE SLAB DEPTHS<br/>AND VOID DATA'''
+
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_with_Drop_Panel_-_Reinforcement_(Half_Section).gif]]</center>
|-
+
 
|colspan="5"|Truck Loading
+
 
|-
+
<center>'''HALF SECTION'''</center>
|T (*)||&nbsp;||"D"||"E"||"F"
+
 
|-
+
 
|17"||colspan="4" align="left"|and less - no voids
+
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_with_Drop_Panel_-_Reinforcement_(Section_Thru_Drop_Panel).gif]]</center>
|-
+
 
|18"||&nbsp;||9"||15"||21"
+
 
|-
+
<center>'''SECTION THRU DROP PANEL'''</center>
|19"||(***)||10"||16"||22"
+
 
|-
+
 
|21"||&nbsp;||12"||18"||24"
+
(1) Use 5 1/4" for computing length of stirrup bar.  Do not detail on plans.
|-
+
 
|23"||&nbsp;||14"||20"||26"
+
(2) Standard 90° hook.
|-
+
 
|25"||&nbsp;||15.7"||22"||28"
+
(3) Optional Const. Joint Key 10" x 2"
|-
+
 
|26"||&nbsp;||16.7"||23"||29"
+
=====751.40.8.9.3.4 Integral Pile Cap Bents without Drop Panel=====
|-
+
 
|28"||&nbsp;||18.7"||25"||31"
+
 
|-
+
'''REINFORCEMENT'''
|30"||&nbsp;||20.85"||27"||33"
+
 
|-
+
 
|colspan="4"|Pedestrian Overpasses
+
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_without_Drop_Panel_-_Reinforcement_(Half_Section).gif]]</center>
|-
+
 
|T (*)||&nbsp;||"D"||"E"
+
 
|-
+
<center>'''HALF SECTION'''</center>
|15"||colspan="3" align="left"|and less - no voids
+
 
|-
+
 
|16"||&nbsp;||8"||14"
+
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_without_Drop_Panel_-_Reinforcement_(Section_Thru_Bent).gif]]</center>
|-
+
 
|17"||&nbsp;||9"||15"
+
 
|-
+
<center>'''SECTION THRU BENT'''</center>
|18"||&nbsp;||10"||16"
+
 
|-
+
 
|20"||&nbsp;||12"||18"
+
(1) Use 5 1/4" for computing length of stirrup bar.  Do not detail on plans.
|}-->
+
 
|-
+
(2) Horizontal except for superelevated structures.
|[[Image:751.40_Slab_Cross_Section_-_Detail_C.gif]]<!--column 1 occupied by cell {|border="3" cellpadding="2" cellspacing="0" style="text-align:center"
+
 
|colspan="5"|'''AVAILABLE SLAB DEPTHS<br/>AND VOID DATA'''
+
(3) Standard 90° hook.
|-
+
 
|colspan="5"|Truck Loading
+
=====751.40.8.9.3.5 Pile Footing Design and Details=====
|-
+
 
|T (*)||&nbsp;||"D"||"E"||"F"
+
'''(1) GENERAL'''
|-
+
 
|17"||colspan="4" align="left"|and less - no voids
+
Number, size and spacing of piling shall be determined by computing the pile loads and applying the proper allowable overstresses.
|-
+
|18"||&nbsp;||9"||15"||21"
+
Cases of Loading (AASHTO Article 3.22)
|-
+
|19"||(***)||10"||16"||22"
+
Group I maximum vertical loads.
|-
+
|21"||&nbsp;||12"||18"||24"
+
Group IV temperature and shrinkage moments with applicable vertical loads.
|-
+
|23"||&nbsp;||14"||20"||26"
+
1983 AASHTO guide specifications for seismic design of highway bridges. (See chapter 4 for earthquake loads combined with applicable vertical loads.) (*) (See Structural Project Manager or Liaison)
|-
+
|25"||&nbsp;||15.7"||22"||28"
+
Internal stresses including the position of the shear line shall then be computed.
|-
+
|26"||&nbsp;||16.7"||23"||29"
+
Long narrow footings are not desirable and care should be taken to avoid the use of an extremely long footing 6~0" wide when a shorter footing 8'-3" or 9'-0" wide could be used.
|-
+
|28"||&nbsp;||18.7"||25"||31"
+
When using the load factor design method for footings, design the number of piles needed based on the working stress design method.
|-
+
|30"||&nbsp;||20.85"||27"||33"
+
 
|-
+
 
|colspan="4"|Pedestrian Overpasses
+
'''ASSUMPTIONS'''
|-
+
(Bents with 2 or more columns)
|T (*)||&nbsp;||"D"||"E"
+
 
|-
+
 
|15"||colspan="3" align="left"|and less - no voids
+
'''SEISMIC PERFORMANCE CATEGORY A'''
|-
+
 
|16"||&nbsp;||8"||14"
+
#Dead and live load moments will be 25% of the moments used for slab and top of Column design.
|-
+
#Temperature moments shall be 50% of the moment at top of Column.
|17"||&nbsp;||9"||15"
+
#Column reinforcement to be same as that required at top of Column. Footing dowel's to be #5 bars, same number as column bars.
|-
+
#Footings to be proportioned for conditions as specified. Do not use ratio of bent height as specified for Intermediate Bents for longitudinal footings dimensions.
|18"||&nbsp;||10"||16"
+
 
|-
+
 
|20"||&nbsp;||12"||18"
+
'''SEISMIC PERFORMANCE CATEGORIES B, C & D'''
|}-->
+
 
|-
+
#For Seismic Performance categories B, C & D, the connection between the bottom of Column and the footing is a fixed connection.
|'''DETAIL "C"'''<!--column 1 occupied by cell {|border="3" cellpadding="2" cellspacing="0" style="text-align:center"
+
#Footing design is based on (Seismic Design of Beam-Column Joint).
|colspan="5"|'''AVAILABLE SLAB DEPTHS<br/>AND VOID DATA'''
+
 
|-
+
(*) The design of all bridges in seismic performance B, C & D are to be designed by earthquake criteria in accordance with [[751.9_Bridge_Seismic_Design|EPG 751.9 Bridge Seismic Design]].
|colspan="5"|Truck Loading
+
 
|-
+
 
|T (*)||&nbsp;||"D"||"E"||"F"
+
'''(2) PILE LOADS'''
|-
+
:P = N/n ± M/S
|17"||colspan="4" align="left"|and less - no voids
+
:P = Pile Loads
|-
+
:N = Vertical Loads
|18"||&nbsp;||9"||15"||21"
+
:n = number of piles
|-
+
:M = overturning moment
|19"||(***)||10"||16"||22"
+
:if minimum eccentricity controls the moment in both directions, it is necessary to use the moment in one direction (direction with less section modulus of Pile group) only for the footing check.
|-
+
:S = Section Modulus of pile group
|21"||&nbsp;||12"||18"||24"
+
 
|-
+
 
|23"||&nbsp;||14"||20"||26"
+
'''AASHTO GROUP I AND IV LOADS'''
|-
 
|25"||&nbsp;||15.7"||22"||28"
 
|-
 
|26"||&nbsp;||16.7"||23"||29"
 
|-
 
|28"||&nbsp;||18.7"||25"||31"
 
|-
 
|30"||&nbsp;||20.85"||27"||33"
 
|-
 
|colspan="4"|Pedestrian Overpasses
 
|-
 
|T (*)||&nbsp;||"D"||"E"
 
|-
 
|15"||colspan="3" align="left"|and less - no voids
 
|-
 
|16"||&nbsp;||8"||14"
 
|-
 
|17"||&nbsp;||9"||15"
 
|-
 
|18"||&nbsp;||10"||16"
 
|-
 
|20"||&nbsp;||12"||18"
 
|}-->
 
|}
 
  
 +
Maximum P = Pile Capacity
 +
Minimum P = 0
  
 +
Tension on a pile will not be allowed for any combination of forces.
 +
 +
Overstress reduction will not be used for loading minimums.
  
{|border="0"
 
  
|colspan="2"|Notes:
+
'''EARTHQUAKE LOADS'''
|-
 
|(*)||Increase the Dimension "T" by 1/2" for #14 bars placed in the top or bottom of the slab.
 
|-
 
|&nbsp;||Increase the Dimension "T" by 1" for #14 bars placed in the top and bottom of the slab.
 
|-
 
|&nbsp;||("T" and "D" are based on 3" clearance which includes the integral wearing surface to the top of the longitudinal bar.)
 
|-
 
|&nbsp;
 
|-
 
|(**)||For Roadways with slab drains, use 10" minimum. For Roadways that require additional reinforcement for resisting moment of the edge beam 20" minimum, refer to this section.
 
|-
 
|&nbsp;
 
|-
 
|(***)||Preferred minimum (Consult the Structural Project Manager prior to the use of a thinner slab.)
 
|}
 
  
 +
'''POINT BEARING PILES'''
  
 +
(**) Maximum P = Pile capacity x 2
 +
:(I.E. for HP 10 x 42 piles, maximum P = 56 x 2 = 112 tons/pile).
 +
 +
Minimum P = Use allowable uplift force specified for piles in [[751.39 Seal Course|EPG 751.39 Seal Course]].
  
'''Voided Slab Spans'''
+
(**) Two (2) is our normal factor of safety.  Under earthquake loadings only the point bearing pile and rock capacities are their ultimate capacities.
  
  
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
+
'''FRICTION PILES'''
  
|Void Dia.<br/>(in.)||Area<br/>(sq.ft.)||Area<br/>(sq.in.)||Moment<br/>of Inertia<br/>(ft.<sup>4</sup>)||Moment<br/>of Inertia<br/>(in.<sup>4</sup>)||Weight<br/>(lb./ft.)
+
Maximum P = Pile capacity
|-
 
|8.00||0.3490||50.2656||0.0096||201.0624||52.35
 
|-
 
|9.00||0.4417||63.6174||0.0155||322.0630||66.26
 
|-
 
|10.00||0.5454||78.5400||0.0236||490.8750||81.81
 
|-
 
|12.00||0.7854||113.0976||0.0490||1017.8784||117.81
 
|-
 
|14.00||1.0690||153.9384||0.0909||1885.7454||160.35
 
|-
 
|15.70||1.3443||193.5932||0.1438||2982.4242||201.66
 
|-
 
|16.70||1.5211||219.0402||0.1841||3818.0075||228.17
 
|-
 
|18.70||1.9072||274.6465||0.2894||6002.5789||286.09
 
|-
 
|20.85||2.3710||341.4310||0.4473||9276.7336||355.65
 
|}
 
  
=====751.40.8.9.1.5 Slab Reinforcement=====
 
  
&nbsp;
+
'''(3) INTERNAL STRESSES'''
 +
::A) Shear Line
 +
::B) Bending
 +
::C) Distribution of Reinforcement
 +
::D) Shear
  
'''HOLLOW SLABS'''
+
=====751.40.8.9.3.6 Pedestal Pile=====
  
 +
'''GENERAL'''
  
<center>[[Image:751.40_Slab_Reinf_-_Positive_Moment.gif]]</center>
+
No concrete bell shall be used without approval of Structural Project Manager or Liaison.
  
  
<center>'''DETAIL "A"<br/>(POSITIVE MOMENT)'''</center>
+
'''SEISMIC PERFORMANCE CATEGORY A'''
  
 +
#Assume column to be "pinned" for belled footing sitting on rock.  All loads will be axial.
 +
#Assume column to be fixed for pedestal pile embedded in rock.
 +
#All earth loads within the diameter of belled footing, or pedestal pile if there is no bell, above ground line shall be included in footing design.
  
<center>[[Image:751.40_Slab_Reinf_-_Negative_Moment.gif]]</center>
+
 
 +
<center>[[Image:751.40_Intermediate_Bents_-_Pedestal_Pile_General_(Category_A)_Elevation.gif]]</center>
 +
 
 +
 
 +
'''SEISMIC PERFORMANCE CATEGORY B, C & D'''
 +
 
 +
See (Seismic Design).
  
  
<center>'''DETAIL "B"<br/>(NEGATIVE MOMENT)'''</center>
+
'''DETAILS'''
 +
 
 +
'''SEISMIC PERFORMANCE CATEGORY A'''
 +
 
 +
 
 +
<center>[[Image:751.40_Intermediate_Bents_-_Pedestal_Pile_Details_(Category_A)_Elevation_&_Section_AA.gif]]</center>
  
  
{|border="3" cellpadding="4" cellspacing="0" align="center" style="text-align:center"
+
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
  
|Longitudinal Reinforcement<br/>(Largest Bar)||width="50"|"G"
+
|Diameter<br/>of Shaft||Minimum<br/>Bell Diameter||Maximum<br/>Bell Diameter||Minimum<br/>(*) Reinf.||Cubic Yards<br/>Concrete per ft.
 
|-
 
|-
|#8||3-5/8"
+
|2'-0"||2'-4"||6'-0"||8-#7||0.1164
 
|-
 
|-
|#9||3-3/4"
+
|2'-6"||2'-10"||7'-6"||8-#9||0.1818
 
|-
 
|-
|#10||3-7/8"
+
|3'-0"||3'-6"||9'-0"||11-#9||0.2618
 
|-
 
|-
|#11||4"
+
|3'-6"||4'-0"||10'-6"||14-#9||0.3563
 
|-
 
|-
|#14||4-3/8"
+
|4'-0"||4'-6"||12'-0"||19-#9||0.4654
|}
 
 
 
 
 
'''Moment Curves'''
 
 
 
{|border="0"
 
 
 
|valign="top"|1.||Determine reinforcing steel from the sum of the dead loads and the live loads + impact (working stress design) or design in accordance with AASHTO Article 8.16 and 8.9 (load factor design).
 
 
|-
 
|-
|valign="top"|2.||Determine the cut-off points for the stress bars in sets of 2 or 3.<br/>Maximum length = 60'-0", see AASHTO Article 8.24 for extension of reinforcement.
+
|4'-6"||5'-0"||13'-0"||24-#9||0.5890
 
|-
 
|-
|3.||Determine the drop panel width:
+
|5'-0"||5'-6"||14'-0"||29-#9||0.7272
 
|-
 
|-
|&nbsp;||Minimum width = Column diameter plus 2~6".<br/>Maximum width = (Parallel to the centerline of roadway) as determined by deign).
+
|5'-6"||6'-0"||15'-0"||35-#9||0.8799
 
|-
 
|-
|&nbsp;||In general, the width of the drop panel normal to centerline bent should be adjusted to 6" increments.
+
|6'-0"||6'-6"||16'-0"||41-#9||1.0472
 
|}
 
|}
  
  
'''SOLID SLABS (BOTTOM)'''
+
Concrete Quantities shown in table are per linear foot of shaft only.  Bell Quantities are not included.
 +
 
 +
(*) Amount of reinforcing may be increased from that shown to meet the individual job requirements.
 +
 
 +
Minimum reinforcement meets AASHTO Spec. 8.18 for reinforcement of compression members.
  
Use AASHTO 3.24.10 Distribution Reinforcement shall be a percentage of positive moment reinforcement (% = 100/√S, with a maximum of 50%).
 
  
  
'''EDGE BEAM'''
+
'''DETAILS'''
  
{|border="0"
+
'''SEISMIC PERFORMANCE CATEGORY B, C & D'''
  
|colspan="3"|Positive Moment:
+
 
|-
+
<center>[[Image:751.40_Intermediate_Bents_-_Pedestal_Pile_Details_(Category_B_C_&_D)_Elevation_&_Section_AA.gif]]</center>
|colspan="3"|The bridge curb is not to be used in determining the resisting moment of the edge beam.
+
 
 +
 
 +
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
 +
 
 +
|Diameter<br/>of Shaft||Minimum<br/>(*) Reinf.||Cubic Yards<br/>Concrete per ft.
 
|-
 
|-
|valign="top"|Dead Load:||colspan="2"|Use the same distribution as for the slab design.<br/>Use for simple spans 0.1 PS.
+
|2'-0"||8-#7||0.1164
 +
|-
 +
|2'-6"||8-#9||0.1818
 +
|-
 +
|3'-0"||11-#9||0.2618
 +
|-
 +
|3'-6"||14-#9||0.3563
 
|-
 
|-
|colspan="3"|Live Load + I: AASHTO Article 3.24.8
+
|4'-0"||19-#9||0.4654
 
|-
 
|-
|&nbsp;||colspan="2"|Use for negative moment on continuous spans 0.1 PS.<br/>Use for positive moment on continuous spans 0.08 PS.
+
|4'-6"||24-#9||0.5890
 
|-
 
|-
|&nbsp;||Where||P = Wheel load in pounds, see this Section.
+
|5'-0"||29-#9||0.7272
 
|-
 
|-
|&nbsp;||&nbsp;||S = Span in feet
+
|5'-6"||35-#9||0.8799
 
|}
 
|}
  
  
<center>[[Image:751.40_Slab_Reinf_-_Edge_Beam_Detail.gif]]</center>
+
Concrete Quantities shown in table are per linear foot of shaft only.
  
=====751.40.8.9.1.6 Shear=====
+
(*) Amount of reinforcing may be increased from that shown to meet the individual job requirements.
  
 +
Minimum reinforcement meets AASHTO Spec. 8.18 for reinforcement of compression members.
  
'''Shear Loads'''
+
(**) Stay in place casing may be used in place of spirals for column diameters greater than 4 foot.
  
The shear in the Hollow Slab should be computed for all loadings H20 and over.
+
=== 751.40.8.10 Prestressed Concrete I-Girders ===
  
  
'''Distribution of Loads'''
+
==== 751.40.8.10.1 Design ====
  
Use the same distribution for the dead and live load as was used for the moment.
+
===== 751.40.8.10.1.1 Girder Design=====
  
 +
'''Geometric Dimensions'''
  
'''Unit Shear Stress'''
+
'''Girder Analysis (Continuous Span Series)'''
  
{|border="0"  
+
Stresses due to dead load weight of slab, girder, diaphragms, haunch and forms will be based on simple spans from centerline to centerline of bearings.
 +
 +
Stresses due to dead load weight of curbs, parapet, rails, future wearing surface and outlets will be based on continuous composite spans with loads equally distributed to all girders.  The span lengths used in these computations will be based on the distance from the centerline of the bearing at the End Bent to the centerline of the Int. Bent, and from centerline of Int. Bent to centerline of Int. Bent.
 +
 +
Stresses due to live load plus impact will be based on continuous composite spans whose lengths are described above for curbs, etc.
 +
 +
The analysis will be made on the basis of transformed areas of all steel (both strands and bars) in the section using concrete with <math>\, n</math> = 6.
 +
 +
In composite design, allowances shall be made for the difference in modulus of elasticity of slab and girder by using the effective slab area as specified for concrete T-Beams as given in the current AASHTO Specifications, multiplied by the factor <math>\, (E_{slab}/E_{girder})</math> .  The area shall include the transformed area of all longitudinal reinforcing bars within the effective width.  The 1" integral wearing surface shall not be used in the effective slab depth.
  
|colspan="4"|Load Factor:
 
|-
 
|&nbsp;||Shear Stress||=||<math>\, Vu = \frac{Vu}{\phi(Bd - voids~area)}</math>
 
|-
 
|colspan="4"|Working Stress:
 
|-
 
|&nbsp;||Shear Stress||=||<math>\, v = \frac{v}{(Bd - Area~of~voids)}</math>
 
|-
 
|colspan="4"|Where "d" = effective depth, <math>\phi</math> = 0.85 for shear
 
|}
 
  
 +
'''Effective Flange Width'''
 +
 +
The effective flange width for Beam Types 2,3,4 & 6 should be calculated using AASHTO 8.10.1.  For Beam Type 7, the effective flange width should be calculated using AASHTO 9.8.3.
 +
 +
 +
'''Continuity at Intermediate Supports'''
 +
 +
Continuity will be obtained at intermediate supports by pouring a concrete diaphragm monolithic with the deck slab and encasing the prestressed girders. Reinforcing bars will tie the slab, diaphragms and girders together.
 +
 +
Reinforcing bars, <math>\, f_y</math> = 60,000 psi, will be placed in the deck slab for tensile
 +
steel.
 +
 +
The ultimate negative moments should be 2.17 times the maximum live load moments including impact and 1.3 times moments for future wearing surface and dead load of barrier or railing.
 +
 +
The area of longitudinal reinforcing steel at the centerline of the intermediate bent should be determined on the basis of a cracked section.  This area of reinforcing bars is to be provided by adding additional bars between the normal longitudinal bars at the top of the slab. #8 maximum bar size for additional bars over bents.
 +
 +
These special negative moment reinforcing bars should be ended by one of the following criteria (whichever is greater):
 +
 +
#Where the stress on the normal longitudinal reinforcing bars does not exceed 24,000 psi. as based on a cracked section, plus 15 bar diameters or development length.
 +
#Not closer to the centerline of the intermediate bent than 1/10 of the span.  (8' min.)
 +
 +
The concrete stress at the bottom of the girder should be checked at a point 70 strand diameters plus 9 inches from the centerline of the intermediate bent to see that the total compressive stress due to prestress and negative moment does not exceed 3,000 psi.  (AASHTO. 9.7.2)
 +
 +
The positive moment at the intermediate bent should be provided for by extending the top two rows of the top strands (both straight or deflected) and if available, the number of bottom strands indicated in tables below bent to form a right angle hook.
 +
 +
 +
'''Design of Negative Moment Reinforcement'''
 +
 +
Since most of the dead load moments are carried by the beam acting as a simple span, the negative design moment over piers is the live load plus impact moment. In most designs, the dead load applied after continuity is achieved should also be considered in the negative design moment. The effect of initial precompression due to prestress in the precast girders may be neglected in the negative moment computation of ultimate strength if the maximum precompression  stress is less than <math>\, 0.4 f'_c</math> and the continuity reinforcement is less than 1.5 percent.
 +
 +
It will usually be found that the depth of the compression block will be less than the thickness of the bottom flange of the precast girder. For this reason, the negative moment reinforcement required can be determined by assuming the beam to be a rectangular section with a width equal to the bottom flange width of the girder. Due to the lateral restraint of the diaphragm concrete, ultimate negative compression failure in the PCA tests always occurred in the girders, even though the diaphragm concrete strength was about 1000 psi less than that of the girder concrete for this reason, it is recommended that the negative moment reinforce-ment  be designed using the compressive strength of the girder concrete.
  
  
<center>[[Image:751.40_Slab_Shear_Stress_Elevation.gif]]</center>
+
<center>[[Image:751.40 prestressed concrete i-girders-rectangular beam curves.gif]]</center>
  
 +
<center>'''Rectangular Beam Curves'''</center>
  
  
'''Allowable Shear Stress'''
 
  
{|border="0"
 
  
|colspan="2"|Load Factor:
+
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 +
|-
 +
!rowspan="2"|Web<br/>Thickness<br/>(Inches)
 +
!colspan="5"|Number of Bottom Strands for Positive Moment<br/>Connection (C) for Closed Diaphragms
 
|-
 
|-
|width="20"|&nbsp;||<math>\, Vc = 2.0\sqrt{f'c}</math>
+
!Beam Type 2<br/>or Modified
 +
!Beam Type 3<br/>or Modified
 +
!Beam Type 4<br/>or Modified
 +
!Beam Type 6<br/>or Modified
 +
!Beam Type 7<br/>or Modified
 
|-
 
|-
|&nbsp;||Where Vc = shear strength provided by concrete
+
|6||6||8||10||--||18
 
|-
 
|-
|&nbsp;
+
|6 1/2||--||--||--||14||--
 
|-
 
|-
|colspan="2"|Working Stress:
+
|7 (A)||8||10||10||--||--
 
|-
 
|-
|&nbsp;||<math>\, Vc = 0.95\sqrt{f'c}</math>
+
|7 1/2 (B)||--||--||--||16||--
 
|-
 
|-
|&nbsp;
+
|8 (A)||8||10||12||--||--
 
|-
 
|-
|&nbsp;||Where Vc = Allowable shear stress carried by concrete
+
|8 1/2 (B)||--||--||--||16||--
 
|}
 
|}
  
  
If shear stress (load) exceeds the allowable shear use one or more of the following solutions.
+
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 +
|-
 +
!rowspan="2"|Web<br/>Thickness<br/>(Inches)
 +
!colspan="5"|Number of Bottom Strands for Positive Moment Connection (C) for<br/>Open Intermediate Diaphragms with Continuous Superstruecture
 +
|-
 +
!Beam Type 2<br/>or Modified
 +
!Beam Type 3<br/>or Modified
 +
!Beam Type 4<br/>or Modified
 +
!Beam Type 6<br/>or Modified
 +
!Beam Type 7<br/>or Modified
 +
|-
 +
|6||12||16||16||--||22
 +
|-
 +
|6 1/2||--||--||--||22||--
 +
|-
 +
|7 (A)||12||16||16||--||--
 +
|-
 +
|7 1/2 (B)||--||--||--||22||--
 +
|-
 +
|8 (A)||12||16||16||--||--
 +
|-
 +
|8 1/2 (B)||--||--||--||22||--
 +
|}
  
# Eliminate some voids and replace remainder.
 
# Shorten alternate voids
 
# Use shear reinforcing in the critical zone.
 
  
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|valign="top"|(A)||align="left" width="400pt" |Modified Beam Type 2, 3 or 4.
 +
|-
 +
|valign="top"|(B)||align="left" width="400pt" |Modified Beam Type 6.
 +
|-
 +
|valign="top"|(C)||align="left" width="400pt" |If available, otherwise bend all bottom strands.
 +
|}
  
<center>[[Image:751.40_Slab_Shear_Stress_Diagram.gif]]</center>
 
  
 +
'''Negative Moment Bar Cut-Off (Working Stress Controlling)'''
  
Note:<br/>Consider a voided slab the same as a regular slab as it pertains to the minimum stirrups (AASHTO - Article 8.19).<br/>i.e. The minimum stirrups are not required if the shear stress is less than allowable.
+
Area of slab bars required and stress in the slab bars are printed in program BR200.
  
=====751.40.8.9.1.7 Camber Deflection=====
+
Determine stress of the area of slab bars input into program at a point where the area required is larger than that input.
  
 +
Interpolate along a straight line to where the stress is 24,000 psi.
  
'''Ultimate Deflection:'''
+
Note: Negative moment bar computations use a cracked section analysis to determine stresses.
  
Compute the "ultimate deflection" at 0.2 points of the spans for the dead loads without the 35# future wearing surface.
+
===== 751.40.8.10.1.2 Allowable Concrete Stresses =====
  
Ultimate deflection (long term) = elastic deflection x 3
+
The following criteria is shown for clarity and is in accordance with AASHTO 9.15.
 +
 +
:<math>\, f'_c</math> = 5,000 psi, &nbsp; <math>\, f'_{ci}</math> = 4,000 psi
  
{|border="0"
 
  
|Ec (Elastic Modulus) =|| <math>\, 4 \times 10^6</math> psi (districts 1 and 4)
+
A. Temporary stresses before losses except as noted:
|-
 
|&nbsp;||<math>\, 6 \times 10^6</math> psi (remainder of districts)
 
|}
 
  
The modulus of elasticity for the use in a continuous structure analysis computer program should be determined as follows:
+
*Compression...<math>\, 0.6 f'_{ci} = 0.6 \times 4,000psi = 2,448psi</math> (*)
  
{|border="0"
+
*Tension
 +
**Precompressed tensile zone ....................
 +
***No temporary allowable stresses are specified. See paragraph "B" below.
 +
***In tension areas with no bonded reinforcement...<math>\, 3 \sqrt{f'_{ci}} = 3 \sqrt{4,000} = 190 psi</math>
 +
***Where the calculated tensile stress exceeds this value, bonded reinforcement shall be provided to resist the total tension force in the concrete computed on the assumption of an uncracked section. The maximum tensile stress shall not exceed...<math>\, 7.5 \sqrt{f'_{ci}} = 7.5 \sqrt{4,000} = 475 psi</math>
  
|<math>\, \Delta_{ULT}</math>||=||<math>\, 3 \times  \Delta_{ELASTIC}</math>
 
|-
 
|<math>\, \Delta_{ELASTIC}</math>||=||<math>\, Coeff./E_c</math>
 
|-
 
|<math>\, \Delta_{ULT}</math>||=||<math>\, (Coeff./E_c \times 3 = Coeff./(E_c / 3)</math>
 
|-
 
|&nbsp;
 
|-
 
|Where:
 
|-
 
|<math>\, \Delta</math>||=||deflection.
 
|-
 
|<math>\, \Delta_{ULT}</math>||=||Ultimate deflection
 
|-
 
|<math>\, \Delta_{ELASTIC}</math>||=||Elastic deflection
 
|}
 
  
 +
B.  Stresses at service loads after losses:
  
'''Example No. 1'''
+
*Compression...<math>\, 0.4 f'_c = 0.4 \times 5,000 = 2,000 psi</math>
  
(Assume bridge is in District 8)
+
*Tension in the precompressed tensile zone...
 +
**(a) For members with bonded reinf. (**)...<math>\, 6 \sqrt {f'_c} = 6 \sqrt{5,000} = 425 psi</math>
 +
**(b) For members without bonded reinf...<math>\, = Zero</math>
  
{|border="0"
+
*Tension in other areas
 +
**Tension in other area is limited by the allowable temporary stresses specified in "A" above.
  
|<math>\, E_c</math>||=|| <math>\, 6 \times 10^6 psi</math>
 
|-
 
|<math>\, \Delta_{ULT}</math>||=||<math>\, Coeff. / (6/3) = Coeff./2</math>
 
|}
 
  
Therefore, use 2 \times 10<sup>6</sup> psi for modulus of elasticity in the structure analysis computer program to get ultimate deflection. (*)
+
C. Cracking stress:
  
 +
*Modulus of rupture from tests or (for normal weight concrete)...<math>\, 7.5 \sqrt{f'_c} = 7.5 \sqrt {5,000} = 530 psi</math>
  
  
'''Example No. 2'''
+
D. Negative moment stresses in girders made continuous after deadload of slab is in place:
  
(Assume bridge is in District 1)
+
*Tension in negative moment reinforcement...<math>\, f_y</math> = 60,000 psi, &nbsp; <math>\, f_s</math> = 24,000 psi
 +
*Compression in concrete at bottom of girder...<math>\, f'_c</math> = 5,000 psi, &nbsp; <math>\, f_c = 0.6 f'_c</math>
  
{|border="0"
+
(*) BR200 allows 2% overstress
  
|<math>\, E_c</math>||=||<math>\, 4 \times 10^6 psi</math>
+
(**)Strands qualify if not debonded at ends.
|-
 
|<math>\, \Delta_{ULT}</math>||=||<math>\, Coeff. / (4/3) = Coeff./1.333</math>
 
|}
 
  
Therefore, use <math>\, 1.333 \times 10^6</math> psi for modulus of elasticity in the structure analysis computer program to get ultimate deflection. (*)
+
===== 751.40.8.10.1.3 Prestress Loss and Prestress Camber =====
  
 +
<math>\, \Bigg[ \cfrac{ \overset{(SH)}{6,000} + \overset{(ES)}{ \frac {Es}{Ec_i}}fc + \overset{(CR_C)}{8.5 fc} + (5,000 - \overset{(CR_s)}{0.1 ES} - 0.05 (SH + CR_c))}{fs_i} \Bigg]</math>
  
  
(*) Gives long term deflection as output.
+
{|
 
+
|rowspan="4" width="375pt"|Reduce to: &nbsp; &nbsp; <math>\, \cfrac {10,700 + (0.9 \left( \frac{E_s}{Ec_i} \right) + 8.08) fc}{fs_i}</math>
=====751.40.8.9.1.8 Slab Construction Joint Details=====
+
|<math>\, SH</math>||width="150pt"|= Shrinkage
 +
|-
 +
|<math>\, ES</math>||width="150pt"|= Elastic Strain
 +
|-
 +
|<math>\, CR_c</math>||width="150pt"|= Concrete Creep
 +
|-
 +
|<math>\, CR_s</math>||width="150pt"|= Steel Creep
 +
|}
  
  
<center>[[Image:751.40_Slab_Const_Jt_Key_(Slab_Depth_17_in_or_more).gif]]</center>
+
{|
 +
|valign="top"| <math>\, CR_c</math>||valign="top"|= <math>\, 12 fc_{ir} - 7 fc_{ds}</math>
 +
|-
 +
|<math>\, CR_c</math>||valign="top"|= <math>\, 12 fc - 7/2 fc = 8.5 fc</math>  &nbsp;(Approximate Estimate)
 +
|-
 +
|<math>\, Ec_i</math>||valign="top"|= <math>\, 150^{1.5} 33 \sqrt{f'c_i}</math>  &nbsp; &nbsp; <math>\, ES = \frac {Es}{Ec_i} fc_{ir} = \frac {Es}{Ec_i} fc</math>  &nbsp;(Approximate Estimate)
 +
|-
 +
|<math>\, fc_{ir}</math> ||valign="top"|= Concrete stress at centroid of P/S steel at point considered due to P/S and dead load at release.
 +
|-
 +
|<math>\, fc</math>||valign="top"|= <math>\, fc_{ir}</math> (Assume <math>\, fc_{ir} = fc</math>)
 +
|-
 +
|<math>\, fc</math>||valign="top"|= <math>\, 0.4(4,000) = 1,600 psi</math> (Estimate average)
 +
|-
 +
|<math>\, fc_{ds}</math> ||valign="top"|= Concrete stress at centroid of P/S Steel (due to dead load)(Assume fcds = 1/2 fc)
 +
|-
 +
|<math>\, fs_i</math> ||valign="top"|= Initial stress in P/S steel
 +
|-
 +
|<math>\, fs_i</math> ||valign="top"|= <math>\, 270,000 psi \times 75% = 202,500 psi</math>
 +
|-
 +
|<math>\, Ec_i</math> ||valign="top"|= <math>\, 150^{1.5} 33 \sqrt{4,000} = 3,834,253.5 psi</math>
 +
|-
 +
|<math>\, Es</math> ||valign="top"|= <math>\, 28,000,000 psi </math> (AASHTO 9.16.2.1)
 +
|-
 +
|<math>\, \frac {Es}{Ec_i}</math> ||= <math>\, 7.30</math>
 +
|}
  
  
<center>'''DETAILS OF SLAB CONSTRUCTION JOINT KEY<br/>(FOR SLAB DEPTHS 17" OR MORE)'''</center>
+
<math>\, \frac {10,700 + (0.9 \times 7.30 + 8.08) 1,600}{202,500} = 16.9%</math>
  
  
 +
<math>\, 202.5ksi \times 16.9% = 34.22ksi</math>
  
<center>[[Image:751.40_Slab_Const_Jt_Key_(Slab_Depth_16.5_in_or_less).gif]]</center>
 
  
 +
Total loss due to all causes, except friction, is 34.22 ksi. (Friction losses are applied to post-tensioned girder only.) Use 8.84% for initial loss and 8.84% for final loss for design.
  
<center>'''DETAILS OF SLAB CONSTRUCTION JOINT KEY<br/>(FOR SLAB DEPTHS 16½" OR LESS)'''</center>
 
  
 +
<math>\, 202.5 ksi \times 8.84% = 17.90 ksi</math> = initial loss
  
 +
<math>\, 202.5 - 17.90 = 184.60ksi</math>
  
<center>[[Image:751.40_Slab_Const_Jt_Void_Spacing.gif]]</center>
+
<math>184.60ksi \times 8.84% = 16.32ksi</math> = final loss
  
 +
<math>17.90 + 16.32 = 34.22ksi \approx 34.22ksi = 202.5ksi \times 16.9%</math> = total loss
  
<center>'''VOID SPACING AT LONGITUDINAL CONSTRUCTION JOINT'''</center>
 
  
 +
In the above design example, if tension exceeds AASHTO Specifications, (425 psi for 5,000 psi concrete) the girder will have to be modified to limit stress to 425 psi.
  
====751.40.8.9.2 End Bents====
 
  
=====751.40.8.9.2.1 Pile Cap Bents=====
+
{|
 
+
|valign="top"| <math>\, f'c</math>||valign="top"|= 6,000 psi
<center>[[Image:751.40_End_Bent_(Pile_Cap_Sections).gif]]</center>
+
|-
 
+
|valign="top"| <math>\, f'c_i</math>||valign="top"|= 4,500 psi
<center>* See Design Layout for maximum slope of spill fill.</center>
+
|-
 
+
|colspan="2" valign="top"|Grade 270 low relaxation strands
{|border="0" align="center" style="text-align:center"
+
|-
 +
|valign="top"|<math>\, fc</math>||valign="top"|= <math>\, 0.4(4,500) = 1,800 psi</math> (Estimated average)
 +
|-
 +
|valign="top"|<math>\, Ec_i</math>||valign="top"|= <math>\, 150^1.5 33 \sqrt{f'c_i} = 4,066.840 psi</math>
 +
|-
 +
|valign="top"|<math>\, \frac{Es}{Ec}</math>||valign="top"|= <math>\, \frac{28,000,000}{4,066,840} = 6.89</math>
 +
|-
 +
|colspan="2" valign="top"|AASHTO 9.16.2.1.3: <math>\, CRc = 12fc - 7/2fc = 8.5fc</math> (approximate estimate)
 +
|}
  
|width="275"|'''SECTION THRU WING'''||width="175" align="right"|'''SECTION A-A'''
 
  
|}
+
<math>\, \Bigg[ \overset{(SH)}{6,000} + \overset{(ES)}{ \frac {Es}{Ec_i}}fc + \overset{CR_c)}{8.5 fc} + (5,000 - \overset{(CR_s)}{0.1ES} - 0.05(SH + CR_c)) \Bigg]</math>
  
  
<center>[[Image:751.40_End_Bent_(Pile_Cap_Elevation).gif]]</center>
+
Reduce to: &nbsp; <math>\, \cfrac{10,700 + (0.9 (\frac{Es}{Ec_i}) + 8.08) fc}{fs_i}</math>
  
  
<center>'''ELEVATION'''</center>
+
{|
 +
|valign="top"| <math>\, fc</math>||valign="top"|= <math>\, 0.4(4,500) = 1,800 psi</math> (estimated average)
 +
|-
 +
|<math>\, \frac{Es}{Ec_i}</math> ||= <math>\, 6.89</math>
 +
|}
  
 +
<math>\, fs_i</math> = Initial stress in low relaxation strands stressed to 75% of ultimate (*)
  
 +
<math>\, fs_i</math> = 270,000 psi \times 75% = 202,500 psi
  
<center>[[Image:751.40_End_Bent_(Pile_Cap_Plan_(SQ)).gif]]</center>
 
  
 +
<math>\, \frac {10,700 + (0.9 \times 6.89 + 8.08) \times 1,800}{202,500} = 18.0%</math>
  
<center>'''PLAN (SQUARE)'''</center>
 
  
 +
<math>\, 202.50 ksi \times 18.0% = 36.45 ksi</math> = total loss except friction
  
{|border="0" align="center"
+
Use 9.44% for initial loss and 9.44% for final loss.
 +
 +
<math>\, 202.50 ksi \times 9.44% = 19.12 ksi</math> = initial loss
  
|width="300"|(1) Wing brace details.||[[Image:751.40_End_Bent_(Pile_Cap_Detail_B).gif]]
+
<math>\, 202.5 - 19.12 = 183.38 ksi</math>
|}
 
  
 +
<math>\, 183.38 ksi \times 9.44% = 17.31 ksi</math> = final loss
  
<center>[[Image:751.40_End_Bent_(Pile_Cap_Plan_(Skewed)).gif]]</center>
+
<math>\, 19.12 + 17.31 = 36.43 ksi \approx 36.45 ksi = 202.5 ksi \times 18.0%</math> = total loss
 +
  
 +
P/s force initial = <math>\, (183.38 ksi)(0.153 in.^2/strands)(no.\ of\ strands)</math>
  
<center>'''PLAN (SKEWED)'''</center>
+
P/s force final = <math>\, ((202.5 - 36.43) ksi)(0.153 in.^2/strand)(no.\ of\ strands)</math>
  
<center>(*) Use the same Dimension (centerline Curb Joint) as the opposite side when the wings are the same length.</center>
 
  
=====751.40.8.9.2.2 Integral Column Bents=====
+
(*) Suggested by FHWA: when using 3/8" round strands, max. <math>\, fs_i = 0.7 \times 250 ksi\ or\ 0.7 \times ultimate\ stress</math>, whichever is smaller. Larger initial stresses will cause debonding.
'''SEISMIC PERFORMANCE CATEGORY A<BR/>(PINNED COLUMN AT TOP AND BOTTOM)'''
 
  
  
<center>[[Image:751.40_End_Bent_(Integral_Column_Part_Section).gif]]</center>
+
'''Prestress Concrete Girder Formula for Stress Calculation'''
  
<center>'''PART SECTION'''</center>
+
(-) Tension; &nbsp; (+) Compression
  
  
{|border="0" style="text-align:center" align="center"
+
'''Temp. Stress'''
  
|rowspan="3"|[[Image:751.40_End_Bent_(Integral_Column_Pinned_Column).gif]]||[[Image:751.40_End_Bent_(Integral_Column_Section_AA).gif]]
+
{|
 +
|width="75pt"|Allow Top||width="250pt"|<math>\, 7.5 \sqrt{f'c_i} = 0.474ksi</math> tension for||width="200pt"|<math>\, f'c_i = 4,000psi</math>
 
|-
 
|-
|'''SECTION A-A'''<!--column 1 occupied by cell [[Image:751.40_End_Bent_(Integral_Column_Pinned_Column).gif]]-->
+
|width="75pt"|Bottom||width="250pt"|<math>\, 0.6 f'c_i = 2.4 ksi</math> compression for||width="200pt"|<math>\, f'c_i = 4,000psi</math>
|-
+
|}
|[[Image:751.40_End_Bent_(Integral_Column_Section_BB).gif]]<!--column 1 occupied by cell [[Image:751.40_End_Bent_(Integral_Column_Pinned_Column).gif]]-->
 
|-
 
|'''PINNED COLUMN'''||'''SECTION B-B'''
 
|}
 
  
 +
:Temp. Top =
 +
::<math>\, \frac{(1.0 - initial\ loss)(P/S\ F)}{Ag} - \frac{(1.0 - initial\ loss)(P/S\ F)(ECC_{nc}}{St_{nc}} + \frac{M_{Gdr}}{St_{nc}}</math>
  
Note:  If the columns at an end bent have excessive moments due to shortness of the Column or length of the span, they should be detailed as "pinned" and designed for vertical reactions only.
 
  
 +
:Temp. Bottom =
 +
::<math>\, \frac{(1.0 - initial\ loss)(P/S\ F)}{Ag} - \frac{(1.0 - initial\ loss)(P/S\ F)(ECC_{nc}}{Sb_{nc}} + \frac{M_{Gdr}}{Sb_{nc}}</math>
  
'''SEISMIC PERFORMANCE CATEGORIES B, C & D<BR/>(PINNED COLUMN AT TOP, FIXED COLUMN AT BOTTOM)'''
 
  
For pinned column conditions at the top, see the above details.<br/>For fixed column conditions at the bottom and column reinforcement details.
+
'''Design Load Stress'''
  
Note:  For details not shown, see integral pile cap details.
+
{|
 +
|width="75pt"|Allow Top||width="250pt"|<math>\, 0.4\ f'c = 2.0 ksi</math> compression for||width="200pt"|<math>\, f'c = 5,000psi</math>
 +
|-
 +
|width="75pt"|Bottom||width="250pt"|<math>\, 6.0 \sqrt{f'c} = 0.424 ksi</math> tension for||width="200pt"|<math>\, f'c = 5,000psi</math>
 +
|}
  
=====751.40.8.9.2.3 Reinforcement - Pile Cap Bents=====
+
:Top final =
 +
::<math>\, Temp.\ Top\ Stress - \frac{(Final\ loss)(P/S\ F)}{A_c} + \frac{(Final\ loss)(P/S\ F)(ECC_c)}{St_c} + \frac{M_{Slb+Dph}}{St_{nc}} + \frac{M_{DLC}}{St_c}{st_c} + \frac{M_{LL+I}}{St_c}</math>
  
  
<center>[[Image:751.40_Reinforcement_-_Pile_Cap_Section_1_(Slab_Depth_less_than_16_in).gif]]</center>
+
:Bottom final =
 +
::<math>\, Temp.\ Bott.\ Stress - \frac{(Final\ loss)(P/S\ F)}{A_c} - \frac{(Final\ loss)(P/S\ F)(ECC_c)}{Sb_c} - \frac{M_{Slb+Dph}}{Sb_{nc}} - \frac{M_{DLC}}{Sb_c} - \frac{M_{LL+I}}{Sb_c}</math>
  
::::::::::'''SECTION THRU END BENT<BR/>(Slab depth less than 16")'''
 
  
 +
::0.153 sq. in. = Area of one 1/2 inch strand
 +
::270 ksi = f's = Ult, Str. P/S Strand
 +
::202.5 ksi = 0.75 (270) = Initial steel stress
  
<center>[[Image:751.40_Reinforcement_-_Pile_Cap_Section_2_(Slab_Depth_16_in_or_more).gif]]</center>
 
  
::::::::::'''SECTION THRU END BENT<BR/>(Slab depth 16" or more)'''
+
:0.0884 = 8.84% Initial loss - low relaxation
 +
:0.0884 = 8.84% Final loss - low relaxation
 +
:4 Str. 2 Draped
 +
:202.5 (0.153) = 30.98 kips/Str. P/s force
 +
:6 Strands (30.98) = 185.90 P/s force
  
  
(**) Development length for top bar minimum.
+
{|
 
+
|<math>\, A_c</math>||= Area Composite
=====751.40.8.9.2.4 Reinforcement - Wing=====
+
|-
 
+
|<math>\, A_g</math>||= Area Girder
 
+
|-
<center>[[Image:751.40_Reinforcement_-_Wing_(Elevation_&_Part_Section).gif]]</center>
+
|<math>\, Ecc_c</math>||= Eccentricity of prestress force of composite section
 
 
{|border="0" style="text-align:center" align="right"
 
 
 
|width="225"|'''ELEVATION OF WING'''||width="375"|'''PART SECTION THRU WING'''
 
 
|-
 
|-
|align="left" colspan="2"|(*) Clip K bars as required to maintain<br/>minimum clearance at bottom of wing.
+
|<math>\, Ecc_{nc}</math>||= Eccentricity of prestress force of non-composite section
|}
+
|-
 
+
|<math>\, M_{DFLC}</math>||= Composite dead load moment
 
+
|-
&nbsp;
+
|<math>\, M_{Gdr}</math>||= Girder dead load moment
&nbsp;
+
|-
 
+
|<math>\, M_{LL+I}</math>||= Live load + impact moment
 
+
|-
<center>[[Image:751.40_Reinforcement_-_Wing_(Section_AA_&_Part_Section_Thru_End).gif]]</center>
+
|<math>\, M_{Slb+Dph}</math>||= Slab + diaphragm moment
 
+
|-
{|border="0" style="text-align:center" align="right"
+
|<math>\, P/S\ F</math>||= Prestress forces in girder
 
+
|-
|width="225"|'''SECTION A-A'''<BR/>(K-bars not shown for clarity)||width="375"|'''PART SECTION THRU<BR/>END OF WING'''
+
|<math>\, Sb_c</math>||= Composite section modulus at bottom of girder
|}
 
 
 
&nbsp;
 
 
 
&nbsp;
 
 
 
Note: See _____ for barrier curb details and spacing of K-bars.
 
 
 
=====751.40.8.9.2.5 Design Assumptions for Integral Piles=====
 
 
 
 
 
'''Seismic Performance Category A'''
 
 
 
Piles may be considered as "pinned" (for superstructure) at the pile cap and designed for vertical loads only unless they fall under the following general conditions in which case they should be checked for the loadings as specified for columns.
 
 
 
{|border="0"
 
 
 
|1.||Height from centerline of slab to "pin" is less than 15'.
 
 
|-
 
|-
|&nbsp;||The location of the pinned joint is arbitratily taken as about 1/3 of the length of long piles or at a point about 10' below the natural ground line.
+
|<math>\, Sb_{nc}</math>||= Non-composite section modulus at bottom of girder
 
|-
 
|-
|2.||Piles having a large gross moment of inertia (cast-in-place concrete) gross I of steel BP = I x n.
+
|<math>\, St_c</math>||= Composite section modulus at top of girder
 
|-
 
|-
|3.||The number of piles used on a fairly long structure is small.
+
|<math>\, St_{nc}</math>||= Non-composite section modulus at top of girder
 
|}
 
|}
  
  
 +
'''Prestress Camber'''
  
'''Seismic Performance Categories B, C & D'''
+
Reference: Computer Program BR139B
  
Piles shall be checked for combined axial and bending stresses for seismic loading conditions. For AASHTO group loads I thru VI as applicable, follow criteria noted above for seismic performance category A.
+
<center>[[Image:751.40 prestressed concrete i-girders-camber diagram.gif]]</center>
  
  
 +
<math>\,
 +
\begin{Bmatrix}
 +
I4 = 107,888 in.^4\\
 +
(non-transformed)\\
 +
Beam\ wt. = 0.541\ (k/ft.)
 +
\end{Bmatrix}
 +
</math> &nbsp; Used to resist uplift before beam is set on bent.
  
====751.40.8.9.3 Intermediate Bents====
 
=====751.40.8.9.3.1 Integral Bents=====
 
  
 +
<math>\,
 +
\begin{Bmatrix}
 +
I4 = 114,383 in.^4\\
 +
(transformed)\\
 +
Slab\ wt. = 0.92\ (k/ft.)\\
 +
Diaphragm\ wt. = 2.65\ (K)
 +
\end{Bmatrix}
 +
</math> &nbsp; Used after beam is in place.
  
<center>[[Image:751.40_Intermediate_Bents_(Integral_Bents_Half_Section).gif]]</center>
 
  
 +
{|
 +
|align="right"|Mult. factor|| &nbsp; <math>\, [1 + (1 - e^{-\phi})] = 1.77</math>
 +
| rowspan="6" align="center" |
 +
{| border="1" cellspacing="0" style="text-align:center"
 +
|rowspan="2"| &nbsp;||colspan="2"|Mult. Factor <math>\, (F)</math>
 +
|-
 +
|<math>\, f'c</math> = 5,000psi||<math>\, f'c</math> = 6,000psi
 +
|-
 +
|Beam Type 3||1.780||1.773
 +
|-
 +
|Beam Type 4||1.772||1.765
 +
|-
 +
|Beam Type 4||1.775||1.768
 +
|-
 +
|Beam Type 6||1.761||1.754
 +
|}
 +
|-
 +
|align="right"|<math>\, F</math>||= 1.77
 +
|-
 +
|align="right"|<math>\, e</math>||=2.718
 +
|-
 +
|align="right"|<math>\, \phi</math>||= \varepsilon\ creep \times E_{28\ days}
 +
|-
 +
|align="right" valign="top"|<math>\, \varepsilon\ creep</math>||width="300pt"|= (See page 3 PCA design of precast prestressed concrete girders. Use 40% factor based on creep at erection for 28 days.)
 +
|}
  
<center>'''HALF SECTION'''</center>
 
  
 +
The following formulas are used to determine:
 +
*Camber due initial strand stress (inch),
 +
*deflection due beam weight (inch),
 +
*camber due strands, beam weight and 28 day creep (inch),
 +
*camber L/4 due strands, beam weight and 28 day creep (inch),
 +
*deflection due to slab weight (inch),
 +
*camber centerline due strands, beam weight, 28 day creep, slab and diaphragm (inch), and
 +
*camber quarterpoint due strands, beam weight, 28 day creep, slab and diaphragm (inch).
  
(*) 25'-0" is the max. column spacing allowed.  However, the footing pressure may be the controlling factor for the column spacing.  It is suggested that a rough check be made of the footing pressure before the spacing is definitely established.
 
  
In congested areas, when it is desired to keep the number of columns to a min., larger column spacings may be desirable.  (consult the Structural Project Manager).
+
Formulas used:
  
In general, use two 2'-6" columns for Roadways thru 44'-0" and additional 2'-6" columns for wider Roadways.
+
Positive deflect up <math>\, \uparrow</math>
  
 +
Negative deflect down <math>\, \downarrow</math>
  
'''SEISMIC PERFORMANCE CATEGORY A'''
 
  
 +
<math>\, \uparrow \triangle_1 = 144 \times 10^3 \times \underset {(a = \big[ L - (centerline\ to\ centerline\ tie\ downs) \big] \div 2)ft.}{ \Bigg[ \frac{F_{01}(e_1)(L_2}{8E_i I} + \frac{F_{02}(e_2 + e_3}{E_i I} \Bigg( \frac{L_2}{8} - \frac{a^2}{6} \Bigg) - \frac{F_{02}(e_3(L^2)}{8E_i I} \Bigg]} </math>
  
<center>[[Image:751.40_Intermediate_Bents_(Integral_Bents_Category_A_Half_Section).gif]]</center>
 
  
 +
Beam weight camber
  
<center>'''HALF SECTION'''</center>
+
<math>\, \downarrow \triangle_2 = \frac{5W_B(L^4)}{384E_iI} (1728 \times 10^3)</math>
  
  
<center>[[Image:751.40_Intermediate_Bents_(Integral_Bents_Category_A_Part_Section_AA).gif]]</center>
+
Slab weight camber
  
 +
<math>\, \downarrow \triangle_s = \Bigg[ \frac{5W_s(L^4)}{384E_fI_{TR}} + \frac{P(L^3)}{48E_fI_{TR}} + \frac{2PsX(3L^2 - 4X^2)}{48E_fI_{TR}} \Bigg] (1728 \times 10^3)</math>
  
<center>'''PART SECTION A-A'''</center>
 
  
=====751.40.8.9.3.2 Integral Column Bent with Drop Panel=====
+
Force straight strands (1/2" low relaxation strands)
 +
 
 +
:<math>\, F_{01} = (no.\ of\ straight\ strands) \times \big[ 31.0 - (17.1 \times 0.153) \big] kips</math>
  
  
{|border="0" align="center"
+
Force draped strands ( 1/2 " low relaxation strands)
  
|[[Image:751.40_Intermediate_Bents_-_Integral_Column_Bents_with_Drop_Panel_(Part_Section).gif]]||valign="top"|'''<u>ATTENTION DETAILER:</u>'''<br/>When detailing Int. Bents on SPS the Section thru drop panel shall be drawn to appropriate grade.
+
:<math>\, F_{02} = (no.\ of\ draped\ strands) \times \big[ 31.0 - (17.1 \times 0.153) \big]  
|-
+
kips</math>
|align="center"|'''PART SECTION'''
 
|}
 
  
  
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Column_Bents_with_Drop_Panel_(Part_Sections_AA).gif]]</center>
+
:<math>\, 270 ksi \times 75% \times (0.153 sq.\ in.) = 31\ kips\ per\ strand</math>
 +
:<math>202.5 \times (1-0.0884) = 184.6 ksi</math>
 +
:<math>184.6 \times (1-0.0884) = 168.28 ksi</math>
 +
:<math>202.5 - 168.28 = 34.22 ksi = Total\ loss</math>
  
 +
:<math>Average\ loss = Totalloss/2 = 34.22/2 = 17.1 ksi</math>
  
{|border="0" align="center" style="text-align:center"
 
  
|valign="top" width="300"|'''PART SECTION A-A<BR/>(FLAT)'''||width="300"|'''PART SECTION A-A<BR/>(GRADE OR V.C.)'''<BR/>D = Diameter of Column
+
{|
 +
|<math>e_1</math>||= dist. centroid beam to centroid straight strand (in.)
 +
|-
 +
|<math>e_2</math>||= dist. centroid beam to low centroid draped at center of beam (in.)
 +
|-
 +
|<math>e_3</math>||= dist. centroid beam to up centroid draped at end of beam (in.)
 +
|-
 +
|<math>L</math>||= length (ft.) (cneterline bearing to centerline bearing).
 +
|-
 +
|<math>I</math>||= moment of inertia (in.<sup>2</sup>) non-transformed.
 +
|-
 +
|<math>I_{TR}</math>||= moment of inertia (in.<sup>2</sup>) transformed.
 +
|-
 +
|<math>Ps</math>||= concentrated loads due to variable slab thickness on each end.
 +
|-
 +
|<math>X</math>||= dist. from centerline brg. to Ps.
 +
|-
 +
|<math>P</math>||= concentrated load due to diaphragm at center of span (kips)
 +
|-
 +
|<math>W_B</math>||= uniform beam load (kips/ft.)
 +
|-
 +
|<math>W_S</math>||= uniform slab load (kips/ft.)
 +
|-
 +
|<math>F</math>||= factor for 28 day creep
 +
|-
 +
|<math>E_i</math>||= modulus of elasticity corresponding to initial girder concrete strength
 +
|-
 +
|<math>E_f</math>||= modulus of elasticity corresponding to final girder concrete strength
 
|}
 
|}
  
  
 +
<math>\, \triangle Centerline = F( \triangle_1 - \triangle_2) - \triangle_s</math>
 +
::<math>\, \triangle\ at\ 0.10 = 0.314 ( \triangle\ at\  Centerline) </math>
 +
::<math>\, \triangle\ at\ 0.20 = 0.593 ( \triangle\ at\  Centerline) </math>
 +
::<math>\, \triangle\ at\ 0.25 = 0.7125 ( \triangle\ at\  Centerline) </math>
 +
::<math>\, \triangle\ at\ 0.30 = 0.813 ( \triangle\ at\  Centerline) </math>
 +
::<math>\, \triangle\ at\ 0.40 = 0.952 ( \triangle\ at\  Centerline) </math>
  
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Column_Bents_with_Drop_Panel_(Part_Plans_Square_&_Skewed).gif]]</center>
 
  
 +
Note: Compute and show on plans camber at  1/4  points for bridges with spans less than 75', 1/10 points for spans 75' and over.
  
{|border="0" align="center" style="text-align:center"
+
===== 751.40.8.10.1.4 Superstructure Design =====
  
|width="175"|'''PART PLAN - SQUARE'''||width="350"|'''PART PLAN - SKEWED'''
+
'''Live Load Distribution'''
|}
+
 
 +
The live load distribution to girders may be assumed to be the same as the
 +
AASHTO distribution for concrete floors on steel I-Beam stringers. These
 +
factors may be found in [[751.40 Widening and Repair #751.40.8.2 Distribution of Loads|EPG 751.40.8.2 Distribution of Loads]].
  
  
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Column_Bents_with_Drop_Panel_(Section_Thru_Drop_Panel).gif]]</center>
+
'''Ultimate Load Capacity'''
  
 +
The ultimate load capacity shall be not less than 1.3 times (the weight of
 +
the girder plus the weight of the slab and diaphragms plus the weight of the
 +
future wearing surface) plus 2.17 times the design live load plus impact.
  
<center>'''SECTION THRU DROP PANEL'''</center>
 
  
 +
'''Ultimate Strength'''
  
{|border="0" align="center"
+
The ultimate moment on a prestressed girder as determined in accordance
 +
with the ultimate load capacity indicated above, shall not be greater than
 +
the ultimate strength determined as follows:
  
|
 
{|border="1" cellspacing="0" cellpadding="3" align="center" style="text-align:center"
 
  
|Largest<br/>Longitudinal<br/>Slab Bar||"a"
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|-
|#8||1-13/16"
+
|Where &nbsp; <math>\, t \le 0.2d</math>|| &nbsp;|| Where &nbsp; <math>\, t > 0.2d</math>
 
|-
 
|-
|#9, #10 & #11||2-1/16"
+
|[[Image:751.40 prestressed concrete i-girders-ultimate strength diagram-1.gif]]|| &nbsp;
 +
|[[Image:751.40 prestressed concrete i-girders-ultimate strength diagram-2.gif]]
 
|-
 
|-
|#14||2-9/16"
+
|<math>\, M_u = A_sf'_s (d -t/2)</math><br/>or<br/><math>\, M_u = 0.85 f'_c bt (d-t/2)</math>
 +
|Use the lesser<br/>in each case
 +
|<math>\, M_u = A_sf'_s (0.9d)</math><br/>or<br/><math>\, M_u = 0.85 f'_c b(0.2d)(0.9d)</math>
 
|}
 
|}
|[[Image:Symbol.gif]]||For Reference Only
 
|-
 
|&nbsp;
 
|-
 
|
 
{|border="1" cellspacing="0" cellpadding="5" align="center" style="text-align:center"
 
  
|Largest<br/>Longitudinal<br/>Slab Bar||"a" (*)
+
 
 +
Where:
 +
{|
 +
|<math>\, A_s</math>||= Area of p/s strands in bottom flange
 
|-
 
|-
|#8 & #9||2-5/8"
+
|<math>\, b</math>, <math>\, b'</math>, <math>\, t</math> & <math>\, d</math>||= as shown above
 
|-
 
|-
|#10 & #11||2-7/8"
+
|<math>\, f'_s</math>||= Ultimate strength of p/s strands
 
|-
 
|-
|#14||3-3/8"
+
|<math>\, f'_c</math>||= Ultimate strength of slab concrete = 4,000 psi
|}
 
 
|}
 
|}
  
  
(*) Based on 3" clearance and #6 stirrups, (includes Integral W.S.) to top longitudinal bar.
+
'''Maximum Prestressing Steel Area'''
  
(1) Standard 90° Hook.
+
:<math>\, A_s = \frac{0.85 f'_c b t}{f'_s}</math> &nbsp; When &nbsp; <math>\, t \le 0.2d</math>
  
(2) Const. joint key D/3 x D/3 x 2", D = Diameter of Column
 
  
=====751.40.8.9.3.3 Integral Pile Cap Bents with Drop Panel=====
+
:<math>\, a_s = \frac{0.85 f._c b (0.2d)}{f'_s}</math> &nbsp; When &nbsp; <math>\, t > 0.2d</math>
  
  
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_with_Drop_Panel_(Part_Section_&_Flat).gif]]</center>
+
In lieu of the above, AASHTO - Article 9.17 & 9.18 may be used. (This is the method used by computer program BR200)
  
{|border="0" align="center" style="text-align:center"
+
===== 751.40.8.10.1.5 Web Reinforcement =====
  
|width="350"|'''PART SECTION'''||width="250"|'''PART SECTION A-A<BR/>(FLAT)'''
+
(5" Min. - 21" Max. bar spacing for #4 bars)
|}
+
(5" Min. - 24" Max. bar spacing for #5 bars)
  
  
{|border="0" align="center"
+
<center>[[Image:751.40 prestressed concrete i-girders-web reinforcement diagram.gif]]</center>
  
|valign="bottom"|Bottom or drop panel to be parallel to top of slab both transversely and longitudinally.||rowspan="5"|[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_with_Drop_Panel_(Part_Section_Grade_or_VC).gif]]
 
|-
 
|(1)Horizontal except for superelevated structures.
 
|-
 
|valign="top"|(2) Use 3" Min. clip on beam for skews above 35°.
 
|-
 
|&nbsp;
 
|-
 
|&nbsp;
 
|-
 
|&nbsp;||align="center"|'''PART SECTION A-A<BR/>(GRADE OR V.C.)
 
|}
 
  
 +
(*) Prestressed concrete members shall be reinforced for diagonal tension stresses. Shear reinforcement shall be placed perpendicular to the axis of the member. The formula to be used to compute areas of web reinforcement is as follows:
  
 +
:<math>\, A_V = \frac{(V_U - V_C)S}{2f_{sy}jd}</math> &nbsp; Where &nbsp; <math>\, V_C = (0.06f'c)b'jd</math> &nbsp; but not more than <math>\, 180 b'jd</math>
  
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_with_Drop_Panel_(Part_Plans_Square_&_Skewed).gif]]</center>
+
:But shall not be less than  &nbsp; <math>\, A_V = \frac{100b's}{60,000} = 0.00167 b's</math>.
  
{|border="0" align="center" style="text-align:center"
 
  
|width="250"|'''PART PLAN - SQUARE'''||width="250"|'''PART PLAN - SKEWED'''
 
|}
 
  
 +
(**) Since large moments and large shears occur in the same area of the girder near the interior supports, the AASHTO formula (AASHTO - 9.20 -Shear) for computing the area of web reinforcement has been modified. The formula to be used to compute areas of web reinforcement near interior supports is as follows:
  
 +
:<math>\, A_V = \frac{(V_U - V_C)S}{f_{sy}jd}; V_C = 180b'jd</math>
  
'''REINFORCEMENT'''
+
The value "jd" is the distance from the slab reinforcement to the center-of-gravity of the compression area under ultimate loads.
  
 +
Use #4 shear reinforcement when possible. Alternate B1 bar will not work with #5.
  
  
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_with_Drop_Panel_-_Reinforcement_(Half_Section).gif]]</center>
+
'''Anchorage Zone Reinforcement - AASHTO Article 9.21.3'''
  
 +
The following detail meets the criteria for anchorage zone reinforcement for pretensioned girders (AASHTO Article 9.21.3) for all MoDOT standard girder shapes.
  
<center>'''HALF SECTION'''</center>
 
  
 +
{|border="0" cellpadding="5" align="center" style="text-align:center" cellspacing="0"
 +
|+'''Standard P/S Girder End Section'''
 +
|[[Image:751.40 prestressed concrete i-girders-standard girder end-end section.gif]]
 +
|[[Image:751.40 prestressed concrete i-girders-standard girder end-end elevation.gif]]
 +
|}
 +
{|border="0" cellpadding="5" align="center" style="text-align:center" cellspacing="0"
 +
|-
 +
|align="right" valign="top"|*
 +
|width="200" align="left"|2 3/4" (Type 2, 3 & 4)<br/>5 1/4" (Type 6)
 +
|-
 +
|align="right" valign="top"|**
 +
|width="200" align="left"|15 1/2" (Type 2, 3 & 4)<br/>22 1/2" (Type 6)
 +
|}
  
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_with_Drop_Panel_-_Reinforcement_(Section_Thru_Drop_Panel).gif]]</center>
 
  
 +
'''Sole Plate Anchor Studs'''
  
<center>'''SECTION THRU DROP PANEL'''</center>
+
The standard 1/2" sole plate will be anchored with four 1/2" x 4" studs.
  
 +
Studs shall be designed to meet the criteria of AASHTO Div. I-A in Seismic Performance Category C or D.
  
(1) Use 5 1/4" for computing length of stirrup bar.  Do not detail on plans.
+
Stud capacity is determined as follows:
  
(2) Standard 90° hook.
+
<math>\, Stud\ Cap. = (n)(As)(0.4Fy)(1.5)</math>
  
(3) Optional Const. Joint Key 10" x 2"
+
Where:
 +
{|
 +
|<math>\, n</math>||= no. of studs
 +
|-
 +
|<math>\, As</math>||= area of stud
 +
|-
 +
|<math>\, Fy</math>||= yield strength of stud (50 ksi)
 +
|-
 +
|<math>\, 0.4Fy</math>||= Allowable Shear in Pins AASHTO Table 10.32.1A
 +
|-
 +
|<math>\, 1.5</math>||= seismic overload factor
 +
|}
  
=====751.40.8.9.3.4 Integral Pile Cap Bents without Drop Panel=====
+
If required, increase the number of 1/2" studs to six and space between open B2 bars. If this is still not adequate, 5/8" studs may be used. The following table may be used as a guide to upper limits of dead load reactions:
  
 +
{|align="center"
 +
|width="300pt"|The minimum 3/16" fillet weld between the<br/>1/2" bearing plate and 1 1/2" sole plate is<br/>adequate for all cases.
 +
| align="center" |
 +
{| border="1" cellspacing="0" style="text-align:center"
 +
|+Seismic Bearing Plate Anchor Design
 +
|rowspan="2" width="50pt"|No. of<br/>Studs||width="50pt"  rowspan="2"|Stud<br/>Dia.||colspan="2"|Max. Allowable D.L. Reaction (Kips)
 +
|-
 +
|A = 0.30||A = 0.36
 +
|-
 +
|4||1/2"||78||65
 +
|-
 +
|6||1/2"||117||98
 +
|-
 +
|4||5/8"||122||102
 +
|-
 +
|6||5/8"||184||153
 +
|}
 +
|}
  
'''REINFORCEMENT'''
+
===== 751.40.8.10.1.6 Strands – Miscellaneous =====
  
 +
'''Detensioning'''
  
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_without_Drop_Panel_-_Reinforcement_(Half_Section).gif]]</center>
+
In all detensioning operations the prestressing forces must be kept symmetrical about the vertical axis of the member and must be applied in such a manner as to prevent any sudden or shock loading.
  
  
<center>'''HALF SECTION'''</center>
+
'''General Information'''  
  
 +
'''Splicing:'''
  
<center>[[Image:751.40_Intermediate_Bents_-_Integral_Pile_Cap_Bents_without_Drop_Panel_-_Reinforcement_(Section_Thru_Bent).gif]]</center>
+
One approved splice per pretensioning strand will be permitted provided the splices are so positioned that none occur within a member. Strands which are being spliced shall have the same "Twist" or "Lay". Allowance shall be made for slippage of the splice in computing strand elongation.
  
 +
'''Wire failure:'''
  
<center>'''SECTION THRU BENT'''</center>
+
Failure of one wire in a seven wire pretensioning strand may be accepted, provided that, it is not more than two percent of the total area of the strands.
  
 +
'''Sand Blasting:'''
  
(1) Use 5 1/4" for computing length of stirrup bar. Do not detail on plans.
+
On structures where it is questionable as to the clarity of areas to be sandblasted: show limits of sandblasted area in a plan view of details on girder ends (bent sheet). However, generally, sandblasting is covered by Missouri Standard Specification 705.4.14.
  
(2) Horizontal except for superelevated structures.
+
==== 751.40.8.10.2 Length ====
  
(3) Standard 90° hook.
 
  
=====751.40.8.9.3.5 Pile Footing Design and Details=====
+
===== 751.40.8.10.2.1 Structure Length =====
  
'''(1) GENERAL'''
+
<center>[[Image:751.40 prestressed concrete i-girders-structure length-integral end bents.gif]]</center>
  
Number, size and spacing of piling shall be determined by computing the pile loads and applying the proper allowable overstresses.
+
<center>(*) Maximum length for End Bent to End Bent = 600 feet.</center>
 
Cases of Loading (AASHTO Article 3.22)
 
 
Group I maximum vertical loads.
 
 
Group IV temperature and shrinkage moments with applicable vertical loads.
 
 
1983 AASHTO guide specifications for seismic design of highway bridges. (See chapter 4 for earthquake loads combined with applicable vertical loads.) (*) (See Structural Project Manager or Liaison)
 
 
Internal stresses including the position of the shear line shall then be computed.
 
 
Long narrow footings are not desirable and care should be taken to avoid the use of an extremely long footing 6~0" wide when a shorter footing 8'-3" or 9'-0" wide could be used.
 
 
When using the load factor design method for footings, design the number of piles needed based on the working stress design method.
 
 
  
 +
<center>'''Typical Continuous Prestressed Structure'''<br/>'''(Integral End Bents)'''</center>
  
'''ASSUMPTIONS'''
 
(Bents with 2 or more columns)
 
  
  
'''SEISMIC PERFORMANCE CATEGORY A'''
+
<center>[[Image:751.40 prestressed concrete i-girders-structure length-non integral end bents.gif]]</center>
  
#Dead and live load moments will be 25% of the moments used for slab and top of Column design.
+
<center>(**) Maximum length for End Bent to End Bent = 800 feet.</center>
#Temperature moments shall be 50% of the moment at top of Column.
 
#Column reinforcement to be same as that required at top of Column. Footing dowel's to be #5 bars, same number as column bars.
 
#Footings to be proportioned for conditions as specified. Do not use ratio of bent height as specified for Intermediate Bents for longitudinal footings dimensions.
 
  
 +
<center>'''Typical Continuous Prestressed Structure'''<br/>'''(Non-Integral End Bents)'''</center>
  
'''SEISMIC PERFORMANCE CATEGORIES B, C & D'''
+
==== 751.40.8.10.3 Miscellaneous Details ====
 
 
#For Seismic Performance categories B, C & D, the connection between the bottom of Column and the footing is a fixed connection.
 
#Footing design is based on (Seismic Design of Beam-Column Joint).
 
  
(*) The design of all bridges in seismic performance B, C & D are to be designed by earthquake criteria in accordance with this bridge manual.
 
  
 +
===== 751.40.8.10.3.1 Shear Blocks =====
  
'''(2) PILE LOADS'''
+
A minimum of two Shear Blocks 12" wide x [[Image:751.40 circled 1.gif]] high by width of diaphragm, will be detailed at effective locations on open diaphragm bent caps when adequate structural restraint cannot be provided for with anchor bolts.
:P = N/n ± M/S
 
:P = Pile Loads
 
:N = Vertical Loads
 
:n = number of piles
 
:M = overturning moment
 
:if minimum eccentricity controls the moment in both directions, it is necessary to use the moment in one direction (direction with less section modulus of Pile group) only for the footing check.
 
:S = Section Modulus of pile group
 
  
  
'''AASHTO GROUP I AND IV LOADS'''
+
<center>[[Image:751.40 prestressed concrete i-girders-miscellaneous details-shear block.gif]]</center>
  
Maximum P = Pile Capacity
 
Minimum P = 0
 
  
Tension on a pile will not be allowed for any combination of forces.
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
|-
Overstress reduction will not be used for loading minimums.
+
|valign="top" align="right"|[[Image:751.40 circled 1.gif]]||align="left" width="400pt" |Height of shear block shall extend a minimum of 1" above the top of the sole plate.
 +
|}
  
 +
===== 751.40.8.10.3.2 Anchor Bolts =====
  
'''EARTHQUAKE LOADS'''
+
'''Simple Spans'''
  
'''POINT BEARING PILES'''
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|colspan="2"|[[Image:751.40 prestressed concrete i-girders-miscellaneous details-anchor bolts.gif]]
 +
|-
 +
!width="50%"|Expansion||width="50%"|Fixed
 +
|-
 +
!colspan="2"|Part Elevation
 +
|}
  
(**) Maximum P = Pile capacity x 2
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
:(I.E. for HP 10 x 42 piles, maximum P = 56 x 2 = 112 tons/pile).
+
|-
+
|valign="top" align="right"|Note:||align="left" width="400pt"|It is permissible for the reinforcing bars and or the strands to come in contact with the materials used in forming A.B. holes.
Minimum P = Use allowable uplift force specified for piles in Bridge Manual 3.71 under seal course design.
+
|-
 +
|valign="top" align="right"|&nbsp;||align="left" width="400pt"|If A.B. holes are formed with galvanized sheet metal, the forms may be left in place.
 +
|-
 +
|valign="top" align="right"|&nbsp;||align="left" width="400pt"|Hole (1 1/2" round) to be grouted with approved non-shirk grout.
 +
|}
  
(**) Two (2) is our normal factor of safety. Under earthquake loadings only the point bearing pile and rock capacities are their ultimate capacities.
+
===== 751.40.8.10.3.3 Dowel Bars =====
  
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|[[Image:751.40 prestressed concrete i-girders-miscellaneous details-dowel bars part elevation.gif]]
 +
|[[Image:751.40 prestressed concrete i-girders-miscellaneous details-dowel bars section a-a.gif]]
 +
|-
 +
!width="50%"|Part Elevation<br/>(Fixed Bent) (*)||width="50%"|Section A-A (*)
 +
|}
  
'''FRICTION PILES'''
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|valign="top" align="right"|(*)||align="left" width="300pt"|Details shown are for SPC A and B only.
 +
|}
  
Maximum P = Pile capacity
+
Dowel bars shall be used for all fixed intermediate bents under prestressed superstructures.
  
  
'''(3) INTERNAL STRESSES'''
+
Seismic Performance Category A:
::A) Shear Line
+
:Use #6 Bars @ 18" Cts. for dowel bars.
::B) Bending
 
::C) Distribution of Reinforcement
 
::D) Shear
 
  
=====751.40.8.9.3.6 Pedestal Pile=====
 
  
'''GENERAL'''
+
Seismic Performance Category B:
 +
:Dowel bars shall be determined by design. (#6 Bars @ 18" Cts. minimum)
 +
:Design dowel bars for shear using service load design.
 +
:Allowable stresses are permitted to increase by 33.3% for earthquake loads.
  
No concrete bell shall be used without approval of Structural Project Manager or Liaison.
 
  
 +
Seismic Performance Categories C & D:
 +
:See Structural Project Manager.
  
'''SEISMIC PERFORMANCE CATEGORY A'''
+
===== 751.40.8.10.3.4 Expansion Device Support Slots =====
 
 
#Assume column to be "pinned" for belled footing sitting on rock. All loads will be axial.
 
#Assume column to be fixed for pedestal pile embedded in rock.
 
#All earth loads within the diameter of belled footing, or pedestal pile if there is no bell, above ground line shall be included in footing design.
 
  
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|[[Image:751.40 prestressed concrete i-girders-miscellaneous details-exp device support holes part plan.gif]]
 +
|-
 +
!Part Plan of P/S Concrete I-Girder @ Expansion Device End
 +
|-
 +
| &nbsp;
 +
|-
 +
|[[Image:751.40 prestressed concrete i-girders-miscellaneous details-exp device support holes part elevation.gif]]
 +
|-
 +
!Part Elevation of P/S Concrete I-Girder @ Expansion Device End
 +
|}
  
<center>[[Image:751.40_Intermediate_Bents_-_Pedestal_Pile_General_(Category_A)_Elevation.gif]]</center>
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|valign="top" align="right"|(*)||align="left" width="300pt"|Show these dimensions on the P/S concrete girder sheet.
 +
|}
  
 +
===751.40.8.11 Open Concrete Intermediate Bents and Piers===
  
'''SEISMIC PERFORMANCE CATEGORY B, C & D'''
+
====751.40.8.11.1 Design====
 +
 
 +
=====751.40.8.11.1.1 General and Unit Stresses=====
  
See (Seismic Design).
+
'''GENERAL'''
  
 +
Use Load Factor design method, except for footing pressure and pile capacity where the Service Load design method shall be used.
  
'''DETAILS'''
+
In some cases, Service Load design method may be permitted on widening projects, see Structural Project Manager.
  
'''SEISMIC PERFORMANCE CATEGORY A'''
+
The terms, Intermediate Bents and Piers, are to be considered interchangeable for EPG 751.40.8.11 Open Concrete Intermediate Bents and Piers.
  
  
<center>[[Image:751.40_Intermediate_Bents_-_Pedestal_Pile_Details_(Category_A)_Elevation_&_Section_AA.gif]]</center>
+
'''DESIGN UNIT STRESSES'''
  
  
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
+
(1) Reinforced Concrete
  
|Diameter<br/>of Shaft||Minimum<br/>Bell Diameter||Maximum<br/>Bell Diameter||Minimum<br/>(*) Reinf.||Cubic Yards<br/>Concrete per ft.
+
:{|
 +
|-
 +
|Class B Concrete (Substructure)||width="100"|<math>\, f_c</math> = 1,200 psi||width="100"|<math>\, f'_c</math> = 3,000 psi
 
|-
 
|-
|2'-0"||2'-4"||6'-0"||8-#7||0.1164
+
|Reinforcing Steel (Grade 60)||<math>\, f_s</math> = 24,000 psi||<math>\, f_y</math> = 60,000 psi
 
|-
 
|-
|2'-6"||2'-10"||7'-6"||8-#9||0.1818
+
|n = 10||&nbsp;
 
|-
 
|-
|3'-0"||3'-6"||9'-0"||11-#9||0.2618
+
|<math>\, E_c = W_1.5 \times 33 \sqrt{f'_c}</math>|| (AASHTO Article 8.7.1) (*)
 
|-
 
|-
|3'-6"||4'-0"||10'-6"||14-#9||0.3563
+
|}
 +
 
 +
 
 +
 
 +
(2) Reinforced Concrete (**)
 +
 
 +
:{|
 
|-
 
|-
|4'-0"||4'-6"||12'-0"||19-#9||0.4654
+
|Class B-1 Concrete (Substructure)||width="100"|<math>\, f_c</math> = 1,600 psi||width="100"|<math>\, f'_c</math> = 4,000 psi
 
|-
 
|-
|4'-6"||5'-0"||13'-0"||24-#9||0.5890
+
|Reinforcing Steel (Grade 60)||<math>\, f_s</math> = 24,000 psi||<math>\, f_y</math> = 60,000 psi
 
|-
 
|-
|5'-0"||5'-6"||14'-0"||29-#9||0.7272
+
|<math>\, n</math> = 8||&nbsp;
 
|-
 
|-
|5'-6"||6'-0"||15'-0"||35-#9||0.8799
+
|<math>\, E_c = W_1.5 \times 33 \sqrt{f'c}</math>|| (AASHTO Article 8.7.1) (*)
 
|-
 
|-
|6'-0"||6'-6"||16'-0"||41-#9||1.0472
 
 
|}
 
|}
  
  
Concrete Quantities shown in table are per linear foot of shaft only.  Bell Quantities are not included.
 
  
(*) Amount of reinforcing may be increased from that shown to meet the individual job requirements.
+
(3) Structural Steel
  
Minimum reinforcement meets AASHTO Spec. 8.18 for reinforcement of compression members.
+
:Structural Carbon Steel  (ASTM A709 Grade 36)
 +
:::::::::<math>\, f_s</math> = 20,000 psi, &nbsp;  <math>\, f_y</math> = 36,000 psi
  
  
  
'''DETAILS'''
+
(4) Overstress
  
'''SEISMIC PERFORMANCE CATEGORY B, C & D'''
+
:The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for Service Load design method.
  
  
<center>[[Image:751.40_Intermediate_Bents_-_Pedestal_Pile_Details_(Category_B_C_&_D)_Elevation_&_Section_AA.gif]]</center>
+
(*) Use <math>\, W = 150 \ pcf, \ E_c = 60,625  \sqrt{f'_c}</math>
 +
 +
(**) May be used for special cases, see Structural Project Manager.
  
 +
=====751.40.8.11.1.2 Loads=====
 +
(1) Dead Loads
 +
 
 +
  
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
+
(2) Live Loads
  
|Diameter<br/>of Shaft||Minimum<br/>(*) Reinf.||Cubic Yards<br/>Concrete per ft.
+
:As specified on the Bridge Memorandum.
|-
+
|2'-0"||8-#7||0.1164
+
:Impact of 30% is to be used for the design of beam, web supporting beam and top of columns. No impact is to be used for bottom of column, tie beam or footing design.
|-
+
|2'-6"||8-#9||0.1818
 
|-
 
|3'-0"||11-#9||0.2618
 
|-
 
|3'-6"||14-#9||0.3563
 
|-
 
|4'-0"||19-#9||0.4654
 
|-
 
|4'-6"||24-#9||0.5890
 
|-
 
|5'-0"||29-#9||0.7272
 
|-
 
|5'-6"||35-#9||0.8799
 
|}
 
  
  
Concrete Quantities shown in table are per linear foot of shaft only.
+
(3) Wind and Frictional Forces
  
(*) Amount of reinforcing may be increased from that shown to meet the individual job requirements.
 
  
Minimum reinforcement meets AASHTO Spec. 8.18 for reinforcement of compression members.
 
  
(**) Stay in place casing may be used in place of spirals for column diameters greater than 4 foot.
+
(4) Temperature and Shrinkage
  
=== 751.40.8.10 Prestressed Concrete I-Girders ===
+
:The effect of normal and parallel components to the bent shall be considered. When bearings with high friction coefficients are used or for long bridge lengths, the columns and footings are to be analyzed for moments normal to the bent due to the horizontal deflection of the top of the bent.
 +
 +
 +
 +
(5) Buoyancy
  
 +
:If specified by the Structural Project Manager, or by the Bridge Memorandum.
 +
  
==== 751.40.8.10.1 Design ====
+
 +
(6) Earth Pressure
  
===== 751.40.8.10.1.1 Girder Design=====
+
:Bents are to be analyzed for moments due to equivalent fluid pressure on columns and web where the ground line at time of construction, or potential changes in the ground line, indicate.  
 +
  
'''Geometric Dimensions'''
+
 +
(7) Earthquake
 +
 
 +
:See Structural Project Manager or Liaison.
 +
  
'''Girder Analysis (Continuous Span Series)'''
+
 +
(8) Special Stability Situations
  
Stresses due to dead load weight of slab, girder, diaphragms, haunch and forms will be based on simple spans from centerline to centerline of bearings.
+
:When indicated by the Bridge Memorandum or by the Structural Project Manager, piers must be analyzed for special loadings as directed (i.e., differential settlement).
 
   
 
   
Stresses due to dead load weight of curbs, parapet, rails, future wearing surface and outlets will be based on continuous composite spans with loads equally distributed to all girders.  The span lengths used in these computations will be based on the distance from the centerline of the bearing at the End Bent to the centerline of the Int. Bent, and from centerline of Int. Bent to centerline of Int. Bent.
+
 
 
   
 
   
Stresses due to live load plus impact will be based on continuous composite spans whose lengths are described above for curbs, etc.
+
(9) Collision
 +
 
 +
:Where the possibility of collision exists from railroad traffic, the appropriate protection system, for example Collision Wall, shall be provided (See the Bridge Memorandum).
 
   
 
   
The analysis will be made on the basis of transformed areas of all steel (both strands and bars) in the section using concrete with <math>\, n</math> = 6.
+
 
 
   
 
   
In composite design, allowances shall be made for the difference in modulus of elasticity of slab and girder by using the effective slab area as specified for concrete T-Beams as given in the current AASHTO Specifications, multiplied by the factor <math>\, (E_{slab}/E_{girder})</math> .  The area shall include the transformed area of all longitudinal reinforcing bars within the effective widthThe 1" integral wearing surface shall not be used in the effective slab depth.
+
(10) Collision Walls
 +
 
 +
:Collision walls are to be designed for the unequal horizontal forces from the earth pressure, if the condition exists (See the Bridge Memorandum).  The vertical force on the collision wall is the dead load weight of the wall (*)If a bent has three or more columns, design the steel in the top of the wall for negative moment.
  
  
'''Effective Flange Width'''
+
(*) For footing design, the eccentricity dead load moment due to an unsymmetrical collision wall shall be considered.
 
The effective flange width for Beam Types 2,3,4 & 6 should be calculated using AASHTO 8.10.1.  For Beam Type 7, the effective flange width should be calculated using AASHTO 9.8.3.
 
  
 +
=====751.40.8.11.1.3 Distribution of Loads=====
  
'''Continuity at Intermediate Supports'''
 
  
Continuity will be obtained at intermediate supports by pouring a concrete diaphragm monolithic with the deck slab and encasing the prestressed girders. Reinforcing bars will tie the slab, diaphragms and girders together.
+
(1) Dead Loads
 
Reinforcing bars, <math>\, f_y</math> = 60,000 psi, will be placed in the deck slab for tensile
 
steel.
 
 
The ultimate negative moments should be 2.17 times the maximum live load moments including impact and 1.3 times moments for future wearing surface and dead load of curb, parapet or safety barrier curb and bridge rail.
 
 
The area of longitudinal reinforcing steel at the centerline of the intermediate bent should be determined on the basis of a cracked section.  This area of reinforcing bars is to be provided by adding additional bars between the normal longitudinal bars at the top of the slab. #8 maximum bar size for additional bars over bents.
 
 
These special negative moment reinforcing bars should be ended by one of the following criteria (whichever is greater):
 
 
#Where the stress on the normal longitudinal reinforcing bars does not exceed 24,000 psi. as based on a cracked section, plus 15 bar diameters or development length.
 
#Not closer to the centerline of the intermediate bent than 1/10 of the span.  (8' min.)
 
 
The concrete stress at the bottom of the girder should be checked at a point 70 strand diameters plus 9 inches from the centerline of the intermediate bent to see that the total compressive stress due to prestress and negative moment does not exceed 3,000 psi.  (AASHTO. 9.7.2)
 
 
The positive moment at the intermediate bent should be provided for by extending the top two rows of the top strands (both straight or deflected) and if available, the number of bottom strands indicated in tables below bent to form a right angle hook.
 
  
 +
:Loads from stringers, girders, etc. shall be concentrated loads applied at the centerline of bearing.  Loads from superstructure, such as concrete slab spans, shall be applied as uniformly distributed loads.
  
'''Design of Negative Moment Reinforcement'''
 
  
Since most of the dead load moments are carried by the beam acting as a simple span, the negative design moment over piers is the live load plus impact moment. In most designs, the dead load applied after continuity is achieved should also be considered in the negative design moment. The effect of initial precompression due to prestress in the precast girders may be neglected in the negative moment computation of ultimate strength if the maximum precompression  stress is less than <math>\, 0.4 f'_c</math> and the continuity reinforcement is less than 1.5 percent.
+
(2) Live Loads
  
It will usually be found that the depth of the compression block will be less than the thickness of the bottom flange of the precast girder. For this reason, the negative moment reinforcement required can be determined by assuming the beam to be a rectangular section with a width equal to the bottom flange width of the girder. Due to the lateral restraint of the diaphragm concrete, ultimate negative compression failure in the PCA tests always occurred in the girders, even though the diaphragm concrete strength was about 1000 psi less than that of the girder concrete for this reason, it is recommended that the negative moment reinforce-ment  be designed using the compressive strength of the girder concrete.
+
:Loads from stringers, girders, etc., shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of bent.
  
  
<center>[[Image:751.40 prestressed concrete i-girders-rectangular beam curves.gif]]</center>
+
(3) Wind and Frictional Forces
  
<center>'''Rectangular Beam Curves'''</center>
 
  
 +
(4) Temperature
  
 +
:Apply at the top of the substructure beam.
  
  
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
(5) Earth Loads
|-
+
:(a) Vertical
!rowspan="2"|Web<br/>Thickness<br/>(Inches)
+
::Vertical earth loads on tie beams shall be applied as uniform loads for a column of earth equal to 3 times the width of the beam.  The weight of earth for footing design shall be that directly above the footing, excluding that occupied by the column.
!colspan="5"|Number of Bottom Strands for Positive Moment<br/>Connection (C) for Closed Diaphragms
 
|-
 
!Beam Type 2<br/>or Modified
 
!Beam Type 3<br/>or Modified
 
!Beam Type 4<br/>or Modified
 
!Beam Type 6<br/>or Modified
 
!Beam Type 7<br/>or Modified
 
|-
 
|6||6||8||10||--||18
 
|-
 
|6 1/2||--||--||--||14||--
 
|-
 
|7 (A)||8||10||10||--||--
 
|-
 
|7 1/2 (B)||--||--||--||16||--
 
|-
 
|8 (A)||8||10||12||--||--
 
|-
 
|8 1/2 (B)||--||--||--||16||--
 
|}
 
  
  
{|border="1" style="text-align:center;" cellpadding="5" align="center"
+
::The earth above the seal courses shall be considered in computing pile loads.  Refer to the Design and Dimension of the Pile Footings portion of [[#751.40.8.13 Concrete Pile Cap Non-Integral End Bents|EPG 751.40.8.13 Concrete Pile Cap Non-Integral End Bents]] or [[751.36 Driven Piles|EPG 751.36 Driven Piles]].
|-
 
!rowspan="2"|Web<br/>Thickness<br/>(Inches)
 
!colspan="5"|Number of Bottom Strands for Positive Moment Connection (C) for<br/>Open Intermediate Diaphragms with Continuous Superstruecture
 
|-
 
!Beam Type 2<br/>or Modified
 
!Beam Type 3<br/>or Modified
 
!Beam Type 4<br/>or Modified
 
!Beam Type 6<br/>or Modified
 
!Beam Type 7<br/>or Modified
 
|-
 
|6||12||16||16||--||22
 
|-
 
|6 1/2||--||--||--||22||--
 
|-
 
|7 (A)||12||16||16||--||--
 
|-
 
|7 1/2 (B)||--||--||--||22||--
 
|-
 
|8 (A)||12||16||16||--||--
 
|-
 
|8 1/2 (B)||--||--||--||22||--
 
|}
 
  
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
:(b) Horizontal
|-
+
<center>
|valign="top"|(A)||align="left" width="400pt" |Modified Beam Type 2, 3 or 4.
 
|-
 
|valign="top"|(B)||align="left" width="400pt" |Modified Beam Type 6.
 
|-
 
|valign="top"|(C)||align="left" width="400pt" |If available, otherwise bend all bottom strands.
 
|}
 
  
 +
[[Image:751.40 Open Concrete Int Bents and Piers- Distribution Loads.gif]]
  
'''Negative Moment Bar Cut-Off (Working Stress Controlling)'''
+
</center>
 +
(*) A factor of 2.0 is applied to the moment to allow for the possibility of the column esisting earth pressure caused by the earth behind the column twice the column width.
  
Area of slab bars required and stress in the slab bars are printed in program BR200.
 
  
Determine stress of the area of slab bars input into program at a point where the area required is larger than that input.
+
(6) Earthquake Loads
 +
 
 +
:See Structural Project Manager or Liaison.
  
Interpolate along a straight line to where the stress is 24,000 psi.
 
  
Note: Negative moment bar computations use a cracked section analysis to determine stresses.
+
(7) Seal Course
  
===== 751.40.8.10.1.2 Allowable Concrete Stresses =====
+
:The weight of the seal course shall not be considered as contributing to the pile loads, except for unusual cases.
  
The following criteria is shown for clarity and is in accordance with AASHTO 9.15.
+
=====751.40.8.11.1.4 Types of Design=====
 
:<math>\, f'_c</math> = 5,000 psi, &nbsp; <math>\, f'_{ci}</math> = 4,000 psi
 
  
 +
'''TYPES OF DESIGN'''
  
A. Temporary stresses before losses except as noted:
+
Rigid frame design is to be used for the design of Intermediate Bents and
 +
Piers.
  
*Compression...<math>\, 0.6 f'_{ci} = 0.6 \times 4,000psi = 2,448psi</math> (*)
 
  
*Tension
+
The joint between the beam and column, and web or tie beam and column,  
**Precompressed tensile zone ....................
+
is assumed to be integral for all phases of design and must be analyzed
***No temporary allowable stresses are specified. See paragraph "B" below.
+
for reinforcement requirements as a "Rigid Frame".
***In tension areas with no bonded reinforcement...<math>\, 3 \sqrt{f'_{ci}} = 3 \sqrt{4,000} = 190 psi</math>
 
***Where the calculated tensile stress exceeds this value, bonded reinforcement shall be provided to resist the total tension force in the concrete computed on the assumption of an uncracked section. The maximum tensile stress shall not exceed...<math>\, 7.5 \sqrt{f'_{ci}} = 7.5 \sqrt{4,000} = 475 psi</math>
 
  
  
B. Stresses at service loads after losses:
+
The joint between the column and footing is assumed to be "fixed",
 +
unless foundation fexibility needs to be considered (consult Structural
 +
Project Manager for this assessment).
  
*Compression...<math>\, 0.4 f'_c = 0.4 \times 5,000 = 2,000 psi</math>
 
  
*Tension in the precompressed tensile zone...
+
If the distance from the ground line to the footing is large (*),  
**(a) For members with bonded reinf. (**)...<math>\, 6 \sqrt {f'_c} = 6 \sqrt{5,000} = 425 psi</math>
+
consideration shall be given to assuming the column to be "fixed" at a
**(b) For members without bonded reinf...<math>\, = Zero</math>
+
point below the ground line.
  
*Tension in other areas
 
**Tension in other area is limited by the allowable temporary stresses specified in "A" above.
 
  
 +
(*) When the distance from the ground line to the top of footing is 10' or more, the unsupported height and the fixed point may be measured from the bottom of the beam to the ground line plus 1/2 of the distance from the ground line to the top of the footing.
  
C.  Cracking stress:
 
  
*Modulus of rupture from tests or (for normal weight concrete)...<math>\, 7.5 \sqrt{f'_c} = 7.5 \sqrt {5,000} = 530 psi</math>
+
'''UNSUPPORTED HEIGHT'''
  
 +
Unsupported height is the distance from the bottom of the beam to the
 +
top of the footing.
  
D.  Negative moment stresses in girders made continuous after deadload of slab is in place:
 
  
*Tension in negative moment reinforcement...<math>\, f_y</math> = 60,000 psi, &nbsp; <math>\, f_s</math> = 24,000 psi
+
'''SINGLE COLUMN'''
*Compression in concrete at bottom of girder...<math>\, f'_c</math> = 5,000 psi, &nbsp; <math>\, f_c = 0.6 f'_c</math>
 
  
(*) BR200 allows 2% overstress
+
Use rigid frame design with the column considered "fixed" at the bottom for all of the conditions.
  
(**)Strands qualify if not debonded at ends.
 
  
===== 751.40.8.10.1.3 Prestress Loss and Prestress Camber =====
+
'''COLUMN DIAMETER CHANGE'''
  
<math>\, \Bigg[ \cfrac{ \overset{(SH)}{6,000} + \overset{(ES)}{ \frac {Es}{Ec_i}}fc + \overset{(CR_C)}{8.5 fc} + (5,000 - \overset{(CR_s)}{0.1 ES} - 0.05 (SH + CR_c))}{fs_i} \Bigg]</math>
+
Use a change in column diameter as required by the Bridge Memorandum or column design.
  
  
{|
+
'''COLUMN SPACING (TRIAL)'''
|rowspan="4" width="375pt"|Reduce to: &nbsp; &nbsp; <math>\, \cfrac {10,700 + (0.9 \left( \frac{E_s}{Ec_i} \right) + 8.08) fc}{fs_i}</math>
+
 
|<math>\, SH</math>||width="150pt"|= Shrinkage
+
(Except Web Supporting Beam type)
|-
+
 
|<math>\, ES</math>||width="150pt"|= Elastic Strain
+
Estimate centerline-centerline column spacing for a two column bent as 72% of the distance from the centerline of the outside girder to the centerline of the outside girder.
|-
 
|<math>\, CR_c</math>||width="150pt"|= Concrete Creep
 
|-
 
|<math>\, CR_s</math>||width="150pt"|= Steel Creep
 
|}
 
  
 +
A three column bent spacing estimation is 44% of the centerline-centerline outside girder spacing.
  
 +
====751.40.8.11.2 Reinforcement====
 +
=====751.40.8.11.2.1 Hammer Head Type=====
 +
<center>
 
{|
 
{|
|valign="top"| <math>\, CR_c</math>||valign="top"|= <math>\, 12 fc_{ir} - 7 fc_{ds}</math>
 
 
|-
 
|-
|<math>\, CR_c</math>||valign="top"|= <math>\, 12 fc - 7/2 fc = 8.5 fc</math>  &nbsp;(Approximate Estimate)
+
|[[Image:751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Part Plan.gif]]||[[Image:751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Section A-A.gif]]
 
|-
 
|-
|<math>\, Ec_i</math>||valign="top"|= <math>\, 150^{1.5} 33 \sqrt{f'c_i}</math>  &nbsp; &nbsp; <math>\, ES = \frac {Es}{Ec_i} fc_{ir} = \frac {Es}{Ec_i} fc</math>  &nbsp;(Approximate Estimate)
+
|PART PLAN||SECTION A-A
 
|-
 
|-
|<math>\, fc_{ir}</math> ||valign="top"|= Concrete stress at centroid of P/S steel at point considered due to P/S and dead load at release.
+
|rowspan="2"|[[Image:751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Part Elev.gif]]||style="text-align:left"|Note:<br>When an expansion device in the slab is used at an intermediate bent, all reinforcement located entirely within the beam shall be epoxy coated.  See details of protective coating and sloping top of beam to drain.
 
|-
 
|-
|<math>\, fc</math>||valign="top"|= <math>\, fc_{ir}</math> (Assume <math>\, fc_{ir} = fc</math>)
+
|[[Image:751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Part Section B-B.gif]]
 
|-
 
|-
|<math>\, fc</math>||valign="top"|= <math>\, 0.4(4,000) = 1,600 psi</math> (Estimate average)
+
|PART ELEVATION||PART SECTION B-B
|-
 
|<math>\, fc_{ds}</math> ||valign="top"|= Concrete stress at centroid of P/S Steel (due to dead load)(Assume fcds = 1/2 fc)
 
|-
 
|<math>\, fs_i</math> ||valign="top"|= Initial stress in P/S steel
 
|-
 
|<math>\, fs_i</math> ||valign="top"|= <math>\, 270,000 psi \times 75% = 202,500 psi</math>
 
|-
 
|<math>\, Ec_i</math> ||valign="top"|= <math>\, 150^{1.5} 33 \sqrt{4,000} = 3,834,253.5 psi</math>
 
 
|-
 
|-
|<math>\, Es</math>||valign="top"|= <math>\, 28,000,000 psi</math> (AASHTO 9.16.2.1)
 
|-
 
|<math>\, \frac {Es}{Ec_i}</math> ||= <math>\, 7.30</math>
 
 
|}
 
|}
 +
</center>
  
 +
(*) Add hooked reinforcement as required by design.
  
<math>\, \frac {10,700 + (0.9 \times 7.30 + 8.08) 1,600}{202,500} = 16.9%</math>
+
(**) See AASHTO Article 8.18.2.3.4 for tie requirements.
  
  
<math>\, 202.5ksi \times 16.9% = 34.22ksi</math>
+
[[Image:751.40 circled 1.gif]] All stirrups in beam to be the same size bar. (Use a min. spacing of 5" (6" for double stirrups), minimum stirrups are #4 at 12" cts., and maximum
 +
stirrups are #6 at 6" cts.)
  
 +
Locate #4 bars (┌─┐) under bearings if required.  (Not required for P/S Double-Tee Girders.)
  
Total loss due to all causes, except friction, is 34.22 ksi. (Friction losses are applied to post-tensioned girder only.) Use 8.84% for initial loss and 8.84% for final loss for design.
 
  
 +
[[Image:751.40 circled 2.gif]] See development length (Other than top bars) or standard hooks in
 +
tension, Ldh.
  
<math>\, 202.5 ksi \times 8.84% = 17.90 ksi</math> = initial loss
 
  
<math>\, 202.5 - 17.90 = 184.60ksi</math>
+
[[Image:751.40 circled 3.gif]] See lap splice class C.
  
<math>184.60ksi \times 8.84% = 16.32ksi</math> = final loss
+
====751.40.8.11.3 Pile Footings====
 +
=====751.40.8.11.3.1 Design and Dimensions=====
  
<math>17.90 + 16.32 = 34.22ksi \approx 34.22ksi = 202.5ksi \times 16.9%</math> = total loss
+
'''GENERAL '''
  
 +
:Number, size and spacing of piling shall be determined by computing the pile loads and applying the proper allowable overstresses.
 +
 +
:Cases of Loading:  (AASHTO Article 3.22)
 +
 +
:Group I and Group II maximum vertical loads (refer to distribution of loads, this Section).
 +
 +
:Group III thru VI wind and/or temperature moments with applicable vertical loads.
  
In the above design example, if tension exceeds AASHTO Specifications, (425 psi for 5,000 psi concrete) the girder will have to be modified to limit stress to 425 psi.
+
:Internal stresses including the position of the shear line shall then be computed.
  
 +
:Long narrow footings are not desirable and care should be taken to avoid the use of an extremely long footing 6~0" wide when a shorter footing 8'-3" or 9'-0" wide could be used.
 +
 +
:Footings are to be designed for the greater of the minimum moment requirements at the bottom of the column, or the moments at the bottom of the footing.
 +
 +
:When using the load factor design method for footings, design the number of piles needed based on the working stress design method.
 +
 
  
{|
+
'''PILE LOADS'''
|valign="top"| <math>\, f'c</math>||valign="top"|= 6,000 psi
+
 
 +
<math>\, P = N/n \pm M/S</math>
 +
:{|
 +
|<math>\, P</math>|| - Pile Loads
 +
|-
 +
|<math>\, N</math>|| - Vertical Loads
 
|-
 
|-
|valign="top"| <math>\, f'c_i</math>||valign="top"|= 4,500 psi
+
|<math>\, n</math>|| - Number of Piles
 
|-
 
|-
|colspan="2" valign="top"|Grade 270 low relaxation strands
+
|<math>\, M</math>|| - Overturning Moment
 
|-
 
|-
|valign="top"|<math>\, fc</math>||valign="top"|= <math>\, 0.4(4,500) = 1,800 psi</math> (Estimated average)
+
|&nbsp;||If minimum eccentricity controls the moment in both directions,
 
|-
 
|-
|valign="top"|<math>\, Ec_i</math>||valign="top"|= <math>\, 150^1.5 33 \sqrt{f'c_i} = 4,066.840 psi</math>
+
|&nbsp;||It is necessary to use the moment in one direction (direction with
 
|-
 
|-
|valign="top"|<math>\, \frac{Es}{Ec}</math>||valign="top"|= <math>\, \frac{28,000,000}{4,066,840} = 6.89</math>
+
|&nbsp;||less section modulus of pile group) only for the footing check.
 
|-
 
|-
|colspan="2" valign="top"|AASHTO 9.16.2.1.3: <math>\, CRc = 12fc - 7/2fc = 8.5fc</math> (approximate estimate)
+
|<math>\, S</math>|| - Section Modulus of Pile Group
 
|}
 
|}
  
  
<math>\, \Bigg[ \overset{(SH)}{6,000} + \overset{(ES)}{ \frac {Es}{Ec_i}}fc + \overset{CR_c)}{8.5 fc} + (5,000 - \overset{(CR_s)}{0.1ES} - 0.05(SH + CR_c)) \Bigg]</math>
+
:'''(A) AASHTO Group I thru VI Loads as applicable'''
  
 +
:Maximum <math>\, P</math> = Pile Capacity
 +
:Minimum <math>\, P = 0</math> (zero)
 +
 +
:Tension on a pile will not be allowed for any combination of forces.
 +
 +
:Pile design force shall be calculated with consideration of AASHTO percentage overstress factors.
  
Reduce to: &nbsp; <math>\, \cfrac{10,700 + (0.9 (\frac{Es}{Ec_i}) + 8.08) fc}{fs_i}</math>
 
  
  
{|
+
:'''(B) Earthquake Loads'''
|valign="top"| <math>\, fc</math>||valign="top"|= <math>\, 0.4(4,500) = 1,800 psi</math> (estimated average)
 
|-
 
|<math>\, \frac{Es}{Ec_i}</math> ||= <math>\, 6.89</math>
 
|}
 
  
<math>\, fs_i</math> = Initial stress in low relaxation strands stressed to 75% of ultimate (*)
+
See Structural Project Manager or Liaison before using the following seismic information.
 +
 
 +
:<u>Point Bearing Pile</u>
 +
 +
::    Maximum <math>\, P = Pile\ capacity\ \times 2</math> (**)
 +
::    (i.e., for HP 10 X 42 piles, Max. <math>\, P = 56\ \times 2 = 112</math> tons/pile)
 +
::    Minimum <math>\, P</math> = Allowable uplift force specified for piles in this
 +
::    Section under Seal Course Design.
 +
 +
::    (**) Two "2" is our normal factor of safety. Under earthquake loadings only the point bearing pile and rock capacities are their ultimate capacities.
 +
 +
:<u>Friction Piles</u>
 +
 +
::    Maximum <math>\, P</math> = Pile Capacity
 +
::    Minimum <math>\, P</math> = Allowable uplift force specified for piles in this
 +
::    Section under Seal Course Design.
 +
::    See combined axial & bending stresses in Cast-In-Place friction piles in liquefaction areas.
  
<math>\, fs_i</math> = 270,000 psi \times 75% = 202,500 psi
 
 
 
<math>\, \frac {10,700 + (0.9 \times 6.89 + 8.08) \times 1,800}{202,500} = 18.0%</math>
 
  
  
<math>\, 202.50 ksi \times 18.0% = 36.45 ksi</math> = total loss except friction
+
'''(1) Shear Line'''
  
Use 9.44% for initial loss and 9.44% for final loss.
+
{|
+
|-
<math>\, 202.50 ksi \times 9.44% = 19.12 ksi</math> = initial loss
+
|width="400"|If the shear line is within the column projected, the footing may be considered satisfactory for all conditions and standard #6 hairpin bars shall be used.
  
<math>\, 202.5 - 19.12 = 183.38 ksi</math>
 
  
<math>\, 183.38 ksi \times 9.44% = 17.31 ksi</math> = final loss
+
If the shear line is outside of the column projected, the footing must be analyzed and reinforced for bending and checked for shear stress (see [[#(4) Shear|(4) Shear]], below).
  
<math>\, 19.12 + 17.31 = 36.43 ksi \approx 36.45 ksi = 202.5 ksi \times 18.0%</math> = total loss
 
 
   
 
   
 +
Footing depths may be increased, in lieu of reinforcement, if an increase would be more economical.  (6'-0" Maximum depth, with 3" increments.)
 +
||[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Internal Stresses.gif]]
 +
|-
 +
|}
 +
 +
 +
'''(2) Bending'''
 +
 +
The critical section for bending shall be taken at the face of the columns (concentric square of equivalent area for round columns).
 +
 +
The reinforcement shall be as indicated for reinforced footings, except that the standard #6 hairpin bars may be used for small footings if they provide sufficient steel area.
 +
 +
 +
'''(3) Distribution of Reinforcement'''
 +
 +
<u>Reinforcement in Bottom of Footing</u>
 +
<center>
 +
[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Distribution of Reinforcement.gif]]
 +
</center>
  
P/s force initial = <math>\, (183.38 ksi)(0.153 in.^2/strands)(no.\ of\ strands)</math>
+
Reinforcement shall be distributed uniformly across the entire width of footing in the long direction. In the short direction, the portion of the total reinforcement given by AASHTO Equation 4.4.11.2.2-1 shall be distributed uniformly over a band width equal to the length of the short side of the footing, <math>\, B</math>.
  
P/s force final = <math>\, ((202.5 - 36.43) ksi)(0.153 in.^2/strand)(no.\ of\ strands)</math>
+
:Band Width Reinforcement = <math>2(total\ reinforcement\ in\ short\ direction)/(\beta + 1)</math>
  
 +
:where <math> \beta = the\ ratio\ of\ fooring\ lenth\ to\ width = L/B</math>
  
(*) Suggested by FHWA: when using 3/8" round strands, max. <math>\, fs_i = 0.7 \times 250 ksi\ or\ 0.7 \times ultimate\ stress</math>, whichever is smaller. Larger initial stresses will cause debonding.
+
The remainder of the reinforcement required in the short direction shall be distributed uniformly outside the center band width of footing.
  
  
'''Prestress Concrete Girder Formula for Stress Calculation'''
+
<u>Reinforcement in Top of Footing</u>
  
(-) Tension; &nbsp; (+) Compression
+
Reinforcement in the top of the footing shall be provided based on a seismic analysis for Seismic Performance Categories B, C and D. This reinforcement shall be at least the equivalent area as the bottom steel in both directions. The top steel shall be placed uniformly outside the column.
  
  
'''Temp. Stress'''
+
<div id="(4) Shear"></div>
 +
'''(4) Shear'''
  
{|
+
(AASHTO Article 8.15.5 or 8.16.6)
|width="75pt"|Allow Top||width="250pt"|<math>\, 7.5 \sqrt{f'c_i} = 0.474ksi</math> tension for||width="200pt"|<math>\, f'c_i = 4,000psi</math>
 
|-
 
|width="75pt"|Bottom||width="250pt"|<math>\, 0.6 f'c_i = 2.4 ksi</math> compression for||width="200pt"|<math>\, f'c_i = 4,000psi</math>
 
|}
 
  
:Temp. Top =
+
The shear capacity of footing in the vicinity of concentrated loads shall be governed by the more severe of the following two conditions.
::<math>\, \frac{(1.0 - initial\ loss)(P/S\ F)}{Ag} - \frac{(1.0 - initial\ loss)(P/S\ F)(ECC_{nc}}{St_{nc}} + \frac{M_{Gdr}}{St_{nc}}</math>
 
  
  
:Temp. Bottom =
+
(i) Beam shear
::<math>\, \frac{(1.0 - initial\ loss)(P/S\ F)}{Ag} - \frac{(1.0 - initial\ loss)(P/S\ F)(ECC_{nc}}{Sb_{nc}} + \frac{M_{Gdr}}{Sb_{nc}}</math>
 
  
 
+
Critical Section at "d" distance from face of column.
'''Design Load Stress'''
 
  
 
{|
 
{|
|width="75pt"|Allow Top||width="250pt"|<math>\, 0.4\ f'c = 2.0 ksi</math> compression for||width="200pt"|<math>\, f'c = 5,000psi</math>
 
 
|-
 
|-
|width="75pt"|Bottom||width="250pt"|<math>\, 6.0 \sqrt{f'c} = 0.424 ksi</math> tension for||width="200pt"|<math>\, f'c = 5,000psi</math>
+
|width="250"|b = Footing Width Service Load||rowspan="6"|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Internal Stresses- Part Plan of Footing- Beam Shear.gif]]
 +
|-
 +
|Service Load
 +
|-
 +
|<math>\, v = V / \left(b d \right)</math>||
 +
|-
 +
|<math>\, v_c = 0.95 \sqrt{f'_c}</math>||
 +
|-
 +
|Load Factor||
 +
|-
 +
|<math>\, V_u / \left(\omega b d \right)</math>||
 +
|-
 +
|<math>\, v_c = 2.0 \sqrt{f'_c}</math>
 +
!style="text-align:center"|PART PLAN OF FOOTING
 +
|-
 
|}
 
|}
  
:Top final =
 
::<math>\, Temp.\ Top\ Stress - \frac{(Final\ loss)(P/S\ F)}{A_c} + \frac{(Final\ loss)(P/S\ F)(ECC_c)}{St_c} + \frac{M_{Slb+Dph}}{St_{nc}} + \frac{M_{DLC}}{St_c}{st_c} + \frac{M_{LL+I}}{St_c}</math>
 
  
  
:Bottom final =
+
(ii)Peripheral Shear
::<math>\, Temp.\ Bott.\ Stress - \frac{(Final\ loss)(P/S\ F)}{A_c} - \frac{(Final\ loss)(P/S\ F)(ECC_c)}{Sb_c} - \frac{M_{Slb+Dph}}{Sb_{nc}} - \frac{M_{DLC}}{Sb_c} - \frac{M_{LL+I}}{Sb_c}</math>
 
  
  
::0.153 sq. in. = Area of one 1/2 inch strand
+
Critical Section at "d/2" distance from face of column.
::270 ksi = f's = Ult, Str. P/S Strand
 
::202.5 ksi = 0.75 (270) = Initial steel stress
 
 
 
 
 
:0.0884 = 8.84% Initial loss - low relaxation
 
:0.0884 = 8.84% Final loss - low relaxation
 
:4 Str. 2 Draped
 
:202.5 (0.153) = 30.98 kips/Str. P/s force
 
:6 Strands (30.98) = 185.90 P/s force
 
  
 +
<math>\, b_o = 4(d + Equiv.\ square\ column\ width)</math>
  
 
{|
 
{|
|<math>\, A_c</math>||= Area Composite
 
 
|-
 
|-
|<math>\, A_g</math>||= Area Girder
+
|width="250"|Service Load||rowspan="5"|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Internal Stresses- Part Plan of Footing- Peripheral Shear.gif]]
 
|-
 
|-
|<math>\, Ecc_c</math>||= Eccentricity of prestress force of composite section
+
|<math>\, v = V / \left(b_o d \right)</math>||
 
|-
 
|-
|<math>\, Ecc_{nc}</math>||= Eccentricity of prestress force of non-composite section
+
|<math>\, v = 1.8 \sqrt{f'_c}</math>||
 
|-
 
|-
|<math>\, M_{DFLC}</math>||= Composite dead load moment
+
|Load Factor||
 
|-
 
|-
|<math>\, M_{Gdr}</math>||= Girder dead load moment
+
|<math>\, V_u / \left(\omega b_o d \right)</math>||
 +
|-
 +
|<math>\, v_c = 4.0 \sqrt{f'c}</math>
 +
!align="center"|PART PLAN OF FOOTING
 +
|}
 +
 
 +
 
 +
If shear stress is excessive, increase footing depth.
 +
 
 +
{|
 +
|valign="top"|[[Image:751.40 circled 1.gif]]||Piles to be considered for shear.  (Center of piles are at or outside the critical section.)
 +
|}
 +
 
 +
 
 +
{|style="text-align:center"
 +
|-
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Side Elev.gif]]||[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Front Elev.gif]]
 +
|-
 +
!SIDE ELEVATION||FRONT ELEVATION
 +
|}
 +
 
 +
 
 +
{|
 +
|valign="top"|[[Image:751.40 circled 1.gif]]||Min. = 1/8 x (Distance from top of beam to bottom of footing.)
 +
|-
 +
|valign="top"|[[Image:751.40 circled 2.gif]]||3'-0" (Min.) & 6'-0" (Max.) for steel HP piles, 14" CIP piles. AASHTO Article 4.5.6.4 shall be considered if piles are situated in cohesive soils.
 +
|-
 +
|valign="top"|&nbsp;||3D (Min.) and 6D (Max.) for 20" and 24" CIP piles. (D = pile diameter)
 +
|-
 +
|valign="top"|[[Image:751.40 circled 3.gif]]||Indicates column diameter, or column length or width on a hammer head pier.
 
|-
 
|-
|<math>\, M_{LL+I}</math>||= Live load + impact moment
+
|valign="top"|[[Image:751.40 circled 4.gif]]||Min. = 2'-6" or column diameter (*) (Or width) for friction piles for SPC A.
 
|-
 
|-
|<math>\, M_{Slb+Dph}</math>||= Slab + diaphragm moment
+
|valign="top"|&nbsp;||Min. = 3'-0" or column diameter (*) (Or width) for steel piles for SPC A.
 
|-
 
|-
|<math>\, P/S\ F</math>||= Prestress forces in girder
+
|valign="top"|&nbsp;||Min. = 3'-0" or column diameter (*) (Or width) for friction piles for SPC B,C,& D.
 
|-
 
|-
|<math>\, Sb_c</math>||= Composite section modulus at bottom of girder
+
|valign="top"|&nbsp;||Min. = 3'-6" or column diameter (*) (Or width) for steel piles for SPC B, C & D.
 
|-
 
|-
|<math>\, Sb_{nc}</math>||= Non-composite section modulus at bottom of girder
+
|valign="top"|[[Image:751.40 circled 5.gif]]||12" for seismic performance category A and 18" for SPC B, C, & D.
 
|-
 
|-
|<math>\, St_c</math>||= Composite section modulus at top of girder
+
|valign="top" align="left"|(*)||For column diameters 4'-0" and greater use a 4'-0" min. footing thickness.
 
|-
 
|-
|<math>\, St_{nc}</math>||= Non-composite section modulus at top of girder
+
|valign="top" align="left"|(**)||Use 18" for steel HP piles, 14" CIP piles, prescase and prestress piles.
 
|}
 
|}
  
 +
<center>
 +
 +
[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Typ Plan of 3 Pile Footing.gif]]
  
'''Prestress Camber'''
+
'''TYPICAL PLAN OF<br>3 PILE FOOTINGS'''<br>(minimum pile spacings)
 +
</center>
  
Reference: Computer Program BR139B
+
NOTES:
  
<center>[[Image:751.40 prestressed concrete i-girders-camber diagram.gif]]</center>
+
Use 3- piles on exterior foorings only.
  
 +
Use only HP 10 x 42 or friction piles on three pile footings.
  
<math>\,
+
<center>
\begin{Bmatrix}
 
I4 = 107,888 in.^4\\
 
(non-transformed)\\
 
Beam\ wt. = 0.541\ (k/ft.)
 
\end{Bmatrix}
 
</math> &nbsp; Used to resist uplift before beam is set on bent.
 
  
 +
[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Typ Plan of Staggered Pile.gif]]
  
<math>\,
+
'''TYPICAL PLAN<br>STAGGERED PILE'''
\begin{Bmatrix}
 
I4 = 114,383 in.^4\\
 
(transformed)\\
 
Slab\ wt. = 0.92\ (k/ft.)\\
 
Diaphragm\ wt. = 2.65\ (K)
 
\end{Bmatrix}
 
</math> &nbsp; Used after beam is in place.
 
  
 +
(7 Pile footings shall not be used.)
 +
</center>
  
 
{|
 
{|
|align="right"|Mult. factor|| &nbsp; <math>\, [1 + (1 - e^{-\phi})] = 1.77</math>
+
|valign="top"|[[Image:751.40 circled 1.gif]]||If horizontal thrust requires pile batter- consult the Structural Project Manager.
| rowspan="6" align="center" |
+
|}
{| border="1" cellspacing="0" style="text-align:center"
+
 
|rowspan="2"| &nbsp;||colspan="2"|Mult. Factor <math>\, (F)</math>
+
(*) The maximum pile spacing is 4'-0".
 +
 
 +
=====751.40.8.11.3.2 Reinforcement=====
 +
 
 +
'''Unreinforced Footing - Use only in Seismic Performance Category A'''
 +
 
 +
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 
|-
 
|-
|<math>\, f'c</math> = 5,000psi||<math>\, f'c</math> = 6,000psi
+
|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Elev 3 Pile Footing.gif]]
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Elev 4 Pile Footing.gif]]
 
|-
 
|-
|Beam Type 3||1.780||1.773
+
!Elevation<br/>(3 Pile Footing)||Elevation<br/>(4 Pile Footing
 
|-
 
|-
|Beam Type 4||1.772||1.765
+
|colspan="2"| &nbsp;
 
|-
 
|-
|Beam Type 4||1.775||1.768
+
|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Plan 3 Pile Footing.gif]]
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Plan 4 Pile Footing.gif]]
 
|-
 
|-
|Beam Type 6||1.761||1.754
+
!Plan<br/>(3 Pile Footing)||Plan<br/>(4 Pile Footing
 
|}
 
|}
 +
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|-
|align="right"|<math>\, F</math>||= 1.77
+
|valign="top" align="right"|(*)||align="left" width="400pt" |See lap splice class C (Other than top bars).
 
|-
 
|-
|align="right"|<math>\, e</math>||=2.718
+
|valign="top" align="right"|Notes:||align="left" width="400pt" |Reiforcement not required by design.  Hairpins are sufficient for renforcing requirements.
 
|-
 
|-
|align="right"|<math>\, \phi</math>||= \varepsilon\ creep \times E_{28\ days}
+
|valign="top" align="right"|&nbsp;||align="left" width="400pt" |The minimum percentage of reinforcement, "P" , is not required to be met, unless scour is anticipated.
 
|-
 
|-
|align="right" valign="top"|<math>\, \varepsilon\ creep</math>||width="300pt"|= (See page 3 PCA design of precast prestressed concrete girders. Use 40% factor based on creep at erection for 28 days.)
+
|valign="top" align="right"|&nbsp;||align="left" width="400pt" |Use for all types of piling, except timber.
 
|}
 
|}
  
  
The following formulas are used to determine:
 
*Camber due initial strand stress (inch),
 
*deflection due beam weight (inch),
 
*camber due strands, beam weight and 28 day creep (inch),
 
*camber L/4 due strands, beam weight and 28 day creep (inch),
 
*deflection due to slab weight (inch),
 
*camber centerline due strands, beam weight, 28 day creep, slab and diaphragm (inch), and
 
*camber quarterpoint due strands, beam weight, 28 day creep, slab and diaphragm (inch).
 
  
 +
'''Reinforced Footing - Seismic Performance Category A'''
 +
 +
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 +
|-
 +
|[[Image:751.40 seismic performance category a footing reinforcement front elevation.gif]]
 +
|[[Image:751.40 seismic performance category a footing reinforcement side elevation.gif]]
 +
|-
 +
!Front Elevation||Side Elevation
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
| &nbsp;
 +
|[[Image:751.40 Open Concrete Int Bents and Piers-reinforcement-seismic performance category a footing reinforcement plan.gif]]
 +
|-
 +
!&nbsp;||Plan
 +
|}
 +
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|valign="top" align="right"|(*)||align="left" width="400pt" |See lap splice class C (Other than top bars).
 +
|-
 +
|valign="top" align="right"|Note:||align="left" width="400pt" |The maximum size of stress steel allowed is #8 bars.
 +
|}
  
Formulas used:
 
  
Positive deflect up <math>\, \uparrow</math>
+
'''Reinforced Footing - Seismic Performance Categorys B, C & D'''
  
Negative deflect down <math>\, \downarrow</math>
+
See Structural Project Manager or Liaison before using the following seismic details.
  
  
<math>\, \uparrow \triangle_1 = 144 \times 10^3 \times \underset {(a = \big[ L - (centerline\ to\ centerline\ tie\ downs) \big] \div 2)ft.}{ \Bigg[ \frac{F_{01}(e_1)(L_2}{8E_i I} + \frac{F_{02}(e_2 + e_3}{E_i I} \Bigg( \frac{L_2}{8} - \frac{a^2}{6} \Bigg) - \frac{F_{02}(e_3(L^2)}{8E_i I} \Bigg]} </math>
+
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 +
|-
 +
|[[Image:751.40 seismic performance category b c & d footing reinforcement front elevation.gif]]
 +
|[[Image:751.40 seismic performance category b c & d footing reinforcement side elevation.gif]]
 +
|-
 +
!Front Elevation||Side Elevation
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
|valign="bottom"|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- typical detail pile channel shear connector.gif]]
 +
|rowspan="2"|[[Image:751.40 seismic performance category b c & d footing reinforcement plan of top reinforcement.gif]]
 +
|-
 +
!Typical Detail<br/>Pile Channel<br/>Shear Connector
 +
|-
 +
! &nbsp;||Plan Showing Top Reinforcement
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
| &nbsp;
 +
|[[Image:751.40 seismic performance category b c & d footing reinforcement plan of bottom reinforcement.gif]]
 +
|-
 +
! &nbsp;||Plan Showing Bottom reinforcement
 +
|}
  
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|valign="top" align="right"|(*)||align="left" width="400pt" |For reinforcement in top of the footing, see lap splice class C (Top bars).
 +
|-
 +
|valign="top" align="right"|(**)||align="left" width="400pt" |Place the top reinforcement uniformly outside the column.
 +
|-
 +
|valign="top" align="right"|(***)||align="left" width="400pt" |Use same area of steel in the top of the footing as is required for the bottom.
 +
|-
 +
|valign="top" align="right"|Notes:||align="left" width="400pt" |For reinforcement in bottom of the footing, see lap splice Class C (Other than top bars).
 +
|-
 +
| &nbsp;||align="left" width="400pt" |The maximum size of stress steel allowed is #8 bars.
 +
|-
 +
| &nbsp;||align="left" width="400pt" |Unreinforced footings shall not be used in seismic performance categories B, C & D.
 +
|}
  
Beam weight camber
+
====751.40.8.11.4 Spread Footings====
 
+
=====751.40.8.11.4.1 Design and Dimensions=====
<math>\, \downarrow \triangle_2 = \frac{5W_B(L^4)}{384E_iI} (1728 \times 10^3)</math>
 
  
  
Slab weight camber
+
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 +
|-
 +
|width="250pt"|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-side elevation.gif]]
 +
|width="250pt"|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-front elevation.gif]]
 +
|-
 +
!Side Elevation||Front Elevation
 +
|}
  
<math>\, \downarrow \triangle_s = \Bigg[ \frac{5W_s(L^4)}{384E_fI_{TR}} + \frac{P(L^3)}{48E_fI_{TR}} + \frac{2PsX(3L^2 - 4X^2)}{48E_fI_{TR}} \Bigg] (1728 \times 10^3)</math>
+
{|align="center"
 +
|-
 +
|d||= column diameter
 +
|-
 +
|L||= footing length
 +
|-
 +
|b||= footing depth
 +
|-
 +
|B||= footing width
 +
|-
 +
|A||= edge distance from column
 +
|}
  
  
Force straight strands (1/2" low relaxation strands)
+
The calculated bearing pressure shall be less than the ultimate capacity of the foundation soil.  The ultimate capacity of the foundation soil can be conservatively estimated as 2.0 times the allowable bearing pressure given on the Bridge Memorandum.  The analysis method of calculating bearing pressures is outlined in the following information.
  
:<math>\, F_{01} = (no.\ of\ straight\ strands) \times \big[ 31.0 - (17.1 \times 0.153) \big] kips</math>
 
  
 +
'''Dimensional Requirements'''
  
Force draped strands ( 1/2 " low relaxation strands)
+
{|
 +
|valign="top"|'''L''' -||Minimum of 1/6 x distance from top of beam to bottom of footing (3" increments);
 +
|-
 +
|valign="top"|'''B''' -||Minimum footing width is column diameter + 2A, (3" increments);
 +
|-
 +
|valign="top"|'''A''' -||Minimum of 12";
 +
|-
 +
|valign="top"|'''b''' -||Minimum of 30" or column diameter, Maximum of 72" at 3" increments; (for column diameters 48" and greater use a 48" minimum footing depth.)
 +
|}
  
:<math>\, F_{02} = (no.\ of\ draped\ strands) \times \big[ 31.0 - (17.1 \times 0.153) \big]
 
kips</math>
 
  
 +
'''Size'''
  
:<math>\, 270 ksi \times 75% \times (0.153 sq.\ in.) = 31\ kips\ per\ strand</math>
+
The size of footing shall be determined by computing the location of the resultant force and by calculating the bearing pressure.
:<math>202.5 \times (1-0.0884) = 184.6 ksi</math>
 
:<math>184.6 \times (1-0.0884) = 168.28 ksi</math>
 
:<math>202.5 - 168.28 = 34.22 ksi = Total\ loss</math>
 
  
:<math>Average\ loss = Totalloss/2 = 34.22/2 = 17.1 ksi</math>
+
Long, narrow footings are to be avoided, especially on foundation material of low capacity.  In general, the length to width ratio should not exceed 2.0, except on structures where the ratio of the longitudinal to transverse loads or some other consideration makes the use of such a ratio limit impractical.
 +
 
 +
 
 +
'''Location of Resultant Force'''
 +
 
 +
 
 +
The location of the resultant force shall be determined by the following equations.
 +
 
 +
The Middle 1/3 is defined as: <math>\, \frac{e_L}{L} + \frac{e_B}{B} \le \frac{1}{6}</math>
 +
 
 +
The Middle 1/2 is defined as: <math>\, \frac{e_L}{L} \le \frac{1}{4}</math> and <math>\, \frac{e_B}{B} \le \frac{1}{4}</math>
 +
 
 +
The Middle 2/3 is defined as: <math>\, \frac{e_L}{L} \le \frac{1}{3}</math> and <math>\, \frac{e_B}{B} \le \frac{1}{3}</math>
 +
 
 +
The following table specifies requirements for the location of the resultant force.
  
  
{|
+
{|border="1" style="text-align:center;" cellpadding="5" align="center"
|<math>e_1</math>||= dist. centroid beam to centroid straight strand (in.)
 
 
|-
 
|-
|<math>e_2</math>||= dist. centroid beam to low centroid draped at center of beam (in.)
+
!width="150pt"|Soil Type||width="150pt"|Resultant Location Group I - VI||width="150pt"|Resultant Location Earthquake Loads Categories B, C and D
 
|-
 
|-
|<math>e_3</math>||= dist. centroid beam to up centroid draped at end of beam (in.)
+
|align="left" width="150pt"|Clay, clay and boulders, cemented gravel, soft shale with allowable bearing values less than 6 tons, etc.
 +
|middle 1/3
 +
|middle 1/2
 
|-
 
|-
|<math>L</math>||= length (ft.) (cneterline bearing to centerline bearing).
+
|align="left" width="150pt"|Rock, hard shale with allowable bearing values of 6 tons or more.
 +
|middle 1/2
 +
|middle 2/3
 +
|}
 +
 
 +
 
 +
'''Bearing Pressure'''
 +
 
 +
The bearing pressure for Group I thru VI loads shall be calculated using service loads and the allowable overstress reduction factors as specified in AASHTO Table 3.21.1A. The calculated bearing pressure shall be less than the allowable pressure given on the Bridge Memorandum.
 +
 
 +
The bearing pressure for Earthquake Loads in Categories B, C, and D shall be  calculated from loads specified in AASHTO Division I-A Seismic Design, Sections 6.2.2, 7.2.1, and 7.2.2.  The seismic design moment shall be the elastic seismic moment (EQ) divided by the modified response modification factor R'.  The modified seismic moment shall then be combined independently with moments from other loads:
 +
 
 +
Group Load = <math>\, 1.0(D + B + SF + E + EQ/R')</math>
 +
 
 +
Where:
 +
{|
 +
|<math>\, D</math>||= dead load
 
|-
 
|-
|<math>I</math>||= moment of inertia (in.<sup>2</sup>) non-transformed.
+
|<math>\, B</math>||= buoyancy
 
|-
 
|-
|<math>I_{TR}</math>||= moment of inertia (in.<sup>2</sup>) transformed.
+
|<math>\, SF</math>||= stream flow pressure
 
|-
 
|-
|<math>Ps</math>||= concentrated loads due to variable slab thickness on each end.
+
|<math>\, EQ</math>||= elastic seismic moment
 
|-
 
|-
|<math>X</math>||= dist. from centerline brg. to Ps.
+
|<math>\, E</math>||= earth pressure
 
|-
 
|-
|<math>P</math>||= concentrated load due to diaphragm at center of span (kips)
+
|<math>\, R'</math>||= R/2 for category B
 
|-
 
|-
|<math>W_B</math>||= uniform beam load (kips/ft.)
+
|&nbsp;||= 1 for categories C and D
 
|-
 
|-
|<math>W_S</math>||= uniform slab load (kips/ft.)
+
|colspan="2"|&nbsp;
 
|-
 
|-
|<math>F</math>||= factor for 28 day creep
+
|<math>\, R</math>||= Response Modification Factor
 
|-
 
|-
|<math>E_i</math>||= modulus of elasticity corresponding to initial girder concrete strength
+
|&nbsp;||= 5 for multi-column bent
 
|-
 
|-
|<math>E_f</math>||= modulus of elasticity corresponding to final girder concrete strength
+
|&nbsp;||= 3 for single-column bent
 
|}
 
|}
  
  
<math>\, \triangle Centerline = F( \triangle_1 - \triangle_2) - \triangle_s</math>
+
The calculated bearing pressure shall be less than the ultimate capacity of the foundation soilThe ultimate capacity of the foundation soil can be conservatively estimated as 2.0 times the allowable bearing pressure given on the Bridge MemorandumThe analysis method of calculating bearing pressures is outlined in the following information.
::<math>\, \triangle\ at\ 0.10 = 0.314 ( \triangle\ at\  Centerline) </math>
 
::<math>\, \triangle\ at\ 0.20 = 0.593 ( \triangle\ at\  Centerline) </math>
 
::<math>\, \triangle\ at\ 0.25 = 0.7125 ( \triangle\ at\ Centerline) </math>
 
::<math>\, \triangle\ at\ 0.30 = 0.813 ( \triangle\ at\ Centerline) </math>
 
::<math>\, \triangle\ at\ 0.40 = 0.952 ( \triangle\ at\  Centerline) </math>
 
  
  
Note: Compute and show on plans camber at  1/4 points for bridges with spans less than 75', 1/10 points for spans 75' and over.
+
<center>See AASHTO 4.4.2 for explanation of notations.</center>
  
===== 751.40.8.10.1.4 Superstructure Design =====
 
  
'''Live Load Distribution'''
+
<center>[[Image:751.40 sketch of dimensions for footings subjected to eccentric loading.gif]]</center>
  
The live load distribution to girders may be assumed to be the same as the
+
<center>'''Sketch of Dimensions for Footings Subjected to Eccentric Loading'''</center>
AASHTO distribution for concrete floors on steel I-Beam stringers. These
 
factors may be found in [[751.40 Widening and Repair #751.40.8.2 Distribution of Loads|EPG 751.40.8.2 Distribution of Loads]].
 
  
  
'''Ultimate Load Capacity'''
+
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 
 
The ultimate load capacity shall be not less than 1.3 times (the weight of
 
the girder plus the weight of the slab and diaphragms plus the weight of the
 
future wearing surface) plus 2.17 times the design live load plus impact.
 
 
 
 
 
'''Ultimate Strength'''
 
 
 
The ultimate moment on a prestressed girder as determined in accordance
 
with the ultimate load capacity indicated above, shall not be greater than
 
the ultimate strength determined as follows:
 
 
 
 
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|Where &nbsp; <math>\, t \le 0.2d</math>|| &nbsp;|| Where &nbsp; <math>\, t > 0.2d</math>
+
!For &nbsp; <math>\, e_L < L/6</math>
 +
!For &nbsp; <math>\, L/6 < e_L < L/2</math>
 
|-
 
|-
|[[Image:751.40 prestressed concrete i-girders-ultimate strength diagram-1.gif]]|| &nbsp;
+
|colspan="2"| &nbsp;
|[[Image:751.40 prestressed concrete i-girders-ultimate strength diagram-2.gif]]
 
 
|-
 
|-
|<math>\, M_u = A_sf'_s (d -t/2)</math><br/>or<br/><math>\, M_u = 0.85 f'_c bt (d-t/2)</math>
+
|<math>\, q_{max} = \frac{Q (1 + \frac{6e_L}{L})}{BL}</math>
|Use the lesser<br/>in each case
+
|<math>\, q_{max} = \frac{2Q}{3B (L/2 - e_L)}</math>
|<math>\, M_u = A_sf'_s (0.9d)</math><br/>or<br/><math>\, M_u = 0.85 f'_c b(0.2d)(0.9d)</math>
 
|}
 
 
 
 
 
Where:
 
{|
 
|<math>\, A_s</math>||= Area of p/s strands in bottom flange
 
 
|-
 
|-
|<math>\, b</math>, <math>\, b'</math>, <math>\, t</math> & <math>\, d</math>||= as shown above
+
|colspan="2"| &nbsp;
 
|-
 
|-
|<math>\, f'_s</math>||= Ultimate strength of p/s strands
+
|<math>\, q_{min} = \frac{Q (1 - \frac{6e_L}{L})}{BL}</math>
 +
|<math>\, q_{min} = L_1 = 3(L/2 - e_L)</math>
 
|-
 
|-
|<math>\, f'_c</math>||= Ultimate strength of slab concrete = 4,000 psi
+
|colspan="2"| &nbsp;
 +
|-
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-plan view 1.gif]]
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-plan view 2.gif]]
 +
|-
 +
!Plan View||Plan View
 +
|-
 +
|colspan="2"| &nbsp;
 +
|-
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure 1.gif]]
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure 2.gif]]
 +
|-
 +
!Bearing Pressure||Bearing Pressure
 
|}
 
|}
  
 +
<center>'''Bearing Pressure for Footing Loaded Eccentrically About One Axis'''</center>
  
'''Maximum Prestressing Steel Area'''
 
  
:<math>\, A_s = \frac{0.85 f'_c b t}{f'_s}</math> &nbsp; When &nbsp; <math>\, t \le 0.2d</math>
 
  
  
:<math>\, a_s = \frac{0.85 f._c b (0.2d)}{f'_s}</math> &nbsp; When &nbsp; <math>\, t > 0.2d</math>
+
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
!colspan="2"|CASE 1||CASE 2
 +
|-
 +
|colspan="2"|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 1 plan view.gif]]
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 2 plan view.gif]]
 +
|-
 +
|colspan="2"|&nbsp;||k, x and y from AASHTO chart
 +
|-
 +
|colspan="2"|<math>\, q_{max} = \frac{R}{BL} (1 + \frac{6e_L}{L} + \frac{6e_B}{B})</math>
 +
|<math>\, q_{max} = \frac{KR}{BL}</math>
 +
|-
 +
!colspan="2"|CASE 1 Plan View||CASE 2 Plan View
 +
|-
 +
|colspan="3"|&nbsp;
 +
|-
 +
!colspan="2"|CASE 3||CASE 4
 +
|-
 +
|colspan="2"|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 3 plan view.gif]]
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 4 plan view.gif]]
 +
|-
 +
|<math>\, r = j/n</math>
 +
|<math>\, s = 1 + r + r^2</math>
 +
|rowspan="3"|<math>\, q_{max} = \frac{3R}{8FG}</math>
 +
|-
 +
|<math>\, g = \frac{n(1 + rs)}{4s}</math>
 +
|<math>\, f = \frac{L(3s - r - 2)}{4s}</math>
 +
|-
 +
|<math>\, q_{max} = \frac{6R}{Lns}</math>
 +
|&nbsp;
 +
|-
 +
!colspan="2"|CASE 3 Plan View||CASE 4 Plan View
 +
|}
  
 +
<center>'''Bearing Pressure for Footing Loaded Eccentrically About Two Axes'''</center>
  
In lieu of the above, AASHTO - Article 9.17 & 9.18 may be used. (This is the method used by computer program BR200)
 
  
===== 751.40.8.10.1.5 Web Reinforcement =====
+
'''Loading Cases'''
  
(5" Min. - 21" Max. bar spacing for #4 bars)
+
Loads for Groups I thru VI shall be calculated for all bridges.
(5" Min. - 24" Max. bar spacing for #5 bars)
 
  
 +
Earthquake loads shall be calculated when the bridge is in Seismic Zones B, C, and D.
 +
 +
Loads for other group loadings shall be used on a case by case basis.
  
<center>[[Image:751.40 prestressed concrete i-girders-web reinforcement diagram.gif]]</center>
 
  
 +
'''Reinforcement'''
  
(*) Prestressed concrete members shall be reinforced for diagonal tension stresses. Shear reinforcement shall be placed perpendicular to the axis of the member. The formula to be used to compute areas of web reinforcement is as follows:
+
The footing is to be designed so that the shear strength of the concrete is adequate to handle the shear stress without the additional help of reinforcement. If the shear stress is too great, the footing depth should be increased.
  
:<math>\, A_V = \frac{(V_U - V_C)S}{2f_{sy}jd}</math> &nbsp; Where &nbsp; <math>\, V_C = (0.06f'c)b'jd</math> &nbsp; but not more than <math>\, 180 b'jd</math>
 
  
:But shall not be less than  &nbsp; <math>\, A_V = \frac{100b's}{60,000} = 0.00167 b's</math>.
 
  
 +
'''Shear'''
  
 +
The shear capacity of the footings in the vicinity of concentrated loads shall be governed by the more severe of the following two conditions.
  
(**) Since large moments and large shears occur in the same area of the girder near the interior supports, the AASHTO formula (AASHTO - 9.20 -Shear) for computing the area of web reinforcement has been modified. The formula to be used to compute areas of web reinforcement near interior supports is as follows:
 
  
:<math>\, A_V = \frac{(V_U - V_C)S}{f_{sy}jd}; V_C = 180b'jd</math>
+
'''Critical section at "d" distance from face of column:'''
  
The value "jd" is the distance from the slab reinforcement to the center-of-gravity of the compression area under ultimate loads.
+
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:center"
 
+
|-
Use #4 shear reinforcement when possible. Alternate B1 bar will not work with #5.
+
|[[Image:751.40 critical section at d dist from face of column.gif]]
 +
|-
 +
!Load Factor
 +
|}
 +
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:left"
 +
|-
 +
|<math>\, V_n = V_u/(\phi bd)</math>
 +
|-
 +
|<math>\, V_c = 2 \sqrt{f'_c}</math>
 +
|-
 +
|<math>\, b</math> = footing width
 +
|}
  
  
'''Anchorage Zone Reinforcement - AASHTO Article 9.21.3'''
+
'''Critical section at "d/2" distance from face of column:'''
  
The following detail meets the criteria for anchorage zone reinforcement for pretensioned girders (AASHTO Article 9.21.3) for all MoDOT standard girder shapes.
+
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:center"
 
+
|-
 
+
|[[Image:751.40 critical section at d divided by 2 dist from face of column.gif]]
{|border="0" cellpadding="5" align="center" style="text-align:center" cellspacing="0"
+
|-
|+'''Standard P/S Girder End Section'''
+
!Load Factor
|[[Image:751.40 prestressed concrete i-girders-standard girder end-end section.gif]]
 
|[[Image:751.40 prestressed concrete i-girders-standard girder end-end elevation.gif]]
 
 
|}
 
|}
{|border="0" cellpadding="5" align="center" style="text-align:center" cellspacing="0"
+
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:left"
 +
|-
 +
|<math>\, V_n = V_u/(\phi b_0d</math>
 +
|-
 +
|<math>\, V_c = 4 \sqrt{f'_c}</math>
 
|-
 
|-
|align="right" valign="top"|*
+
|<math>\, b_0 = 4(d + Equivalent\ square\ column\ width)</math>
|width="200" align="left"|2 3/4" (Type 2, 3 & 4)<br/>5 1/4" (Type 6)
 
 
|-
 
|-
|align="right" valign="top"|**
+
|colspan="2"|If shear stress is excessive, increase footing depth.
|width="200" align="left"|15 1/2" (Type 2, 3 & 4)<br/>22 1/2" (Type 6)
 
 
|}
 
|}
  
  
'''Sole Plate Anchor Studs'''
 
  
The standard 1/2" sole plate will be anchored with four 1/2" x 4" studs.
+
'''Bending'''
 +
 
 +
If the shear line is within the projected equivalent square column, the footing may be considered satisfactory for all conditions. (minimum reinforcement required)
 +
 
 +
If the shear line is outside of the projected column, the footing must be analyzed and reinforced for bending and checked for shear stress.
 +
 
 +
<center>[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-shear line diagrams.gif]]</center>
 +
 
 +
The critical section for bending shall be taken at the face of the equivalent square column. The equivalent square column is the theoretical square column which has a cross sectional area equal to the round section of the actual column and placed concentrically.  
 +
 
 +
 
 +
'''Reinforcement in Bottom of Footing'''
  
Studs shall be designed to meet the criteria of AASHTO Div. I-A in Seismic Performance Category C or D.
+
The bearing pressure used to design bending reinforcement for Group I thru VI loads shall be calculated using Load Factor Loads.
  
Stud capacity is determined as follows:
+
The bearing pressure used to design bending reinforcement for Earthquake Loads in Categories B, C, and D shall be calculated from the same loads as specified in AASHTO Division 1-A Seismic Design for ultimate bearing pressure.
  
<math>\, Stud\ Cap. = (n)(As)(0.4Fy)(1.5)</math>
+
The bottom reinforcement shall be designed using ultimate strength design.  
  
Where:
 
{|
 
|<math>\, n</math>||= no. of studs
 
|-
 
|<math>\, As</math>||= area of stud
 
|-
 
|<math>\, Fy</math>||= yield strength of stud (50 ksi)
 
|-
 
|<math>\, 0.4Fy</math>||= Allowable Shear in Pins AASHTO Table 10.32.1A
 
|-
 
|<math>\, 1.5</math>||= seismic overload factor
 
|}
 
  
If required, increase the number of 1/2" studs to six and space between open B2 bars. If this is still not adequate, 5/8" studs may be used.  The following table may be used as a guide to upper limits of dead load reactions:
+
'''Distribution of Reinforcement'''
  
{|align="center"
+
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:center"
|width="300pt"|The minimum 3/16" fillet weld between the<br/>1/2" bearing plate and 1 1/2" sole plate is<br/>adequate for all cases.
 
| align="center" |
 
{| border="1" cellspacing="0" style="text-align:center"
 
|+Seismic Bearing Plate Anchor Design
 
|rowspan="2" width="50pt"|No. of<br/>Studs||width="50pt"  rowspan="2"|Stud<br/>Dia.||colspan="2"|Max. Allowable D.L. Reaction (Kips)
 
 
|-
 
|-
|A = 0.30||A = 0.36
+
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-distribution of reinforcement.gif]]
 
|-
 
|-
|4||1/2"||78||65
+
|L = Footing Length
 
|-
 
|-
|6||1/2"||117||98
+
|B = Footing Width
|-
 
|4||5/8"||122||102
 
|-
 
|6||5/8"||184||153
 
|}
 
 
|}
 
|}
  
===== 751.40.8.10.1.6 Strands – Miscellaneous =====
+
Reinforcement shall be distributed uniformly across the entire width of footing in the long direction. In the short direction, the portion of the total reinforcement given by AASHTO Equation 4.4.11.2.2-1 shall be distributed uniformly over a band width equal to the length of the short side of the footing, B.
  
'''Detensioning'''
+
:<math>\, Band\ Width\ Reinforcement = 2(total\ reinforcement\ in\ short\ direction)/(\beta + 1)</math>
 +
:<math>\, \beta = the\ ratio\ of\ footing\ length\ to\ width = L/B</math>
  
In all detensioning operations the prestressing forces must be kept symmetrical about the vertical axis of the member and must be applied in such a manner as to prevent any sudden or shock loading.
 
  
 +
'''Reinforcement in Top of Footing'''
  
'''General Information'''
+
Reinforcement in the top of the footing shall be provided for Seismic Performance Categories B, C, and D.  This reinforcement shall be the equivalent area as the bottom steel in both directions.  The top steel shall be placed uniformly outside the column.
  
'''Splicing:'''
 
  
One approved splice per pretensioning strand will be permitted provided the splices are so positioned that none occur within a member. Strands which are being spliced shall have the same "Twist" or "Lay". Allowance shall be made for slippage of the splice in computing strand elongation.
+
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 +
|+'''Reinforcement Details - Seismic Performance Category A'''
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-SPC A reinforcement details-front elevation.gif]]
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-SPC A reinforcement details-side elevation.gif]]
 +
|-
 +
!Front Elevation||Side Elevation
 +
|}
  
'''Wire failure:'''
 
  
Failure of one wire in a seven wire pretensioning strand may be accepted, provided that, it is not more than two percent of the total area of the strands.
+
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 +
|+'''Reinforcement Details - Seismic Performance Categorys B, C & D'''
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-SPC b c & d reinforcement details-front elevation.gif]]
 +
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-SPC b c & d reinforcement details-side elevation.gif]]
 +
|-
 +
!Front Elevation||Side Elevation
 +
|}
  
'''Sand Blasting:'''
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|valign="top" align="right"|(*)||align="left" width="400pt" |Use same area of steel in the top of the footing as is required for the bottom.
 +
|}
  
On structures where it is questionable as to the clarity of areas to be sandblasted: show limits of sandblasted area in a plan view of details on girder ends (bent sheet). However, generally, sandblasting is covered by Missouri Standard Specification 705.4.14.
+
===751.40.8.12 Concrete Pile Cap Intermediate Bents===
  
==== 751.40.8.10.2 Length ====
+
====751.40.8.12.1 Design====
  
 +
=====751.40.8.12.1.1 Unit Stresses=====
  
===== 751.40.8.10.2.1 Structure Length =====
 
  
<center>[[Image:751.40 prestressed concrete i-girders-structure length-integral end bents.gif]]</center>
+
{|border="0"
  
<center>(*) Maximum length for End Bent to End Bent = 600 feet.</center>
+
|(1)||Reinforced Concrete
 
 
<center>'''Typical Continuous Prestressed Structure'''<br/>'''(Integral End Bents)'''</center>
 
 
 
 
 
 
 
<center>[[Image:751.40 prestressed concrete i-girders-structure length-non integral end bents.gif]]</center>
 
 
 
<center>(**) Maximum length for End Bent to End Bent = 800 feet.</center>
 
 
 
<center>'''Typical Continuous Prestressed Structure'''<br/>'''(Non-Integral End Bents)'''</center>
 
 
 
==== 751.40.8.10.3 Miscellaneous Details ====
 
 
 
 
 
===== 751.40.8.10.3.1 Shear Blocks =====
 
 
 
A minimum of two Shear Blocks 12" wide x [[Image:751.40 circled 1.gif]] high by width of diaphragm, will be detailed at effective locations on open diaphragm bent caps when adequate structural restraint cannot be provided for with anchor bolts.
 
 
 
 
 
<center>[[Image:751.40 prestressed concrete i-girders-miscellaneous details-shear block.gif]]</center>
 
 
 
 
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|valign="top" align="right"|[[Image:751.40 circled 1.gif]]||align="left" width="400pt" |Height of shear block shall extend a minimum of 1" above the top of the sole plate.
+
|&nbsp;||Class B Concrete (Substructure)||<math>\, f_c</math> = 1,200 psi||<math>\, f'_c</math> = 3,000 psi
 +
|-
 +
|&nbsp;||Reinforcing Steel (Grade 60||<math>\, f_s</math> = 24,000 psi||<math>\, f_y</math> = 60,000 psi
 +
|-
 +
|&nbsp;||<math>\, n</math> = 10
 +
|-
 +
|&nbsp;||colspan="3"|<math>\, E_c = 3,122 ksi (Ec = W^{1.5} \times 33 \sqrt{f'_c}, Ec = 57,000 \sqrt{f'c}</math>
 +
|-
 +
|&nbsp;
 +
|-
 +
|(2)||Structural Steel
 +
|-
 +
|&nbsp;||Structural Carbon Steel (ASTM A709 Grade 36)||<math>\, f_s</math> = 20,000 psi||<math>\, f_y</math> = 36,000 psi
 +
|-
 +
|&nbsp;
 +
|-
 +
|(3)||Piling
 +
|-
 +
|&nbsp;
 +
|-
 +
|(4)||Overstress
 +
|-
 +
|&nbsp;||colspan="3"|The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for service loads.
 
|}
 
|}
  
===== 751.40.8.10.3.2 Anchor Bolts =====
+
=====751.40.8.12.1.2 Loads=====
 +
 
  
'''Simple Spans'''
+
{|border="0"
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
|(1)||Dead Loads
 
|-
 
|-
|colspan="2"|[[Image:751.40 prestressed concrete i-girders-miscellaneous details-anchor bolts.gif]]
+
|&nbsp;
 
|-
 
|-
!width="50%"|Expansion||width="50%"|Fixed
+
|(2)||Live Load
 
|-
 
|-
!colspan="2"|Part Elevation
+
|&nbsp;||As specified on Bridge Memorandum.
|}
 
 
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|valign="top" align="right"|Note:||align="left" width="400pt"|It is permissible for the reinforcing bars and or the strands to come in contact with the materials used in forming A.B. holes.
+
|&nbsp;||Impact of 30% is to be used for design of the beam.  No impact is to be used for design of any other portion of bent including the piles.
 
|-
 
|-
|valign="top" align="right"|&nbsp;||align="left" width="400pt"|If A.B. holes are formed with galvanized sheet metal, the forms may be left in place.
+
|&nbsp;
 
|-
 
|-
|valign="top" align="right"|&nbsp;||align="left" width="400pt"|Hole (1 1/2" round) to be grouted with expansive type mortar.
+
|(3)||Temperature, Wind and Frictional Loads
 
|}
 
|}
  
===== 751.40.8.10.3.3 Dowel Bars =====
+
=====751.40.8.12.1.3 Distribution of Loads=====
 +
 
 +
{|border="0"
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
|(1)||Dead Loads
 
|-
 
|-
|[[Image:751.40 prestressed concrete i-girders-miscellaneous details-dowel bars part elevation.gif]]
+
|&nbsp;||Loads from stringers, girders, etc. shall be concentrated loads applied at the intersection of centerline of stringer and centerline of bearing. Loads from concrete slab spans shall be applied as uniformly, distributed loads along the centerline of bearing.
|[[Image:751.40 prestressed concrete i-girders-miscellaneous details-dowel bars section a-a.gif]]
 
 
|-
 
|-
!width="50%"|Part Elevation<br/>(Fixed Bent) (*)||width="50%"|Section A-A (*)
+
|&nbsp;
|}
 
 
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|valign="top" align="right"|(*)||align="left" width="300pt"|Details shown are for SPC A and B only.
+
|(2)||Live Load
 +
|-
 +
|&nbsp;||Loads from stringers, girders, etc. shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of bearing.  For concrete slab spans distribute two wheel lines over 10'-0" (normal to centerline of roadway) of substructure beam.  This distribution shall be positioned on the beam on the same basis as used for wheel lines in Traffic Lanes for Substructure Design.
 +
|-
 +
|&nbsp;
 +
|-
 +
|(3)||Temperature, Wind and Frictional Loads
 
|}
 
|}
  
Dowel bars shall be used for all fixed intermediate bents under prestressed superstructures.
+
=====751.40.8.12.1.4 Design Assumptions=====
  
 +
'''LOADINGS'''
  
Seismic Performance Category A:
+
{|border="0"
:Use #6 Bars @ 18" Cts. for dowel bars.
 
  
 
+
|(1)||colspan="2"|Beam
Seismic Performance Category B:
+
|-
:Dowel bars shall be determined by design. (#6 Bars @ 18" Cts. minimum)
+
|&nbsp;||colspan="2"|The beam shall be assumed continuous over supports at centerline of piles.
:Design dowel bars for shear using service load design.
+
|-
:Allowable stresses are permitted to increase by 33.3% for earthquake loads.
+
|&nbsp;||colspan="2"|Intermediate bent beam caps shall be designed so that service dead load moments do not exceed the cracking moment of the beam cap (AASHTO Article 8.13.3, Eq. 8-2).
 
 
 
 
Seismic Performance Categories C & D:
 
:See Structural Project Manager.
 
 
 
===== 751.40.8.10.3.4 Expansion Device Support Slots =====
 
 
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|[[Image:751.40 prestressed concrete i-girders-miscellaneous details-exp device support holes part plan.gif]]
+
|&nbsp;
 
|-
 
|-
!Part Plan of P/S Concrete I-Girder @ Expansion Device End
+
|(2)||colspan="2"|Piles
 
|-
 
|-
| &nbsp;
+
|&nbsp;||(a)||Bending
 
|-
 
|-
|[[Image:751.40 prestressed concrete i-girders-miscellaneous details-exp device support holes part elevation.gif]]
+
|colspan="2"|&nbsp;||Stresses in the piles due to bending need not be considered in design calculations for Seismic Performance Category A.
 
|-
 
|-
!Part Elevation of P/S Concrete I-Girder @ Expansion Device End
+
|&nbsp;||(b)||Dead Loads, etc.
|}
 
 
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|valign="top" align="right"|(*)||align="left" width="300pt"|Show these dimensions on the P/S concrete girder sheet.
+
|colspan="2"|&nbsp;||Dead load of superstructure and substructure will be distributed equally to all piles which are under the main portion of the bent.
 
|}
 
|}
  
 +
====751.40.8.12.2 Reinforcement====
 +
=====751.40.8.12.2.1 General=====
  
===751.40.8.11 Open Concrete Intermediate Bents and Piers===
+
'''PRESTRESS DOUBLE-TEE STRUCTURES'''
  
====751.40.8.11.1 Design====
 
  
=====751.40.8.11.1.1 General and Unit Stresses=====
+
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Bents_with_3_thru_6_in_crown).gif]]</center>
  
'''GENERAL'''
+
<center>'''BENTS WITH 3" THRU 6" CROWN'''</center>
  
Use Load Factor design method, except for footing pressure and pile capacity where the Service Load design method shall be used.
 
  
In some cases, Service Load design method may be permitted on widening projects, see Structural Project Manager.
+
{|border="0" align="center" style="text-align:center"
  
The terms, Intermediate Bents and Piers, are to be considered interchangeable for this Manual Section.
+
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Section_AA).gif]]
 +
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Section_BB).gif]]
 +
|-
 +
|'''SECTION A-A'''||'''SECTION B-B'''
 +
|}
  
  
'''DESIGN UNIT STRESSES'''
+
{|border="0"
  
 
+
|(*)||Channel shear connectors are to be used in Seismic Performance Categories B, C & D.  For details not shown, see [[751.9_Bridge_Seismic_Design|EPG 751.9 Bridge Seismic Design]].
(1) Reinforced Concrete
 
 
 
:{|
 
 
|-
 
|-
|Class B Concrete (Substructure)||width="100"|<math>\, f_c</math> = 1,200 psi||width="100"|<math>\, f'_c</math> = 3,000 psi
+
|valign="top"|(**)||2'-6" Min. for Seismic Performance Category A.<br/>2'-9" Min. for Seismic Performance Categories, B, C & D.
|-
 
|Reinforcing Steel (Grade 60)||<math>\, f_s</math> = 24,000 psi||<math>\, f_y</math> = 60,000 psi
 
|-
 
|n = 10||&nbsp;
 
|-
 
|<math>\, E_c = W_1.5 \times 33 \sqrt{f'_c}</math>|| (AASHTO Article 8.7.1) (*)
 
 
|-
 
|-
 +
|colspan="2"|Note:  Use square ends on Prestress Double-Tee Structures.
 
|}
 
|}
 +
 +
 +
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Bents_with_crown_over_6_in).gif]]</center>
 +
 +
<center>'''BENTS WITH CROWN OVER 6"'''</center>
  
  
  
(2) Reinforced Concrete (**)
+
{|border="0" align="center" style="text-align:center"
  
:{|
+
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Bents_with_crown_over_6_in)_(Section_AA).gif]]||[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Bents_with_crown_over_6_in)_(Section_BB).gif]]
|-
 
|Class B-1 Concrete (Substructure)||width="100"|<math>\, f_c</math> = 1,600 psi||width="100"|<math>\, f'_c</math> = 4,000 psi
 
|-
 
|Reinforcing Steel (Grade 60)||<math>\, f_s</math> = 24,000 psi||<math>\, f_y</math> = 60,000 psi
 
|-
 
|<math>\, n</math> = 8||&nbsp;
 
|-
 
|<math>\, E_c = W_1.5 \times 33 \sqrt{f'c}</math>|| (AASHTO Article 8.7.1) (*)
 
 
|-
 
|-
 +
|'''SECTION A-A'''||'''SECTION B-B'''
 
|}
 
|}
  
  
 +
{|border="0"
  
(3) Structural Steel
+
|(*)||Channel shear connectors are to be used in Seismic Performance Categories B, C & D.
 +
|-
 +
|valign="top"|(**)||2'-6" Min. for Seismic Performance Category A.<br/>2'-9" Min. for Seismic Performance Categories, B, C & D.
 +
|-
 +
|colspan="2"|Note:  Use square ends on Prestress Double-Tee Structures.
 +
|}
  
:Structural Carbon Steel  (ASTM A709 Grade 36)
+
=====751.40.8.12.2.2 Anchorage of Piles for Seismic Performance Categories B, C & D=====
:::::::::<math>\, f_s</math> = 20,000 psi, &nbsp;  <math>\, f_y</math> = 36,000 psi
 
  
  
 +
'''STEEL PILE'''
  
(4) Overstress
 
 
:The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for Service Load design method.
 
  
 +
{|border="0" align="center" style="text-align:center"
  
(*) Use <math>\, W = 150 \ pcf, \ E_c = 60,625  \sqrt{f'_c}</math>
+
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_Steel_Pile_(Part_Elevation).gif]]
+
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_Steel_Pile_(Sec_thru_beam).gif]]
(**) May be used for special cases, see Structural Project Manager.
+
|-
 +
|'''PART ELEVATION'''||'''SECTION THRU BEAM'''
 +
|-
 +
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_Steel_Pile_(Part_Plan).gif]]
 +
|-
 +
|'''PART PLAN'''
 +
|}
  
=====751.40.8.11.1.2 Loads=====
 
(1) Dead Loads
 
 
 
 
  
(2) Live Loads
 
  
:As specified on the Design Layout.
+
'''CAST-IN-PLACE PILE'''
 
:Impact of 30% is to be used for the design of beam, web supporting beam and top of columns. No impact is to be used for bottom of column, tie beam or footing design.
 
 
  
  
(3) Wind and Frictional Forces
+
{|border="0" align="center" style="text-align:center"
  
 +
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_CIP_Pile_(Part_Elevation).gif]]
 +
|width="300"|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_CIP_Pile_(Sec_thru_beam).gif]]
 +
|-
 +
|'''PART ELEVATION'''||'''SECTION THRU BEAM'''
 +
|-
 +
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_CIP_Pile_(Part_Plan).gif]]
 +
|-
 +
|'''PART PLAN'''
 +
|}
  
 +
=====751.40.8.12.2.3 Beam Reinforcement Special Cases=====
  
(4) Temperature and Shrinkage
 
  
:The effect of normal and parallel components to the bent shall be considered. When bearings with high friction coefficients are used or for long bridge lengths, the columns and footings are to be analyzed for moments normal to the bent due to the horizontal deflection of the top of the bent.
+
'''SPECIAL CASE I'''
 
 
 
(5) Buoyancy
 
  
:If specified by the Structural Project Manager, or by the Design Layout.
 
 
  
+
If centerline bearing is 12" or less on either side of centerline piles, for all piles (as shown above), use 4-#6 top and bottom and #4 at 12" cts. (stirrups), regardless of pile size.
(6) Earth Pressure
 
  
:Bents are to be analyzed for moments due to equivalent fluid pressure on columns and web where the ground line at time of construction, or potential changes in the ground line, indicate.
 
 
  
+
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_Beam_Reinf_(Special_Case_I).gif]]</center>
(7) Earthquake
 
  
:See Structural Project Manager or Liaison.
 
 
  
 
(8) Special Stability Situations
 
  
:When indicated by the Design Layout or by the Structural Project Manager, piers must be analyzed for special loadings as directed (i.e., differential settlement).
+
'''SPECIAL CASE II'''
 
  
 
(9) Collision
 
  
:Where the possibility of collision exists from railroad traffic, the appropriate protection system, for example Collision Wall, shall be provided (See the Design Layout).
+
When beam reinforcement is to be designed assuming piles to take equal force, design for negative moment in the beam over the interior piles.
 
  
 
(10) Collision Walls
 
  
:Collision walls are to be designed for the unequal horizontal forces from the earth pressure, if the condition exists (See the Design Layout). The vertical force on the collision wall is the dead load weight of the wall (*). If a bent has three or more columns, design the steel in the top of the wall for negative moment.
+
[[Image:751.40_Conc_Pile_Cap_Int_Bents_Beam_Reinf_(Special_Case_II).gif]]
  
  
(*) For footing design, the eccentricity dead load moment due to an unsymmetrical collision wall shall be considered.
+
(*) Dimensions shown are for illustration purposes only.
  
=====751.40.8.11.1.3 Distribution of Loads=====
+
====751.40.8.12.3 Details====
 +
=====751.40.8.12.3.1 Sway Bracing=====
  
 +
Refer to [[751.32 Concrete Pile Cap Intermediate Bents#751.32.3.2.1 Sway Bracing|EPG 751.32.3.2.1 Sway Bracing]].
  
(1) Dead Loads
+
=====751.40.8.12.3.2 Miscellaneous Details for Prestressed Girder=====
  
:Loads from stringers, girders, etc. shall be concentrated loads applied at the centerline of bearing.  Loads from superstructure, such as concrete slab spans, shall be applied as uniformly distributed loads.
+
'''PRESTRESSED GIRDERS (INTEGRAL INT. BENT)'''
  
  
(2) Live Loads
+
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_Misc_Details_PS_Girders_(Integral_Int_Bent)_Jt_Filler_Detail.gif]]</center>
  
:Loads from stringers, girders, etc., shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of bent.
 
  
 +
<center>'''DETAIL OF JOINT FILLER AT INT. BENTS<br/>(Continuous Spans - No Longitudinal Beam Steps)'''</center>
  
(3) Wind and Frictional Forces
 
  
 +
{|border="0"
  
(4) Temperature
+
|(*)||¼ Joint Filler for a P/S Double Tee Structure
 +
|-
 +
|&nbsp;||½ Joint Filler for a P/S I-Girder Structure
 +
|}
  
:Apply at the top of the substructure beam.
 
  
 +
'''PRESTRESSED GIRDERS (NON-INTEGRAL INT. BENT)'''
  
(5) Earth Loads
 
:(a) Vertical
 
::Vertical earth loads on tie beams shall be applied as uniform loads for a column of earth equal to 3 times the width of the beam.  The weight of earth for footing design shall be that directly above the footing, excluding that occupied by the column.
 
  
 +
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_Misc_Details_PS_Girders_(Non_Integral_Int_Bent)_Jt_Filler_Detail.gif]]</center>
  
::The earth above the seal courses shall be considered in computing pile loads.  Refer to the Design and Dimension of the Pile Footings portion of this Manual Section.
 
  
 +
<center>'''DETAIL OF JOINT FILLER AT INT. BENTS<br/>Longitudinal Beam Step and Shear Blocks shown)'''</center>
  
:(b) Horizontal
 
<center>
 
 
[[Image:751.40 Open Concrete Int Bents and Piers- Distribution Loads.gif]]
 
  
</center>
+
'''DETAILS OF CONST. JOINT KEY'''
(*) A factor of 2.0 is applied to the moment to allow for the possibility of the column esisting earth pressure caused by the earth behind the column twice the column width.
 
  
 +
{|border="0" align="center" style="text-align:center"
  
(6) Earthquake Loads
+
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Misc_Details_Const_Jt_Key_(Part_Elevation).gif]]
 +
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Misc_Details_Const_Jt_Key_(Part_Section_PS_I_Girders).gif]]
 +
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Misc_Details_Const_Jt_Key_(Part_Section_Dbl_Tee_Girders).gif]]
 +
|-
 +
|'''PART ELEVATION'''||'''PART SECTION THRU KEYS<BR/>(P/S I-GIRDERS)'''||'''PART SECTION THRU KEYS<BR/>(P/S DOUBLE TEE GIRDERS)'''
 +
|}
  
:See Structural Project Manager or Liaison.
 
  
 +
===751.40.8.13 Concrete Pile Cap Non-Integral End Bents===
  
(7) Seal Course
+
====751.40.8.13.1 Design====
  
:The weight of the seal course shall not be considered as contributing to the pile loads, except for unusual cases.
+
=====751.40.8.13.1.1 Unit Stresses=====
  
=====751.40.8.11.1.4 Types of Design=====
+
{|border="0"
  
'''TYPES OF DESIGN'''
+
|(1)||Reinforced Concrete
 
+
|-
Rigid frame design is to be used for the design of Intermediate Bents and
+
|&nbsp;||Class B Concrete (Substructure)||<math>\, f_c</math> = 1,200 psi||<math>\, f'_c</math> = 3,000 psi
Piers.
+
|-
 +
|&nbsp;||Reinforcing Steel (Grade 60)||<math>\, f_s</math> = 24,000 psi||<math>\, f_y</math> = 60,000 psi
 +
|-
 +
|&nbsp;||<math>\, n</math> = 10
 +
|-
 +
|&nbsp;||colspan="3"|<math>\, E_c = W^{1.5} \times 33 \sqrt{f'_c}</math> AASHTO Article 8.7.1) (*)
 +
|-
 +
|&nbsp;
 +
|-
 +
|(2)||Structural Steel
 +
|-
 +
|&nbsp;||Structural Carbon Steel (ASTM A709 Grade 36)||<math>\, f_s</math> = 20,000 psi||<math>\, f_y</math> = 36,000 psi
 +
|-
 +
|&nbsp;
 +
|-
 +
|(3)||Piling
 +
|-
 +
|&nbsp;
 +
|-
 +
|(4)||Overstress
 +
|-
 +
|&nbsp;||colspan="3"|The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for Service Loads design method.
 +
|-
 +
|(*)||colspan="3"| <math>\, E_c = 57,000 \sqrt{f'c} W</math> = 145 pcf., <math>\, Ec = 60,625 \sqrt{f'c}</math> for <math>\, W</math> = 150 pcf.
 +
|}
  
 +
=====751.40.8.13.1.2 Loads=====
  
The joint between the beam and column, and web or tie beam and column,
 
is assumed to be integral for all phases of design and must be analyzed
 
for reinforcement requirements as a "Rigid Frame".
 
  
 +
{|border="0"
  
The joint between the column and footing is assumed to be "fixed",
+
|(1)||Dead Loads
unless foundation fexibility needs to be considered (consult Structural
+
|-
Project Manager for this assessment).
+
|&nbsp;
 +
|-
 +
|(2)||Live Load
 +
|-
 +
|&nbsp;||As specified on the Bridge Memorandum
 +
|-
 +
|&nbsp;||Impact of 30% is to be used for design of the beam.  No impact is to be used for design of any other portion of bent including the piles.
 +
|-
 +
|&nbsp;
 +
|-
 +
|(3)||Temperature, Wind and Frictional Loads
 +
|-
 +
|&nbsp;||Wind and temperature forces can be calculated based on longitudinal force distribution.
 +
|}
  
 
+
=====751.40.8.13.1.3 Distribution of Loads=====
If the distance from the ground line to the footing is large (*),
 
consideration shall be given to assuming the column to be "fixed" at a
 
point below the ground line.
 
  
  
(*) When the distance from the ground line to the top of footing is 10' or more, the unsupported height and the fixed point may be measured from the bottom of the beam to the ground line plus 1/2 of the distance from the ground line to the top of the footing.
+
{|border="0"
  
 +
|(1)||Dead Loads
 +
|-
 +
|&nbsp;||Loads from stringers, girders, etc. shall be concentrated loads applied at the intersection of centerline of stringer and centerline of bearing.
 +
|-
 +
|&nbsp;
 +
|-
 +
|(2)||Live Load
 +
|-
 +
|&nbsp;||Loads from stringers, girders, etc. shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of earing.
 +
|-
 +
|&nbsp;
 +
|-
 +
|(3)||Temperature
 +
|-
 +
|&nbsp;||The force due to expansion or contraction applied at bearing pads are not used for stability or pile bearing computations.  However, the movement due to temperature should be considered in the bearing pad design and expansion device design.
 +
|-
 +
|&nbsp;
 +
|-
 +
|(4)||Wing with Detached Wing Wall
 +
|}
  
'''UNSUPPORTED HEIGHT'''
+
<center>[[Image:751.40_Detached_Wing_Wall_Section_AA.gif]]</center>
 
 
Unsupported height is the distance from the bottom of the beam to the
 
top of the footing.
 
  
 +
<center>'''SECTION A-A'''</center>
  
'''SINGLE COLUMN'''
 
  
Use rigid frame design with the column considered "fixed" at the bottom for all of the conditions.
+
<center>[[Image:751.40_Detached_Wing_Wall_Detail_B.gif]]</center>
  
 +
<center>'''DETAIL B'''</center>
  
'''COLUMN DIAMETER CHANGE'''
 
  
Use a change in column diameter as required by the Design Layout or column design.
+
{|border="0"
  
 +
|(*)||Detached wing wall shown is for illustration purpose only.  Design detached wing wall as a retaining wall.
 +
|-
 +
|(**)||See retaining wall design.
 +
|}
  
'''COLUMN SPACING (TRIAL)'''
+
=====751.40.8.13.1.4 Design Assumptions - Loadings=====
  
(Except Web Supporting Beam type)
 
  
Estimate centerline-centerline column spacing for a two column bent as 72% of the distance from the centerline of the outside girder to the centerline of the outside girder.
+
{|border="0"
  
A three column bent spacing estimation is 44% of the centerline-centerline outside girder spacing.
+
|'''1)'''||colspan="3"|'''Piles'''
 
 
====751.40.8.11.2 Reinforcement====
 
=====751.40.8.11.2.1 Hammer Head Type=====
 
<center>
 
{|
 
 
|-
 
|-
|[[Image:751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Part Plan.gif]]||[[Image:751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Section A-A.gif]]
+
|&nbsp;||valign="top"|a.||colspan="2"|Stresses in the piles due to bending need not be considered in design calculations except for seismic design in categories B, C and D.
 
|-
 
|-
|PART PLAN||SECTION A-A
+
|&nbsp;||b.||colspan="2"|The following four loading cases should be considered.
 
|-
 
|-
|rowspan="2"|[[Image:751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Part Elev.gif]]||style="text-align:left"|Note:<br>When an expansion device in the slab is used at an intermediate bent, all reinforcement located entirely within the beam shall be epoxy coated.  See details of protective coating and sloping top of beam to drain.
+
|&nbsp;||&nbsp;||colspan="2"|
 +
{|border="1" style="text-align:center" cellpadding="5" cellspacing="0"
 +
 
 +
|Case||Vertical Loads||Horizontal Loads||Special Consideration
 
|-
 
|-
|[[Image:751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Part Section B-B.gif]]
+
|I||DL + E + SUR||EP + SUR||-
 
|-
 
|-
|PART ELEVATION||PART SECTION B-B
+
|II||DL + LL + E + SUR||EP + SUR||-
 
|-
 
|-
 +
|III||DL + LL + E||EP||-
 +
|-
 +
|IV||DL + LL + E||None||Allow 25% Overstress
 
|}
 
|}
</center>
 
 
(*) Add hooked reinforcement as required by design.
 
 
(**) See AASHTO Article 8.18.2.3.4 for tie requirements.
 
 
 
[[Image:751.40 circled 1.gif]] All stirrups in beam to be the same size bar. (Use a min. spacing of 5" (6" for double stirrups), minimum stirrups are #4 at 12" cts., and maximum
 
stirrups are #6 at 6" cts.)
 
 
Locate #4 bars (┌─┐) under bearings if required.  (Not required for P/S Double-Tee Girders.)
 
 
 
[[Image:751.40 circled 2.gif]] See development length (Other than top bars) or standard hooks in
 
tension, Ldh.
 
 
 
[[Image:751.40 circled 3.gif]] See lap splice class C.
 
 
====751.40.8.11.3 Pile Footings====
 
=====751.40.8.11.3.1 Design and Dimensions=====
 
 
'''GENERAL '''
 
 
:Number, size and spacing of piling shall be determined by computing the pile loads and applying the proper allowable overstresses.
 
 
:Cases of Loading:  (AASHTO Article 3.22)
 
 
:Group I and Group II maximum vertical loads (refer to distribution of loads, this Section).
 
 
:Group III thru VI wind and/or temperature moments with applicable vertical loads.
 
 
:Internal stresses including the position of the shear line shall then be computed.
 
 
:Long narrow footings are not desirable and care should be taken to avoid the use of an extremely long footing 6~0" wide when a shorter footing 8'-3" or 9'-0" wide could be used.
 
 
:Footings are to be designed for the greater of the minimum moment requirements at the bottom of the column, or the moments at the bottom of the footing.
 
 
:When using the load factor design method for footings, design the number of piles needed based on the working stress design method.
 
 
 
 
'''PILE LOADS'''
 
 
<math>\, P = N/n \pm M/S</math>
 
:{|
 
|<math>\, P</math>|| - Pile Loads
 
 
|-
 
|-
|<math>\, N</math>|| - Vertical Loads
+
|&nbsp;||&nbsp;||colspan="2"|Where,
 
|-
 
|-
|<math>\, n</math>|| - Number of Piles
+
|&nbsp;||&nbsp;||LL||= live load
 
|-
 
|-
|<math>\, M</math>|| - Overturning Moment
+
|&nbsp;||&nbsp;||DL||= dead load of superstructure, substructure and one half of the apporach slab
 
|-
 
|-
|&nbsp;||If minimum eccentricity controls the moment in both directions,
+
|&nbsp;||&nbsp;||SUR||= two feet of live load surcharge
 
|-
 
|-
|&nbsp;||It is necessary to use the moment in one direction (direction with
+
|&nbsp;||&nbsp;||E||= dead load of earth fill
 
|-
 
|-
|&nbsp;||less section modulus of pile group) only for the footing check.
+
|&nbsp;||&nbsp;||EP||= equivalent fluid pressure of earth
 +
|-
 +
|&nbsp;||&nbsp;||colspan="2"|Maximum pile pressure = pile capacity
 +
|-
 +
|&nbsp;||&nbsp;||colspan="2"|Minimum pile pressure = 0 (tension on a pile will not be allowed for any combination of forces exept as noted)
 
|-
 
|-
|<math>\, S</math>|| - Section Modulus of Pile Group
+
|&nbsp;
|}
 
 
 
 
 
:'''(A) AASHTO Group I thru VI Loads as applicable'''
 
 
 
:Maximum <math>\, P</math> = Pile Capacity
 
:Minimum <math>\, P = 0</math> (zero)
 
 
:Tension on a pile will not be allowed for any combination of forces.
 
 
:Pile design force shall be calculated with consideration of AASHTO percentage overstress factors.
 
 
 
 
 
 
 
:'''(B) Earthquake Loads'''
 
 
 
See Structural Project Manager or Liaison before using the following seismic information.
 
 
 
:<u>Point Bearing Pile</u>
 
 
::    Maximum <math>\, P = Pile\ capacity\ \times 2</math>  (**)
 
::    (i.e., for HP 10 X 42 piles, Max. <math>\, P = 56\ \times 2 = 112</math> tons/pile)
 
::    Minimum <math>\, P</math> = Allowable uplift force specified for piles in this
 
::    Section under Seal Course Design.
 
 
::    (**) Two "2" is our normal factor of safety. Under earthquake loadings only the point bearing pile and rock capacities are their ultimate capacities.
 
 
:<u>Friction Piles</u>
 
 
::    Maximum <math>\, P</math> = Pile Capacity
 
::    Minimum <math>\, P</math> = Allowable uplift force specified for piles in this
 
::    Section under Seal Course Design.
 
::    See combined axial & bending stresses in Cast-In-Place friction piles in liquefaction areas.
 
 
 
 
 
 
 
'''(1) Shear Line'''
 
 
 
{|
 
 
|-
 
|-
|width="400"|If the shear line is within the column projected, the footing may be considered satisfactory for all conditions and standard #6 hairpin bars shall be used.
+
|'''2)'''||colspan="3"|'''Analysis Procedure'''
 
 
 
 
If the shear line is outside of the column projected, the footing must be analyzed and reinforced for bending and checked for shear stress (see following sheet, this Bridge Manual Section).
 
 
 
 
Footing depths may be increased, in lieu of reinforcement, if an increase would be more economical.  (6'-0" Maximum depth, with 3" increments.)
 
||[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Internal Stresses.gif]]
 
 
|-
 
|-
|}
+
|&nbsp;||a.||colspan="2"|''Find the lateral stiffness of a pile, <math>\, K_\delta</math>'':
 
 
'''(2) Bending'''
 
 
The critical section for bending shall be taken at the face of the columns (concentric square of equivalent area for round columns).
 
 
The reinforcement shall be as indicated for reinforced footings, except that the standard #6 hairpin bars may be used for small footings if they provide sufficient steel area.
 
 
 
'''(3) Distribution of Reinforcement'''
 
 
<u>Reinforcement in Bottom of Footing</u>
 
<center>
 
[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Distribution of Reinforcement.gif]]
 
</center>
 
 
 
Reinforcement shall be distributed uniformly across the entire width of footing in the long direction. In the short direction, the portion of the total reinforcement given by AASHTO Equation 4.4.11.2.2-1 shall be distributed uniformly over a band width equal to the length of the short side of the footing, <math>\, B</math>.
 
 
 
:Band Width Reinforcement = <math>2(total\ reinforcement\ in\ short\ direction)/(\beta + 1)</math>
 
 
 
:where <math> \beta = the\ ratio\ of\ fooring\ lenth\ to\ width = L/B</math>
 
 
 
The remainder of the reinforcement required in the short direction shall be distributed uniformly outside the center band width of footing.
 
 
 
 
 
<u>Reinforcement in Top of Footing</u>
 
 
 
Reinforcement in the top of the footing shall be provided based on a seismic analysis for Seismic Performance Categories B, C and D. This reinforcement shall be at least the equivalent area as the bottom steel in both directions. The top steel shall be placed uniformly outside the column.
 
 
 
 
 
 
 
'''(4) Shear'''
 
 
 
(AASHTO Article 8.15.5 or 8.16.6)
 
 
 
The shear capacity of footing in the vicinity of concentrated loads shall be governed by the more severe of the following two conditions.
 
 
 
 
 
(i) Beam shear
 
 
 
Critical Section at "d" distance from face of column.
 
 
 
{|
 
 
|-
 
|-
|width="250"|b = Footing Width Service Load||rowspan="6"|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Internal Stresses- Part Plan of Footing- Beam Shear.gif]]
+
|&nbsp;||&nbsp;||colspan="2"|With fixed pile-head (i.e., only translation movement is allowed but no rotation allowed): The lateral stiffness of a pile can be estimated using Figures 1 and 3 or 2 and 3 for pile in cohesionless or cohesive soil, respectively. The method of using Figures 1, 2, and 3 to find lateral stiffness is called Linear Subgrade Modulus Method.  Usually the significant soil-pile interaction zone for pile subjected to lateral movement is confined to a depth at the upper 5 to 10 pile diameters.  Therefore, simplified single layer stiffness chart shown in Figure 3 is appropriate for lateral loading.  The coefficient <math>\, f</math> in Figures 1 and 2 is used to define the subgrade modulus <math>\, E_s</math> at depth “z” representing the soil stiffness per unit pile length.  For the purpose of selecting an appropriate <math>\, f</math> value, the soil condition at the upper 5 pile diameters should be used.  Since soil property, friction angle <math>\, \phi</math>, or cohesion c, is needed when Figure 1 or 2 is used, determine soil properties based on available soil boring data.  If soil boring data is not available, one can conservatively use <math>\, f</math> value of 0.1 in Figure 3.  Designer may also use soil properties to convert SPT N value to friction angle <math>\, \phi</math>, or cohesion c, for granular or cohesive soil, respectively.  Figures 1 and 2 were based on test data for smaller-diameter (12 inches) piles, but can be used for piles up to about 24 inches in diameter.  In Figure 2, the solid line (by Lam et al. 1991) shall be used in design.
 
|-
 
|-
|Service Load
+
|&nbsp;||b.||colspan="2"|''Find the axial stiffness of a pile, <math>\, K_a</math>'':
 
|-
 
|-
|<math>\, v = V / \left(b d \right)</math>||
+
|&nbsp;||&nbsp;||colspan="2"|For friction pile, <math>\, K_a</math> may be determined based on a secant stiffness approach as described in [[751.9_Bridge_Seismic_Design|EPG 751.9 Bridge Seismic Design]] or by the in-house computer program “SPREAD” where <math>\, K_a</math> is calculated as:
 
|-
 
|-
|<math>\, v_c = 0.95 \sqrt{f'_c}</math>||
+
|&nbsp;||&nbsp;||colspan="2"|<math>\, \frac{1}{K_a} = \frac{1}{AE / L'} + \frac{1}{K_{Q_f}} + \frac{1}{K_{Q_b}}</math> &nbsp;  Equation (1)
 
|-
 
|-
|Load Factor||
+
|&nbsp;||&nbsp;||colspan="2"|Where:
 
|-
 
|-
|<math>\, V_u / \left(\omega b d \right)</math>||
+
|&nbsp;||&nbsp;||<math>\, A</math>||= cross sectional area of pile
 
|-
 
|-
|<math>\, v_c = 2.0 \sqrt{f'_c}</math>
+
|&nbsp;||&nbsp;||<math>\, E</math>||= elastic modulus of pile
!style="text-align:center"|PART PLAN OF FOOTING
 
 
|-
 
|-
|}
+
|&nbsp;||&nbsp;||<math>\, L'</math>||= total length of pile
 
 
 
 
 
 
(ii)Peripheral Shear
 
 
 
 
 
Critical Section at "d/2" distance from face of column.
 
 
 
<math>\, b_o = 4(d + Equiv.\ square\ column\ width)</math>
 
 
 
{|
 
 
|-
 
|-
|width="250"|Service Load||rowspan="5"|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Internal Stresses- Part Plan of Footing- Peripheral Shear.gif]]
+
|&nbsp;||&nbsp;||<math>\, K_{Q_f}</math>||= secant stiffness due to ultimate friction capacity of the pile as described in [[751.9 LFD Seismic#751.9.2.6.3 Pile Axial Stiffness|EPG 751.9.2.6.3 Pile Axial Stiffness]]
 
|-
 
|-
|<math>\, v = V / \left(b_o d \right)</math>||
+
|&nbsp;||&nbsp;||<math>\, K_{Q_f}</math> ||= secant stiffness due to ultimate bearing capacity of the pile as described in [[751.9 LFD Seismic#751.9.2.6.3 Pile Axial Stiffness|EPG 751.9.2.6.3 Pile Axial Stiffness]]
 
|-
 
|-
|<math>\, v = 1.8 \sqrt{f'_c}</math>||
+
|&nbsp;||colspan="3"|For HP bearing pile on rock <math>\, K_a</math> shall be calculated as:
 
|-
 
|-
|Load Factor||
+
|&nbsp;||&nbsp;||colspan="2"|<math>\, \frac{1}{K_a} = \frac{1}{AE / L'} + \frac{1}{K_{Q_f}}</math> &nbsp;  Equation (2)
 
|-
 
|-
|<math>\, V_u / \left(\omega b_o d \right)</math>||
+
|&nbsp;||&nbsp;||colspan="2"|Or Conservatively, <math>\, K_a</math> may be determined as:
 
|-
 
|-
|<math>\, v_c = 4.0 \sqrt{f'c}</math>
+
|&nbsp;||&nbsp;||colspan="2"|<math>\, K_a = \frac{AE}{L'}</math> &nbsp;  Equation (3)
!align="center"|PART PLAN OF FOOTING
 
|}
 
 
 
 
 
If shear stress is excessive, increase footing depth.
 
 
 
{|
 
|valign="top"|[[Image:751.40 circled 1.gif]]||Piles to be considered for shear.  (Center of piles are at or outside the critical section.)
 
|}
 
 
 
 
 
{|style="text-align:center"
 
 
|-
 
|-
|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Side Elev.gif]]||[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Front Elev.gif]]
+
|&nbsp;
 
|-
 
|-
!SIDE ELEVATION||FRONT ELEVATION
+
|align="center" colspan="4"|[[Image:751.40_Subgrade_Modulus_with_Depth_for_Sand.gif]]
|}
 
 
 
 
 
{|
 
|valign="top"|[[Image:751.40 circled 1.gif]]||Min. = 1/8 x (Distance from top of beam to bottom of footing.)
 
 
|-
 
|-
|valign="top"|[[Image:751.40 circled 2.gif]]||3'-0" (Min.) & 6'-0" (Max.) for steel HP piles, 14" CIP piles. AASHTO Article 4.5.6.4 shall be considered if piles are situated in cohesive soils.
+
|&nbsp;
 
|-
 
|-
|valign="top"|&nbsp;||3D (Min.) and 6D (Max.) for 20" and 24" CIP piles. (D = pile diameter)
+
|align="center" colspan="4"|'''Recommended Coefficient <math>f</math> of Variation in Subgrade Modulus with Depth for Sand'''
 
|-
 
|-
|valign="top"|[[Image:751.40 circled 3.gif]]||Indicates column diameter, or column length or width on a hammer head pier.
+
|&nbsp;
 
|-
 
|-
|valign="top"|[[Image:751.40 circled 4.gif]]||Min. = 2'-6" or column diameter (*) (Or width) for friction piles for SPC A.
+
|align="center" colspan="4"|[[Image:751.40_Subgrade_Modulus_with_Depth_for_Clay.gif]]
 
|-
 
|-
|valign="top"|&nbsp;||Min. = 3'-0" or column diameter (*) (Or width) for steel piles for SPC A.
+
|&nbsp;
 
|-
 
|-
|valign="top"|&nbsp;||Min. = 3'-0" or column diameter (*) (Or width) for friction piles for SPC B,C,& D.
+
|align="center" colspan="4"|'''Recommended Coefficient <math>\, f</math> of Variation in Subgrade Modulus with Depth for Clay'''
 
|-
 
|-
|valign="top"|&nbsp;||Min. = 3'-6" or column diameter (*) (Or width) for steel piles for SPC B, C & D.
+
|&nbsp;
 
|-
 
|-
|valign="top"|[[Image:751.40 circled 5.gif]]||12" for seismic performance category A and 18" for SPC B, C, & D.
+
|align="center" colspan="4"|[[Image:751.40_Lateral_Embedded_Pile-Head_Stiffness.gif]]
 
|-
 
|-
|valign="top" align="left"|(*)||For column diameters 4'-0" and greater use a 4'-0" min. footing thickness.
+
|align="center" colspan="4"|
|-
+
{|border="0" align="center" style="text-align:center" cellpadding="5"
|valign="top" align="left"|(**)||Use 18" for steel HP piles, 14" CIP piles, prescase and prestress piles.
 
|}
 
  
<center>
+
|'''PILE HEAD AT<br/>GRADE LEVEL'''||&nbsp;||'''EMBEDDED PILE HEAD'''
 
 
[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Typ Plan of 3 Pile Footing.gif]]
 
 
 
'''TYPICAL PLAN OF<br>3 PILE FOOTINGS'''<br>(minimum pile spacings)
 
</center>
 
 
 
NOTES:
 
 
 
Use 3- piles on exterior foorings only.
 
 
 
Use only HP 10 x 42 or friction piles on three pile footings.
 
 
 
<center>
 
 
 
[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Typ Plan of Staggered Pile.gif]]
 
 
 
'''TYPICAL PLAN<br>STAGGERED PILE'''
 
 
 
(7 Pile footings shall not be used.)
 
</center>
 
 
 
{|
 
|valign="top"|[[Image:751.40 circled 1.gif]]||If horizontal thrust requires pile batter- consult the Structural Project Manager.
 
 
|}
 
|}
 
(*) The maximum pile spacing is 4'-0".
 
 
=====751.40.8.11.3.2 Reinforcement=====
 
 
'''Unreinforced Footing - Use only in Seismic Performance Category A'''
 
 
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 
 
|-
 
|-
|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Elev 3 Pile Footing.gif]]
+
|&nbsp;
|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Elev 4 Pile Footing.gif]]
 
 
|-
 
|-
!Elevation<br/>(3 Pile Footing)||Elevation<br/>(4 Pile Footing
+
|align="center" colspan="4"|'''Lateral Embedded Pile-Head Stiffness'''
 
|-
 
|-
|colspan="2"| &nbsp;
+
|&nbsp;
 
|-
 
|-
|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Plan 3 Pile Footing.gif]]
+
|&nbsp;||c.||colspan="2"|''Find the equivalent cantilever pile length, <math>\, L</math>''
|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Plan 4 Pile Footing.gif]]
 
 
|-
 
|-
!Plan<br/>(3 Pile Footing)||Plan<br/>(4 Pile Footing
+
|&nbsp;||&nbsp;||colspan="2"|For the structural model used in the structural analyses of loading cases I through IV.  As shown in figure below, length L can be calculated as:
|}
 
 
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|valign="top" align="right"|(*)||align="left" width="400pt" |See lap splice class C (Other than top bars).
+
|&nbsp;||&nbsp;||colspan="2"|<math>\, L = \Bigg(\frac{12EI}{K_\delta}\Bigg)^{1/3}</math> &nbsp;  Equation (4)
 
|-
 
|-
|valign="top" align="right"|Notes:||align="left" width="400pt" |Reiforcement not required by design.  Hairpins are sufficient for renforcing requirements.
+
|&nbsp;
 
|-
 
|-
|valign="top" align="right"|&nbsp;||align="left" width="400pt" |The minimum percentage of reinforcement, "P" , is not required to be met, unless scour is anticipated.
+
|colspan="4" align="center"|[[Image:751.40_Structural_Model.gif]]
 
|-
 
|-
|valign="top" align="right"|&nbsp;||align="left" width="400pt" |Use for all types of piling, except timber.
+
|&nbsp;
|}
 
 
 
 
 
 
 
'''Reinforced Footing - Seismic Performance Category A'''
 
 
 
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 
 
|-
 
|-
|[[Image:751.40 seismic performance category a footing reinforcement front elevation.gif]]
+
|colspan="4" align="center|'''Structural Model'''
|[[Image:751.40 seismic performance category a footing reinforcement side elevation.gif]]
 
 
|-
 
|-
!Front Elevation||Side Elevation
+
|&nbsp;
 
|-
 
|-
|colspan="2"| &nbsp;
+
|&nbsp;||d.||colspan="2"|''Find the equivalent pile area, <math>\, A_e</math> :
 
|-
 
|-
| &nbsp;
+
|&nbsp;||&nbsp;||colspan="2"|Once the equivalent cantilever pile length has been determined from step (c) above, the equivalent axial rigidity of the pile, <math>\, A_e \times E_e</math> , can be calculated as <math>\, A_e \times E = K_a L</math>. Then, the equivalent pile area, <math>\, A_e</math> , is equal to
|[[Image:751.40 Open Concrete Int Bents and Piers-reinforcement-seismic performance category a footing reinforcement plan.gif]]
 
 
|-
 
|-
!&nbsp;||Plan
+
|&nbsp;||&nbsp;||colspan="2"|<math>\, A_e = \frac{K_aL}{E}</math> &nbsp;  Equation (5)
|}
 
 
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|valign="top" align="right"|(*)||align="left" width="400pt" |See lap splice class C (Other than top bars).
+
|&nbsp;
 
|-
 
|-
|valign="top" align="right"|Note:||align="left" width="400pt" |The maximum size of stress steel allowed is #8 bars.
+
|&nbsp;||e.||colspan="2"|''Perform structural analyses for loading cases I through IV.
|}
 
 
 
 
 
'''Reinforced Footing - Seismic Performance Categorys B, C & D'''
 
 
 
See Structural Project Manager or Liaison before using the following seismic details.
 
 
 
 
 
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 
 
|-
 
|-
|[[Image:751.40 seismic performance category b c & d footing reinforcement front elevation.gif]]
+
|&nbsp;||&nbsp;||colspan="2"|Use computer programs STRUCT3D, SAP2000 or any other program capable of running static analysis.
|[[Image:751.40 seismic performance category b c & d footing reinforcement side elevation.gif]]
 
 
|-
 
|-
!Front Elevation||Side Elevation
+
|&nbsp;
 
|-
 
|-
|colspan="2"| &nbsp;
+
|&nbsp;||f.||colspan="2"|''Check abutment movement at the top of backwall and at the bottom of beam cap''
 
|-
 
|-
|valign="bottom"|[[Image:751.40 Open Concrete Int Bents and Piers- Pile Footings- typical detail pile channel shear connector.gif]]
+
|&nbsp;||&nbsp;||colspan="2"|Maximum movement away from the backfill shall not be greater than 1/8". Maximum movement toward the backfill shall not be greater than 1/4".
|rowspan="2"|[[Image:751.40 seismic performance category b c & d footing reinforcement plan of top reinforcement.gif]]
 
 
|-
 
|-
!Typical Detail<br/>Pile Channel<br/>Shear Connector
+
|&nbsp;
 
|-
 
|-
! &nbsp;||Plan Showing Top Reinforcement
+
|&nbsp;||g.||colspan="2"|''Check pile axial loads from the analysis with the allowable pile axial load capacity.
 
|-
 
|-
|colspan="2"| &nbsp;
+
|&nbsp;
 
|-
 
|-
| &nbsp;
+
|&nbsp;||h.||colspan="2"|''Check overturning of bent''
|[[Image:751.40 seismic performance category b c & d footing reinforcement plan of bottom reinforcement.gif]]
 
 
|-
 
|-
! &nbsp;||Plan Showing Bottom reinforcement
+
|&nbsp;||&nbsp;||colspan="2"|Conservatively, use the same equivalent cantilever pile length, <math>\, L</math>.  Check overturning of bent at the bottom of toe pile for loading cases I and II(Figure of Structural model).
|}
+
|-
 +
|&nbsp;||&nbsp;||colspan="2"|
 +
{|border="1" style="text-align:center" cellpadding="5" cellspacing="0"
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
|Case I||Point of<br/>Investigation||Vertical Loads||Horizontal Loads||Factor of Safety (**)
 
|-
 
|-
|valign="top" align="right"|(*)||align="left" width="400pt" |For reinforcement in top of the footing, see lap splice class C (Top bars).
+
|I||Toe Pile||DL + E||EP + SUR||1.2
 
|-
 
|-
|valign="top" align="right"|(**)||align="left" width="400pt" |Place the top reinforcement uniformly outside the column.
+
|II||Toe Pile||DL + LL + E||EP + SUR||1.5
 +
|}
 
|-
 
|-
|valign="top" align="right"|(***)||align="left" width="400pt" |Use same area of steel in the top of the footing as is required for the bottom.
+
|&nbsp;
 
|-
 
|-
|valign="top" align="right"|Notes:||align="left" width="400pt" |For reinforcement in bottom of the footing, see lap splice Class C (Other than top bars).
+
|'''5)'''||colspan="3"|'''Deadman Anchorage System'''
 
|-
 
|-
| &nbsp;||align="left" width="400pt" |The maximum size of stress steel allowed is #8 bars.
+
|&nbsp;||colspan="3"|Deadman anchorage can be used when the abutment movement exceeds the allowable movement.
 
|-
 
|-
| &nbsp;||align="left" width="400pt" |Unreinforced footings shall not be used in seismic performance categories B, C & D.
+
|&nbsp;||colspan="3"|The size and location of deadman anchorage shall be designed appropriately to maintain the stability of the abutment.
|}
 
 
 
====751.40.8.11.4 Spread Footings====
 
=====751.40.8.11.4.1 Design and Dimensions=====
 
 
 
 
 
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 
 
|-
 
|-
|width="250pt"|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-side elevation.gif]]
+
|&nbsp;||colspan="3"|The deadman forces may be used to resist overturning with the approval of the Structural Project Manager.
|width="250pt"|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-front elevation.gif]]
 
 
|-
 
|-
!Side Elevation||Front Elevation
+
|&nbsp;
|}
 
 
 
{|align="center"
 
 
|-
 
|-
|d||= column diameter
+
|'''6)'''||colspan="3"|'''Passive Pressure Shear Key (if applicable)'''
 
|-
 
|-
|L||= footing length
+
|&nbsp;||colspan="3"|Passive pressure shear key may be used when the abutment movement exceeds the allowable movement.
 
|-
 
|-
|b||= footing depth
+
|&nbsp;||colspan="3"|The passive resistance of soil to the lateral force at shear keys may be used with the approval of structural project manager.
|-
 
|B||= footing width
 
|-
 
|A||= edge distance from column
 
 
|}
 
|}
  
 +
=====751.40.8.13.1.5 Deadman Anchors=====
  
The calculated bearing pressure shall be less than the ultimate capacity of the foundation soil.  The ultimate capacity of the foundation soil can be conservatively estimated as 2.0 times the allowable bearing pressure given on the Design Layout. The analysis method of calculating bearing pressures is outlined in the following information.
+
'''Design Assumptions'''
 +
 
 +
 
 +
<center>[[Image:751.40_Deadman_Anchor_Design_Assumption_Detail.gif]]</center>
  
  
'''Dimensional Requirements'''
+
{|border="0" cellpadding="3"
  
{|
+
|&nbsp;||Length of Deadman = <math>\, (F_E + F_S / (P_P - P_A)</math>
|valign="top"|'''L''' -||Minimum of 1/6 x distance from top of beam to bottom of footing (3" increments);
 
 
|-
 
|-
|valign="top"|'''B''' -||Minimum footing width is column diameter + 2A, (3" increments);
+
|&nbsp;||Number of tie rods required = <math>\, (F_E + F_S) / F_R</math>
 
|-
 
|-
|valign="top"|'''A''' -||Minimum of 12";
+
|&nbsp;||<math>\, P_A</math> = Active earth pressure on deadman, in lb./ft. = (120 pcf) <math>\, K_A hT</math>
 +
|-
 +
|(**)||<math>\, P_P</math> = Passive earth pressure on deadman, in lb./ft. = (120 pcf) <math>\, K_P hT</math>
 +
|-
 +
|&nbsp;||<math>\, F_E</math> = Earth pressure on end bent, in lb. = 0.5(120 pcf)<math>\, K_A H^2</math> (length of beam)
 +
|-
 +
|&nbsp;||<math>\, F_S</math> = Surcharge on end bent, in lb. = <math>\, (120 pcf)(2')K_A H (length\ of\ beam)</math>
 +
|-
 +
|&nbsp;||<math>\, K_A = Tan^2 (45^\circ - \phi/2)</math>
 +
|-
 +
|&nbsp;||<math>\, K_P = Tan^2 (45^\circ - \phi/2)</math>
 +
|-
 +
|valign="top"|(***)||<math>\, F_R</math> = 8.0 kips for 7/8" Ø tie rod and 10.50 kips for 1" Ø tie rods<br/>(Capacity of the tie rods based on a maximum skew of 30°.)
 +
|-
 +
|&nbsp;
 +
|-
 +
|align="right"|*||If the number of 7/8" Ø tie rods causes too long of a deadman, then try 1" Ø tie rods.
 +
|-
 +
|align="right"|**||For seismic loads only, use <math>\, P_P</math> = 4 kips/sq.ft. as the ultimate capacity of compacted fill.
 
|-
 
|-
|valign="top"|'''b''' -||Minimum of 30" or column diameter, Maximum of 72" at 3" increments; (for column diameters 48" and greater use a 48" minimum footing depth.)
+
|align="right"|***||For seismic loads only, the allowable stress in the tie rod may be taken as the yield stress of the rod.
 
|}
 
|}
  
  
'''Size'''
+
Notes:
  
The size of footing shall be determined by computing the location of the resultant force and by calculating the bearing pressure.
+
No more than 20% of deadman may fall outside of the roadway shoulders.  To prevent more than 20% limit, using a deeper deadman to reduce its length.  If this is not possible, the total passive pressure resistance should be calculated by summing the resistance from the different fill depths.
  
Long, narrow footings are to be avoided, especially on foundation material of low capacityIn general, the length to width ratio should not exceed 2.0, except on structures where the ratio of the longitudinal to transverse loads or some other consideration makes the use of such a ratio limit impractical.
+
When deadman anchors are to be used, design the piles for a factor of safety of 1.0 for sliding and design deadman anchors to resist all horizontal earth forces with a factor of safety of 1.0This will result in a factor of safety for sliding of 2.0. For special cases, see the Structural Project Manager.
  
  
'''Location of Resultant Force'''
+
'''Design Example'''
  
 +
{|border="0"
  
The location of the resultant force shall be determined by the following equations.  
+
|colspan="2"|Assume:
 
+
|-
The Middle 1/3 is defined as: <math>\, \frac{e_L}{L} + \frac{e_B}{B} \le \frac{1}{6}</math>
+
|width="25"|&nbsp;||Roadway width = 36', Out-Out slab width = 36' + 2 x 16" = 38.67'
 
+
|-
The Middle 1/2 is defined as: <math>\, \frac{e_L}{L} \le \frac{1}{4}</math> and <math>\, \frac{e_B}{B} \le \frac{1}{4}</math>
+
|width="25"|&nbsp;||Skew = <math>\, 15^\circ</math>, Length of Beam = <math>\, (38.67')/(Cos 15^\circ) = 40.03'</math>
 
+
|-
The Middle 2/3 is defined as: <math>\, \frac{e_L}{L} \le \frac{1}{3}</math> and <math>\, \frac{e_B}{B} \le \frac{1}{3}</math>
+
|width="25"|&nbsp;||Beam depth = <math>\, 3^\prime-0^{\prime\prime} </math>, <math>\, \phi = 27^\circ</math>, <math>\, H = 8.20'</math>
 
 
The following table specifies requirements for the location of the resultant force.
 
 
 
 
 
{|border="1" style="text-align:center;" cellpadding="5" align="center"
 
 
|-
 
|-
!width="150pt"|Soil Type||width="150pt"|Resultant Location Group I - VI||width="150pt"|Resultant Location Earthquake Loads Categories B, C and D
+
|&nbsp;
 
|-
 
|-
|align="left" width="150pt"|Clay, clay and boulders, cemented gravel, soft shale with allowable bearing values less than 6 tons, etc.
+
|width="25"|&nbsp;||<math>\, \frac{H}{3} = \frac{8.20'}{3} = 2.73'</math>
|middle 1/3
 
|middle 1/2
 
 
|-
 
|-
|align="left" width="150pt"|Rock, hard shale with allowable bearing values of 6 tons or more.
+
|width="25"|&nbsp;||<math>\, 3^\prime - 2.73^\prime = 0.27^\prime < 9^{\prime\prime}</math>, use <math>\, 9^{\prime\prime}</math>
|middle 1/2
+
|-
|middle 2/3
+
|width="25"|&nbsp;||<math>\, h = H - (Beam\ depth) + 9^{\prime\prime} = 8.20^\prime - 3^\prime + 0.75 = 5.95^\prime</math>
 +
|-
 +
|width="25"|&nbsp;||Assume <math>\, T = 2^\prime-0^{\prime\prime} </math> (Deadman anchor depth)
 
|}
 
|}
  
  
'''Bearing Pressure'''
+
{|border="0" cellpadding="5"
  
The bearing pressure for Group I thru VI loads shall be calculated using service loads and the allowable overstress reduction factors as specified in AASHTO Table 3.21.1A. The calculated bearing pressure shall be less than the allowable pressure given on the Design Layout.
+
|colspan="4"|Determine Earth and Surcharge Forces
 
+
|-
The bearing pressure for Earthquake Loads in Categories B, C, and D shall be  calculated from loads specified in AASHTO Division I-A Seismic Design, Sections 6.2.2, 7.2.1, and 7.2.2.  The seismic design moment shall be the elastic seismic moment (EQ) divided by the modified response modification factor R'. The modified seismic moment shall then be combined independently with moments from other loads:
+
|width="25"|&nbsp;||<math>\, K_A</math>||=||<math>\, Tan^2 (45^\circ - \varnothing/2) = Tan^2 (45^\circ - 27^\circ/2) = 0.3755</math>
 
+
|-
Group Load = <math>\, 1.0(D + B + SF + E + EQ/R')</math>
+
|width="25"|&nbsp;||<math>\, K_P</math>||=||<math>\, Tan^2 (45^\circ - \varnothing/2) = Tan^2 (45^\circ - 27^\circ/2) = 2.6629</math>
 
+
|-
Where:
+
|width="25"|&nbsp;||<math>\, F_e</math>||=||<math>\, \frac{1}{2} (120 K_AH^2)(Length\,of\,Beam)</math>
{|
+
|-
|<math>\, D</math>||= dead load
+
|width="25" colspan="2"|&nbsp;||=||<math>\, (60 lb./cu.ft.)(0.3755)(8.20')^2(40.03')</math>
 
|-
 
|-
|<math>\, B</math>||= buoyancy
+
|width="25" colspan="2"|&nbsp;||=||<math>\, 60,842 lbs.</math>
 
|-
 
|-
|<math>\, SF</math>||= stream flow pressure
+
|width="25"|&nbsp;||<math>\, F_s</math>||=||<math>\, (2')(120 K_AH)</math><math>(Length\,of\,Beam)</math>
 
|-
 
|-
|<math>\, EQ</math>||= elastic seismic moment
+
|width="25" colspan="2"|&nbsp;||=||<math>\, (240 lb./cu.ft.)(0.3755)(8.20')(40.03')</math>
 
|-
 
|-
|<math>\, E</math>||= earth pressure
+
|width="25" colspan="2"|&nbsp;||=||<math>\, 297,582 lbs.</math>
 
|-
 
|-
|<math>\, R'</math>||= R/2 for category B
+
|width="25"|&nbsp;||<math>\, P_A</math>||=||<math>\, 120 K_Ah\;T</math>
 
|-
 
|-
|&nbsp;||= 1 for categories C and D
+
|width="25" colspan="2"|&nbsp;||=||<math>\, (120 lb./cu.ft.)(0.3755)(5.95')(2.0')</math>
 
|-
 
|-
|colspan="2"|&nbsp;
+
|width="25" colspan="2"|&nbsp;||=||<math>\, 536 lbs.\,per\,foot\,of\,Deadman</math>
 
|-
 
|-
|<math>\, R</math>||= Response Modification Factor
+
|width="25"|&nbsp;||<math>\, P_P</math>||=||<math>\, 120 K_Ph\;T</math>
 
|-
 
|-
|&nbsp;||= 5 for multi-column bent
+
|width="25" colspan="2"|&nbsp;||=||<math>\, (120 lb./cu.ft.)(2.6629)(5.95')(2.0')</math>
 
|-
 
|-
|&nbsp;||= 3 for single-column bent
+
|width="25" colspan="2"|&nbsp;||=||<math>\, 3,803 lbs.\,per\,foot\,of\,Deadman</math>
 
|}
 
|}
  
  
The calculated bearing pressure shall be less than the ultimate capacity of the foundation soil.  The ultimate capacity of the foundation soil can be conservatively estimated as 2.0 times the allowable bearing pressure given on the Design Layout.  The analysis method of calculating bearing pressures is outlined in the following information.
+
{|border="0"
  
 +
|colspan="2"|Determine number of Tie Rods required
 +
|-
 +
|width="25"|&nbsp;||Try 7/8"Ø Rods: <math>\, F_R = 8.0</math> kips
 +
|-
 +
|width="25"|&nbsp;||Number of Rods required = <math>\, (F_E + F_S)/F_R = (60,642 + 29,582)/8,000 = 11.29</math>
 +
|-
 +
|width="25"|&nbsp;||Use 12-7/8"Ø Rie Rods.
 +
|}
  
<center>See AASHTO 4.4.2 for explanation of notations.</center>
+
{|border="0"
  
 +
|colspan="2"|Determine length of Deadman
 +
|-
 +
|width="25"|&nbsp;||Length of Deadman required = <math>\, (F_E + F_S)/(P_P - P_A = {(60,642 + 29,582) lbs.}/{(3,803 - 536) lb/ft.} = 27.62'</math>
 +
|-
 +
|width="25"|&nbsp;||Tie Rod spacing = <math>\, (27.62^\prime - 2.0^\prime )/11 = 2.33^\prime  say 2^\prime-4^{\prime\prime} > 12^{\prime\prime}</math> minimum, ok.
 +
|-
 +
|width="25"|&nbsp;||Length of Deadman provided = <math>\, (2'-4^{\prime\prime})(11) + 2.0^\prime = 27^\prime-8^{\prime\prime}</math>
 +
|}
 +
 +
 +
<center>[[Image:751.40_Deadman_Anchor_Design_Example_Detail_1.gif]]</center>
 +
 +
 +
<center><math>\, \phi = 27^\circ</math></center>
 +
 +
 +
<center><math>\, 45^\circ - \frac{\phi}{2} = 31.5^\circ</math></center>
  
<center>[[Image:751.40 sketch of dimensions for footings subjected to eccentric loading.gif]]</center>
 
 
<center>'''Sketch of Dimensions for Footings Subjected to Eccentric Loading'''</center>
 
  
 +
{|border="0" cellpadding="5"
  
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
+
|1)||colspan="2"|Check tie rod skew angle at Fill Face of End Bent
 
|-
 
|-
!For &nbsp; <math>\, e_L < L/6</math>
+
|&nbsp;|| <math>\, (5.5\ spacing)(30.5^{\prime\prime} - 28^{\prime\prime}) = 13.75^{\prime\prime}, tan</math> || <math>\, \phi = 13.75^{\prime\prime}/(24.33 \times 12^{\prime\prime}) = 0.471</math>
!For &nbsp; <math>\, L/6 < e_L < L/2</math>
 
 
|-
 
|-
|colspan="2"| &nbsp;
+
|colspan="2"|&nbsp;||<math>\, \phi = 2.70^\circ < 30^\circ</math>, tie capacity ok.
 
|-
 
|-
|<math>\, q_{max} = \frac{Q (1 + \frac{6e_L}{L})}{BL}</math>
+
|&nbsp;
|<math>\, q_{max} = \frac{2Q}{3B (L/2 - e_L)}</math>
 
 
|-
 
|-
|colspan="2"| &nbsp;
+
|colspan="3" align="center"|[[Image:751.40_Deadman_Anchor_Design_Example_Detail_2.gif]]
 
|-
 
|-
|<math>\, q_{min} = \frac{Q (1 - \frac{6e_L}{L})}{BL}</math>
+
|&nbsp;
|<math>\, q_{min} = L_1 = 3(L/2 - e_L)</math>
 
 
|-
 
|-
|colspan="2"| &nbsp;
+
|2)||colspan="2"|Check criteria for Deadman Anchors extending into Fill Slope
 
|-
 
|-
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-plan view 1.gif]]
+
|&nbsp;
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-plan view 2.gif]]
 
 
|-
 
|-
!Plan View||Plan View
+
|colspan="3" align="center"|[[Image:751.40_Deadman_Anchor_Design_Example_Detail_3.gif]]
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure 1.gif]]
 
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure 2.gif]]
 
|-
 
!Bearing Pressure||Bearing Pressure
 
 
|}
 
|}
  
<center>'''Bearing Pressure for Footing Loaded Eccentrically About One Axis'''</center>
 
  
 +
:{|border="0"
  
 
+
|A)||colspan="3"|Extension of Deadman into Fill Slope
 
 
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
!colspan="2"|CASE 1||CASE 2
+
|&nbsp;||colspan="3"|Length of Deadman extending into Fill Slope = <math>\, 1.08^\prime tan 15^\circ +</math>
 
|-
 
|-
|colspan="2"|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 1 plan view.gif]]
+
|&nbsp;||width="10"|&nbsp;||colspan="2"| <math>\, (13.83^\prime - ((15.04^\prime + 3.87^\prime) - 24.33^\prime  tan 15^\circ)) = 1.73^\prime</math>
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 2 plan view.gif]]
 
 
|-
 
|-
|colspan="2"|&nbsp;||k, x and y from AASHTO chart
+
|colspan="2"|&nbsp;||colspan="2"|0.2 (Length of Deadman) = <math>\, 0.2 (27.67^\prime) = 5.53^\prime</math>
 
|-
 
|-
|colspan="2"|<math>\, q_{max} = \frac{R}{BL} (1 + \frac{6e_L}{L} + \frac{6e_B}{B})</math>
+
|colspan="2"|&nbsp;||width="60"|&nbsp;||<math>\, 1.73^\prime < 5.53^\prime</math>
|<math>\, q_{max} = \frac{KR}{BL}</math>
 
 
|-
 
|-
!colspan="2"|CASE 1 Plan View||CASE 2 Plan View
+
|&nbsp;||colspan="3"|Length of Deadman extending into Fill Slope <math>\, < 0.2</math> (Length of Deadman), ok
 
|-
 
|-
|colspan="3"|&nbsp;
+
|&nbsp;
 
|-
 
|-
!colspan="2"|CASE 3||CASE 4
+
|colspan="4"|Note: See below for Section A-A details.
 
|-
 
|-
|colspan="2"|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 3 plan view.gif]]
+
|&nbsp;
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 4 plan view.gif]]
 
 
|-
 
|-
|<math>\, r = j/n</math>
+
|B)||colspan="3"|Cover of Deadman in Fill Slope
|<math>\, s = 1 + r + r^2</math>
 
|rowspan="3"|<math>\, q_{max} = \frac{3R}{8FG}</math>
 
 
|-
 
|-
|<math>\, g = \frac{n(1 + rs)}{4s}</math>
+
|&nbsp;||colspan="3"|<math>\, 1.44^\prime \times (cos 15^\circ) = 1.39^\prime</math>
|<math>\, f = \frac{L(3s - r - 2)}{4s}</math>
 
|-
 
|<math>\, q_{max} = \frac{6R}{Lns}</math>
 
|&nbsp;
 
|-
 
!colspan="2"|CASE 3 Plan View||CASE 4 Plan View
 
 
|}
 
|}
  
<center>'''Bearing Pressure for Footing Loaded Eccentrically About Two Axes'''</center>
 
  
 +
<center>[[Image:751.40_Deadman_Anchor_Design_Example_Detail_4.gif]]</center>
  
'''Loading Cases'''
+
<center>'''SECTION A-A<BR/>DETAIL AT FILL SLOPE'''</center>
  
Loads for Groups I thru VI shall be calculated for all bridges.
 
  
Earthquake loads shall be calculated when the bridge is in Seismic Zones B, C, and D.
+
Note:
 
Loads for other group loadings shall be used on a case by case basis.
 
  
 +
(*) Fill slope shown is for illustration purpose only, see roadway plans.
  
'''Reinforcement'''
+
====751.40.8.13.2 Reinforcement====
 +
=====751.40.8.13.2.1 Wide Flange Beams, Plate Girders and Prestressed Girders=====
  
The footing is to be designed so that the shear strength of the concrete is adequate to handle the shear stress without the additional help of reinforcement. If the shear stress is too great, the footing depth should be increased.
 
  
 +
'''END BENT WITH EXPANSION DEVICE'''
  
  
'''Shear'''
+
{|border="0" cellpadding="5" align="center" style="text-align:center"
  
The shear capacity of the footings in the vicinity of concentrated loads shall be governed by the more severe of the following two conditions.
+
|[[Image:751.40_Reinf_End_Bent_With_Exp_Device_Sec_AA.gif]]
 
+
|rowspan="4"|[[Image:751.40_Reinf_End_Bent_With_Exp_Device_Part_Elevation.gif]]
 
 
'''Critical section at "d" distance from face of column:'''
 
 
 
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|[[Image:751.40 critical section at d dist from face of column.gif]]
+
|'''SECTION A-A'''
 
|-
 
|-
!Load Factor
+
|&nbsp;
|}
 
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:left"
 
 
|-
 
|-
|<math>\, V_n = V_u/(\phi bd)</math>
+
|&nbsp;
 
|-
 
|-
|<math>\, V_c = 2 \sqrt{f'_c}</math>
+
|&nbsp;||'''PART ELEVATION'''
|-
 
|<math>\, b</math> = footing width
 
 
|}
 
|}
  
 +
Notes:
  
'''Critical section at "d/2" distance from face of column:'''
+
(1) See details for reinforcement of end bent backwall.
  
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:center"
+
(2) #6-H bars and #4-H bars in backwall of skewed bridges shall be bent in field if required.
|-
 
|[[Image:751.40 critical section at d divided by 2 dist from face of column.gif]]
 
|-
 
!Load Factor
 
|}
 
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:left"
 
|-
 
|<math>\, V_n = V_u/(\phi b_0d</math>
 
|-
 
|<math>\, V_c = 4 \sqrt{f'_c}</math>
 
|-
 
|<math>\, b_0 = 4(d + Equivalent\ square\ column\ width)</math>
 
|-
 
|colspan="2"|If shear stress is excessive, increase footing depth.
 
|}
 
  
 +
(3) Center #5 bars in backwall.
  
 +
Epoxy coat all reinforcing in end bents with expansion devices.  See ______ for details of protective coating and sloping top of beam to drain.
  
'''Bending'''
 
 
If the shear line is within the projected equivalent square column, the footing may be considered satisfactory for all conditions. (minimum reinforcement required)
 
  
If the shear line is outside of the projected column, the footing must be analyzed and reinforced for bending and checked for shear stress.
 
  
<center>[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-shear line diagrams.gif]]</center>
+
{|border="0" cellpadding="5" align="center" style="text-align:center"
  
The critical section for bending shall be taken at the face of the equivalent square column. The equivalent square column is the theoretical square column which has a cross sectional area equal to the round section of the actual column and placed concentrically.  
+
|rowspan="2"|[[Image:751.40_Reinf_End_Bent_With_Exp_Device_Part_Plan_BB.gif]]
 +
|width="250"|[[Image:751.40_Reinf_End_Bent_With_Exp_Device_Detail_of_-5_Shape_19_Bar.gif]]
 +
|-
 +
|'''DETAIL OF #5 BARS<br/>SHAPE 19'''<!--cell 1 occupied by [[Image:751.40_Reinf_End_Bent_With_Exp_Device_Part_Plan_BB.gif]]-->
 +
|-
 +
|'''PART PLAN B-B'''
 +
|}
  
  
'''Reinforcement in Bottom of Footing'''
+
'''END BENT WITHOUT EXPANSION DEVICE'''
  
The bearing pressure used to design bending reinforcement for Group I thru VI loads shall be calculated using Load Factor Loads.
 
  
The bearing pressure used to design bending reinforcement for Earthquake Loads in Categories B, C, and D shall be calculated from the same loads as specified in AASHTO Division 1-A Seismic Design for ultimate bearing pressure.
+
{|border="0" cellpadding="5" align="center" style="text-align:center"
  
The bottom reinforcement shall be designed using ultimate strength design.  
+
|[[Image:751.40_Reinf_End_Bent_Without_Exp_Device_Sec_AA.gif]]
 
+
|rowspan="4"|[[Image:751.40_Reinf_End_Bent_Without_Exp_Device_Part_Elevation.gif]]
 
 
'''Distribution of Reinforcement'''
 
 
 
{|border="0" cellpadding="4" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-distribution of reinforcement.gif]]
+
|'''SECTION A-A'''
 
|-
 
|-
|L = Footing Length
+
|&nbsp;
 +
|-
 +
|&nbsp;
 
|-
 
|-
|B = Footing Width
+
|&nbsp;||'''PART ELEVATION'''
 
|}
 
|}
  
Reinforcement shall be distributed uniformly across the entire width of footing in the long direction.  In the short direction, the portion of the total reinforcement given by AASHTO Equation 4.4.11.2.2-1 shall be distributed uniformly over a band width equal to the length of the short side of the footing, B.
 
  
:<math>\, Band\ Width\ Reinforcement = 2(total\ reinforcement\ in\ short\ direction)/(\beta + 1)</math>
+
{|border="0" cellpadding="5" align="center" style="text-align:center"
:<math>\, \beta = the\ ratio\ of\ footing\ length\ to\ width = L/B</math>
 
  
 +
|[[Image:751.40_Reinf_End_Bent_Without_Exp_Device_Part_Plan_BB.gif]]
 +
|valign="top"|
 +
{|border="0" cellpadding="3" style="text-align:left"
  
'''Reinforcement in Top of Footing'''
+
|valign="top"|(1)||#5 Dowel bars are 2'-6" long and placed parallel to centerline roadway.
 
+
|-
Reinforcement in the top of the footing shall be provided for Seismic Performance Categories B, C, and D.  This reinforcement shall be the equivalent area as the bottom steel in both directions.  The top steel shall be placed uniformly outside the column.
+
|valign="top"|(2)||#6-H bars and #4-H bars in backwall of skewed bridges shall be bent in field.
 
+
|-
 
+
|valign="top"|(3)||For skewed bridges with no expansion device place a #4 bar along skew.
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
+
|-
|+'''Reinforcement Details - Seismic Performance Category A'''
+
|valign="top"|(4)||See details of end bent backwall for reinforcement.
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-SPC A reinforcement details-front elevation.gif]]
 
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-SPC A reinforcement details-side elevation.gif]]
 
 
|-
 
|-
!Front Elevation||Side Elevation
+
|valign="top"|(5)||Seal joint with joint sealant. See special provisions.
|}
 
 
 
 
 
{|border="0" cellpadding="1" cellspacing="0" align="center" style="text-align:center"
 
|+'''Reinforcement Details - Seismic Performance Categorys B, C & D'''
 
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-SPC b c & d reinforcement details-front elevation.gif]]
 
|[[Image:751.40 Open Concrete Int Bents and Piers- spread footings-SPC b c & d reinforcement details-side elevation.gif]]
 
 
|-
 
|-
!Front Elevation||Side Elevation
+
|colspan="2"|Note:  See Structural Project Manager before using this detail.
 
|}
 
|}
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
|-
 
|-
|valign="top" align="right"|(*)||align="left" width="400pt" |Use same area of steel in the top of the footing as is required for the bottom.
+
|'''PART PLAN B-B
 
|}
 
|}
  
===751.40.8.12 Concrete Pile Cap Intermediate Bents===
 
  
====751.40.8.12.1 Design====
+
'''END BENT WING'''
  
=====751.40.8.12.1.1 Unit Stresses=====
 
  
 +
{|border="0" cellpadding="5" align="center" style="text-align:center"
  
{|border="0"
+
|[[Image:751.40_Reinf_End_Bent_Wing_Sec_AA.gif]]|
 
+
|rowspan="3"|[[Image:751.40_Reinf_End_Bent_Wing_Typ_Elevation.gif]]
|(1)||Reinforced Concrete
 
 
|-
 
|-
|&nbsp;||Class B Concrete (Substructure)||<math>\, f_c</math> = 1,200 psi||<math>\, f'_c</math> = 3,000 psi
+
|'''SECTION A-A'''
 
|-
 
|-
|&nbsp;||Reinforcing Steel (Grade 60||<math>\, f_s</math> = 24,000 psi||<math>\, f_y</math> = 60,000 psi
+
|&nbsp;
 
|-
 
|-
|&nbsp;||<math>\, n</math> = 10
+
|&nbsp;||'''TYPICAL ELEVATION OF WING'''
 +
|}
 +
 
 +
Note:  (1) Development length
 +
 
 +
 
 +
{|border="0" cellpadding="5" align="center" style="text-align:center"
 +
 
 +
|valign="top"|
 +
{|border="1" cellpadding="5" align="center" style="text-align:center"
 +
 
 +
|h||(2)||(3)
 
|-
 
|-
|&nbsp;||colspan="3"|<math>\, E_c = 3,122 ksi (Ec = W^{1.5} \times 33 \sqrt{f'_c}, Ec = 57,000 \sqrt{f'c}</math>
+
|2' or less||#4 @ 12"||#6 @ 6"
 
|-
 
|-
|&nbsp;
+
|Over 2' to 4'||#5 @ 6"||#7 @ 6"
 
|-
 
|-
|(2)||Structural Steel
+
|Over 4' to 6'||#7 @ 5"||#8 @ 5"
 +
|}
 +
|[[Image:751.40_Reinf_End_Bent_Wing_Sec_BB.gif]]
 
|-
 
|-
|&nbsp;||Structural Carbon Steel (ASTM A709 Grade 36)||<math>\, f_s</math> = 20,000 psi||<math>\, f_y</math> = 36,000 psi
+
|&nbsp;||'''SECTION B-B'''
 
|-
 
|-
|&nbsp;
+
|[[Image:751.40_Reinf_End_Bent_Wing_Part_Sec_With_Passive_Pressure.gif]]
 +
|rowspan="2"|[[Image:751.40_Reinf_End_Bent_Wing_Horiz_Sec_Thru_Wing.gif]]
 
|-
 
|-
|(3)||Piling
+
|'''PART SECTION THRU BENTS<br/>WITH PASSIVE PRESSURE'''
 
|-
 
|-
|&nbsp;
+
|&nbsp;||'''HORIZONTAL SECTION THRU WING'''<br/>(K bars not shown for clarity)
|-
 
|(4)||Overstress
 
|-
 
|&nbsp;||colspan="3"|The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for service loads.
 
 
|}
 
|}
  
=====751.40.8.12.1.2 Loads=====
+
 
 +
'''END BENT BEAM HEEL'''
  
  
{|border="0"
+
{|border="0" cellpadding="5" align="center" style="text-align:center"
  
|(1)||Dead Loads
+
|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Elev_AA.gif]]
 +
|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Square.gif]]
 
|-
 
|-
|&nbsp;
+
|'''ELEVATION A-A (TYP.)'''||'''PART PLAN OF BEAM (SQUARE)'''
 
|-
 
|-
|(2)||Live Load
+
|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_thru_15_deg.gif]]
 +
|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_thru_15_deg_(2).gif]]
 
|-
 
|-
|&nbsp;||As specified on Design Layout.
+
|colspan="2"|'''PART PLAN OF BEAM - SKEWS THRU 15° - LEFT ADVANCE SHOWN'''
|-
 
|&nbsp;||Impact of 30% is to be used for design of the beam.  No impact is to be used for design of any other portion of bent including the piles.
 
|-
 
|&nbsp;
 
|-
 
|(3)||Temperature, Wind and Frictional Loads
 
 
|}
 
|}
  
=====751.40.8.12.1.3 Distribution of Loads=====
 
  
{|border="0"
+
{|border="0" cellpadding="5" align="center" style="text-align:center"
  
|(1)||Dead Loads
+
|rowspan="2"|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_over_15_deg_(1).gif]]
 +
|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_over_15_deg_(Sec_BB).gif]]
 +
|rowspan="2"|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_over_15_deg_(2).gif]]
 
|-
 
|-
|&nbsp;||Loads from stringers, girders, etc. shall be concentrated loads applied at the intersection of centerline of stringer and centerline of bearing.  Loads from concrete slab spans shall be applied as uniformly, distributed loads along the centerline of bearing.
+
|'''SECTION B-B''' <!--column 1 occupied by cell [[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_over_15_deg_(1).gif]]-->
 
|-
 
|-
|&nbsp;
+
|colspan="3"|'''PART PLAN OF BEAM - SKEWS OVER 15° - LEFT ADVANCE SHOWN'''
|-
 
|(2)||Live Load
 
|-
 
|&nbsp;||Loads from stringers, girders, etc. shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of bearing.  For concrete slab spans distribute two wheel lines over 10'-0" (normal to centerline of roadway) of substructure beam.  This distribution shall be positioned on the beam on the same basis as used for wheel lines in Traffic Lanes for Substructure Design.
 
|-
 
|&nbsp;
 
|-
 
|(3)||Temperature, Wind and Frictional Loads
 
 
|}
 
|}
  
=====751.40.8.12.1.4 Design Assumptions=====
 
  
'''LOADINGS'''
+
Note:
 +
 
 +
Vertical spacing for #7 bars shown in Elevation A-A is typical for all types of end bent beams.
 +
 
 +
For a long distance between heel pile and bearing beam investigate for use of larger bars; e.g. larger skews where the shear line does not fall within the bearing beam.
 +
 
  
{|border="0"
+
{|border="1" cellpadding=6" cellspacing="1" align="center" style="text-align:center"
  
|(1)||colspan="2"|Beam
+
|rowspan="2" width="150"|Pile Load Not Greater||rowspan="2" width="150"|(1)<math>*</math> Hair-Pin Stirrups||colspan="4"|(2) Horizontal Rebar around Heel Pile
 
|-
 
|-
|&nbsp;||colspan="2"|The beam shall be assumed continuous over supports at centerline of piles.
+
|width="75"|Skew thru 30° <!--column 1 occupied by cell Pile Load Not Greater--> <!--column 2 occupied by cell (1)* Hair-Pin Stirrups-->||width="75"|Skew 31° thru 45°||width="75"|Skew 46° thru 60°||width="75"|Skew over 60°
 
|-
 
|-
|&nbsp;||colspan="2"|Intermediate bent beam caps shall be designed so that service dead load moments do not exceed the cracking moment of the beam cap (AASHTO Article 8.13.3, Eq. 8-2).
+
|140 kips||#6 @ 9"||5-#7||5-#7||5-#8||By Design
 
|-
 
|-
|&nbsp;
+
|194 kips||#6 @ 6"||5-#7||5-#8||By Design||By Design
|-
 
|(2)||colspan="2"|Piles
 
|-
 
|&nbsp;||(a)||Bending
 
|-
 
|colspan="2"|&nbsp;||Stresses in the piles due to bending need not be considered in design calculations for Seismic Performance Category A.
 
|-
 
|&nbsp;||(b)||Dead Loads, etc.
 
|-
 
|colspan="2"|&nbsp;||Dead load of superstructure and substructure will be distributed equally to all piles which are under the main portion of the bent.
 
 
|}
 
|}
  
====751.40.8.12.2 Reinforcement====
 
=====751.40.8.12.2.1 General=====
 
  
'''PRESTRESS DOUBLE-TEE STRUCTURES'''
+
<math>*</math>  Use 21" horizontal leg.
  
  
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Bents_with_3_thru_6_in_crown).gif]]</center>
+
'''END BENT BACKWALL'''
  
<center>'''BENTS WITH 3" THRU 6" CROWN'''</center>
 
  
 +
<center>[[Image:751.40_Reinf_End_Bent_Backwall_Part_Section.gif]]</center>
  
{|border="0" align="center" style="text-align:center"
+
<center>'''PART SECTION THRU BACKWALL AND BEAM'''</center>
  
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Section_AA).gif]]
 
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Section_BB).gif]]
 
|-
 
|'''SECTION A-A'''||'''SECTION B-B'''
 
|}
 
  
 +
{|border="1" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
  
{|border="0"
+
|colspan="4"|'''V-BAR SIZE AND SPACING'''
 
+
|-
|(*)||Channel shear connectors are to be used in Seismic Performance Categories B, C & D.  For details not shown, see this Section.
+
|h<br/>(feet)||t<br/>(inch)||Fill Face<br/>Reinforcement||Front Face<br/>Reinforcement
 +
|-
 +
|1-6||12||#5 @ 12"||#5 @ 12"
 +
|-
 +
|7||12||#5 @ 12"||#5 @ 12"
 +
|-
 +
|8||12||#5 @ 12"||#5 @ 12"
 +
|-
 +
|9||12||#6 @ 12"||#5 @ 12"
 +
|-
 +
|10||12||#6 @ 10"||#5 @ 12"
 +
|-
 +
|11||15||#6 @ 10"||#5 @ 12"
 +
|-
 +
|12||15||#6 @ 8"||#5 @ 12"
 
|-
 
|-
|valign="top"|(**)||2'-6" Min. for Seismic Performance Category A.<br/>2'-9" Min. for Seismic Performance Categories, B, C & D.
+
|13||18||#6 @ 8"||#5 @ 12"
 
|-
 
|-
|colspan="2"|Note:  Use square ends on Prestress Double-Tee Structures.
+
|14||18||#6 @ 6"||#5 @ 12"
 
|}
 
|}
  
  
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Bents_with_crown_over_6_in).gif]]</center>
+
Note:
  
<center>'''BENTS WITH CROWN OVER 6"'''</center>
+
All reinforcement is grade 60.
  
 +
Design is based on 45 lbs. per cu. ft. equivalent fluid pressure and 90 lbs. per sq. ft. live load surcharge.
  
 +
Epoxy coat all reinforcing steel in beam and backwall on non-integral end bents with expansion devices.
  
{|border="0" align="center" style="text-align:center"
+
=== 751.40.8.14 Concrete Pile Cap Integral End Bents ===
  
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Bents_with_crown_over_6_in)_(Section_AA).gif]]||[[Image:751.40_Conc_Pile_Cap_Int_Bents_PS_Dbl_Tee_(Bents_with_crown_over_6_in)_(Section_BB).gif]]
 
|-
 
|'''SECTION A-A'''||'''SECTION B-B'''
 
|}
 
  
 +
==== 751.40.8.14.1 Design ====
  
{|border="0"
 
  
|(*)||Channel shear connectors are to be used in Seismic Performance Categories B, C & D.
+
===== 751.40.8.14.1.1 Design Unit Stresses =====
|-
 
|valign="top"|(**)||2'-6" Min. for Seismic Performance Category A.<br/>2'-9" Min. for Seismic Performance Categories, B, C & D.
 
|-
 
|colspan="2"|Note:  Use square ends on Prestress Double-Tee Structures.
 
|}
 
  
=====751.40.8.12.2.2 Anchorage of Piles for Seismic Performance Categories B, C & D=====
+
#Reinforced Concrete
 +
#*Class B Concrete (Substructure) &nbsp; <math>\, f_c</math> &nbsp; = 1,200 psi, &nbsp; <math>\, f'_c</math> &nbsp; = 3,000 psi
 +
#*Reinforcing Steel (Grade 60) &nbsp; &nbsp; &nbsp; &nbsp; <math>\, f_s</math> &nbsp; = 24,000 psi &nbsp; <math>\, f_y</math> &nbsp; = 60,000 psi
 +
#*<math>\, n</math> &nbsp; = 10
 +
#*<math>\, E_c</math> &nbsp; =<math>\, w^{1.5} \times 33 \sqrt{f'_c}</math> &nbsp; (AASHTO Article 8.7.1)(*)
 +
#Structural Steel
 +
#*Structural Carbon Steel  (ASTM A709 Grade 36) &nbsp; <math>\, f_s</math> &nbsp; = 20,000 psi &nbsp; <math>\, f_y</math> &nbsp; = 36,000 psi
 +
#Piling
 +
#*See the Bridge Memorandum if pile capacity is indicated.
 +
#Overstress
 +
#*The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for Service Loads design method.
  
 +
(*) &nbsp; <math>\, E_c = 57,000 \sqrt {f'_c} for\ W = 145 pcf,\ E_c = 60,625 \sqrt{f'_c} for W = 150 pcf </math>
  
'''STEEL PILE'''
+
===== 751.40.8.14.1.2 Loads =====
  
 +
#Dead Loads
 +
#Live Load
 +
#*As specified on the Bridge Memorandum.
 +
#*Impact of 30% is to be used for design of the beam. No impact is to be used for design of any other portion of bent including the piles.
 +
#Temperature, Wind and Frictional Loads
  
{|border="0" align="center" style="text-align:center"
+
===== 751.40.8.14.1.3 Distribution of Loads =====
  
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_Steel_Pile_(Part_Elevation).gif]]
+
#Dead Loads
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_Steel_Pile_(Sec_thru_beam).gif]]
+
#*Loads from stringers, girders, etc. shall be concentrated loads applied at the intersection of centerline of stringer and centerline of bearing.  Loads from concrete slab spans shall be applied as uniformly, distributed loads along the centerline of bearing.
|-
+
#Live Load
|'''PART ELEVATION'''||'''SECTION THRU BEAM'''
+
#*Loads from stringers, girders, etc. shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of bearing. For concrete slab spans distribute two wheel lines over 10'-0" (normal to centerline of roadway) of substructure beam.  This distribution shall be positioned on the beam on the same basis as used for wheel lines in Traffic Lanes for Substructure Design.
|-
+
#Wing with Detached Wing Wall
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_Steel_Pile_(Part_Plan).gif]]
+
#*When wing length, L, is greater than 17 feet, use maximum length of 10 feet rectangular wing wall combined with a detached wing wall.  When detached wing walls are used, no portion of the bridge live load shall be assumed distributed to the detached wing walls.  Design detached wing wall as a retaining wall. (The weight of barrier or railing on top of the wall shall be included in Dead Load.)
|-
 
|'''PART PLAN'''
 
|}
 
  
 +
===== 751.40.8.14.1.4 Design Examples =====
  
 +
Design H-bar and F-bar of an intermediate wing as shown in the figures below (wing length = 12.5', wing thickness = 24", wing height = 8'-4"), a Seismic Force of &nbsp; <math>\, \omega</math> = 12.21 kips/ft. is applied on the wall.
  
'''CAST-IN-PLACE PILE'''
 
  
 
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
{|border="0" align="center" style="text-align:center"
+
|-
 
+
|[[Image:751.40 conc pile cap int end bents-section near intermediate wing.gif]]
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_CIP_Pile_(Part_Elevation).gif]]
+
|[[Image:751.40 conc pile cap int end bents-intermediate wing sectin b-b.gif]]
|width="300"|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_CIP_Pile_(Sec_thru_beam).gif]]
+
|-
 +
!Section Near Intermediate Wing
 +
!Section B-B
 +
|-
 +
|colspan="2"| &nbsp;
 
|-
 
|-
|'''PART ELEVATION'''||'''SECTION THRU BEAM'''
+
|rowspan="2"|[[Image:751.40 conc pile cap int end bents-intermediate wing sectin c-c.gif]]
 +
|[[Image:751.40 conc pile cap int end bents-interior wing design.gif]]
 
|-
 
|-
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Reinf_CIP_Pile_(Part_Plan).gif]]
+
!Interior Wing Design
 
|-
 
|-
|'''PART PLAN'''
+
!Section C-C
 
|}
 
|}
  
=====751.40.8.12.2.3 Beam Reinforcement Special Cases=====
 
  
 +
Solve:  Assume #6 V bar, #8 H bar, #6 F bar
  
'''SPECIAL CASE I'''
+
{|
 
+
|valign="top" rowspan="14"|1.)||Design H-bar for bending
 
+
|-
If centerline bearing is 12" or less on either side of centerline piles, for all piles (as shown above), use 4-#6 top and bottom and #4 at 12" cts. (stirrups), regardless of pile size.
+
|<math>\, d = 24in. - 2in. (clr.) - 0.75in. (V\ Bar) - 0.5 \times 1in. (H\ bar) = 20.75in.</math>.
 
+
|-
 
+
| <math>\, \ell = 11ft.,</math> &nbsp; <math>\, \omega = 12.21 kips/ft.,</math> &nbsp;  <math>\, b = 8ft. 4in. = 100in. </math>
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_Beam_Reinf_(Special_Case_I).gif]]</center>
+
|-
 
+
|&nbsp;
 
+
|-
 
+
|At Section A-A:
'''SPECIAL CASE II'''
+
|-
 
+
|<math>\, Mu = (1.0)( \omega \ell^2 / 2) = 12.21 \times 11^2/2 = 738.705 kip-ft.</math>
 
+
|-
When beam reinforcement is to be designed assuming piles to take equal force, design for negative moment in the beam over the interior piles.
+
|<math>\, Ru = Mu/( \phi bd^2) = 738.705 \times 12,000/(0.9 \times 100in. \times (20.75)^2) = 228.85 psi</math>
 
+
|-
 
+
|Use <math>\, f-c = 3 kisi,</math> &nbsp; <math>\, fy = 60 ksi</math>
[[Image:751.40_Conc_Pile_Cap_Int_Bents_Beam_Reinf_(Special_Case_II).gif]]
+
|-
 
+
|<math>\, m = fy/(0.85 f'c) = 60/(0.85 \times 3) = 23.53</math>
 
+
|-
(*) Dimensions shown are for illustration purposes only.
+
|<math>\, \rho = (1/m)[1 - \sqrt{1 - 2 Rum/fy}] = (1 - \sqrt{1 - 2 \times 228.85 \times 23.53/60000})/23.53 = 0.004003</math>
 
+
|-
====751.40.8.12.3 Details====
+
|As (Req'd) = <math>\, \rho\ bd = 0.004003 \times 100in. \times 20.75in. = 8.31 sq.\ in.</math>
=====751.40.8.12.3.1 Sway Bracing=====
+
|-
 
+
|Try No. 8 @ 9", USE &nbsp; <math>\, \frac{100in - 3in. (clr.) - 2in. (clr.) - 1in (No.\ 8\ bar)}{9in} = 10.44\ spacing</math>
'''(Use when specified on Design Layout)'''
+
|-
 
+
|Say 11 spacings, 12 bars (Each Face)
 
+
|-
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_Sway_Bracing_(Steel_&_CIP_Pile).gif]]</center>
+
|Total Area = <math>\, 12 (0.7854) = 9.42 sq.\ in. > 8.31 sq.\ in.,</math> &nbsp; USE 12-No. 8 H-bar (Each Face)
 
 
{|border="0" align="center" style="text-align:center"
 
 
 
|width="250"|'''STEEL BEARING PILE'''||width="250"|'''CAST-IN-PLACE PILE'''
 
 
|}
 
|}
  
  
 
+
{|
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_Sway_Bracing_(Alternate_Steel_Pile).gif]]</center>
+
|valign="top" rowspan="22"|2.)||Design F-bar for shear
 
 
 
 
<center>'''ALTERNATE STEEL BEARING PILE'''</center>
 
 
 
 
 
Attention Designers and Detailers:
 
 
 
{|border="0"
 
 
 
|(1)||Omit sway bracing if less than 10'-0" (Cast-In-Place piles only).
 
 
|-
 
|-
|valign="top"|(2)||When angle slope of bracing becomes less than 15° to the horizontal, omit the diagonal angles and use the horizontal angles only (Except on four pile bents, then use alternate shown above).
+
|<math>\, Vu \le \phi (Vc = Vs),\ \phi = 0.85</math> &nbsp; (AASHTO Article 8.16.6.1.1)
|}
 
 
 
Note:  In case of a large number of piles, see the Structural Project Manager.
 
 
 
=====751.40.8.12.3.2 Miscellaneous Details for Prestressed Girder=====
 
 
 
'''PRESTRESSED GIRDERS (INTEGRAL INT. BENT)'''
 
 
 
 
 
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_Misc_Details_PS_Girders_(Integral_Int_Bent)_Jt_Filler_Detail.gif]]</center>
 
 
 
 
 
<center>'''DETAIL OF JOINT FILLER AT INT. BENTS<br/>(Continuous Spans - No Longitudinal Beam Steps)'''</center>
 
 
 
 
 
{|border="0"
 
 
 
|(*)||¼ Joint Filler for a P/S Double Tee Structure
 
 
|-
 
|-
|&nbsp;||½ Joint Filler for a P/S I-Girder Structure
+
| &nbsp;
|}
 
 
 
 
 
'''PRESTRESSED GIRDERS (NON-INTEGRAL INT. BENT)'''
 
 
 
 
 
<center>[[Image:751.40_Conc_Pile_Cap_Int_Bents_Misc_Details_PS_Girders_(Non_Integral_Int_Bent)_Jt_Filler_Detail.gif]]</center>
 
 
 
 
 
<center>'''DETAIL OF JOINT FILLER AT INT. BENTS<br/>Longitudinal Beam Step and Shear Blocks shown)'''</center>
 
 
 
 
 
'''DETAILS OF CONST. JOINT KEY'''
 
 
 
{|border="0" align="center" style="text-align:center"
 
 
 
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Misc_Details_Const_Jt_Key_(Part_Elevation).gif]]
 
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Misc_Details_Const_Jt_Key_(Part_Section_PS_I_Girders).gif]]
 
|[[Image:751.40_Conc_Pile_Cap_Int_Bents_Misc_Details_Const_Jt_Key_(Part_Section_Dbl_Tee_Girders).gif]]
 
 
|-
 
|-
|'''PART ELEVATION'''||'''PART SECTION THRU KEYS<BR/>(P/S I-GIRDERS)'''||'''PART SECTION THRU KEYS<BR/>(P/S DOUBLE TEE GIRDERS)'''
+
|At Section A-A:
|}
 
 
 
 
 
===751.40.8.13 Concrete Pile Cap Non-Integral End Bents===
 
 
 
====751.40.8.13.1 Design====
 
 
 
=====751.40.8.13.1.1 Unit Stresses=====
 
 
 
{|border="0"
 
 
 
|(1)||Reinforced Concrete
 
 
|-
 
|-
|&nbsp;||Class B Concrete (Substructure)||<math>\, f_c</math> = 1,200 psi||<math>\, f'_c</math> = 3,000 psi
+
|<math>\, Vu = 1.0 \times (\omega \ell) = (12.21 kips/ft.)(11ft.) = 134.11 kips</math>
 
|-
 
|-
|&nbsp;||Reinforcing Steel (Grade 60)||<math>\, f_s</math> = 24,000 psi||<math>\, f_y</math> = 60,000 psi
+
|<math>\, Vc = bd(\vartheta c) = bd(2 \sqrt{f'c} = (100in. \times 20.75in.)(2 \times \sqrt{3000})/1000 = 227.30 kips</math>
 
|-
 
|-
|&nbsp;||<math>\, n</math> = 10
+
|<math>\, \phi\ Vc = 0.85 Vc = 0.85 \times 227.30 kips = 193.20 kips</math>
 
|-
 
|-
|&nbsp;||colspan="3"|<math>\, E_c = W^{1.5} \times 33 \sqrt{f'_c}</math> AASHTO Article 8.7.1) (*)
+
|<math>\, \phi\ Vc = 193.20 kips > Vu = 134.11 kips,</math> &nbsp; No &nbsp; <math>\, Vs</math> &nbsp; needed by AASHTO Article 8.16.6.3.1.
 +
|-
 +
|Minimum shear reinforcement is required by AASHTO Article 8.19.1.1(a).(ACI 318-95 11.5.5.1)
 
|-
 
|-
 
|&nbsp;
 
|&nbsp;
 
|-
 
|-
|(2)||Structural Steel
+
|F-bar is a single group of parallel bars, all bent up at the same distance from support (no "spacing" along the "L" direction of the wing).
 +
|-
 +
|Try No. 6 @ 12" F-bar (each face).
 +
|-
 +
|Try <math>\, (100in. - 3in. - 2in. - 1in. )/12in = 7.83,</math> say 8 spacing, 9 bars (each face).
 +
|-
 +
| &nbsp;
 +
|-
 +
|Since seismic force is a cyclic loading, assume one bar works at any instance.
 
|-
 
|-
|&nbsp;||Structural Carbon Steel (ASTM A709 Grade 36)||<math>\, f_s</math> = 20,000 psi||<math>\, f_y</math> = 36,000 psi
+
|<math>\, Av (provided) = 1 \times 9 \times (0.4418 sq.\ in.) = 3.98 sq.\ in.</math>
 
|-
 
|-
|&nbsp;
+
| &nbsp;
 
|-
 
|-
|(3)||Piling
+
|<math>\, Vs = Av (Fy\ Sin 45^\circ) = (3.98 sq.\ in.)(60 ksi)(Sin 45^\circ) = 168.7 kips</math>
 
|-
 
|-
|&nbsp;
+
|Check &nbsp; <math>3 \sqrt{f'c} b_\omega d = 3 \sqrt{3000} \times 100in. \times 20.75in. / 1000 = 341.0 kips</math>
 
|-
 
|-
|(4)||Overstress
+
| &nbsp;
 
|-
 
|-
|&nbsp;||colspan="3"|The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for Service Loads design method.
+
|<math>\, Vs = Av (fy\ Sin 45^\circ) \le 3 \sqrt{f'c} b_\omega d,</math> &nbsp; O.K. by AASHTO Article 8.16.6.3.4.
 
|-
 
|-
|(*)||colspan="3"| <math>\, E_c = 57,000 \sqrt{f'c} W</math> = 145 pcf., <math>\, Ec = 60,625 \sqrt{f'c}</math> for <math>\, W</math> = 150 pcf.
+
|USE 9 No. 6 F-bars (each face).
 
|}
 
|}
  
=====751.40.8.13.1.2 Loads=====
+
==== 751.40.8.14.2 Reinforcement ====
  
  
{|border="0"
+
===== 751.40.8.14.2.1 Earthquake Loads at End Bent – Intermediate Wing (Seismic Shear Wall) =====
  
|(1)||Dead Loads
+
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|-
|&nbsp;
+
|[[Image:751.40 conc pile cap int end bents-section near intermediate wing(seismic).gif]]
 +
|[[Image:751.40 conc pile cap int end bents-intermediate wing sectin b-b(seismic).gif]]
 
|-
 
|-
|(2)||Live Load
+
!Section Near Intermediate Wing
 +
!Section B-B
 
|-
 
|-
|&nbsp;||As specified on the Design Layout
+
|colspan="2"| &nbsp;
 
|-
 
|-
|&nbsp;||Impact of 30% is to be used for design of the beam.  No impact is to be used for design of any other portion of bent including the piles.
+
|[[Image:751.40 conc pile cap int end bents-intermediate wing sectin a-a(seismic).gif]]
 +
|&nbsp;
 
|-
 
|-
 +
!Section A-A
 
|&nbsp;
 
|&nbsp;
 +
|}
 +
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 +
|-
 +
|valign="top" align="right"|*||align="left" width="400pt"|Use 1.25 x development length for seismic design.
 
|-
 
|-
|(3)||Temperature, Wind and Frictional Loads
+
|valign="top" align="right"|**||align="left" width="400pt"|Additional reinforcing steel by design if required.
 
|-
 
|-
|&nbsp;||Wind and temperature forces can be calculated based on longitudinal force distribution.
+
|valign="top" align="right"|Note:||align="left" width="400pt"|Make sure reinforcement does not interfere with girders.
 
|}
 
|}
  
=====751.40.8.13.1.3 Distribution of Loads=====
+
=== 751.40.8.15 Cast-In-Place Concrete Retaining Walls ===
 +
 
 +
==== 751.40.8.15.1 Loads ====
  
 +
'''Dead Loads'''
  
{|border="0"
+
Dead loads shall be determined from the unit weights in [[751.2 Loads#751.2.1.1 Dead Load |EPG 751.2.1.1 Dead Load]].
  
|(1)||Dead Loads
+
'''Equivalent Fluid Pressure (Earth Pressures)'''
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||Loads from stringers, girders, etc. shall be concentrated loads applied at the intersection of centerline of stringer and centerline of bearing.
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;
+
|AASHTO 3.20.1
|-
+
|}
|(2)||Live Load
+
 
|-
+
For determining equivalent earth pressures for Group Loadings I through VI the Rankine Formula for Active Earth Pressure shall be used.
|&nbsp;||Loads from stringers, girders, etc. shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of earing.
+
 
|-
+
Rankine Formula: <math>P_a = \frac{1}{2}C_a\gamma_sH^2</math> where:
|&nbsp;
+
:''C<sub>a</sub>'' = <math>\cos\delta\Bigg[\frac{\cos\delta - \sqrt{\cos^2\delta - \cos^2\phi}}{\cos\delta + \sqrt{\cos^2\delta - \cos^2\phi}}\Bigg]</math> = coefficient of active earth pressure
|-
+
 
|(3)||Temperature
+
:''P<sub>a</sub>'' = equivalent active earth pressure
|-
+
 
|&nbsp;||The force due to expansion or contraction applied at bearing pads are not used for stability or pile bearing computations. However, the movement due to temperature should be considered in the bearing pad design and expansion device design.
+
:''H'' = height of the soil face at the vertical plane of interest
|-
+
 
|&nbsp;
+
:<math>\boldsymbol{\gamma_s}</math> = unit weight of soil
|-
+
 
|(4)||Wing with Detached Wing Wall
+
:<math>\boldsymbol{\delta}</math>= slope of fill in degrees
|}
+
 
 +
:<math>\boldsymbol{\phi}</math> = angle of internal friction of soil in degrees
 +
[[image:751.24.1.2.jpg|center|485px]]
 +
 
 +
'''Example'''
 +
 
 +
Given:
 +
 
 +
:''δ'' = 3:1 (H:V) slope
 +
 
 +
:''ϕ'' = 25°
 +
 
 +
:''γ<sub>s</sub>'' = 0.120 kcf
 +
 
 +
:''H'' = 10 ft
 +
 
 +
''δ'' = arctan<math>\Big[\frac{1}{3}\Big]</math> = 18.4°
 +
 
 +
''C<sub>a</sub>'' = <math>\cos (18.4^\circ)\Bigg[\frac{\cos(18.4^\circ) - \sqrt{\cos^2(18.4^\circ) - \cos^2(25^\circ)}}{\cos(18.4^\circ) + \sqrt{\cos^2(18.4^\circ) - \cos^2(25^\circ)}}\Bigg]</math> = 0.515
 +
 
 +
''P<sub>a</sub>'' = (1/2)(0.515)(0.120 kips/ft<sup>3</sup>)(10 ft)<sup>2</sup> = 3.090 kips per foot of wall length
 +
 
 +
The ''ϕ'' angle shall be determined by the Materials Division from soil tests. If the ''ϕ'' angle cannot be provided by the [http://sp/sites/cm/Pages/default.aspx Construction and Materials Division] a ''ϕ'' angle of 27 degrees shall be used.
 +
 
 +
Drainage shall be provided to relieve water pressure from behind all cast-in-place concrete retaining walls. If adequate drainage can not be provided then walls shall be designed to resist the maximum anticipated water pressure.
 +
 
 +
'''Surcharge Due to Point, Line and Strip Loads'''
 +
 
 +
Surcharge due to point and line loads on the soil being retained shall be included as dead load surcharge. The effect of these loads on the wall may be calculated using Figure 5.5.2B from AASHTO.
 +
 
 +
Surcharge due to strip loads on the soil being retained shall be included as a dead load surcharge load. The following procedure as described in ''Principles of Foundation Engineering'' by Braja M. Das (1995) shall be applied to calculate these loads when strip loads are applicable. An example of this application is when a retaining wall is used in front of an abutment so that the wall is retaining the soil from behind the abutment as a strip load on the soil being retained by the wall.
 +
 
 +
[[image:751.24.1.2 retaining.jpg|center|255px|thumb|<center>'''Retaining Wall in front of an Abutment'''</center>]]
 +
 
 +
The portion of soil that is in the active wedge must be determined because the surcharge pressure only affects the wall if it acts on the active wedge. The actual failure surface in the backfill for the active state can be represented by ABC shown in the figure below. An approximation to the failure surface based on Rankine's active state is shown by dashed line AD. This approximation is slightly unconservative because it neglects friction at the pseudo-wall to soil interface.
 +
 
 +
The following variables are shown in the figure below:
 +
 
 +
:''β'' = slope of the active failure plane in degrees
 +
:''δ'' = slope of fill in degrees
 +
:''H'' = height of the pseudo-wall (fom the bottom of the footing).
 +
:''L<sub>1</sub>'' = distance from back of stem to back of footing heel
 +
:''L<sub>2</sub>'' = distance from footing heel to intersection of failure plane with ground surface
 +
 
 +
[[image:751.24.1.2 wedges.jpg|center|575px|thumb|<center>'''Determination of Active Wedges'''</center>]]
 +
 
 +
In order to determine ''β'', the following equation which has been derived from Rankine's active earth pressure theory must be solved by iteration:
 +
 
 +
:<math>\tan (-\beta) + \frac{1}{\tan (\beta - \phi)} - \frac{1}{\tan (\beta - \delta)} + \frac{1}{\tan (90^\circ + \phi + \delta - \beta)} = 0</math>
 +
 
 +
:''ϕ'' = angle of internal friction of soil in degrees
  
<center>[[Image:751.40_Detached_Wing_Wall_Section_AA.gif]]</center>
+
A good estimate for the first iteration is to let ''β'' = 45° + (ϕ/2). In lieu of iterating the above equation a conservative estimate for ''β'' is 45°. Once β has been established, an estimate of L<sub>1</sub> is needed to determine L<sub>2</sub>. From the geometry of the variables shown in the above figure:
  
<center>'''SECTION A-A'''</center>
+
:<math>L_2 = H\frac{\cos\delta\cos\beta}{\sin(\beta - \delta)}</math>
  
 +
The resultant pressure due to the strip load surcharge and its location are then determined. The following variables are shown in the figure below:
  
<center>[[Image:751.40_Detached_Wing_Wall_Detail_B.gif]]</center>
+
:''q'' = load per unit area
 +
:''P<sub>s</sub>'' = resultant pressure on wall due only to surcharge earth pressure
 +
:<math>\bar{z}</math> = location of P<sub>s</sub> measured from the bottom of the footing
 +
:''L<sub>3</sub>'' = distance from back of stem to where surcharge pressure begins
  
<center>'''DETAIL B'''</center>
+
[[image:751.24.1.2 surcharge.jpg|center|625px|thumb|<center>'''Surcharge Pressure on Retaining Wall'''</center>]]
  
 +
From the figure:
  
{|border="0"
+
:P<sub>s</sub> = <math>\frac{q}{90}\big[H(\theta_2 - \theta_1)\big]</math> where
  
|(*)||Detached wing wall shown is for illustration purpose only.  Design detached wing wall as a retaining wall.
+
:<math>\theta_1 = \arctan\Big[\frac{L_3}{H}\Big] \ and \ \theta_2 = \arctan\Big[\frac{L_2}{H}\Big]</math>
|-
 
|(**)||See retaining wall design.
 
|}
 
  
=====751.40.8.13.1.4 Design Assumptions - Loadings=====
+
:<math>\bar{z} = \frac{H^2(\theta_2 - \theta_1) - (R - Q) + 57.03L_4H}{2H(\theta_2 - \theta_1)}</math> where
  
 +
:<math>R = (L_2)^2(90^\circ - \theta_2) \ and \ Q = (L_3)^2(90^\circ - \theta_1)</math>
  
{|border="0"
+
When applicable, P<sub>s</sub> is applied to the wall in addition to other earth pressures. The wall is then designed as usual.
  
|'''1)'''||colspan="3"|'''Piles'''
+
'''Live Load Surcharge'''
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"  
 
|-
 
|-
|&nbsp;||valign="top"|a.||colspan="2"|Stresses in the piles due to bending need not be considered in design calculations except for seismic design in categories B, C and D.
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||b.||colspan="2"|The following four loading cases should be considered.
+
|AASHTO 3.20.3 & 5.5.2
|-
+
|}
|&nbsp;||&nbsp;||colspan="2"|
+
Live load surcharge pressure of not less than two feet of earth shall be applied to the structure when highway traffic can come within a horizontal distance equal to one-half of the wall height, measured from the plane where earth pressure is applied.
{|border="1" style="text-align:center" cellpadding="5" cellspacing="0"
+
 
 +
[[image:751.24.1.2 live load1.jpg|center|475px]]
 +
 
 +
[[image:751.24.1.2 live load surcharge.jpg|center|575px|thumb|<Center>'''Live Load Surcharge'''</center>]]
 +
 
 +
:''P<sub>LLS</sub>'' = (2 ft.) ''γ<sub>s</sub> C<sub>a</sub> H'' = pressure due to live load surcharge only
 +
 
 +
:''γ<sub>s</sub>'' = unit weight of soil (Note: AASHTO 5.5.2 specifies a minimum of 125 pcf for live load surcharge, MoDOT policy allows 120 pcf as given from the unit weights in [[751.2 Loads#751.2.1.1 Dead Load |EPG 751.2.1.1 Dead Load]].)
 +
:''C<sub>a</sub>'' = coefficient of active earth pressure
 +
 
 +
:''H'' = height of the soil face at the vertical plane of interest
 +
 
 +
The vertical live load surcharge pressure should only be considered when checking footing bearing pressures, when designing footing reinforcement, and when collision loads are present.
 +
 
 +
'''Live Load Wheel Lines'''
  
|Case||Vertical Loads||Horizontal Loads||Special Consideration
+
Live load wheel lines shall be applied to the footing when the footing is used as a riding or parking surface.
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|I||DL + E + SUR||EP + SUR||-
+
|'''Additional Information'''
 
|-
 
|-
|II||DL + LL + E + SUR||EP + SUR||-
+
|AASHTO 3.24.5.1.1 & 5.5.6.1
 +
|}
 +
 
 +
Distribute a LL<sub>WL</sub> equal to 16 kips as a strip load on the footing in the following manner.
 +
 
 +
 
 +
:P = LL<sub>WL</sub>/E
 +
 
 +
::where E = 0.8X + 3.75
 +
 
 +
::::X = distance in ft. from the load to the front face of the wall
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|III||DL + LL + E||EP||-
+
|'''Additional Information'''
 
|-
 
|-
|IV||DL + LL + E||None||Allow 25% Overstress
+
|AASHTO 3.24.2 & 3.30
 
|}
 
|}
 +
 +
Two separate placements of wheel lines shall be considered, one foot from the barrier or wall and one foot from the toe of the footing.
 +
 +
[[image:751.24.1.2 wheel.jpg|center|350px]]
 +
 +
'''Collision Forces'''
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|Where,
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||&nbsp;||LL||= live load
+
|AASHTO Figure 2.7.4B
 +
|}
 +
 
 +
Collision forces shall be applied to a wall that can be hit by traffic. Apply a point load of 10 kips to the wall at a point 3 ft. above the finished ground line.
 +
 
 +
[[image:751.24.1.2 collision section.jpg|center|450px|thumb|<center>'''Section'''</center>]]
 +
 
 +
Distribute the force to the wall in the following manner:
 +
 
 +
:Force per ft of wall = (10 kips)/2L
 +
 
 +
[[image:751.24.1.2 collision profile.jpg|center|350px|thumb|<center>'''Profile'''</center>]]
 +
 
 +
When considering collision loads, a 25% overstress is allowed for bearing pressures and a factor of safety of 1.2 shall be used for sliding and overturning.
 +
 
 +
'''Wind and Temperature Forces'''
 +
 
 +
These forces shall be disregarded except for special cases, consult the Structural Project Manager.
 +
 
 +
When walls are longer than 84 ft., an expansion joint shall be provided.
 +
 
 +
Contraction joint spacing shall not exceed 28 feet.
 +
 
 +
'''Seismic Loads'''
 +
 
 +
Retaining walls in Seismic Performance Category A (SPC A) and SPC B that are located adjacent to roadways may be designed in accordance with AASHTO specifications for SPC A. Retaining walls in SPC B which are located under a bridge abutment or in a location where failure of the wall may affect the structural integrity of a bridge shall be designed to AASHTO specifications for SPC B. All retaining walls located in SPC C and SPC D shall be designed in accordance to
 +
AASHTO specifications for the corresponding SPC.
 +
 
 +
In seismic category B, C and D determine equivalent fluid pressure from Mononobe-Okabe static method.
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||&nbsp;||DL||= dead load of superstructure, substructure and one half of the apporach slab
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||&nbsp;||SUR||= two feet of live load surcharge
+
|1992 AASHTO Div. IA Eqns. C6-3 and C6-4
 +
|}
 +
''P<sub>AE</sub>'' = equivalent active earth pressure during an earthquake
 +
 
 +
''P<sub>AE</sub>'' = 0.5 γ<sub>s</sub>H<sup>2</sup>(1 - k<sub>v</sub>)K<sub>AE</sub> where
 +
 
 +
''K<sub>AE</sub>'' = seismic active pressure coefficient
 +
 
 +
:<math>K_{AE} = \frac{\cos^2(\phi - \theta - \beta)}{\cos\theta\cos^2\beta\cos(\delta + \beta + \theta)\Big\{1 + \sqrt{\frac{\sin(\phi + \delta)\sin(\phi - \theta - i)}{\cos(\delta + \beta + \theta)\cos(i - \beta)}}\Big\}^2}</math>
 +
 
 +
 
 +
''γ<sub>s</sub>'' = unit weight of soil
 +
 
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||&nbsp;||E||= dead load of earth fill
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||&nbsp;||EP||= equivalent fluid pressure of earth
+
|AASHTO 5.2.2.3 & Div. IA 6.4.3
|-
+
|}
|&nbsp;||&nbsp;||colspan="2"|Maximum pile pressure = pile capacity
+
''k<sub>v</sub>'' = vertical acceleration coefficient
 +
 
 +
''k<sub>h</sub>'' = horizontal acceleration coefficient which is equal to 0.5A for all walls,
 +
:::but 1.5A for walls with battered piles where
 +
:::A = seismic acceleration coefficient
 +
 
 +
The following variables are shown in the figure below:
 +
 
 +
''ϕ'' = angle of internal friction of soil
 +
 
 +
''θ'' = <math>\arctan\ \Big(\frac{k_h}{1 - k_v}\Big)</math>
 +
 
 +
''β'' = slope of soil face
 +
 
 +
''δ'' = angle of friction between soil and wall in degrees
 +
 
 +
''i'' = backfill slope angle in degrees
 +
 
 +
''H'' = distance from the bottom of the part of the wall to which the pressure is applied to the top of the fill at the location where the earth pressure is to be found.
 +
 
 +
[[image:751.24.1.2 active soil.jpg|center|450px|thumb|<center>'''Active Soil Wedge'''</center>]]
 +
 
 +
<div id="Group Loads"></div>
 +
'''Group Loads'''
 +
 
 +
For SPC A and B (if wall does not support an abutment), apply AASHTO Group I Loads only. Bearing capacity, stability and sliding shall be calculated using working stress loads. Reinforced concrete design shall be calculated using load factor design loads.
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|Minimum pile pressure = 0 (tension on a pile will not be allowed for any combination of forces exept as noted)
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;
+
|AASHTO Table 3.22.1A
 +
|}
 +
 
 +
AASHTO Group I Load Factors for Load Factor Design of concrete:
 +
''γ'' = 1.3
 +
 
 +
''β<sub>D</sub>'' = 1.0 for concrete weight
 +
 
 +
''β<sub>D</sub>'' = 1.0 for flexural member
 +
 
 +
''β<sub>E</sub>'' = 1.3 for lateral earth pressure for retaining walls
 +
 
 +
''β<sub>E</sub>'' = 1.0 for vertical earth pressure
 +
 
 +
''β<sub>LL</sub>'' = 1.67 for live load wheel lines
 +
 
 +
''β<sub>LL</sub>'' = 1.67 for collision forces
 +
 
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|'''2)'''||colspan="3"|'''Analysis Procedure'''
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||a.||colspan="2"|''Find the lateral stiffness of a pile, <math>\, K_\delta</math>'':
+
|AASHTO 5.14.2
 +
|}
 +
 
 +
''β<sub>E</sub>'' = 1.67 for vertical earth pressure resulting from live load surcharge
 +
 
 +
''β<sub>E</sub>'' = 1.3 for horizontal earth pressure resulting from live load surcharge
 +
 
 +
For SPC B (if wall supports an abutment), C, and D apply AASHTO Group I Loads and seismic loads in accordance with AASHTO Division IA - Seismic Design Specifications.
 +
 
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|With fixed pile-head (i.e., only translation movement is allowed but no rotation allowed): The lateral stiffness of a pile can be estimated using Figures 1 and 3 or 2 and 3 for pile in cohesionless or cohesive soil, respectively.  The method of using Figures 1, 2, and 3 to find lateral stiffness is called Linear Subgrade Modulus Method.  Usually the significant soil-pile interaction zone for pile subjected to lateral movement is confined to a depth at the upper 5 to 10 pile diameters.  Therefore, simplified single layer stiffness chart shown in Figure 3 is appropriate for lateral loading.  The coefficient <math>\, f</math> in Figures 1 and 2 is used to define the subgrade modulus <math>\, E_s</math> at depth “z” representing the soil stiffness per unit pile length.  For the purpose of selecting an appropriate <math>\, f</math> value, the soil condition at the upper 5 pile diameters should be used.  Since soil property, friction angle <math>\, \phi</math>, or cohesion c, is needed when Figure 1 or 2 is used, determine soil properties based on available soil boring data.  If soil boring data is not available, one can conservatively use <math>\, f</math> value of 0.1 in Figure 3.  Designer may also use soil properties to convert SPT N value to friction angle <math>\, \phi</math>, or cohesion c, for granular or cohesive soil, respectively.  Figures 1 and 2 were based on test data for smaller-diameter (12 inches) piles, but can be used for piles up to about 24 inches in diameter.  In Figure 2, the solid line (by Lam et al. 1991) shall be used in design.
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||b.||colspan="2"|''Find the axial stiffness of a pile, <math>\, K_a</math>'':
+
|AASHTO Div. IA 4.7.3
 +
|}
 +
 
 +
When seismic loads are considered, load factor for all loads = 1.0.
 +
 
 +
==== 751.40.8.15.3 Unit Stresses ====
 +
 
 +
'''Concrete'''
 +
Concrete for retaining walls shall be Class B Concrete (f'c = 3000 psi) unless the footing is used as a riding surface in which case Class B-1 Concrete (f'c = 4000 psi) shall be used.
 +
 
 +
'''Reinforcing Steel'''
 +
 
 +
Reinforcing Steel shall be Grade 60 (fy = 60,000 psi).
 +
 
 +
'''Pile Footing'''
 +
 
 +
For steel piling material requirements, see the unit stresses in [[751.50 Standard Detailing Notes#A1. Design Specifications, Loadings & Unit Stresses and Standard Plans|EPG 751.50 Standard Detailing Notes]].
 +
 
 +
'''Spread Footing'''
 +
 
 +
For foundation material capacity, see Foundation Investigation Geotechnical Report.
 +
 
 +
==== 751.40.8.15.4 Design ====
 +
 
 +
For epoxy coated reinforcement requirements, see [[751.5 Structural Detailing Guidelines#751.5.9.2.2 Epoxy Coated Reinforcement Requirements|EPG 751.5.9.2.2 Epoxy Coated Reinforcement Requirements]].
 +
 
 +
If the height of the wall or fill is a variable dimension, then base the structural design of the wall, toe, and heel on the high quarter point between expansion joints.
 +
 
 +
[[image:751.24.3.2.jpg|center|600px|thumb|<center>'''Fig. 40.8.15.4.1'''</center>]]
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|For friction pile, <math>\, K_a</math> may be determined based on a secant stiffness approach as described in Bridge Manual Section 6.1 – Seismic Design or by the in-house computer program “SPREAD” where <math>\, K_a</math> is calculated as:
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|<math>\, \frac{1}{K_a} = \frac{1}{AE / L'} + \frac{1}{K_{Q_f}} + \frac{1}{K_{Q_b}}</math> &nbsp;  Equation (1)
+
|AASHTO 5.5.5
 +
|}
 +
 
 +
===== 751.40.8.15.4.1 Spread Footings =====
 +
 
 +
'''Location of Resultant'''
 +
 
 +
The resultant of the footing pressure must be within the section of the footing specified in the following table.
 +
 
 +
{| border="1" class="wikitable" style="margin: 1em auto 1em auto"
 +
|+
 +
! style="background:#BEBEBE" |When Retaining Wall is Built on: !! style="background:#BEBEBE"|AASHTO Group Loads I-VI !! style="background:#BEBEBE"|For Seismic Loads
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|Where:
+
| align="center" |Soil<sup>a</sup> || align="center"|Middle 1/3|| align="center"|Middle 1/2 <sup>b</sup>
 
|-
 
|-
|&nbsp;||&nbsp;||<math>\, A</math>||= cross sectional area of pile
+
| align="center"|Rock<sup>c</sup> || align="center"|Middle 1/2||align="center"|Middle 2/3
 
|-
 
|-
|&nbsp;||&nbsp;||<math>\, E</math>||= elastic modulus of pile
+
|colspan="3"|<sup>'''a'''</sup> Soil is defined as clay, clay and boulders, cemented gravel, soft shale, etc. with allowable bearing values less than 6 tons/sq. ft.
 
|-
 
|-
|&nbsp;||&nbsp;||<math>\, L'</math>||= total length of pile
+
|colspan="3"|<sup>'''b'''</sup> MoDOT is more conservative than AASHTO in this requirement.
 
|-
 
|-
|&nbsp;||&nbsp;||<math>\, K_{Q_f}</math>||= secant stiffness due to ultimate friction capacity of the pile as described in Bridge Manual Section 6.1
+
|colspan="3"|<sup>'''c'''</sup> Rock is defined as rock or hard shale with allowable bearing values of 6 tons/sq. ft. or more.
 +
|}
 +
 
 +
Note: The location of the resultant is not critical when considering collision loads.
 +
 
 +
'''Factor of Safety Against Overturning'''
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||&nbsp;||<math>\, K_{Q_f}</math> ||= secant stiffness due to ultimate bearing capacity of the pile as described in Bridge Manual Section 6.1
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||colspan="3"|For HP bearing pile on rock <math>\, K_a</math> shall be calculated as:
+
|AASHTO 5.5.5
 +
|}
 +
 
 +
AASHTO Group Loads I - VI:
 +
* F.S. for overturning ≥ 2.0 for footings on soil.
 +
* F.S. for overturning ≥ 1.5 for footings on rock.
 +
 
 +
For seismic loading, F.S. for overturning may be reduced to 75% of the value for AASHTO Group Loads I - VI. For seismic loading:
 +
* F.S. for overturning ≥ (0.75)(2.0) = 1.5 for footings on soil.
 +
* F.S. for overturning ≥ (0.75)(1.5) = 1.125 for footings on rock.
 +
 
 +
For collision forces:
 +
* F.S. for overturning ≥ 1.2.
 +
 
 +
'''Factor of Safety Against Sliding'''
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|<math>\, \frac{1}{K_a} = \frac{1}{AE / L'} + \frac{1}{K_{Q_f}}</math> &nbsp;  Equation (2)
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|Or Conservatively, <math>\, K_a</math> may be determined as:
+
|AASHTO 5.5.5
 +
|}
 +
 
 +
Only spread footings on soil need be checked for sliding because spread footings on rock or shale are embedded into the rock.
 +
* F.S. for sliding ≥ 1.5 for AASHTO Group Loads I - VI.
 +
* F.S. for sliding ≥ (0.75)(1.5) = 1.125 for seismic loads.
 +
* F.S. for sliding ≥ 1.2 for collision forces.
 +
 
 +
The resistance to sliding may be increased by:
 +
* adding a shear key that projects into the soil below the footing.
 +
* widening the footing to increase the weight and therefore increase the frictional resistance to sliding.
 +
 
 +
'''Passive Resistance of Soil to Lateral Load'''
 +
 
 +
The Rankine formula for passive pressure can be used to determine the passive resistance of soil to the lateral force on the wall. This passive pressure is developed at shear keys in retaining walls and at end abutments.
 +
 
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"  
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|<math>\, K_a = \frac{AE}{L'}</math> &nbsp;  Equation (3)
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;
+
|AASHTO 5.5.5A
 +
|}
 +
 
 +
The passive pressure against the front face of the wall and the footing of a retaining wall is loosely compacted and should be neglected when considering sliding.
 +
 
 +
Rankine Formula: <math>P_p = \frac{1}{2}C_p\gamma_s[H^2-H_1^2]</math> where thefollowing variables are defined in the figure below
 +
:
 +
:''C<sub>p</sub>'' = <math>\tan \big( 45^\circ + \frac{\phi}{2}\big)</math>
 +
 
 +
:''y<sub>1</sub> = <math>\frac{H_1y_2^2 + \frac{2}{3}y_2^3}{H^2 - H_1^2}</math>
 +
 
 +
:''P<sub>p</sub>'' = passive force at shear key in pounds per foot of wall length
 +
 
 +
:''C<sub>p</sub>'' = coefficient of passive earth pressure
 +
 
 +
:<math>\boldsymbol{\gamma_s}</math> = unit weight of soil
 +
 
 +
:''H'' = height of the front face fill less than 1 ft. min. for erosion
 +
 
 +
:''H<sub>1</sub>'' = H minus depth of shear key
 +
 
 +
:''y<sub>1</sub>'' = location of ''P<sub>p</sub>'' from bottom of footing
 +
 
 +
:<math>\boldsymbol{\phi}</math> = angle of internal friction of soil
 +
 
 +
[[image:751.24.3.2.1 passive.jpg|center|500px]]
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|align="center" colspan="4"|[[Image:751.40_Subgrade_Modulus_with_Depth_for_Sand.gif]]
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;
+
|AASHTO 5.5.2
 +
|}
 +
The resistance due to passive pressure in front of the shear key shall be neglected unless the key extends below the depth of frost penetration.
 +
{|style="padding: 0.3em; margin-right:7px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="left"
 
|-
 
|-
|align="center" colspan="4"|'''Recommended Coefficient <math>f</math> of Variation in Subgrade Modulus with Depth for Sand'''
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;
+
|[http://sp/sites/cm/Pages/default.aspx MoDOT Materials Division]
 +
|}
 +
 
 +
Frost line is set at 36 in. at the north border of Missouri and at 18 in. at the south border.
 +
 
 +
'''Passive Pressure During Seismic Loading'''
 +
 
 +
During an earthquake, the passive resistance of soil to lateral loads is slightly decreased. The Mononobe-Okabe static method is used to determine the equivalent fluid pressure.
 +
 
 +
:''P<sub>PE</sub>'' = equivalent passive earth pressure during an earthquake
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|align="center" colspan="4"|[[Image:751.40_Subgrade_Modulus_with_Depth_for_Clay.gif]]
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;
+
|1992 AASHTO Div. IA Eqns. C6-5 and C6-6
 +
|}
 +
:<math>P_{PE} = \frac{1}{2}\gamma_sH^2(1 - k_v)K_{PE}</math> where:
 +
 
 +
:''K<sub>PE</sub>'' = seismic passive pressure coefficient
 +
 
 +
:<math>K_{PE} = \frac{\cos^2(\phi - \theta - \beta)}{\cos\theta\cos^2\beta\cos(\delta + \beta + \theta)\Bigg[1 + \sqrt{\frac{\sin(\phi + \delta)\sin(\phi - \theta - i)}{\cos(\delta + \beta + \theta)\cos(i - \beta)}}\Bigg]^2}</math>
 +
 
 +
::<math>\boldsymbol{\gamma}_s</math> = unit weight of soil
 +
 
 +
:''H'' = height of soil at the location where the earth pressure is to be found
 +
 
 +
:''k<sub>V</sub>'' = vertical acceleration coefficient
 +
 
 +
:<math>\boldsymbol{\phi}</math> = angle of internal friction of soil
 +
 
 +
:<math>\boldsymbol{\theta} =  arctan \big[\frac{k_h}{1 - k_V}\big]</math>
 +
 
 +
:''k<sub>H</sub>'' = horizontal acceleration coefficient
 +
 
 +
:<math>\boldsymbol{\beta}</math> = slope of soil face in degrees
 +
 
 +
:''i'' = backfill slope angle in degrees
 +
 
 +
:<math>\boldsymbol{\delta}</math> = angle of friction between soil and wall
 +
 
 +
'''Special Soil Conditions'''
 +
 
 +
Due to creep, some soft clay soils have no passive resistance under a continuing load. Removal of undesirable material and replacement with suitable material such as sand or crushed stone is necessary in such cases. Generally, this condition is indicated by a void ratio above 0.9, an angle of internal friction (<math>\boldsymbol{\phi}</math>) less than 22°, or a soil shear less than 0.8 ksf. Soil shear is determined from a standard penetration test.
 +
 
 +
:Soil Shear <math>\Big(\frac{k}{ft^2}\Big) = \frac{blows \ per\ 12\ in.}{10}</math>
 +
 
 +
'''Friction'''
 +
 
 +
In the absence of tests, the total shearing resistance to lateral loads between the footing and a soil that derives most of its strength from internal friction may be taken as the normal force times a coefficient of friction. If the plane at
 +
which frictional resistance is evaluated is not below the frost line then this resistance must be neglected.
 +
 
 +
[[image:751.24.3.2.1 friction 2016.jpg|center|450px|thumb|<center>'''When A Shear Key Is Not Used'''</center>]]
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|align="center" colspan="4"|'''Recommended Coefficient <math>\, f</math> of Variation in Subgrade Modulus with Depth for Clay'''
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;
+
|AASHTO 5.5.2B
|-
+
|}
|align="center" colspan="4"|[[Image:751.40_Lateral_Embedded_Pile-Head_Stiffness.gif]]
+
 
|-
+
Sliding is resisted by the friction force developed at the interface between the soil and the concrete footing along the failure plane. The coefficient of friction for soil against concrete can be taken from the table below. If soil data
|align="center" colspan="4"|
+
is not readily available or is inconsistent, the friction factor (f) can be taken as
{|border="0" align="center" style="text-align:center" cellpadding="5"
+
 
 +
: ''f'' =<math>tan \Big(\frac{2\phi}{3}\Big)</math> where <math>\boldsymbol{\phi}</math> is the angle of internal friction of the soil (''Civil Engineering Reference Manual'' by Michael R. Lindeburg, 6th ed., 1992).
  
|'''PILE HEAD AT<br/>GRADE LEVEL'''||&nbsp;||'''EMBEDDED PILE HEAD'''
+
{| border="1" class="wikitable" style="margin: 1em auto 1em auto"
|}
+
|+
 +
!style="background:#BEBEBE" colspan="2"|Coefficient of Friction Values for Soil Against Concrete
 
|-
 
|-
|&nbsp;
+
! style="background:#BEBEBE" |Soil Type<sup>a</sup> !! style="background:#BEBEBE"|Coefficient of Friction
 
|-
 
|-
|align="center" colspan="4"|'''Lateral Embedded Pile-Head Stiffness'''
+
| align="center" |coarse-grained soil without silt || align="center"|0.55
 
|-
 
|-
|&nbsp;
+
| align="center"|coarse-grained soil with silt  || align="center"|0.45
 
|-
 
|-
|&nbsp;||c.||colspan="2"|''Find the equivalent cantilever pile length, <math>\, L</math>''
+
|align="center"|silt (only)|| align="center"|0.35
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|For the structural model used in the structural analyses of loading cases I through IV. As shown in figure below, length L can be calculated as:
+
|align="center"|clay|| align="center"|0.30<sup>b</sup>
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|<math>\, L = \Bigg(\frac{12EI}{K_\delta}\Bigg)^{1/3}</math> &nbsp;  Equation (4)
+
|colspan="2"|<sup>'''a'''</sup> It is not necessary to check rock or shale for sliding due to embedment.
 
|-
 
|-
|&nbsp;
+
|colspan="2"|<sup>'''b'''</sup> Caution should be used with soils with <math>\boldsymbol{\phi}</math> < 22° or soil shear < 0.8 k/sq.ft. (soft clay soils). Removal and replacement of such soil with suitable material should be considered.
 +
|}
 +
 
 +
[[image:751.24.3.2.1 soil and soil.jpg|center|450px|thumb|<center>'''When A Shear Key Is Used'''</center>]]
 +
 
 +
When a shear key is used, the failure plane is located at the bottom of the shear key in the front half of the footing. The friction force resisting sliding in front of the shear key is provided at the interface between the stationary layer of soil and the moving layer of soil, thus the friction angle is the internal angle of friction of the soil (soil against soil). The friction force resisting sliding on the rest of the footing is of that between the concrete and soil. Theoretically
 +
the bearing pressure distribution should be used to determine how much normal load exists on each surface, however it is reasonable to assume a constant distribution. Thus the normal load to each surface can be divided out between the two surfaces based on the fractional length of each and the total frictional force will be the sum of the normal load on each surface
 +
multiplied by the corresponding friction factor.
 +
 
 +
'''Bearing Pressure'''
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|colspan="4" align="center"|[[Image:751.40_Structural_Model.gif]]
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;
+
|AASHTO 4.4.7.1.2 & 4.4.8.1.3
 +
|}
 +
 
 +
:'''Group Loads I - VI'''
 +
 
 +
:The bearing capacity failure factor of safety for Group Loads I - VI must be greater than or equal to 3.0. This factor of safety is figured into the allowable bearing pressure given on the "Design Layout Sheet".
 +
 
 +
:The bearing pressure on the supporting soil shall not be greater than the allowable bearing pressure given on the "Design Layout Sheet".
 +
 
 +
:'''Seismic Loads'''
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|colspan="4" align="center|'''Structural Model'''
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;
+
|AASHTO Div. IA 6.3.1(B) and AASHTO 5.5.6.2
 +
|}
 +
 
 +
:When seismic loads are considered, AASHTO allows the ultimate bearing capacity to be used. The ultimate capacity of the foundation soil can be conservatively estimated as 2.0 times the allowable bearing pressure given on the "Design Layout".
 +
 
 +
:'''Stem Design'''
 +
 +
:The vertical stem (the wall portion) of a cantilever retaining wall shall be designed as a cantilever supported at the base.
 +
 
 +
:'''Footing Design'''
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||d.||colspan="2"|''Find the equivalent pile area, <math>\, A_e</math> :
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||&nbsp;||colspan="2"|Once the equivalent cantilever pile length has been determined from step (c) above, the equivalent axial rigidity of the pile, <math>\, A_e \times E_e</math> , can be calculated as <math>\, A_e \times E = K_a L</math>. Then, the equivalent pile area, <math>\, A_e</math> , is equal to
+
|AASHTO 5.5.6.1
|-
+
|}
|&nbsp;||&nbsp;||colspan="2"|<math>\, A_e = \frac{K_aL}{E}</math> &nbsp;  Equation (5)
+
 
|-
+
::'''Toe'''
|&nbsp;
+
 
|-
+
::The toe of the base slab of a cantilever wall shall be designed as a cantilever supported by the wall. The critical section for bending moments shall be taken at the front face of the stem. The critical section for shear shall be taken at a distance d (d = effective depth) from the front face of the stem.
|&nbsp;||e.||colspan="2"|''Perform structural analyses for loading cases I through IV.
+
 
|-
+
::'''Heel'''
|&nbsp;||&nbsp;||colspan="2"|Use computer programs STRUCT3D, SAP2000 or any other program capable of running static analysis.
+
 
|-
+
::The rear projection (heel) of the base slab shall be designed to support the entire weight of the superimposed materials, unless a more exact method is used. The heel shall be designed as a cantilever supported by the wall. The critical section for bending moments and shear shall be taken at the back face of the stem.
|&nbsp;
+
 
|-
+
:'''Shear Key Design'''
|&nbsp;||f.||colspan="2"|''Check abutment movement at the top of backwall and at the bottom of beam cap''
+
 
|-
+
:The shear key shall be designed as a cantilever supported at the bottom of the footing.
|&nbsp;||&nbsp;||colspan="2"|Maximum movement away from the backfill shall not be greater than 1/8". Maximum movement toward the backfill shall not be greater than 1/4".
+
 
|-
+
===== 751.40.8.15.4.2 Pile Footings =====
|&nbsp;
+
 
|-
+
Footings shall be cast on piles when specified on the "Design Layout Sheet". If the horizontal force against the retaining wall cannot otherwise be resisted, some of the piles shall be driven on a batter.
|&nbsp;||g.||colspan="2"|''Check pile axial loads from the analysis with the allowable pile axial load capacity.
+
 
|-
+
:'''Pile Arrangement'''
|&nbsp;
+
 
|-
+
:For retaining walls subject to moderate horizontal loads (walls 15 to 20 ft. tall), the following layout is suggested.
|&nbsp;||h.||colspan="2"|''Check overturning of bent''
+
 
|-
+
[[image:751.24.3.2.2 batter piles.jpg|center|300px|thumb|<center>'''Section'''</center>]]
|&nbsp;||&nbsp;||colspan="2"|Conservatively, use the same equivalent cantilever pile length, <math>\, L</math>.  Check overturning of bent at the bottom of toe pile for loading cases I and II(Figure of Structural model).
+
 
|-
+
[[image:751.24.3.2.2 plan 2016.jpg|center|450px|thumb|<center>'''Plan'''</center>]]
|&nbsp;||&nbsp;||colspan="2"|
+
 
{|border="1" style="text-align:center" cellpadding="5" cellspacing="0"
+
:For higher walls and more extreme conditions of loading, it may be necessary to:
 +
 
 +
:* use the same number of piles along all rows
 +
 
 +
:* use three rows of piles
 +
 
 +
:* provide batter piles in more than one row
 +
 
 +
::'''Loading Combinations for Stability and Bearing'''
 +
 
 +
::The following table gives the loading combinations to be checked for stability and pile loads. These abbreviations are used in the table:
 +
 
 +
:::DL = dead load weight of the wall elements
 +
 
 +
:::SUR = two feet of live load surcharge
 +
 
 +
:::E = earth weight
 +
 
 +
:::EP = equivalent fluid earth pressure
 +
 
 +
:::COL = collision force
 +
 
 +
:::EQ = earthquake inertial force of failure wedge
  
|Case I||Point of<br/>Investigation||Vertical Loads||Horizontal Loads||Factor of Safety (**)
+
{| border="1" class="wikitable" style="margin: 1em auto 1em auto"
 +
|+
 +
!style="background:#BEBEBE" rowspan="2"|Loading Case !!style="background:#BEBEBE" rowspan="2"|Vertical Loads !!style="background:#BEBEBE" rowspan="2"|Horizontal Loads !!style="background:#BEBEBE" rowspan="2"|Overturning Factor of Safety !!style="background:#BEBEBE" colspan="2"|Sliding Factor of Safety
 
|-
 
|-
|I||Toe Pile||DL + E||EP + SUR||1.2
+
!style="background:#BEBEBE" |Battered Toe Piles !!style="background:#BEBEBE" |Vertical Toe Piles
 
|-
 
|-
|II||Toe Pile||DL + LL + E||EP + SUR||1.5
+
|align="center"|I<sup>a</sup>||align="center"| DL+SUR+E ||align="center"|EP+SUR||align="center"| 1.5||align="center"| 1.5||align="center"|2.0
|}
 
 
|-
 
|-
|&nbsp;
+
|align="center"|II||align="center"| DL+SUR+E ||align="center"|EP+SUR+COL||align="center"| 1.2|| align="center"|1.2||align="center"| 1.2
 
|-
 
|-
|'''5)'''||colspan="3"|'''Deadman Anchorage System'''
+
|align="center"|III||align="center"| DL+E||align="center"| EP||align="center"| 1.5||align="center"| 1.5||align="center"| 2.0
 
|-
 
|-
|&nbsp;||colspan="3"|Deadman anchorage can be used when the abutment movement exceeds the allowable movement.
+
|align="center"|IV<sup>b</sup>||align="center"| DL+E ||align="center"|None||align="center"| -||align="center"| -||align="center"| -
 
|-
 
|-
|&nbsp;||colspan="3"|The size and location of deadman anchorage shall be designed appropriately to maintain the stability of the abutment.
+
|align="center"|V<sup>c</sup>||align="center"| DL+E||align="center"| EP+EQ||align="center"| 1.125||align="center"| 1.125||align="center"| 1.5
 
|-
 
|-
|&nbsp;||colspan="3"|The deadman forces may be used to resist overturning with the approval of the Structural Project Manager.
+
|colspan="6"|<sup>'''a'''</sup> Load Case I should be checked with and without the vertical surcharge.
 
|-
 
|-
|&nbsp;
+
|colspan="6"|<sup>'''b'''</sup> A 25% overstress is allowed on the heel pile in Load Case IV.
 
|-
 
|-
|'''6)'''||colspan="3"|'''Passive Pressure Shear Key (if applicable)'''
+
|colspan="6"|<sup>'''c'''</sup> The factors of safety for earthquake loading are 75% of that used in Load Case III. Battered piles are not recommended for use in seismic performance categories B, C, and D. Seismic design of retaining walls is not required in SPC A and B. Retaining walls in SPC B located under a bridge abutment shall be designed to AASHTO Specifications for SPC B.
|-
 
|&nbsp;||colspan="3"|Passive pressure shear key may be used when the abutment movement exceeds the allowable movement.
 
|-
 
|&nbsp;||colspan="3"|The passive resistance of soil to the lateral force at shear keys may be used with the approval of structural project manager.
 
 
|}
 
|}
  
=====751.40.8.13.1.5 Deadman Anchors=====
+
::'''Pile Properties and Capacities'''
 +
 
 +
::For Load Cases I-IV in the table above, the allowable compressive pile force may be taken from the pile capacity table in the Piling Section of the Bridge Manual which is based in part on AASHTO 4.5.7.3. Alternatively, the allowable compressive pile capacity of a friction pile may be determined from the ultimate frictional and bearing capacity between the soil and pile divided by a safety factor of 3.5 (AASHTO Table 4.5.6.2.A). The maximum amount of tension allowed on a heel pile is 3 tons.
 +
 
 +
::For Load Case V in the table above, the allowable compressive pile force may be taken from the pile capacity table in the Piling Section of the Bridge Manual multiplied by the appropriate factor (2.0 for steel bearing piles, 1.5 for friction piles). Alternatively, the allowable compressive pile capacity of a friction pile may be determined from the ultimate frictional and bearing capacity between the soil and pile divided by a safety factor of 2.0. The allowable tension force on a bearing or friction pile will be equal to the ultimate friction capacity between the soil and pile divided by a safety factor of 2.0.
 +
 
 +
::To calculate the ultimate compressive or tensile capacity between the soil and pile requires the boring data which includes the SPT blow counts, the friction angle, the water level, and the soil layer descriptions.
 +
 
 +
::Assume the vertical load carried by battered piles is the same as it would be if the pile were vertical. The properties of piles may be found in the Piling Section of the Bridge Manual.
  
'''Design Assumptions'''
+
:::'''Neutral Axis of Pile Group'''
  
 +
:::Locate the neutral axis of the pile group in the repetitive strip from the toe of the footing at the bottom of the footing.
  
<center>[[Image:751.40_Deadman_Anchor_Design_Assumption_Detail.gif]]</center>
+
:::'''Moment of Inertia of Pile Group'''
  
 +
:::The moment of inertia of the pile group in the repetitive strip about the neutral axis of the section may be determined using the parallel axis theorem:
  
{|border="0" cellpadding="3"
+
::::I = Σ(I<sub>A</sub>) + Σ(Ad<sup>2</sup>) where :
  
|&nbsp;||Length of Deadman = <math>\, (F_E + F_S / (P_P - P_A)</math>
+
::::''I<sub>A</sub>'' = moment of inertia of a pile about its neutral axis
|-
+
 
|&nbsp;||Number of tie rods required = <math>\, (F_E + F_S) / F_R</math>
+
::::''A'' = area of a pile
 +
 
 +
::::''d'' = distance from a pile's neutral axis to pile group's neutral axis
 +
 
 +
:::''I<sub>A</sub>'' may be neglected so the equation reduces to:
 +
 
 +
::::''I'' =  Σ(Ad<sup>2</sup>)
 +
 
 +
::'''Resistance To Sliding'''
 +
 
 +
::Any frictional resistance to sliding shall be ignored, such as would occur between the bottom of the footing and the soil on a spread footing.
 +
 
 +
::'''Friction or Bearing Piles With Batter (Case 1)'''
 +
 
 +
::Retaining walls using friction or bearing piles with batter should develop lateral strength (resistance to sliding) first from the batter component of the pile and second from the passive pressure against the shear key and the piles.
 +
 
 +
::'''Friction or Bearing Piles Without Batter (Case 2)'''
 +
 
 +
::Retaining walls using friction or bearing piles without batter due to site constrictions should develop lateral strength first from the passive pressure against the shear key and second from the passive pressure against the pile below the bottom of footing. In this case, the shear key shall be placed at the front face of the footing.
 +
 
 +
::'''Concrete Pedestal Piles or Drilled Shafts (Case 3)'''
 +
 
 +
::Retaining walls using concrete pedestal piles should develop lateral strength first from passive pressure against the shear key and second from passive pressure against the pile below the bottom of the footing. In this case, the shear key shall be placed at the front of the footing. Do not batter concrete pedestal piles.
 +
 
 +
[[image:751.24.3.2.2 cases.jpg|center|450px]]
 +
 
 +
::'''Resistance Due to Passive Pressure Against Pile'''
 +
 
 +
::The procedure below may be used to determine the passive pressure resistance developed in the soil against the piles. The procedure assumes that the piles develop a local failure plane.
 +
 
 +
:::''F'' = the lateral force due to passive pressure on pile
 +
 
 +
:::<math>F = \frac{1}{2}\gamma_s C_P H^2 B </math> , where: <math> C_P = tan^2\Big[45 + \frac{\phi}{2}\Big]</math>
 +
 
 +
:::<math>\boldsymbol{\gamma_s}</math> = unit weight of soil
 +
 
 +
:::''H'' = depth of pile considered for lateral resistance (H<sub>max</sub>= 6B)
 +
 
 +
:::''C<sub>P</sub>'' = coefficient of active earth pressure
 +
 
 +
:::''B'' = width of pile
 +
 
 +
:::<math>\boldsymbol{\phi}</math> = angle of internal friction of soil
 +
 
 +
[[image:751.24.3.2.2 resistance passive.jpg|center|450px]]
 +
 
 +
::'''Resistance Due to Pile Batter'''
 +
 
 +
::Use the horizontal component (due to pile batter) of the allowable pile load as the lateral resistance of the battered pile. (This presupposes that sufficient lateral movement of the wall can take place before failure to develop the ultimate strength of both elements.)
 +
 
 +
[[image:751.24.3.2.2 12.jpg|center|125px]]
 +
 
 +
:::''b'' = the amount of batter per 12 inches.
 +
 
 +
:::<math> c = \sqrt{(12 in.)^2 + b^2}</math>
 +
 
 +
:::<math>P_{HBatter} = P_T \Big(\frac{b}{c}\Big)</math> (# of battered piles) where:
 +
 
 +
:::''P<sub>HBatter</sub>'' = the horizontal force due to the battered piles
 +
 
 +
:::''P<sub>T</sub>'' = the allowable pile load
 +
 
 +
::Maximum batter is 4" per 12".
 +
 
 +
::'''Resistance Due to Shear Keys'''
 +
 
 +
::A shear key may be needed if the passive pressure against the piles and the horizontal force due to batter is not sufficient to attain the factor of safety against sliding. The passive pressure against the shear key on a pile footing is found in the same manner as for spread footings.
 +
 
 +
::'''Resistance to Overturning'''
 +
 
 +
::The resisting and overturning moments shall be computed at the centerline of the toe pile at a distance of 6B (where B is the width of the pile) below the bottom of the footing. A maximum of 3 tons of tension on each heel pile may be assumed to resist overturning. Any effects of passive pressure, either on the shear key or on the piles, which resist overturning, shall be ignored.
 +
 
 +
[[image:751.24.3.2.2 resistance overturning.jpg|center|450px]]
 +
 
 +
::'''Pile Properties'''
 +
 
 +
:::'''Location of Resultant'''
 +
 
 +
:::The location of the resultant shall be evaluated at the bottom of the footing and can be determined by the equation below:
 +
 
 +
::::<math>e = \frac{\Sigma M}{\Sigma V}</math>  where:
 +
 
 +
::::e = the distance between the resultant and the neutral axis of the pile group
 +
 
 +
::::''ΣM'' = the sum of the moments taken about the neutral axis of the pile group at the bottom of the footing
 +
 
 +
::::''ΣV'' = the sum of the vertical loads used in calculating the moment
 +
 
 +
:::'''Pile Loads'''
 +
 
 +
:::The loads on the pile can be determined as follows:
 +
 
 +
::::<math>P = \frac{\Sigma V}{A} \pm \frac{Mc}{I}</math> where:
 +
 
 +
:::::''P'' = the force on the pile
 +
 
 +
:::::''A'' = the areas of all the piles being considered
 +
 
 +
:::::''M'' = the moment of the resultant about the neutral axis
 +
 
 +
:::::''c'' = distance from the neutral axis to the centerline of the pile being investigated
 +
 
 +
:::::''I'' = the moment of inertia of the pile group
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||<math>\, P_A</math> = Active earth pressure on deadman, in lb./ft. = (120 pcf) <math>\, K_A hT</math>
+
|'''Additional Information'''
 
|-
 
|-
|(**)||<math>\, P_P</math> = Passive earth pressure on deadman, in lb./ft. = (120 pcf) <math>\, K_P hT</math>
+
|AASHTO 5.5.6.2
|-
+
|}
|&nbsp;||<math>\, F_E</math> = Earth pressure on end bent, in lb. = 0.5(120 pcf)<math>\, K_A H^2</math> (length of beam)
+
 
 +
:::'''Stem Design'''
 +
 
 +
:::The vertical stem (the wall portion) of a cantilever retaining wall shall be designed as a cantilever supported at the base.
 +
 
 +
:::'''Footing Design'''
 +
 
 +
::::'''Toe'''
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 
|-
 
|-
|&nbsp;||<math>\, F_S</math> = Surcharge on end bent, in lb. = <math>\, (120 pcf)(2')K_A H (length\ of\ beam)</math>
+
|'''Additional Information'''
 
|-
 
|-
|&nbsp;||<math>\, K_A = Tan^2 (45^\circ - \phi/2)</math>
+
|AASHTO 5.5.6.1
 +
|}
 +
 
 +
::::The toe of the base slab of a cantilever wall shall be designed as a cantilever supported by the wall. The critical section for bending moments shall be taken at the front face of the stem. The critical section for shear shall be taken at a distance d (d = effective depth) from the front face of the stem.
 +
 
 +
::::'''Heel'''
 +
::::The top reinforcement in the rear projection (heel) of the base slab shall be designed to support the entire weight of the superimposed materials plus any tension load in the heel piles (neglect compression loads in the pile), unless a more exact method is used. The bottom reinforcement in the heel of the base slab shall be designed to support the maximum compression load in the pile neglecting the weight of the superimposed materials. The heel shall be designed as a cantilever supported by the wall. The critical sections for bending moments and shear shall be taken at the back face of the stem.
 +
 
 +
:::'''Shear Key Design'''
 +
:::The shear key shall be designed as a cantilever supported at the bottom of the footing.
 +
 
 +
=====751.40.8.15.4.3 Counterfort Walls=====
 +
 
 +
'''Assumptions:'''
 +
 
 +
(1) Stability
 +
The external stability of a counterfort retaining wall shall be determined in the same manner as described for cantilever retaining walls. Therefore refer to previous pages for the criteria for location of resultant, factor of safety for sliding and bearing pressures.
 +
 +
(2) Stem
 +
 +
[[image:751.24.3.2.3 counterfort.jpg|center|800px]]
 +
 
 +
:<math>P = C_a \boldsymbol \gamma_s</math>
 +
 
 +
:where:
 +
::''C<sub>a</sub>'' = coefficient of active earth pressure
 +
 
 +
::<math>\boldsymbol \gamma_s</math> = unit weigt of soil
 +
 
 +
Design the wall to support horizontal load from the earth pressure and the liveload surcharge (if applicable) as outlined on the previous pages and as designated in AASHTD Section 3.20, except that maximum horizontal loads shall be the calculated equivalent fluid pressure at 3/4  height of wall [(0.75 H)P] which shall be considered applied uniformly from the lower quarter point to the bottom of wall.
 +
 
 +
In addition, vertical steel In the fill face of the bottom quarter of the wall shall be that required by the vertical cantilever wall with the equivalent fluid pressure of that (0.25 H) height.
 +
 
 +
Maximum concrete stress shall be assumed as the greater of the two thus obtained.
 +
 +
The application of these horizontal pressures shall be as follows:
 +
 +
[[image:751.24.3.2.3 counterfort wall.jpg|center|800px|thumb|<center>'''Counterfort Wall Section'''</center> <center>Moments are to be determined by analysis as a continuous beam.  The counterforts are to be spaced so as to produce approximately equal positive and negative moments.</center>]]
 +
 
 +
(3)  Counterfort
 +
Counterforts shall be designed as T-beams, of which the wall is the flange and the counterfort is the stem.  For this reason the concrete stresses ane normally low and will not control.
 +
 
 +
For the design of reinforcing steel in the back of the counterfort, the effective d shall be the perpendicular distance from the front face of the wall (at point that moment is considered), to center of reinforcing steel.
 +
 
 +
[[image:751.24.3.2.3 moment.jpg|center|500px]]
 +
 
 +
(4) Footing
 +
 
 +
The footing of the counterfort walls shall be designed as a continuous beam of spans equal to the distance between the counterforts.
 +
 
 +
The rear projection or heel shall be designed to support the entire weight of the superimposed materials, unless a more exact method is used. Refer to AASHTD Section 5.5.6.
 +
 
 +
Divide footing (transversely) into four (4) equal sections for design footing pressures.
 +
 
 +
Counterfort walls on pile are very rare and are to be treated as special cases.  See Structural Project Manager.
 +
 
 +
(5)  Sign-Board type walls
 +
 
 +
The Sign-Board type of retaining walls are a special case of the counterfort retaining walls.  This type of wall is used where the soiI conditions are such that the footings must be placed a great distance below the finished ground line.  For this situation, the wall is discontinued approximately 12 in. below the finished ground line or below the frost line.
 +
 
 +
Due to the large depth of the counterforts, it may be more economical to use a smaller number of counterforts than would otherwise be used.
 +
 +
All design assumptions that apply to counterfort walls will apply to sign-board walls with the exception of the application of horizontal forces for the stem (or wall design), and the footing design which shall be as follows:
 +
 
 +
:'''Wall'''
 +
 
 +
[[image:751.24.3.2.3 load.jpg|center|550px]]
 +
 
 +
:'''Footing'''
 +
 
 +
:The individual footings shall be designed transversely as cantilevers supported by the wall.  Refer to AASHTO Section 5.
 +
 
 +
==== 751.40.8.15.5 Example 1:  Spread Footing Cantilever Wall ====
 +
 
 +
[[image:751.24.3.3.jpg|center|750px|thumb|<Center>'''Typical Section thru Wall</center><center>(Spread Footing)</center>''']]
 +
 
 +
:f'<sub>c</sub> = 3,000 psi
 +
:f<sub>y</sub> = 60,000 psi
 +
:''φ'' = 24 in.
 +
:''γ<sub>s</sub>'' = 120 pcf (unit wgt of soil)
 +
:Allowable soil pressure = 2 tsf
 +
:''γ<sub>c</sub>'' = 150 pcf (unit wgt of concr.)
 +
:Retaining wall is located in Seismic Performance Category (SPC) B.
 +
:A = 0.1 (A = seismic acceleration coefficient)
 +
 
 +
{| style="margin: 1em auto 1em auto"
 
|-
 
|-
|&nbsp;||<math>\, K_P = Tan^2 (45^\circ - \phi/2)</math>
+
|<math>P_a = \frac{1}{2}\gamma_s C_a H^2</math>||width=50| ||<math>P_p = \frac{1}{2}\gamma_s C_p H_2^2 - H_1^2</math>
 +
|}
 +
 
 +
'''Assumptions'''
 +
 
 +
* Retaining wall is under an abutment or in a location where failure of the wall may affect the structural integrity of a bridge. Therefore, it must be designed for SPC B.
 +
 
 +
* Design is for a unit length (1 ft.) of wall.
 +
 
 +
* Sum moments about the toe at the bottom of the footing for overturning.
 +
 
 +
*For Group Loads I-VI loading:
 +
:* F.S. for overturning ≥ 2.0 for footings on soil.
 +
:* F.S. for sliding ≥ 1.5.
 +
* Resultant to be within middle 1/3 of footing.
 +
 
 +
* For earthquake loading:
 +
:* F.S. for overturning ≥ 0.75(2.0) = 1.5.
 +
:* F.S. for sliding ≥ 0.75(1.5) = 1.125.
 +
:* Resultant to be within middle 1/2 of footing.
 +
 
 +
* Base of footing is below the frost line.
 +
 
 +
* Neglect top one foot of fill over toe when determining passive pressure and soil weight.
 +
 
 +
* Use of a shear key shifts the failure plane to "B" where resistance to sliding is provided by passive pressure against the shear key, friction of soil along failure plane "B" in front of the key, and friction between soil and concrete along the footing behind the key.
 +
 
 +
* Soil cohesion along failure plane is neglected.
 +
 
 +
* Footings are designed as cantilevers supported by the wall.
 +
:* Critical sections for bending are at the front and back faces of the wall.
 +
:* Critical sections for shear are at the back face of the wall for the heel and at a distance d (effective depth) from the front face for the toe.
 +
 
 +
* Neglect soil weight above toe of footing in design of the toe.
 +
 
 +
* The wall is designed as a cantilever supported by the footing.
 +
 
 +
* Load factors for AASHTO Groups I - VI for design of concrete:
 +
:* ''γ'' = 1.3.
 +
:* ''β<sub>E</sub>'' = 1.3 for horizontal earth pressure on retaining walls.
 +
:* ''β<sub>E</sub>'' = 1.0 for vertical earth pressure.
 +
 
 +
* Load factor for earthquake loads = 1.0.
 +
 
 +
'''Lateral Pressures Without Earthquake'''
 +
 
 +
:''C<sub>a</sub>'' = <math>\cos\delta\Bigg[\frac{\cos\delta - \sqrt{\cos^2\delta - \cos^2\phi}}{\cos\delta + \sqrt{\cos^2\delta - \cos^2\phi}}\Bigg]</math>
 +
 
 +
:''C<sub>a</sub>'' = <math>\cos 18.435^\circ \Bigg[\frac{\cos\ 18.435^\circ - \sqrt{\cos^2\ 18.435^\circ - \cos^2\ 24^\circ }}{\cos\ 18.435^\circ  + \sqrt{\cos^2\ 18.435^\circ  - \cos^2\ 24^\circ }}\Bigg]</math> = 0.546
 +
 
 +
:<math>C_p = tan^2 \big( 45^\circ + \frac{\phi}{2}\big)  = tan^2 \big( 45^\circ + \frac{24^\circ}{2}\big) = 2.371</math>
 +
 
 +
:<math>P_A = \frac{1}{2}\big[0.120\frac{k}{ft^3}\big](1 ft)(0.546)(10.667 ft)^2 = 3.726k</math>
 +
 
 +
:<math>P_P = \frac{1}{2}\big[0.120\frac{k}{ft^3}\big](1 ft)(2.371)\big[(5.0)^2 - (2.5)^2\big] = 2.668k</math>
 +
 
 +
:<math>P_{AV} = P_A (sin \delta) = 3.726k (sin 18.435^\circ ) = 1.178k</math>
 +
 
 +
:<math>P_{AH} = P_A (cos \delta) = 3.726k (cos 18.435^\circ ) = 3.534k</math>
 +
 
 +
{| border="1" class="wikitable" style="margin: 1em auto 1em auto"
 +
|+
 +
!style="background:#BEBEBE" |Load !!style="background:#BEBEBE" |Area (ft<sup>2</sup>) !!style="background:#BEBEBE" |Force (k) = (Unit Wgt.)(Area) !!style="background:#BEBEBE" |Arm (ft.) !!style="background:#BEBEBE"|Moment (ft-k)
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|-
 +
|align="center"|(1)||align="center"| (0.5)(6.667ft)(2.222ft) = 7.407||align="center"| 0.889||align="center"| 7.278 ||align="center"|6.469
 
|-
 
|-
|valign="top"|(***)||<math>\, F_R</math> = 8.0 kips for 7/8" Ø tie rod and 10.50 kips for 1" Ø tie rods<br/>(Capacity of the tie rods based on a maximum skew of 30°.)
+
|align="center"|(2)||align="center"| (6.667ft)(6.944ft) = 46.296||align="center"| 5.556||align="center"| 6.167||align="center"| 34.259
|-
+
|-
|&nbsp;
+
|align="center"|(3) ||align="center"|(0.833ft)(8.000ft) + (0.5)(0.083ft)(8.000ft) = 7.000||align="center"|1.050||align="center"| 2.396||align="center"| 2.515
|-
+
|-
|align="right"|*||If the number of 7/8" Ø tie rods causes too long of a deadman, then try 1" Ø tie rods.
+
|align="center"|(4) ||align="center"|(1.500ft)(9.500ft) = 14.250||align="center"| 2.138 ||align="center"|4.750 ||align="center"|10.153
|-
+
|-
|align="right"|**||For seismic loads only, use <math>\, P_P</math> = 4 kips/sq.ft. as the ultimate capacity of compacted fill.
+
|align="center"|(5) ||align="center"|(2.500ft)(1.000ft) = 2.500||align="center"| 0.375||align="center"| 2.500||align="center"| 0.938
|-
+
|-
|align="right"|***||For seismic loads only, the allowable stress in the tie rod may be taken as the yield stress of the rod.
+
|align="center"|(6) ||align="center"|(1.000ft)(1.917ft)+(0.5)(0.010ft)(1.000ft) = 1.922||align="center"|<u>0.231</u>||align="center"| 0.961||align="center"|<u>0.222</u>
|}
+
|-
 +
|align="center"|Σ ||align="center"| -  ||align="center"|ΣV = 10.239 ||align="center"| - ||align="center"|ΣM<sub>R</sub> = 54.556
 +
|-
 +
|align="center"|P<sub>AV</sub>||align="center"| -  ||align="center"|<u>1.178</u>||align="center"| 9.500 ||align="center"|<u>11.192</u>
 +
|-
 +
|align="center"|Σ resisting ||align="center"| - ||align="center"|ΣV = 11.417||align="center"| - ||align="center"| ΣM<sub>R</sub> = 65.748
 +
|-
 +
|align="center"|P<sub>AH</sub> ||align="center"| - ||align="center"|3.534 ||align="center"|3.556 ||align="center"|12.567
 +
|-
 +
|align="center"|P<sub>P</sub>||align="center"| -  ||align="center"|2.668 ||align="center"|1.389<sup>1</sup>||align="center"| -
 +
|-
 +
|colspan="5"|'''<sup>1</sup>''' The passive capacity at the shear key is ignored in overturning checks,since this capacity is considered in the factor of safety against sliding. It is assumed that a sliding and overturning failure will not occur simultaneously. The passive capacity at the shear key is developed only if the wall does slide.
 +
|}
 +
 
 +
[[image:751.24.3.3 passive.jpg|right|150px]]
 +
<math>\bar{y} = \frac{H_1y^2 + \frac{2}{3}y^3}{H_2^2 - H_1^2} = \frac{(2.5 ft)(2.5 ft)^2 + \frac{2}{3}(2.5 ft)^3}{(5.0 ft)^2 - (2.5 ft)^2}</math> = 1.389 ft.
 +
 
 +
:'''Overturning'''
 +
 
 +
:F.S. = <math>\frac{M_R}{M_{OT}} = \frac{65.748(ft-k)}{12.567(ft-k)} = 5.232 \ge 2.0 </math> <u>o.k.</u>
 +
 
 +
:where: M<sub>OT</sub> = overturning moment; M<sub>R</sub> = resisting moment
 +
 
 +
:'''Resultant Eccentricity'''
 +
 
 +
:<math>\bar{x} = \frac{(65.748 - 12.567)(ft-k)}{11.417k}</math> = 4.658 ft.
 +
 
 +
:<math>e = \frac{9.500 ft}{2} - 4.658 ft. = 0.092 ft.</math>
 +
:<math>\frac{L}{6} =\frac{9.500 ft}{6} = 1.583 ft > e</math> <u>o.k.</u>
 +
 
 +
:'''Sliding'''
 +
 
 +
:Check if shear key is required for Group Loads I-VI:
 +
 
 +
:F.S. = <math>\frac{\Sigma V(tan\phi_{s-c})}{P_{AH}} = \frac{11.042k(tan \frac{2}{3}(24^\circ)}{3.534k} </math>= 0.896 <u>no good - shear key req'd</u>
 +
 
 +
:where: ''φ<sub>s-c</sub>'' = angle of friction between soil and concrete = (2/3)''φ<sub>s-s</sub>''
 +
 
 +
:F.S. = <math>\frac{P_P + (\Sigma V) \Big(\frac{L_2}{L_1} tan \phi_{s-s}+\frac{L_3}{L_1} tan \phi_{s-c}\Big)}{P_{AH}}</math>
 +
 
 +
:where: ''φ<sub>s-s</sub>''  = angle of internal friction of soil
 +
 
 +
:F.S. = <math>\frac{2.668k + (11.417k) \Big[\Big(\frac{2 ft}{9.50 ft}\Big) tan 24^\circ + \Big(\frac{7.50 ft}{9.50 ft} tan \Big(\frac{2}{3}(24^\circ)\Big)\Big]}{3.534 k}</math> = 1.789 ≥ 1.5  <u>o.k.</u>
 +
 
 +
:'''Footing Pressure'''
 +
 
 +
:<math>P = \frac{\Sigma V}{bL} \Big[1 \pm \frac{6e}{L}\Big]</math>
 +
 
 +
:P<sub>H</sub> = pressure at heel <math>P_H = \frac{11.417 k}{(1 ft)9.50 ft} \Big[1 - \frac{6 (0.092 ft)}{9.50 ft}\Big]</math> = 1.132 k/ft<sup>2</sup>
 +
 
 +
:P<sub>T</sub> = pressure at toe <math>P_T = \frac{11.417 k}{(1 ft)9.50 ft} \Big[1 + \frac{6 (0.092 ft)}{9.50 ft}\Big]</math> = 1.272 k/ft<sup>2</sup>
 +
 
 +
:Allowable pressure = 2 tons/ft<sup>2</sup> = 4 k/ft<sup>2</sup> ≥ 1.272 k/ft<sup>2</sup> <u>o.k.</u>
 +
 
 +
'''Lateral Pressures With Earthquake'''
 +
 
 +
k<sub>h</sub> = 0.5A = 0.5 (0.1) = 0.05
 +
 
 +
k<sub>v</sub> = 0
 +
 
 +
<math>\theta = arctan \Big[\frac{k_h}{1 - k_v}\Big] = arctan \Big[\frac{0.05}{1 - 0}\Big] = 2.862^\circ</math>
 +
 
 +
:'''Active Pressure on Psuedo-Wall'''
 +
 
 +
:''δ'' = ''φ'' = 24° (''δ'' is the angle of friction between the soil and the wall. In this case, ''δ'' = ''φ'' = because the soil wedge considered is next to the soil above the footing.)
 +
 
 +
:''i'' = 18.435°
 +
 
 +
:''β'' = 0°
 +
 
 +
:<math>K_{AE} = \frac{cos^2(\phi - \theta - \beta)}{cos \theta cos^2 \beta cos(\delta + \beta + \theta)\Big(1 + \sqrt\frac{sin(\phi + \delta) sin (\phi - \theta - i)}{cos (\delta + \beta + \theta) cos(I - \beta)}\Big)^2}</math>
 +
 
 +
:<math>K_{AE} = \frac{cos^2(24^\circ - 2.862^\circ - 0^\circ)}{cos (2.862^\circ) cos^2 (0^\circ) cos(24^\circ + 0^\circ + 2.862^\circ)\Big(1 + \sqrt\frac{sin(24^\circ + 24^\circ) sin (24^\circ - 2.862^\circ - 18.435^\circ)}{cos (24^\circ + 0^\circ + 2.862^\circ) cos(18.435^\circ - 0^\circ)}\Big)^2}</math>
 +
 
 +
:K<sub>AE</sub> = 0.674
 +
 
 +
:P<sub>AE</sub> = ½''γ<sub>s</sub>H<sup>2</sup>''(1 − ''k<sub>v</sub>'')''K<sub>AE</sub>''
 +
 
 +
:P<sub>AE</sub> =  ½[0.120 k/ft<sup>3</sup>](10.667 ft)<sup>2</sup>(1 ft.)(1 - 0)(0.674) = 4.602k
 +
 
 +
:P<sub>AEV</sub> = P<sub>AE</sub>(sin''δ'') = 4.602k(sin24°) = 1.872k
 +
 
 +
:P<sub>AEH</sub> = P<sub>AE</sub>(cos''δ'') = 4.602k(cos 24°) = 4.204k
 +
 
 +
:P'<sub>AH</sub> = P<sub>AEH</sub> − P<sub>AH</sub> = 4.204k − 3.534k = 0.670k
 +
 
 +
:P'<sub>AV</sub> = P<sub>AEV</sub> − P<sub>AV</sub> = 1.872k − 1.178k = 0.694k
 +
 
 +
:where: P'<sub>AH</sub> and P'<sub>AV</sub> are the seismic components of the active force.
 +
 
 +
:'''Passive Pressure on Shear Key'''
 +
 
 +
:''δ'' = ''φ'' = 24° (''δ'' = ''φ'' because the soil wedge considered is assumed to form in front of the footing.)
 +
 
 +
:''i'' = 0
 +
 
 +
:''β'' = 0
 +
 
 +
:<math>K_{PE} = \frac{cos^2(\phi - \theta + \beta)}{cos \theta cos^2 \beta cos(\delta - \beta + \theta)\Big(1 - \sqrt\frac{sin(\phi - \delta) sin (\phi - \theta + i)}{cos (\delta - \beta + \theta) cos(I - \beta)}\Big)^2}</math>
 +
 
 +
:<math>K_{PE} = \frac{cos^2(24^\circ - 2.862^\circ + 0^\circ)}{cos (2.862^\circ) cos^2 (0^\circ) cos(24^\circ - 0^\circ + 2.862^\circ)\Big(1 - \sqrt\frac{sin(24^\circ - 24^\circ) sin (24^\circ - 2.862^\circ + 0^\circ)}{cos (24^\circ - 0^\circ + 2.862^\circ) cos(0^\circ - 0^\circ)}\Big)^2}</math>
 +
 
 +
:K<sub>PE</sub> = 0.976
 +
 
 +
:P<sub>PE</sub> = ½''γ<sub>s</sub>H<sup>2</sup>''(1 − ''k<sub>v</sub>'')''K<sub>PE</sub>''
 +
 
 +
:P<sub>PE</sub> =  ½[0.120 k/ft<sup>3</sup>][(5.0 ft)<sup>2</sup> - (2.5 ft<sup>2</sup>)](1 ft.)(1 - 0)(0.976) = 1.098k
 +
 
 +
{| border="1" class="wikitable" style="margin: 1em auto 1em auto"
 +
|+
 +
!style="background:#BEBEBE" |Load !!style="background:#BEBEBE" |Force (k) !!style="background:#BEBEBE" |Arm (ft) !!style="background:#BEBEBE" |Moment (ft-k)
 +
|-
 +
|align="center"|Σ (1) thru (6) ||align="center"| 10.239||align="center"| - ||align="center"| 54.556
 +
|-
 +
|align="center"|P<sub>AV</sub>||align="center"| 1.178 ||align="center"|9.500||align="center"| 11.192
 +
|-
 +
|align="center"|P'<sub>AV</sub> ||align="center"|0.694 ||align="center"|9.500||align="center"| 6.593
 +
|-
 +
|align="center"|Σ<sub>resisting</sub> ||align="center"|ΣV = 12.111 ||align="center"| - ||align="center"|ΣM<sub>R</sub> = 72.341
 +
|-
 +
|align="center"|P<sub>AH</sub> ||align="center"|3.534 ||align="center"|3.556 ||align="center"|12.567
 +
|-
 +
|align="center"|P'<sub>AH</sub> ||align="center"|0.670||align="center"| 6.400<sup>a</sup>||align="center"| 4.288
 +
|-
 +
|align="center"|P<sub>PEV</sub> ||align="center"|0.447<sup>b</sup>||align="center"| 0.000||align="center"| 0.000
 +
|-
 +
|align="center"|P<sub>PEH</sub> ||align="center"|1.003<sup>b</sup> ||align="center"|1.389<sup>c</sup>||align="center"| <u>0.000</u>
 +
|-
 +
|align="center"| - ||align="center"| - ||align="center"| - ||align="center"|ΣM<sub>OT</sub> = 16.855
 +
|-
 +
|colspan="4"|<sup>'''a'''</sup> P'<sub>AH</sub> acts at 0.6H of the wedge face (1992 AASHTO Div. IA Commentary).
 +
|-
 +
|colspan="4"|<sup>'''b'''</sup> P<sub>PEH</sub> and P<sub>PEH</sub> are the components of P<sub>PE</sub> with respect to ''δ'' (the friction angle). P<sub>PE</sub> does not contribute to overturning.
 +
|-
 +
|colspan="4"|<sup>'''c'''</sup> The line of action of P<sub>PEH</sub> can be located as was done for P<sub>P</sub>.
 +
|}
 +
 
 +
:'''Overturning'''
 +
 
 +
:<math>F.S._{OT} = \frac{72.341ft-k}{16.855ft-k} = 4.292 > 1.5</math> <u>o.k.</u>
 +
 
 +
:'''Resultant Eccentricity'''
 +
 
 +
:<math>\bar{x} = \frac{72.341ft-k - 16.855ft-k}{12.111k} = 4.581 ft.</math>
 +
 
 +
:<math>e = \frac{9.5 ft.}{2}\ - 4.581 ft. = 0.169 ft.</math>
 +
 
 +
:<math>\frac{L}{4} = \frac{9.5 ft.}{4} = 2.375 ft. > e</math> <u>o.k.</u>
 +
 
 +
 
 +
:'''Sliding'''
 +
 
 +
:<math>F.S. = \frac{1.003k + 12.111k \Big[(\frac{2}{9.5})tan 24^\circ + (\frac{7.5}{9.5}) tan \Big( \frac{2}{3}(24^\circ) \Big)\Big]}{4.204 k} = 1.161 > 1.125</math> <u>o.k.</u>
 +
 
 +
 
 +
:'''Footing Pressure'''
 +
 
 +
:for e ≤ L/6:
 +
 
 +
:<math>P = \frac{\Sigma V}{bL} \Big[ 1 \pm \frac{6e}{L}\Big] </math>
 +
 
 +
:<math>P_H = pressure\ at\ heel\ P_H = \frac{12.111 k}{(1 ft.)9.50 ft.} \Big[1 - \frac{6(0.169 ft.)}{9.50 ft}\Big]</math> = 1.139 k/ft<sup>2</sup>
 +
 
 +
:<math>P_TH = pressure\ at\ toe\ P_T = \frac{12.111 k}{(1 ft.)9.50 ft.} \Big[1 + \frac{6(0.169 ft.)}{9.50 ft}\Big]</math> = 1.411 k/ft<sup>2</sup>
 +
 
 +
:Allowable soil pressure for earthquake = 2 (allowable soil pressure)
 +
 
 +
:(2)[4 k/ft<sup>2</sup>] = 8 k/ft<sup>2</sup> > 1.411 k/ft<sup>2</sup> <u>o.k.</u>
 +
 
 +
'''Reinforcement-Stem'''
 +
 
 +
[[image:751.24.3.3 reinforcement stem.jpg|center|200px]]
 +
 
 +
d = 11" - 2" - (1/2)(0.5") = 8.75"
 +
 
 +
b = 12"
 +
 
 +
f'<sub>c</sub> = 3,000 psi
 +
 
 +
:'''Without Earthquake'''
 +
 
 +
:P<sub>AH</sub> = ½ [0.120 k/ft<sup>3</sup>](0.546)(6.944 ft.)<sup>2</sup>(1 ft.)(cos 18.435°) = 1.499k
 +
 
 +
:''γ'' = 1.3
 +
 
 +
:''β<sub>E</sub>'' = 1.3 (active lateral earth pressure)
 +
 
 +
:M<sub>u</sub> = (1.3)(1.3)(1.499k)(2.315ft) = 5.865 (ft-k)
 +
 
 +
:'''With Earthquake'''
 +
 
 +
:k<sub>h</sub> = 0.05
 +
 
 +
:k<sub>v</sub> = 0
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 +
|-
 +
|'''Additional Information'''
 +
|-
 +
|1992 AASHTO Div. IA Commentary
 +
|}
 +
 
 +
:''θ'' = 2.862°
 +
 
 +
:''δ'' = ''φ''/2 = 24°/2 = 12° for angle of friction between soil and wall. This criteria is used only for seismic loading if the angle of friction is not known.
 +
 
 +
:''φ'' = 24°
 +
 
 +
:''i'' = 18.435°
 +
 
 +
:''β'' = 0°
 +
 
 +
:K<sub>AE</sub> = 0.654
 +
 
 +
:P<sub>AEH</sub> = 1/2 ''γ<sub>s''</sub>K<sub>AE</sub>H<sup>2</sup>cos''δ''
 +
 
 +
:P<sub>AEH</sub> = 1/2 [0.120k/ft](0.654)(6.944 ft.)<sup>2</sup>(1 ft.) cos(12°) = 1.851k
 +
 
 +
:M<sub>u</sub> = (1.499k)(2.315 ft.) + (1.851k − 1.499k)(0.6(6.944 ft.)) = 4.936(ft−k)
 +
 
 +
:The moment without earthquake controls:
 +
 
 +
:<math>R_n = \frac{M_u}{\phi bd^2} = \frac{5.865(ft-k)}{0.9(1 ft.)(8.75 in.)^2}\Big(1000 \frac{lb}{k}\Big)</math> = 85.116 psi
 +
 
 +
:''ρ'' = <math>\frac{0.85f'_c}{f_y} \Big[1 - \sqrt{1 - \frac{2R_n}{0.85f'_c}}\Big]</math>
 +
 
 +
:''ρ'' = <math>\frac{0.85 (3.000 psi}{60,000 psi} \Bigg[1 - \sqrt{1 - \frac{2 (85.116 psi}{0.85 (3000 psi)}}\Bigg]</math> = 0.00144
 +
 
 +
{|style="padding: 0.3em; margin-left:5px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="160px" align="right"
 +
|-
 +
|'''Additional Information'''
 +
|-
 +
|AASHTO 8.17.1.1 & 8.15.2.1.1
 +
|}
 +
 
 +
:''ρ<sub>min</sub>'' = <math> 1.7 \Bigg[\frac{h}{d}\Bigg]^2 \frac{\sqrt{f'_c}}{f_y} = 1.7 \Bigg[\frac{11 in.}{8.75 in.}^2 \frac{\sqrt{3000 psi}}{60,000 psi}\Bigg]</math> = 0.00245
 +
 
 +
:Use ''ρ'' = 4/3 ''ρ'' = 4/3 (0.00144) = 0.00192
 +
 
 +
:''A<sub>S<sub>Req</sub></sub>'' = ''ρbd'' = 0.00192 (12 in.)(8.75 in.) = 0.202 in.<sup>2</sup>/ft
 +
 
 +
:One #4 bar has A<sub>S</sub> = 0.196 in<sup>2</sup>
 +
 
 +
:<math>\frac{s}{0.196 in.^2} = \frac{12 in.}{0.202 in.^2}</math>
 +
 
 +
:''s'' = 11.64 in.
 +
 
 +
:<u>Use #4's @ 10" cts.</u>
 +
 
 +
:'''Check Shear'''
 +
 
 +
:V<sub>u</sub> ≥ ''φ'' V<sub>n</sub>
 +
 
 +
::'''Without Earthquake'''
 +
 
 +
::V<sub>u,</sub> = (1.3)(1.3)(1.499k) = 2.533k
 +
 
 +
::'''With Earthquake'''
 +
 
 +
::V<sub>u</sub> = 1.851k
 +
 
 +
:The shear force without earthquake controls.
 +
 
 +
:<math>\frac{\nu_u}{\phi} = \frac{2.533k}{0.85(12 in.)(8.75 in.)} (1000 lb/k)</math> = 28.4 psi
 +
 
 +
:<math>\nu_c = 2 \sqrt{3,000 psi}</math> = 109.5 psi > 28.4 psi <u>o.k.</u>
 +
 
 +
'''Reinforcement-Footing-Heel'''
 +
 
 +
[[image:751.24.3.3 heel.jpg|center|250px]]
 +
 
 +
Note: Earthquake will not control and will not be checked.
 +
 
 +
''β<sub>E</sub>'' = 1.0 (vertical earth pressure)
 +
 
 +
d = 18" - 3" - (1/2)(0.750") = 14.625"
 +
 
 +
b = 12"
 +
 
 +
''f'<sub>c</sub>'' = 3,000 psi
 +
 
 +
''M<sub>u</sub>'' = 1.3 [(5.556k + 1.500k)(3.333ft) + 0.889k(4.444ft) + 1.178k(6.667ft)]
 +
 
 +
''M<sub>u</sub>'' = 45.919(ft−k)
 +
 
 +
<math>R_n = \frac{45.919(ft-k)}{0.9(1 ft.)(14.625 in.)^2}(1000\frac{lb}{k})</math> = 238.5 psi
 +
 
 +
''ρ'' = <math>\frac{0.85(3000)psi}{60,000 psi} \Bigg[ 1 - \sqrt{1 - \frac{2(238.5 psi)}{0.85(3000psi)}}\Bigg]</math> = 0.00418
 +
 
 +
''ρ<sub>min</sub>'' = <math> 1.7 \Big[\frac{18 in.}{14.625 in.}\Big]^2 \frac{\sqrt{3000 psi}}{60,000 psi}</math> = 0.00235
 +
 
 +
''A<sub>S<sub>Req</sub></sub>'' = 0.00418 (12 in.) (14.625 in.) = 0.734 in<sup>2</sup>/ft.
 +
 
 +
 
 +
<u>Use #6's @ 7" cts.</u>
 +
 
 +
:'''Check Shear'''
 +
 
 +
:Shear shall be checked at back face of stem.
 +
 
 +
:''V<sub>u</sub>'' = 1.3 (5.556k + 1.500k + 0.889k + 1.178k) = 11.860k
 +
 
 +
:<math>\frac{\nu_u}{\phi} = \frac{11.860k}{0.85(12 in.)(14.625 in.)}(1000 \frac{lb}{k} ) = 79.5 psi < 2 \sqrt{3,000 psi}</math> = 109.5 psi  o.k.
 +
 
 +
'''Reinforcement-Footing-Toe'''
 +
 
 +
[[image:751.24.3.3. toe.jpg|center|350px]]
 +
 
 +
d = 18" - 4" = 14"
 +
 
 +
b = 12"
 +
 
 +
:'''Without Earthquake'''
 +
 
 +
::'''Apply Load Factors'''
 +
 
 +
::load 4 (weight) = 0.431k(1.3)(1.0) = 0.560k
 +
 
 +
::''β<sub>E</sub>'' = 1.3 for lateral earth pressure for retaining walls.
 +
 
 +
::''β<sub>E</sub>'' = 1.0 for vertical earth pressure.
 +
 
 +
::''ΣM<sub>OT</sub>'' = 12.567(ft−k)(1.3)(1.3) = 21.238(ft−k)
 +
 
 +
::''ΣM<sub>R</sub>'' = [54.556(ft−k) + 11.192(ft−k)](1.3)(1.0) = 85.472(ft−k)
 +
 
 +
::''ΣV'' = 11.417k(1.3)(1.0) = 14.842k
 +
 
 +
:<math>\bar{x} = \frac{85.472(ft-k) - 21.238(ft-k)}{14.842k}</math> = 4.328 ft.
 +
 
 +
:''e'' = (9.5 ft./2) − 4.328 ft. = 0.422 ft.
 +
 
 +
:<math>P_H = \frac{14.842k}{(1 ft.)(9.5 ft.)} \Big[1 - \frac{6(0.422 ft.)}{9.5 ft.}\Big]</math> = 1.146k/ft<sup>2</sup>
 +
 
 +
:<math>P_T = \frac{14.842k}{(1 ft.)(9.5 ft.)} \Big[1 + \frac{6(0.422 ft.)}{9.5 ft.}\Big]</math> = 1.979k/ft<sup>2</sup>
 +
 
 +
:<math>P =\Bigg[\frac{1.979 \frac{k}{ft.} - 1.146 \frac{k}{ft.}}{9.5 ft.}\Bigg](7.583 ft.) + 1.146\frac{k}{ft.}</math> = 1.811k/ft.
 +
 
 +
:<math>M_u = 1.811\frac{k}{ft.}\frac{(1.917 ft.)^2}{2} + \frac{1}{2}(1.917 ft.)^2\Big[1.979\frac{k}{ft.} - 1.811\frac{k}{ft.}\Big]\frac{2}{3} - 0.560k(0.958 ft.)</math>
 +
 
 +
:''M<sub>u</sub>'' = 2.997(ft−k)
 +
 
 +
:'''With Earthquake'''
 +
 
 +
:''P<sub>H</sub>'' = 1.139 k/ft
 +
 
 +
:''P<sub>T</sub>'' = 1.411 k/ft
 +
 
 +
:<math>P = \Bigg[\frac{1.411\frac{k}{ft.} - 1.139\frac{k}{ft.}}{9.5 ft.}\Bigg](7.583 ft.) + 1.139\frac{k}{ft.}</math> = 1.356 k/ft
 +
 
 +
:<math>M_u = 1.356\frac{k}{ft.}\frac{(1.917 ft.)^2}{2} + \frac{1}{2}(1.917 ft.)^2 \Bigg[1.411\frac{k}{ft.} - 1.356\frac{k}{ft.}\Bigg]\frac{2}{3} - 0.431k (0.958 ft.)</math>
 +
 
 +
:''M<sub>u</sub>'' = 2.146(ft−k)
 +
 
 +
:The moment without earthquake controls.
 +
 
 +
:<math>R_n = \frac{2.997(ft-k)}{0.9(1 ft.)(14.0 in.)^2}(1000\frac{lb}{k})</math> = 16.990 psi
 +
 
 +
:''ρ'' = <math>\frac{0.85(3000 psi)}{60,000 psi}\Bigg[1 - \sqrt{1 - \frac{2(16.990 psi)}{0.85(3000psi)}}\Bigg]</math> = 0.000284
 +
 
 +
:''ρ<sub>min</sub>'' = <math>1.7\Big[\frac{18 in.}{14.0 in.}\Big]^2 \frac{\sqrt{3,000 psi}}{60,000 psi}</math> = 0.00257
 +
 
 +
:Use ''ρ'' = 4/3 ''ρ'' = <math>\frac{4}{3}(0.000284)</math> = 0.000379
 +
 
 +
:''A<sub>S<sub>Req</sub></sub>'' = 0.000379 (12 in.)(14.0 in.) = 0.064 in.<sup>2</sup>/ft.
 +
 
 +
 
 +
:<math>\frac{12 in.}{0.064 in.^2} = \frac{s}{0.196 in.^2}</math>
 +
 
 +
:''s'' = 36.8 in.
 +
 
 +
:Minimum is # 4 bars at 12 inches. These will be the same bars that are in the back of the stem. Use the smaller of the two spacings.
 +
 
 +
:<u>Use # 4's @ 10" cts.</u>
 +
 
 +
:'''Check Shear'''
 +
 
 +
:Shear shall be checked at a distance "d" from the face of the stem.
 +
 
 +
::'''Without Earthquake'''
 +
 
 +
::<math>P_d =\Bigg[\frac{1.979\frac{k}{ft.} - 1.146\frac{k}{ft.}}{9.5 ft.}\Bigg](8.750 ft.) + 1.146\frac{k}{ft.}</math> = 1.913k/ft.
 +
 
 +
::<math>V_u =\frac{1.979\frac{k}{ft.} + 1.913\frac{k}{ft.}}{2}(0.750 ft.) - 1.3\Big[0.225\frac{k}{ft.}\Big](0.750 ft.)</math> = 1.240k
 +
 
 +
::'''With Earthquake'''
 +
 
 +
::<math>P_d =\Bigg[\frac{1.411\frac{k}{ft.} - 1.139\frac{k}{ft.}}{9.5 ft.}\Bigg](8.750 ft.) + 1.139\frac{k}{ft.}</math> = 1390k/ft.
 +
 
 +
::<math>V_u =\frac{1.411\frac{k}{ft.} + 1.139\frac{k}{ft.}}{2}(0.750 ft.) - \Big[0.225\frac{k}{ft.}\Big](0.750 ft.)</math> = 0.788k
 +
 
 +
:Shear without earthquake controls.
 +
 
 +
:<math>\frac{\nu_u}{\phi} = \frac{1.240k}{0.85(12 in.)(14.0 in.)}(1000\frac{lb}{k} ) = 8.7 psi < 2\sqrt{3000 psi}</math> = 109.5 psi <u>o.k.</u>
 +
 
 +
'''Reinforcement-Shear Key'''
 +
 
 +
[[image:751.24.3.3 shear key.jpg|center|250px]]
 +
 
 +
The passive pressure is higher without earthquake loads.
 +
 
 +
''γ'' = 1.3
 +
 
 +
''β<sub>E</sub>'' = 1.3 (lateral earth pressure)
 +
 
 +
d = 12"-3"-(1/2)(0.5") = 8.75"
 +
 
 +
b = 12"
 +
 
 +
''M<sub>u</sub> = (3.379k)(1.360 ft.)(1.3)(1.3) = 7.764(ft−k)
 +
 
 +
<math>R_n = \frac{7.764(ft-k)}{0.9(1 ft.)(8.75 in.)^2} (1000\frac{lb}{k})</math> = 112.677 psi
 +
 
 +
''ρ'' = <math>\frac{0.85(3000 psi)}{60,000 psi}\Bigg[1 - \sqrt{1 - \frac{2(112.677 psi)}{0.85(3000psi)}}\Bigg]</math> = 0.00192
 +
 
 +
''ρ<sub>min</sub> = <math>1.7\Big[\frac{12 in.}{8.75 in.}\Big]^2 \frac{\sqrt{3000 psi}}{60,000 psi}</math> = 0.00292
 +
 
 +
Use ''ρ'' = 4/3 ''ρ'' = 4/3 (0.00192) = 0.00256
 +
 
 +
A<sub>S<sub>Req</sub></sub> = 0.00256(12 in.)(8.75 in.) = 0.269 in.<sup>2</sup>/ft.
 +
 
 +
 
 +
<u>Use # 4 @ 8.5 in cts.</u>
 +
 
 +
Check Shear
 +
 
 +
:<math>\frac{\nu_u}{\phi} = \frac{1.3(3.379k)(1.3)}{0.85(12 in.)(8.75.)}(1000\frac{lb}{k} ) = 64.0 psi < 2\sqrt{3000 psi}</math> = 109.5 psi <u>o.k.</u>
 +
 
 +
'''Reinforcement Summary'''
 +
 
 +
[[Image:751.24.3.3 summary.jpg|500px|center]]
 +
 
 +
==== 751.40.8.15.6 Example 2: L-Shaped Cantilever Wall ====
 +
 
 +
[[image:751.24.3.4.jpg|center|650px|thumb|<center>'''Typical Section thru Wall</center><center>(Spread Footing)</center>''']]
 +
 
 +
''f'<sub>c</sub>'' = 4000 psi
 +
 
 +
''f<sub>y</sub>'' = 60,000 psi
 +
 
 +
''φ'' = 29°
 +
 
 +
''γ<sub>s</sub> = 120 pcf
 +
 
 +
Allowable soil pressure = 1.5 tsf = 3.0 ksf
 +
 
 +
Retaining wall is located in Seismic Performance Category (SPC) A.
 +
 
 +
<math>\delta = tan^{-1}\frac{1}{2.5}</math> = 21.801°
 +
 
 +
<math>C_a = cos \delta\Bigg[\frac{cos \delta - \sqrt{cos^2\delta - cos^2\phi}}{cos \delta + \sqrt{cos^2\delta - cos^2\phi}}\Bigg]</math> = 0.462
 +
 
 +
<math>C_p = tan^2\Big[45 + \frac{\phi}{2}\Big]</math> = 2.882
 +
 
 +
''P<sub>A</sub>'' = 1/2 ''γ<sub>s</sub>'' C<sub>a</sub>H<sup>2</sup> = 1/2 (0.120 k/ft<sup>3</sup>)(0.462)(4.958 ft.)<sup>2</sup> = 0.681k
 +
 
 +
For sliding, P<sub>P</sub> is assumed to act only on the portion of key below the frost line that is set at an 18 in. depth on the southern border.
 +
 
 +
''P<sub>P</sub>'' = 1/2 (0.120 k/ft<sup>3</sup>)(2.882)[(2.458 ft.)<sup>2</sup> − (1.500 ft.)<sup>2</sup>] = 0.656k
 +
 
 +
'''Assumptions'''
 +
 
 +
* Design is for a unit length (1 ft.) of wall.
 +
 
 +
* Sum moments about the toe at the bottom of the footing for overturning.
 +
 
 +
* F.S. for overturning ≥ 2.0 for footings on soil.
 +
 
 +
* F.S. for sliding ≥ 1.5 for footings on soil.
 +
 
 +
* Resultant of dead load and earth pressure to be in back half of the middle third of the footing if subjected to frost heave.
 +
 
 +
* For all loading combinations the resultant must be in the middle third of the footing except for collision loads.
 +
 
 +
* The top 12 in. of the soil is not neglected in determining the passive pressure because the soil there will be maintained.
 +
 
 +
* Frost line is set at 18 in. at the south border for Missouri.
 +
 
 +
* Portions of shear key which are above the frost line are assumed not to resist sliding by passive pressure.
 +
 
 +
* Use of a shear key shifts the failure plane to "B" where resistance to sliding is also provided by friction of soil along the failure plane in front of the shear key. Friction between the soil and concrete behind the shear key will be neglected.
 +
 
 +
* Soil cohesion along the failure plane is neglected.
 +
 
 +
* Live loads can move to within 1 ft. of the stem face and 1 ft. from the toe.
 +
 
 +
* The wall is designed as a cantilever supported by the footing.
 +
 
 +
* Footing is designed as a cantilever supported by the wall. Critical sections for bending and shear will be taken at the face of the wall.
 +
 
 +
* Load factors for AASHTO Groups I-VI for design of concrete are:
 +
 
 +
::*''γ'' = 1.3.
 +
 
 +
::*''β<sub>E</sub>'' = 1.3 for horizontal earth pressure on retaining walls.
 +
 
 +
::*''β<sub>E</sub>'' = 1.0 for vertical earth pressure.
 +
 
 +
::*''β<sub>LL</sub>'' = 1.67 for live loads and collision loads.
 +
 
 +
'''Dead Load and Earth Pressure - Stabilty and Pressure Checks'''
 +
 
 +
{| border="1" class="wikitable" style="margin: 1em auto 1em auto"
 +
|+
 +
|-
 +
!colspan="4" style="background:#BEBEBE" |Dead Load and Earth Pressure - Stabilty and Pressure Checks
 +
|-
 +
!style="background:#BEBEBE" |Load !!style="background:#BEBEBE" |Force (k) !!style="background:#BEBEBE" |Arm (in.) !!style="background:#BEBEBE"|Moment (ft-k)
 +
|-
 +
|align="center"|(1)||align="center"| (0.833 ft.)(5.167 ft.)(0.150k/ft<sup>3</sup>) = 0.646||align="center"| 5.333||align="center"| 3.444
 +
|-
 +
|align="center"|(2)||align="center"| (0.958ft)(5.750ft)(0.150k/ft3) = 0.827||align="center"| 2.875||align="center"| 2.376
 +
|-
 +
|align="center"| (3)||align="center"|  (1.000ft)(1.500ft)(0.150k/ft3) = 0.22534.259||align="center"| 4.250 ||align="center"| 0.956
 +
|-
 +
|align="center" colspan="3"|ΣV = 1.698 ||align="center"| ΣM<sub>R</sub> = 6.776
 +
|-
 +
|align="center"| P<sub>AV</sub>||align="center"|  0.253 ||align="center"| 5.750 ||align="center"| 1.455
 +
|-
 +
|align="center" colspan="3"| ΣV = 1.951||align="center"|  ΣM<sub>R</sub> = 8.231
 +
|-
 +
|align="center"| P<sub>AH</sub> ||align="center"| 0.633 ||align="center"| 1.653 ||align="center"| 1.045
 +
|-
 +
|align="center"| P<sub>P</sub>||align="center"|  0.656 ||align="center"| 1.06<sup>1</sup>||align="center"| -
 +
|-
 +
|colspan="4" align="right"|ΣM<sub>OT</sub> = 1.045
 +
|-
 +
|colspan="4"|<sup>'''1'''</sup> The passive pressure at the shear key is ignored in overturning checks.
 +
|}
 +
 
 +
:'''Overturning'''
 +
 
 +
:<math>F.S. = \frac{\Sigma M_R}{\Sigma M_{OT}} = \frac{8.231(ft-k)}{1.045(ft-k)}</math> = 7.877 ≥ 2.0 <u>o.k.</u>
 +
 
 +
:'''Location of Resultant'''
 +
 
 +
:MoDOT policy is that the resultant must be in the back half of the middle third of the footing when considering dead and earth loads:
 +
 
 +
:<math>\Bigg[\frac{5.750 ft.}{2} = 2.875 ft.\Bigg] \le \bar{x} \le \Bigg[\Bigg(\frac{5.750 ft.}{2} + \frac{5.750 ft.}{6}\Bigg) = 3.833 ft.\Bigg] </math>
 +
 
 +
:<math>\bar{x} = \frac{M_{NET}}{\Sigma V} = \frac{8.231(ft-k) - 1.045(ft-k)}{1.951k}</math> = 3.683 ft. <u>o.k.</u>
 +
 
 +
:'''Sliding'''
 +
 
 +
:<math>F.S. = \frac{P_P + \Sigma V \Bigg[\Big(\frac{L_2}{L_1}\Big)tan\phi_{s-s} + \Big(\frac{L_3}{L_1}\Big)tan\phi_{s-c}\Bigg]}{P_{AH}}</math>
 +
 
 +
:where:
 +
::''φ<sub>s-s</sub>'' = angle of internal friction of soil
 +
 
 +
::''φ<sub>s-c</sub>'' = angle of friction between soil and concrete = (2/3)''φ<sub>s-s</sub>''
 +
 
 +
:<math>F.S. = \frac{0.656k +(1.951k)\Big[\Big(\frac{3.75 ft.}{5.75 ft.}\Big)tan 29^\circ + \Big(\frac{1 ft.}{5.75 ft.}\Big) tan\Big(\frac{2}{3}(29^\circ)\Big)\Big]}{0.633 k}</math> = 2.339 ≥ 1.5 <u>o.k.</u>
 +
 
 +
:'''Footing Pressure'''
 +
 
 +
:<math>P = \frac{\Sigma V}{bL} \Big[1 \pm \frac{6e}{L}\Big]</math>
 +
 
 +
:<math>e = \bar{x} - \frac{L}{2} = 3.683 ft. - \frac{5.75 ft.}{2}</math> = 0.808 ft.
 +
 
 +
:Heel: <math>P_H = \frac{1.951k}{(1 ft.)(5.75 ft.)}\Big[1 + \frac{6(0.808 ft.)}{5.75 ft.}\Big]</math> = 0.625 ksf < 3.0 ksf <u>o.k.</u>
 +
 
 +
:Toe: <math>P_T = \frac{1.951k}{(1 ft.)(5.75 ft.)}\Big[1 - \frac{6(0.808 ft.)}{5.75 ft.}\Big]</math> = 0.053 ksf < 3.0 ksf <u>o.k.</u>
 +
 
 +
'''Dead Load, Earth Pressure, and Live Load - Stability and Pressure Checks'''
 +
 
 +
Stability is not an issue because the live load resists overturning and increases the sliding friction force.
 +
 
 +
[[image:751.24.3.4 checks.jpg|center|250px]]
 +
 
 +
The live load will be distributed as:
 +
 
 +
<math> F_{LL} = \frac{LL_{WL}}{E}</math>
 +
 
 +
:where E = 0.8X + 3.75
 +
 
 +
::X = distance in feet from the load to the front face of wall
 +
 
 +
The live load will be positioned as shown by the dashed lines above. The bearing pressure and resultant location will be determined for these two positions.
 +
 
 +
:'''Live Load 1 ft From Stem Face'''
 +
 
 +
::'''Resultant Eccentricity'''
 +
 
 +
::X = 1 ft.
 +
 
 +
::E = 0.8(1 ft.) + 3.75 = 4.55 ft.
 +
 
 +
::<math>F_{LL} = \frac{16k}{4.55 ft.} (1 ft.)</math> = 3.516k
 +
 
 +
::<math>\bar{x} = \frac{M_{NET}}{\Sigma V} = \frac{8.231(ft-k) + (3.516k)(3.917 ft.) - 1.045(ft-k)}{1.951k + 3.516k}</math> = 3.834 ft.
 +
 
 +
::<math>e = \bar{x} - \frac{L}{2} = 3.834 ft. - \frac{5.75 ft.}{2} = 0.959 ft. \le \frac{L}{6}</math> = 5.75 ft. <u>o.k.</u>
 +
 
 +
::'''Footing Pressure'''
 +
 
 +
::<math>P = \frac{\Sigma V}{bL} \Big[1 \pm \frac{6e}{L}\Big]</math>
 +
 
 +
::Allowable Pressure = 3.0 ksf
 +
 
 +
::Heel: <math>P_H = \frac{5.467k}{(1 ft.)(5.75 ft.)}\Big[1 + \frac{6(0.959 ft.)}{5.75 ft.}\Big]</math> = 1.902 ksf
 +
 
 +
::Toe: <math>P_T = \frac{5.467k}{(1 ft.)(5.75 ft.)}\Big[1 - \frac{6(0.959 ft.)}{5.75 ft.}\Big]</math> = 0.000ksf
 +
 
 +
:'''Live Load 1 ft From Toe'''
 +
 
 +
::'''Resultant Eccentricity'''
 +
 
 +
::X = 3.917 ft.
 +
 
 +
::E = 0.8(3.917 ft.) + 3.75 = 6.883 ft.
 +
 
 +
::<math>F_{LL} = \frac{16k}{6.883 ft} (1 ft.)</math> = 2.324k
 +
 
 +
::<math>x = \frac{8.231(ft-k) + (2.324k)(1ft.) - 1.045(ft-k)}{1.951k + 2.324k}</math> = 2.225 ft.
 +
 
 +
::<math>e = \frac{L}{2} - \bar{x} = \frac{5.75 ft.}{2} - 2.225 ft. = 0.650 ft. \le \frac{L}{6} = \frac{5.75 ft.}{6}</math> = 0.958 ft. <u>o.k.</u>
 +
 
 +
::'''Footing Pressure'''
 +
 
 +
::Allowable Pressure = 3.0ksf
 +
 
 +
::Heel: <math>P_H = \frac{4.275k}{(1 ft.)(5.75 ft.}\Big[1 - \frac{6 (0.650 ft.)}{5.75 ft.}\Big]</math> = 0.239ksf <u>o.k.</u>
 +
 
 +
::Toe: <math>P_T = \frac{4.275k}{(1 ft.)(5.75 ft.}\Big[1 + \frac{6 (0.650 ft.)}{5.75 ft.}\Big]</math> = 1.248ksf <u>o.k.</u>
 +
 
 +
'''Dead Load, Earth Pressure, Collision Load, and Live Load - Stability and Pressure Checks'''
 +
 
 +
During a collision, the live load will be close to the wall so check this combination when the live load is one foot from the face of the stem. Sliding (in either direction) will not be an issue. Stability about the heel should be checked although it is unlikely to be a problem. There are no criteria for the location of the resultant, so long as the footing pressure does not exceed 125% of the allowable. It is assumed that the distributed collision force will develop an equal and opposite force on the fillface of the back wall unless it exceeds the passive pressure that can be developed by soil behind the wall.
 +
 
 +
''F<sub>LL</sub>'' = 3.516k
 +
 
 +
[[image:751.24.3.4 collision.jpg|center|250px]]
 +
 
 +
''F<sub>COLL</sub>'' = <math>\frac{10k}{2(3 ft.)}(1 ft.)</math> = 1.667k
 +
 
 +
<math>C_P = cos \delta \Bigg[\frac{cos \delta + \sqrt{cos^2 \delta - cos^2 \phi}}{cos \delta - \sqrt{cos^2 \delta - cos^2 \phi}}\Bigg]</math> = 1.867
 +
 
 +
<math>P_{PH} = \frac{1}{2}\gamma_s C_P H^2 cos\delta = \frac{1}{2}(0.120kcf)(1.867)(4.958ft)^2 cos(21.801^\circ)</math>
 +
 
 +
''P<sub>PH</sub>'' = 2.556k > ''F<sub>COLL</sub>''  Thus the soil will develop an equal but opp. force.
 +
 
 +
:'''Overturning About the Heel'''
 +
 
 +
:F.S. = <math>\frac{(0.646k)(0.417 ft.) + (0.827k)(2.875 ft.) + (0.225k)(1.500 ft.) + (3.516k)(1.833 ft.) + (1.667k)\big(\frac{4.958 ft.}{3}\big)}{(1.667k)(3.958 ft.)}</math>
 +
 
 +
:F.S. = <math>\frac{12.184(ft-k)}{6.598(ft-k)}</math> = 1.847 ≥ 1.2 <u>o.k.</u>
 +
 
 +
:'''Footing Pressure'''
 +
 
 +
:<math>\bar{x} = \frac{12.184(ft-k) - 6.598(ft-k)}{1.951k + 3.516k}</math> = 1.022 ft. from heel
 +
 
 +
:''e'' = <math>\frac{5.75 ft.}{2} - 1.022 ft.</math> = 1.853 ft.
 +
 
 +
:Allowable Pressure = (1.25)(3.0ksf) = 3.75ksf
 +
 
 +
:Heel: <math> P_H =\frac {2(\Sigma V)}{3b[\frac{L}{2} - e]} = \frac {2(5.467k)}{3(1 ft.)\big[\frac{5.75 ft.}{2} - 1.853 ft.\big]}</math> = 3.566ksf <u>o.k.</u>
 +
 
 +
'''Stem Design-Steel in Rear Face'''
 +
 
 +
[[image:751.24.3.4 steel in rear face.jpg|center|250px]]
 +
 
 +
''γ'' = 1.3
 +
 
 +
''β<sub>E</sub>'' = 1.3 (active lateral earth pressure)
 +
 
 +
d = 10 in. − 2 in. − (0.5 in./2) = 7.75 in.
 +
 
 +
<math>P_{AH} = \frac{1}{2}\gamma_s C_a H^2 cos\delta = \frac{1}{2}\Bigg[0.120 \frac{k}{ft^3}\Bigg](0.462)(4 ft.)^2(1 ft.) cos 21.801^\circ</math>
 +
 
 +
''P<sub>AH</sub>'' = 0.412k
 +
 
 +
''M<sub>u</sub>'' = (1.333 ft.)(0.412k)(1.3)(1.3) = 0.928(ft−k)
 +
 
 +
<math>R_n = \frac{M_u}{\phi b d^2} = \frac{0.928(ft-k)}{(0.9)(1 ft.)(7.75 in.)^2}\Big(1000\frac{lb}{k}\Big)</math> = 17.160psi
 +
 
 +
<math>\rho = \frac{0.85f_c}{f_y}\Bigg[1 - \sqrt{1 - \frac{2R_n}{0.85 f_c}}\Bigg]</math>
 +
 
 +
<math>\rho = \frac{4000 psi}{60,000 psi}\Bigg[1 - \sqrt{1 - \frac{2(17.160 psi)}{0.85 (4000psi)}}\Bigg]</math> = 0.000287
 +
 
 +
<math>\rho_{min} = 1.7 \Bigg[\frac{h}{d}\Bigg]^2 \frac{\sqrt{f_c}}{f_y}</math>
 +
 
 +
<math>\rho_{min} = 1.7 \Bigg[\frac{10 in.}{7.75 in.}\Bigg]^2 \frac{\sqrt{4000 psi}}{60000 psi}</math> = 0.00298
 +
 
 +
Use ''ρ'' = (4/3)ρ = (4/3)(0.000287) = 0.000382
 +
 
 +
<math>A_{S_{Req}} = \rho bd = 0.000382(12 in.)(7.75 in.) = 0.036 \frac{in^2}{ft.}</math>
 +
 
 +
One #4 bar has A<sub>S</sub> = 0.196 in<sup>2</sup>, so the required minimum of one #4 bar every 12 in. controls.
 +
 
 +
<u>Use #4's @ 12 in. (min)</u>
 +
 
 +
(These bars are also the bars in the bottom of the footing so the smaller of the two required spacings will be used.)
 +
 
 +
:'''Check Shear'''
 +
 
 +
:<math>\frac{\nu_u}{\phi} \le V_n</math>
 +
 
 +
:<math>\frac{\nu_u}{\phi} = \frac{(1.3)(1.3)(0.412k)}{0.85(12 in.)(7.75 in.)}(1000\frac{lb}{k})</math>  = 8.8 psi
 +
 
 +
:<math>\nu_c = 2 \sqrt{f'_c}</math>
 +
 
 +
:<math>\nu_c = 2 \sqrt{4, 000 psi}</math> = 126.5 psi > 8.8 psi <u>o.k.</u>
 +
 
 +
'''Stem Design-Steel in Front Face (Collision Loads)'''
 +
 
 +
[[image:751.24.3.4 steel in front face.jpg|center|300px]]
 +
 
 +
 
 +
The soil pressure on the back of the stem becomes passive soil pressure during a collision, however this pressure is ignored for reinforcement design.
 +
 
 +
''γ'' = 1.3
 +
 
 +
''β<sub>LL</sub>'' = 1.67
 +
 
 +
<math>d = 10 in. - 1.5 in. - 0.5 in. - \frac{0.5 in.}{2}</math> = 7.75 in.
 +
 
 +
<math>F_{COLL} = \frac{10k}{2L} = \frac{10k}{(2)(3 ft.)}</math> = 1.667 k/ft.
 +
 
 +
''M<sub>u</sub>'' = 1.667k/ft. (1 ft.)(3 ft.)(1.3)(1.67) = 10.855(ft−k)
 +
 
 +
<math>R_n = \frac{10.855(ft-k)}{0.9(1 ft.)(7.75 in.)^2} (1000\frac{lb}{k})</math> = 200.809 psi
 +
 
 +
<math>\rho = \frac{0.85(4000 psi)}{60,000 psi}\Bigg[1 - \sqrt{1 - \frac{2(200.809 psi)}{0.85(4000psi)}}\Bigg]</math> = 0.00345
 +
 
 +
<math>\rho_{min} = 1.7\Bigg[\frac{10 in.}{7.75 in.}\Bigg]^2 \frac{\sqrt{4000 psi}}{60,000 psi}</math> = 0.00298
 +
 
 +
<math>A_{S_{Req}} = 0.00345 (12 in.)(7.75 in.) = 0.321 \frac{in.^2}{ft.}</math>
 +
 
 +
One #4 bar has A<sub>S</sub> = 0.196 in<sup>2</sup>.
 +
 
 +
<math>\frac{s}{0.196 in.^2} = \frac{12 in.}{0.321 in.^2}</math>
 +
 
 +
''s'' = 7.3 in.
 +
 
 +
<u>Use #4's @ 7 in.</u>
 +
 
 +
:'''Check Shear'''
 +
 
 +
:<math>\frac{\nu_u}{\phi} = \frac{(1.3)(1.67)(1.667k)}{(0.85)(12 in.)(7.75 in.)} (1000\frac{lb}{k})</math> = 45.8 psi < 126.5 psi <u>o.k.</u>
 +
 
 +
'''Footing Design - Bottom Steel'''
 +
 
 +
It is not considered necessary to design footing reinforcement based upon a load case which includes collision loads.
 +
 
 +
:'''Dead Load and Earth Pressure Only'''
 +
 
 +
[[image:751.24.3.4 dead load.jpg|center|250px]]
 +
 
 +
:''Footing wt.'' = <math>\Big[\frac{11.5}{12}ft.\Big](4.917 ft.)\Big[0.150 \frac{k}{ft.^3}\Big](1 ft.)</math> = 0.707k
 +
 
 +
:''β<sub>E</sub>'' = 1.3 (lateral earth pressure)
 +
 
 +
:''γ'' = 1.3
 +
 
 +
:Apply Load Factors:
 +
 
 +
:''ΣV'' = 1.951k (1.3) = 2.536k
 +
 
 +
:''ΣM<sub>R</sub>'' = 8.231(ft−k)(1.3) = 10.700(ft−k)
 +
 
 +
:''ΣM<sub>OT</sub>'' = 1.045(ft−k)(1.3)(1.3) = 1.766(ft−k)
 +
 
 +
:''Footing wt.'' = 0.707k (1.3) = 0.919k
 +
 
 +
:<math>\bar{x} = \frac{10.700(ft-k) - 1.766(ft-k)}{2.536k}</math> = 3.523 ft.
 +
 
 +
:<math>e = 3.523 ft. - \frac{5.75ft}{2}</math> = 0.648 ft.
 +
 
 +
:<math>P_H = \frac{2.536k}{(1 ft.)(5.75 ft.)}\Bigg[1 + \frac{6(0.648 ft.)}{5.75 ft.}\Bigg]</math> = 0.739 ksf
 +
 
 +
:<math>P_T = \frac{2.536k}{(1 ft.)(5.75 ft.)}\Bigg[1 - \frac{6(0.648 ft.)}{5.75 ft.}\Bigg]</math> = 0.143ksf
 +
 
 +
:<math>P_W = 0.143 ksf + [0.739 ksf - 0.143 ksf]\Bigg[\frac{4.917 ft.}{5.75 ft.}\Bigg]</math> = 0.653 ksf
 +
 
 +
:Moment at Wall Face:
 +
 
 +
:<math>M_W = \Big[0.143\frac{k}{ft.}\Big]\Bigg[\frac{(4.917 ft.)^2}{2}\Bigg] + \frac{1}{3}(4.917 ft.)^2 \Bigg[0.653\frac{k}{ft.} - 0.143\frac{k}{ft.}\Bigg]\frac{1}{2} -  0.919k \Bigg[\frac{4.917 ft.}{2}\Bigg]</math> = 1.524(ft−k)
 +
 
 +
:'''Dead Load, Earth Pressure, and Live Load'''
 +
 
 +
::'''Live Load 1 ft. From Stem Face'''
 +
 
 +
[[image:751.24.3.4 live load.jpg|center|300px]]
 +
 
 +
::''β<sub>E</sub>'' = 1.3 (lateral earth pressure)
 +
 
 +
::''β<sub>LL</sub>'' = 1.67
 +
 
 +
::''γ'' = 1.3
 +
 
 +
::Apply Load Factors:
 +
 
 +
::''F<sub>LL</sub>'' = 3.516k(1.3)(1.67) = 7.633k
 +
 
 +
::''ΣV'' = 7.633k + 1.951k(1.3) = 10.169k
 +
 
 +
::''ΣM<sub>OT</sub>'' = 1.045(ft−k)(1.3)(1.3) = 1.766(ft−k)
 +
 
 +
::''ΣM<sub>R</sub>'' = 8.231(ft−k)(1.3) + 3.917 ft.(7.633k) = 40.599(ft−k)
 +
 
 +
::<math>\bar{x} = \frac{40.599(ft-k) - 1.766(ft-k)}{10.169k}</math> = 3.819 ft.
 +
 
 +
::''e'' = 3.819 ft. − (5.75 ft./2) = 0.944 ft.
 +
 
 +
::<math>P_T = \Bigg[\frac{10.169k}{(1 ft.)(5.75 ft.)}\Bigg]\Bigg[{1 - \frac{ 6(0.944 ft.)}{5.75 ft.}}\Bigg]</math> = 0.026 ksf
 +
 
 +
::<math>P_H = \Bigg[\frac{10.169k}{(1 ft.)(5.75 ft.)}\Bigg]\Bigg[{1 + \frac{ 6(0.944 ft.)}{5.75 ft.}}\Bigg]</math> = 3.511 ksf
 +
 
 +
::<math>P_W = 0.026 ksf + [3.511 ksf - 0.026 ksf]\Big[\frac{4.917 ft.}{5.75 ft.}\Big]</math> = 3.006 ksf
 +
 
 +
::<math>P_{LL} = 0.026 ksf + [3.511 ksf - 0.026 ksf]\Bigg[\frac{3.917 ft.}{5.75 ft.}\Bigg] </math> = 2.400 ksf
 +
 
 +
::Footing wt. from face of wall to toe:
 +
 
 +
::''Footing wt.'' = <math>1.3\Bigg[\frac{11.5}{12} ft.\Bigg](4.917 ft.)\Bigg[0.150 \frac{k}{ft^3}\Bigg](1 ft.)</math> = 0.919k
 +
 
 +
::Footing wt. from LL<sub>WL</sub> to toe:
 +
 
 +
::''Footing wt.'' = <math>1.3\Bigg[\frac{11.5}{12} ft.\Bigg](3.917 ft.)\Bigg[0.150 \frac{k}{ft^3}\Bigg](1 ft.)</math> = 0.732k
 +
 
 +
::Moment at Wall Face:
 +
 
 +
::''M<sub>W</sub> = <math>0.026\frac{k}{ft} \frac{(4.917 ft.)^2}{2} - 7.633k (1 ft.) + \frac{1}{2}\Bigg[3.006\frac{k}{ft} - 0.026\frac{k}{ft}\Bigg](4.917 ft.)^2\Big[\frac{1}{3}\Big] - 0.919k\frac{(4.917 ft.)}{2}</math>
 +
 
 +
::M<sub>W</sub> = 2.430(ft−k)
 +
 
 +
::Moment at LL<sub>WL</sub>:
 +
 
 +
::''M<sub>LL</sub>'' = <math>0.026\frac{k}{ft} \frac{(3.917 ft.)^2}{2} - 0.732k \frac{(3.917 ft.)}{2} + \frac{1}{2}\Bigg[2.400\frac{k}{ft} - 0.026\frac{k}{ft}\Bigg](3.917 ft.)^2\Big[\frac{1}{3}\Big] </math> = 4.837(ft−k)
 +
 
 +
::'''Live Load 1 ft. From Toe'''
 +
 
 +
[[image:751.24.3.4 toe.jpg|center|250px]]
 +
 
 +
::Apply Load Factors:
 +
 
 +
::''F<sub>LL</sub>'' = 2.324k(1.3)(1.67) = 5.045k
 +
 
 +
::''ΣV'' = 5.045k + 1.951k(1.3) = 7.581k
 +
 
 +
::''ΣM<sub>OT</sub>'' = 1.045(ft−k)(1.3)(1.3) = 1.766(ft−k)
 +
 
 +
::''ΣM<sub>R</sub>'' = 8.231(ft−k)(1.3) + 5.045k(1ft.) = 15.745(ft−k)
 +
 
 +
::<math>\bar{x} = \frac{15.745(ft-k)- 1.766(ft-k)}{7.581k}</math> = 1.844 ft.
 +
 
 +
::<math>e = \frac{5.75 ft.}{2} - 1.844 ft.</math> = 1.031 ft.
 +
 
 +
::''P<sub>H</sub>'' = 0 ksf
 +
 
 +
::<math>P_T = \frac{2(7.581k)}{3(1 ft.)\big[\frac{5.75 ft.}{2} - 1.031 ft.\big]}</math> = 2.741 ksf
 +
 
 +
::''L<sub>1</sub>'' = 3[(L/2)− e]
 +
 
 +
::''L<sub>1</sub>'' = 3[(5.75 ft./2)− 1.031 ft.] = 5.532 ft.
 +
 
 +
::<math>P_W = 2.741 ksf \Big[\frac{0.615 ft.}{5.532 ft.}\Big]</math> = 0.305 ksf
 +
 
 +
::<math>P_{LL} = 2.741 ksf \Big[\frac{4.432 ft.}{5.532 ft.}\Big]</math> = 2.196 ksf
 +
 
 +
::Moment at Wall Face:
 +
 
 +
::''M<sub>W</sub>'' = <math> -5.045k (3.917 ft.) - 0.919k\Bigg[\frac{4.917 ft.}{2}\Bigg] + \frac{1}{2}(0.305\frac{k}{ft.})(4.917 ft.)^2 + \frac{1}{2}(4.917 ft.)^2 \Bigg[2.741\frac{k}{ft.} - 0.305\frac{k}{ft.}\Bigg]\Bigg[\frac{2}{3}\Bigg]</math> = 1.298(ft−k)
 +
 
 +
::Moment at LL<sub>WL</sub>:
 +
 
 +
::''M<sub>LL</sub>'' = <math>-0.187k(0.5 ft.) + 2.196\frac{k}{ft.}\frac{(1 ft.)^2}{2} +\frac{1}{2}(1 ft.)\Bigg[2.741\frac{k}{ft.}  - 2.196\frac{k}{ft.}\Bigg]\Bigg[\frac{2}{3}\Bigg](1 ft.)</math> = 1.186(ft−k)
 +
 
 +
:'''Design Flexural Steel in Bottom of Footing'''
 +
 
 +
:''d'' = 11.5 in. − 4 in. = 7.500 in.
 +
 
 +
:''M<sub>u</sub>'' = 4.837(ft−k) (controlling moment)
 +
 
 +
:<math>R_n = \frac{4.837(ft-k)}{0.9(1 ft.)(7.5 in.)^2}</math> = 0.096 ksi
 +
 
 +
:<math>\rho = \frac{0.85(4000 psi)}{60,000 psi}\Bigg[1 - \sqrt{1 - \frac{2(0.096 ksi)}{0.85(4 ksi)}}\Bigg] </math> = 0.00162
 +
 
 +
:<math>\rho_{min} = 1.7\Bigg[\frac{11.5 in.}{7.5 in.}\Bigg]^2\frac{\sqrt{4000 psi}}{60,000 psi}</math> = 0.00421
 +
 
 +
:Use ''ρ'' = (4/3)''ρ'' = (4/3)(0.00162) = 0.00216
 +
 
 +
:''A<sub>S<sub>Req</sub></sub>'' = 0.00216(12 in.)(7.5 in.) = 0.194 in<sup>2</sup>/ft.
 +
 
 +
 
 +
:<math>\frac{s}{0.196 in^2} = \frac{12 in.}{0.194 in^2}</math>
 +
 
 +
:''s'' = 12.1 in.
 +
 
 +
:<u>Use #4's @ 12 in. cts.</u> (Also use this spacing in the back of the stem.)
 +
 
 +
:'''Check Shear'''
 +
 
 +
::'''Dead Load and Earth Pressure Only'''
 +
 
 +
::<math>V_W = 0.143\frac{k}{ft.}(4.917 ft.) + \frac{1}{2}(4.917 ft.)\Big[0.653\frac{k}{ft.} - 0.143\frac{k}{ft.}\Big] - 0.919k</math>
 +
 
 +
::''V<sub>W</sub>'' = 1.038k
 +
 
 +
::'''Live Load 1 ft. From Stem Face'''
 +
 
 +
::Shear at the wall can be neglected for this loading case.
 +
 
 +
::<math>V_{LL} = 0.026\frac{k}{ft.}(3.917 ft.) + \frac{1}{2}(3.917 ft.)\Big[2.400\frac{k}{ft.} - 0.026\frac{k}{ft.}\Big] - 0.732k</math>
 +
 
 +
::''V<sub>LL</sub>'' = 4.019k
 +
 
 +
::'''Live Load 1 ft. From Toe'''
 +
 
 +
::<math>V_W = 0.305\frac{k}{ft.}(4.917 ft.) + \frac{1}{2}(4.917 ft.)\Big[2.741\frac{k}{ft.} - 0.305\frac{k}{ft.}\Big] - 0.919k - 5.045k</math>
 +
 
 +
::''V<sub>W</sub>'' = 1.525k
 +
 
 +
::<math>V_{LL} = 2.196\frac{k}{ft.}(1ft) + \frac{1}{2}(1ft)\Big[2.741\frac{k}{ft.} - 2.196\frac{k}{ft.}\Big] - 0.187k</math>
 +
 
 +
::''V<sub>LL</sub>'' = 2.282k
 +
 
 +
:Use ''V<sub>U</sub>'' = 4.019k
 +
 
 +
:<math>\frac{\nu_u}{\phi} = \frac{4019(lbs)}{0.85(12 in.)(7.5 in.)} = 52.5 psi < 2\sqrt{4000 psi}</math> = 126.5 psi
 +
 
 +
'''Shear Key Design'''
 +
 
 +
[[image:751.24.3.4 shear key.jpg|center|300px]]
 +
 
 +
For concrete cast against and permanently exposed to earth, minimum cover for reinforcement is 3 inches.
 +
 
 +
<math>d = 12 in. - 3 in. - \frac{1}{2}\Big[\frac{1}{2}in.\Big]</math> = 8.75 in.
 +
 
 +
<math>P_1 = 0.120\frac{k}{ft^3}(1 ft.)(2.882)\Big[\frac{11.5}{12}ft.\Big]</math> = 0.331 k/ft.
 +
 
 +
<math>P_2 = 0.120\frac{k}{ft^3}(1 ft.)(2.882)\Big[\frac{29.5}{12}ft.\Big]</math> = 0.850 k/ft.
 +
 
 +
<math>M_u = (1.3)(1.3)\Bigg\{0.331\frac{k}{ft.}\frac{(1.5 ft.)^2}{2} + \frac{1}{2}(1.5 ft.)\Big[0.850\frac{k}{ft.} - 0.331\frac{k}{ft}\Big]\Big[\frac{2}{3}\Big](1.5 ft.)\Bigg\}</math>
 +
 
 +
''M<sub>u</sub>'' = 1.287(ft−k)
 +
 
 +
<math>R_n = \frac{1.287(ft-k)}{0.9(1ft.)(8.75in.)^2}</math> = 0.0187 ksi
 +
 
 +
<math>\rho = \frac{0.85(4000psi)}{60,000psi}\Bigg[1 - \sqrt{1 - \frac{2(0.0187ksi)}{0.85(4ksi)}}\Bigg]</math> = 0.000312
 +
 
 +
<math>\rho_{min} = 1.7\Big[\frac{12in.}{8.75in.}\Big]^2\frac{\sqrt{4000psi}}{60,000psi}</math> = 0.00337
 +
 
 +
Use ''ρ'' = (4/3)''ρ'' = (4/3)(0.000312) = 0.000416
 +
 
 +
''A<sub>S<sub>Req</sub></sub>'' = 0.000416 (12 in.)(8.75 in.) = 0.0437 in<sup>2</sup>/ft.
 +
 
 +
 
 +
<math>\frac{s}{0.196 in.^2} = \frac{12in.}{0.0437in.^2}</math>
 +
 
 +
''s'' = 53.8 in.
 +
 
 +
<u>Use #4's @ 18 in. cts. (min)</u>
 +
 
 +
:'''Check Shear'''
 +
 
 +
:''V'' = 0.886k
 +
 
 +
:<math>\frac{\nu_u}{\phi} = \frac{(1.3)(1.3)(886 lbs)}{0.85(12 in.)(8.75 in.)}</math> = 16.8 psi < 126.5 psi <u>o.k.</u>
 +
 
 +
'''Reinforcement Summary'''
 +
 
 +
[[image:751.24.3.4 summary.jpg|center|400px]]
 +
 
 +
==== 751.40.8.15.7 Example 3: Pile Footing Cantilever Wall ====
 +
 
 +
[[image:751.24.3.5.jpg|center|850px]]
 +
 
 +
''f’<sub>c</sub>'' = 3,000 psi
 +
 
 +
''f<sub>y</sub>'' = 60,000 psi
 +
 
 +
''φ'' = 27°
 +
 
 +
''γ<sub>s</sub>'' = 120 pcf
 +
 
 +
Pile type: HP 10 x 42
 +
 
 +
Allowable pile bearing = 56 tons
 +
 
 +
Pile width = 10 inches
 +
 
 +
Toe pile batter = 1:3
 +
 
 +
See [[751.12 Barriers, Railings, Curbs and Fences|EPG 751.12 Barriers, Railings, Curbs and Fences]] for weight and centroid of barrier.
 +
 
 +
'''Assumptions'''
 +
 
 +
:* Retaining wall is located such that traffic can come within half of the wall height to the plane where earth pressure is applied.
 +
 
 +
:* Reinforcement design is for one foot of wall length.
 +
 
 +
:* Sum moments about the centerline of the toe pile at a distance of 6B (where B is the pile width) below the bottom of the footing for overturning.
 +
 
 +
:* Neglect top one foot of fill over toe in determining soil weight and passive pressure on shear key.
 +
 
 +
:* Neglect all fill over toe in designing stem reinforcement.
 +
 
 +
:* The wall is designed as a cantilever supported by the footing.
 +
 
 +
:* Footing is designed as a cantilever supported by the wall.
 +
 
 +
:* Critical sections for bending are at the front and back faces of the wall.
 +
 
 +
:* Critical sections for shear are at the back face of the wall for the heel and at a distance d (effective depth) from the front face for the toe.
 +
 
 +
:* For load factors for design of concrete, see [[#Group Loads|EPG 751.24.1.2 Group Loads]].
 +
 
 +
<math>C_A = cos\delta\Bigg[\frac{cos\delta - \sqrt{cos^2\delta - cos^2\phi}}{cos\delta + \sqrt{cos^2\delta - cos^2\phi}}\Bigg]</math>
 +
 
 +
''δ'' = 0, ''ϕ'' = 27° so ''C<sub>A</sub>'' reduces to:
 +
 
 +
<math>C_A = \frac{1 - sin\phi}{1 + sin\phi} = \frac{1 - sin 27^\circ}{1 + sin 27^\circ}</math> = 0.376
 +
 +
<math>C_P = tan^2\Bigg[45^\circ + \frac{\phi}{2}\Bigg] = tan^2\Bigg[ 45^\circ + \frac{27^\circ}{2}\Bigg]</math> = 2.663
 +
 
 +
Table 751.24.3.5.1 is for stability check (moments taken about C.L. of toe pile at a depth of 6B below the bottom of the footing).
 +
 
 +
{| border="1" class="wikitable" style="margin: 1em auto 1em auto" style="text-align:center"
 +
|+ '''''Table 751.24.3.5.1'''''
 +
! style="background:#BEBEBE" colspan="2"|Load !! style="background:#BEBEBE"|Force (kips/ft) !! style="background:#BEBEBE"|Arm about C.L. of toe pile at 6B below footing (ft.) !! style="background:#BEBEBE"|Moment (ft-kips) per foot of wall length
 +
|-
 +
|rowspan="5"|'''Dead Load'''||(1)|| 0.340|| 2.542|| 0.864
 +
|-
 +
|(2)|| (1.333 ft.)(7.000 ft.)(0.150k/ft<sup>3</sup>) = 1.400 ||2.833|| 3.966
 +
|-
 +
|(3)|| (3.000 ft.)(8.500 ft.)(0.150k/ft<sup>3</sup>) = 3.825|| 4.417|| 16.895
 +
|-
 +
|(4)|| (1.000 ft.)(1.750 ft.)(0.150k/ft<sup>3</sup>) = <u>0.263</u>|| 4.417|| <u>1.162</u>
 +
|-
 +
|Σ||ΣV = 5.828 || - ||ΣM<sub>R</sub> = 22.887
 +
|-
 +
|rowspan="3"|'''Earth Load'''||(5)|| (7.000 ft.)(5.167 ft.)(0.120k/ft<sup>3</sup>) = 4.340|| 6.083|| 26.400
 +
|-
 +
|(6)|| (2.000 ft.)(2.000 ft.)(0.120k/ft<sup>3</sup>) = <u>0.480</u>|| 1.167|| <u>0.560</u>
 +
|-
 +
|Σ ||ΣV = 4.820|| - ||ΣM<sub>R</sub> = 26.960
 +
|-
 +
|rowspan="2"|'''Live Load Surcharge'''||P<sub>SV</sub>|| (2.000 ft.)(5.167 ft.)(0.120k/ft<sub>3</sub>) = 1.240|| 6.083|| M<sub>R</sub> = 7.543
 +
|-
 +
|P<sub>SH</sub>||(2.000 ft.)(0.376)(10.000 ft.)(0.120k/ft<sup>3</sup>) = 0.902||10.000|| M<sub>OT</sub> = 9.020
 +
|-
 +
|rowspan="2"|'''Earth Pressure'''||P<sub>A</sub>||2.256<sup>'''1'''</sup>|| 8.333|| M<sub>OT</sub> = 18.799
 +
|-
 +
|P<sub>P</sub>|| 3.285<sup>'''2'''</sup> || - || -
 +
|-
 +
|colspan="2"|'''Collision Force''' (F<sub>COL</sub>)||(10.000k)/[2(7.000 ft.)] = 0.714|| 18.000 ||M<sub>OT</sub> = 12.852
 +
|-
 +
|colspan="2"|'''Heel Pile Tension''' (P<sub>HV</sub>)||(3.000 tons)(2 k/ton)(1 pile)/(12.000 ft.) = 0.500|| 7.167|| M<sub>R</sub> = 3.584
 +
|-
 +
|colspan="2"|'''Toe Pile Batter''' (P<sub>BH</sub>)|| 5.903<sup>'''3'''</sup>|| - || -
 +
|-
 +
|colspan="2"|'''Passive Pile Pressure''' (P<sub>pp</sub>)|| 0.832<sup>'''4'''</sup>|| - || -
 +
|-
 +
|colspan="5" align="left"|<sup>'''1'''</sup> <math>P_A = \frac{1}{2}\gamma_S C_A H^2 = \frac{1}{2}\Bigg[0.120\frac{k}{ft^3}\Bigg](0.376)(10 ft.)^3 = 2.256\frac{k}{ft}</math>
 +
|-
 +
|colspan="5" align="left"|<sup>'''2'''</sup> <math>P_P = \frac{1}{2}\gamma_S C_A\Big[H_2^2 - H_1^2\Big] = \frac{1}{2}\Bigg[0.120\frac{k}{ft^3}\Bigg](2.663)[(6.75 ft.)^2 - (5 ft.)^2] = 3.285\frac{k}{ft}</math>
 +
|-
 +
|colspan="5" align="left"|<sup>'''3'''</sup> <math>P_{BH} = \Big(56 \frac{tons}{pile}\Big)\Big( 2 \frac{k}{ton}\Big)(2 piles)\Bigg(\frac{4 in.}{\sqrt{(12 in.)^2 + (4 in.)^2}}\Bigg)\Big(\frac{1}{12 ft.}\Big) = 5.903 \frac{k}{ft}</math>
 +
|-
 +
|colspan="5" align="left"|<sup>'''4'''</sup> <math>P_{PP} = \frac{1}{2}(2.663)(5 ft.)^2\Big(0.120 \frac{k}{ft^3}\Big)(0.833 ft.)(3 piles)\Big(\frac{1}{12 ft.}\Big) = 0.832\frac{k}{ft}</math>
 +
|}
 +
 
 +
 
 +
Table 751.24.3.5.2 is for bearing pressure checks (moments taken about C.L of toe pile at the bottom of the footing).
 +
 
 +
{| border="1" class="wikitable" style="margin: 1em auto 1em auto" style="text-align:center"
 +
|+ '''''Table 751.24.3.5.2'''''
 +
! style="background:#BEBEBE" colspan="2"|Load !! style="background:#BEBEBE"|Force (kips/ft) !! style="background:#BEBEBE"|Arm about C.L. of toe pile at 6B below footing (ft.) !! style="background:#BEBEBE"|Moment (ft-kips) per foot of wall length
 +
|-
 +
|rowspan="5"|'''Dead Load'''||(1)|| 0.340|| 0.875|| 0.298
 +
|-
 +
|(2)|| (1.333 ft.)(7.000 ft.)(0.150k/ft<sup>3</sup>) = 1.400 ||1.167|| 1.634
 +
|-
 +
|(3)|| (3.000 ft.)(8.500 ft.)(0.150k/ft<sup>3</sup>) = 3.825|| 2.750|| 10.519
 +
|-
 +
|(4)|| (1.000 ft.)(1.750 ft.)(0.150k/ft<sup>3</sup>) = <u>0.263</u>|| 2.750|| <u>0.723</u>
 +
|-
 +
|Σ||ΣV = 5.828 || - ||ΣM<sub>R</sub> = 13.174
 +
|-
 +
|rowspan="3"|'''Earth Load'''||(5)|| (7.000 ft.)(5.167 ft.)(0.120k/ft<sup>3</sup>) = 4.340|| 4.417|| 19.170
 +
|-
 +
|(6)|| (2.000 ft.)(2.000 ft.)(0.120k/ft<sup>3</sup>) = <u>0.480</u>|| -0.500|| <u>-0.240</u>
 +
|-
 +
|Σ ||ΣV = 4.820|| - ||ΣM<sub>R</sub> = 18.930
 +
|-
 +
|rowspan="2"|'''Live Load Surcharge'''||P<sub>SV</sub>|| (2.000 ft.)(5.167 ft.)(0.120k/ft<sub>3</sub>) = 1.240|| 4.417|| M<sub>R</sub> = 5.477
 +
|-
 +
|P<sub>SH</sub>||(2.000 ft.)(0.376)(10.000 ft.)(0.120k/ft<sup>3</sup>) = 0.902||5.000|| M<sub>OT</sub> = 4.510
 +
|-
 +
|rowspan="2"|'''Earth Pressure'''||P<sub>A</sub>||2.256|| 3.333|| M<sub>OT</sub> = 7.519
 +
|-
 +
|P<sub>P</sub>|| 3.285 || - || -
 +
|-
 +
|colspan="2"|'''Collision Force''' (F<sub>COL</sub>)||(10.000k)/[2(7.000 ft.)] = 0.714|| 13.000 ||M<sub>OT</sub> = 9.282
 +
|-
 +
|colspan="2"|'''Heel Pile Tension''' (P<sub>HV</sub>)||(3.000 tons)(2 k/ton)(1 pile)/(12.000 ft.) = 0.500|| 5.500|| M<sub>R</sub> = 2.750
 +
|-
 +
|colspan="2"|'''Toe Pile Batter''' (P<sub>BH</sub>)|| 5.903|| - || -
 +
|-
 +
|colspan="2"|'''Passive Pile Pressure''' (P<sub>pp</sub>)|| 0.832|| - || -
 +
|}
 +
 
 +
Investigate a representative 12 ft. strip. This will include one heel pile and two toe piles. The assumption is made that the stiffness of a batter pile in the vertical direction is the same as that of a vertical pile.
 +
 
 +
Neutral Axis Location = [2piles(1.5 ft.) + 1pile(7 ft.)] / (3 piles) = 3.333 ft. from the toe.
 +
 
 +
[[image:751.24.3.5 neutral axis.jpg|center|350px]]
 +
 
 +
''I ''= Ad<sup>2</sup>
 +
 
 +
For repetitive 12 ft. strip:
 +
 
 +
:Total pile area = 3A
 +
 
 +
:''I ''= 2A(1.833 ft.)<sup>2</sup> + A(3.667 ft.)<sup>2</sup> = 20.167(A)ft.<sup>2</sup>
 +
 
 +
For a 1 ft. unit strip:
 +
 
 +
:<math>I = \frac{20.167(A)ft.^2}{12 ft.} = 1.681(A)ft.^2</math>
 +
 
 +
:Total pile area = (3A/12 ft.) = 0.250A
 +
 
 +
:'''Case I'''
 +
 
 +
:F.S. for overturning ≥ 1.5
 +
 
 +
:F.S. for sliding ≥ 1.5
 +
 
 +
::'''Check Overturning'''
 +
 
 +
::Neglect resisting moment due to P<sub>SV</sub> for this check.
 +
 
 +
::''ΣM<sub>R</sub>'' = 22.887(ft−k) + 26.960(ft−k) + 3.584(ft−k)
 +
 
 +
::''ΣM<sub>R</sub>'' = 53.431(ft−k)
 +
 
 +
::''ΣM<sub>OT</sub>'' = 9.020(ft−k) + 18.799(ft−k) = 27.819(ft−k)
 +
 
 +
::''F.S.<sub>OT</sub>'' = <math>\frac{\Sigma M_R}{\Sigma M_{OT}} = \frac{53.431(ft-k)}{27.819(ft-k)}</math> = 1.921 > 1.5 <u>o.k.</u>
 +
 
 +
::'''Check Pile Bearing'''
 +
 
 +
::Without P<sub>SV</sub> :
 +
 
 +
::''ΣV'' = 5.828k + 4.820k = 10.648k
 +
 
 +
::''e'' = <math>\frac{\Sigma M}{\Sigma V} = \frac{(13.174 + 18.930)(ft-k) - (4.510 + 7.519)(ft-k)}{10.648k}</math> = 1.885 ft.
 +
 
 +
::Moment arm = 1.885 ft. - 1.833 ft. = 0.052 ft.
 +
 
 +
::<math>P_T = \frac{\Sigma V}{A} - \frac{M_c}{I} = \frac{10.648k}{0.250A} - \frac{10.648k(0.052 ft.)(1.833 ft.)}{1.681(A)ft^2}</math>
 +
 
 +
::<math>P_T = \frac{41.988}{A} k</math>
 +
 
 +
::<math>P_H = \frac{10.648k}{0.250A} + \frac{10.648k(0.052 ft.)(3.667 ft.)}{1.681(A)ft^2}</math>
 +
 
 +
::<math>P_H = \frac{43.800}{A} k</math>
 +
 
 +
::Allowable pile load = 56 tons/pile. Each pile has area A, so:
 +
 
 +
::<math>P_T = 41.988\frac{k}{pile} = 20.944\frac{tons}{pile} </math> <u> o.k.</u>
 +
 
 +
::<math>P_H = 43.800\frac{k}{pile} = 21.900\frac{tons}{pile} </math> <u> o.k.</u>
 +
 
 +
::With P<sub>SV</sub>:
 +
 
 +
::''ΣV'' = 5.828k + 4.820k + 1.240k = 11.888k
 +
 
 +
::<math>e = \frac{(13.174 + 18.930 + 5.477)(ft-k) - (4.510 + 7.519)(ft-k)}{11.888k}</math> = 2.149 ft.
 +
 
 +
::Moment arm = 2.149 ft. - 1.833 ft. = 0.316 ft.
 +
 
 +
::<math>P_T = \frac{11.888k}{0.250A} - \frac{11.888k(0.316 ft.)(1.833 ft.)}{1.681(A)ft^2} = 43.456k = 21.728\frac{tons}{pile}</math> <u> o.k.</u>
 +
 
 +
::<math>P_H = \frac{11.888k}{0.250A} + \frac{11.888k(0.316 ft.)(3.667 ft.)}{1.681(A)ft^2} = 55.747k = 27.874\frac{tons}{pile}</math> <u> o.k.</u>
 +
 
 +
::'''Check Sliding'''
 +
 
 +
::<math>F.S._{Sliding} = \frac{3.285k + 5.903k + 0.832k}{0.902 k + 2.256k}</math> = 3.173 ≥ 1.5 <u> o.k.</u>
 +
 
 +
:'''Case II'''
 +
 
 +
:F.S. for overturning ≥ 1.2
 +
 
 +
:F.S. for sliding ≥ 1.2
 +
 
 +
::'''Check Overturning'''
 +
 
 +
::''ΣM<sub>R</sub> ''= (22.887 + 26.960 + 7.543 + 3.584)(ft−k) = 60.974(ft−k)
 +
 
 +
::''ΣM<sub>OT</sub>'' = (9.020 + 18.799 + 12.852)(ft−k) = 40.671(ft−k)
 +
 
 +
::<math>F.S._{OT} = \frac{\Sigma M_R}{\Sigma M_{OT}} = \frac{60.974(ft-k)}{40.671(ft-k)}</math> = 1.499 ≥ 1.2  <u> o.k.</u>
 +
 
 +
::'''Check Pile Bearing'''
 +
 
 +
::<math>e = \frac{\Sigma M}{\Sigma V} = \frac{(13.174 + 18.930 + 5.477)(ft-k) - (4.510 + 7.519 + 9.282)(ft-k)}{(5.828 + 4.820 + 1.240)k}</math> = 1.369 ft.
 +
 
 +
::Moment arm = 1.833 ft. - 1.369 ft. = 0.464 ft.
 +
 
 +
::<math>P_T = \frac{\Sigma V}{A} + \frac{M_c}{I} = \frac{11.888k}{0.250A} + \frac{11.888k(0.464 ft.)(1.833 ft.)}{1.681(A)ft^2}</math>
 +
 
 +
::<math>P_T = 53.567\frac{k}{pile} = 26.783\frac{tons}{pile} \le 56\frac{tons}{pile}</math> <u> o.k.</u>
 +
 
 +
::<math>P_H = \frac{11.888k}{0.250A} - \frac{11.888k(0.464 ft.)(3.667 ft.)}{1.681(A)ft^2}</math> = 35.519k
 +
 
 +
::<math>P_H = 17.760\frac{tons}{pile} \le 56\frac{tons}{pile} </math> <u> o.k.</u>
 +
 
 +
::'''Check Sliding'''
 +
 
 +
::<math>F.S._{Sliding} = \frac{3.285k + 5.903k + 0.832k}{0.902k + 2.256k + 0.714k}</math> = 2.588 ≥ 1.2 <u> o.k.</u>
 +
 
 +
:'''Case III'''
 +
 
 +
:F.S. for overturning ≥ 1.5
 +
 
 +
:F.S. for sliding ≥ 1.5
 +
 
 +
::'''Check Overturning'''
 +
 
 +
::''ΣM<sub>R</sub>'' = (22.887 + 26.960 + 3.584)(ft−k) = 53.431(ft−k)
 +
 
 +
::''ΣM<sub>OT</sub>'' = 18.799(ft−k)
 +
 
 +
::<math>F.S._{OT} = \frac{\Sigma M_R}{\Sigma M_{OT}} = \frac{53.431(ft-k)}{18.799(ft-k)}</math> = 2.842 ≥ 1.5 <u> o.k.</u>
 +
 
 +
::'''Check Pile Bearing'''
 +
 
 +
::<math>e = \frac{\Sigma M}{\Sigma V} = \frac{(13.174 + 18.930)(ft-k) - 7.519(ft-k)}{(5.828 + 4.820)k}</math> = 2.309 ft.
 +
 
 +
::Moment arm = 2.309 ft. - 1.833 ft. = 0.476 ft.
 +
 
 +
::<math>P_T = \frac{10.648k}{0.250A} - \frac{10.648k(0.476 ft.)(1.833 ft.)}{1.681(A)ft^2}</math> = 37.065k
 +
 
 +
::<math>P_T = 18.532\frac{tons}{pile} \le 56\frac{tons}{pile}</math> <u> o.k.</u>
 +
 
 +
::<math>P_H = \frac{10.648k}{0.250A} + \frac{10.648k(0.476 ft.)(3.667 ft.)}{1.681(A)ft^2}</math> = 53.649k
 +
 
 +
::<math>P_H = 26.825\frac{tons}{pile} \le 56\frac{tons}{pile} </math> <u> o.k.</u>
 +
 
 +
::'''Check Sliding'''
 +
 
 +
::<math>F.S._{Sliding} = \frac{3.285k+5.903k+0.832k}{2.256k}</math> = 4.441 ≥ 1.5 <u> o.k.</u>
 +
 
 +
:'''Case IV'''
 +
 
 +
::'''Check Pile Bearing'''
 +
 
 +
::<math>e = \frac{\Sigma M}{\Sigma V} = \frac{(13.174 + 18.930)(ft-k)}{5.828k + 4.820k}</math> = 3.015 ft.
 +
 
 +
::Moment arm = 3.015 ft. - 1.833 ft. = 1.182 ft.
 +
 
 +
::<math>P_H = \frac{\Sigma V}{A} + \frac{M_c}{I} = \frac{10.648k}{0.250A} + \frac{10.648k(1.182 ft.)(3.667 ft.)}{1.681(A)ft^2}</math>
 +
 
 +
::<math>P_H = 70.047k = 35.024 \frac{tons}{pile}</math>
 +
 
 +
::25% overstress is allowed on the heel pile:
 +
 
 +
::<math>P_H = 35.024\frac{tons}{pile} \le 1.25 (56\frac{tons}{pile}) = 70 \frac{tons}{pile}</math> <u> o.k.</u>
 +
 
 +
::<math>P_T = \frac{10.648k}{0.250A} - \frac{10.648k(1.182 ft.)(1.833 ft.)}{1.681(A)ft^2}</math> = 28.868k
 +
 
 +
::<math>P_T = 14.434\frac{tons}{pile} \le 56\frac{tons}{pile} </math> <u> o.k.</u>
 +
 
 +
:'''Reinforcement - Stem'''
 +
 
 +
[[image:751.24.3.5 reinforcement stem.jpg|300px|center]]
 +
 
 +
:b = 12 in.
 +
 
 +
:cover = 2 in.
 +
 
 +
:h = 16 in.
 +
 
 +
:d = 16 in. - 2 in. - 0.5(0.625 in.) = 13.688 in.
 +
 
 +
:''F<sub>Collision</sub>'' = 0.714k/ft
 +
 
 +
::<math>P_{LL} = \gamma_s C_A H(2.000 ft.) = (2.000 ft.)(0.376)(7.000 ft.)(0.120 \frac{k}{ft^3}) = 0.632\frac{k}{ft}</math>
 +
 
 +
::<math>P_{A_{Stem}} = \frac{1}{2} \gamma_s C_A H^2 = \frac{1}{2}\Big[0.120 \frac{k}{ft^3}\Big](0.376)(7.000 ft.)^2 = 1.105\frac{k}{ft} </math>
 +
 
 +
:::'''Apply Load Factors'''
 +
 
 +
:::''F<sub>Col.</sub>'' = ''γβ<sub>LL</sub>''(0.714k) = (1.3)(1.67)(0.714k) = 1.550k
 +
 
 +
:::''P<sub>LL</sub>'' = ''γβ<sub>E</sub>'' (0.632k) = (1.3)(1.67)(0.632k) = 1.372k
 +
 
 +
:::''P<sub>A<sub>Stem</sub></sub>'' = ''γβ<sub>E</sub>'' (1.105k) = (1.3)(1.3)(1.105k) = 1.867k
 +
 
 +
::''M<sub>u</sub>'' = (10.00 ft.)(1.550k) + (3.500 ft.)(1.372k) + (2.333 ft.)(1.867k)
 +
 
 +
::''M<sub>u</sub>''  = 24.658(ft−k)
 +
 
 +
::<math>R_n = \frac{M_u}{\phi b d^2} = \frac{24.658(ft-k)}{(0.9)(1 ft.)(13.688 in.)^2}</math> = 0.146ksi
 +
 
 +
::<math>\rho = \frac{0.85f'_c}{f_y}\Bigg[1 - \sqrt{1 - \frac{2R_n}{0.85f'_c}}\Bigg] =
 +
\frac{0.85(3 ksi)}{60 ksi}\Bigg[1 - \sqrt{1 - \frac{2(0.146 ksi)}{0.85(3 ksi)}}\Bigg]</math> = 0.00251
 +
 
 +
::<math>\rho_{min} = 1.7\Big[\frac{h}{d}\Big]^2 \frac{\sqrt{f'_c}}{f_y} = 1.7\Big[\frac{16 in.}{13.688 in.}\Big]^2 \frac{\sqrt{3000 psi}}{60,000 psi}</math> = 0.00212
 +
 
 +
::''ρ'' = 0.00251
 +
 
 +
::<math>A_{S_{Req.}} = \rho bd = (0.00251)(12 in.)(13.688 in.) = 0.412 \frac{in^2}{ft.}</math>
 +
 
 +
::One #5 bar has A<sub>S</sub> = 0.307 in<sup>2</sup>
 +
 
 +
::<math>\frac{s}{0.307 in^2} = \frac{12 in.}{0.412 in^2}</math>
 +
 
 +
::''s'' = 8.9 in.
 +
 
 +
::<u>Use # 5 bars @ 8.5 in. cts.</u>
 +
 
 +
:::'''Check Shear'''
 +
 
 +
:::''V<sub>u</sub>'' ≤ ''φV<sub>n</sub>''
 +
 
 +
:::''V<sub>u</sub>'' = ''F<sub>Collision</sub>'' + ''P<sub>LL</sub>'' + ''P<sub>A<sub>Stem</sub></sub>'' = 1.550k + 1.372k + 1.867k = 4.789k
 +
 
 +
 
 +
:::<math>\frac{\nu_u}{\phi} = \frac{v_u}{\phi bd} = \frac{4789 lbs}{0.85(12 in.)(13.688 in.)}</math> = 34.301 psi
 +
 
 +
:::<math> \nu_n = \nu_c = 2\sqrt{f'_c} = 2\sqrt{3000psi}</math> = 109.5 psi > 34.3 psi <u>o.k.</u>
 +
 
 +
::'''Reinforcement - Footing - Top Steel'''
 +
 
 +
[[image:751.24.3.5 footing.jpg|300px|center]]
 +
 
 +
::b = 12 in.
 +
 
 +
::cover = 3 in.
 +
 
 +
::h = 36 in.
 +
 
 +
::d = 36 in. - 3 in. - 0.5(0.5 in.) = 32.750 in.
 +
 
 +
::Design the heel to support the entire weight of the superimposed materials.
 +
 
 +
::Soil(1) = 4.340k/ft.
 +
 
 +
::LL<sub>s</sub> = 1.240k/ft.
 +
 
 +
::<math>Slab \ wt. = (3.000 ft.)\Big[0.150 \frac{k}{ft^3}\Big](5.167 ft.)</math> = 2.325k/ft.
 +
 
 +
:::'''Apply Load Factors'''
 +
 
 +
:::Soil(1) = ''γβ<sub>E</sub>''(4.340k) = (1.3)(1.0)(4.340k) = 5.642k
 +
 
 +
:::''LL<sub>s</sub>'' = ''γβ<sub>E</sub>''(1.240k) = (1.3)(1.67)(1.240k) = 2.692k
 +
 
 +
:::Slab wt. = ''γβ<sub>D</sub>''(2.325k) = (1.3)(1.0)(2.325k) = 3.023k
 +
 
 +
::''M<sub>u</sub>'' = (2.583 ft.)(5.642k + 2.692k + 3.023k) = 29.335(ft−k)
 +
 
 +
::<math>R_n = \frac{M_u}{\phi bd^2} = \frac{29.335(ft-k)}{(0.9)(1 ft.)(32.750 in.)^2}</math> = 0.0304 ksi
 +
 +
::<math>\rho = \frac{0.85(3ksi)}{60ksi}\Bigg[1 - \sqrt{1 - \frac{2(0.0304ksi)}{0.85(3ksi)}}\Bigg]</math> = 0.000510
 +
 
 +
::<math>\rho_{min} = 1.7\Big[\frac{36 in.}{32.750 in.}\Big]^2 \frac{\sqrt{3000 psi}}{60,000psi}</math> = 0.00188
 +
 
 +
::Use ''ρ'' = 4/3 ''ρ'' = 4/3 (0.000510) = 0.000680
 +
 
 +
::<math>A_{S_{Req}} = \rho bd = (0.000680)(12 in.)(32.750 in.) = 0.267\frac{in^2}{ft.}</math>
 +
 
 +
::One #4 bar has A<sub>s</sub> = 0.196 in.<sup>2</sup>
 +
 
 +
::<math>\frac{s}{0.196 in^2} = \frac{12 in}{0.267 in.^2}</math>
 +
 
 +
::''s'' = 8.8 in.
 +
 
 +
::<u>Use #4 bars @ 8.5 in. cts.</u>
 +
 
 +
:::'''Check Shear'''
 +
 
 +
:::<math>V_u = Soil(1) + LL_s + Slab \ wt. = 5.642k + 2.692k + 3.023k = 11.357k</math>
 +
 
 +
:::<math>\frac{\nu_u}{\phi} = \frac{V_u}{\phi bd} = \frac{11357 lbs}{(0.85)(12 in.)(32.750 in.)}</math> = 33.998 psi ≤ 109.5 psi = ''ν<sub>c</sub>''  <u>o.k.</u>
 +
 
 +
::'''Reinforcement - Footing - Bottom Steel'''
 +
 
 +
::Design the flexural steel in the bottom of the footing to resist the largest moment that the heel pile could exert on the footing. The largest heel pile bearing force was in Case IV. The heel pile will cause a larger moment about the stem face than the toe pile (even though there are two toe piles for every one heel pile) because it has a much longer moment arm about the stem face.
 +
 
 +
[[image: 751.24.3.5 heel pile.jpg|center|300px]]
 +
 
 +
::Pile is embedded into footing 12 inches.
 +
 
 +
::''b'' = 12 in.
 +
 
 +
::''h'' = 36 in.
 +
 
 +
::''d'' = 36 in. - 4 in. = 32 in.
 +
 
 +
:::'''Apply Load Factors to Case IV Loads'''
 +
 
 +
:::<math>\Sigma V = \gamma \beta_D\Big[5.828 \frac{k}{ft.}\Big] + \gamma \beta_E \Big[4.820 \frac{k}{ft.}\Big]</math>
 +
 
 +
:::<math>\Sigma V = 1.3(1.0)\Big[5.828\frac{k}{ft.}\Big] + 1.3(1.0)\Big[4.820\frac{k}{ft.}\Big]</math>
 +
 
 +
:::''ΣV'' = 13.842 k/ft.
 +
 
 +
:::<math>\Sigma M = \gamma \beta_D\Big[13.174\frac{(ft-k)}{ft.}\Big] + \gamma \beta_E\Big[18.930\frac{(ft-k)}{ft.}\Big]</math>
 +
 
 +
:::<math>\Sigma M = (1.3)(1.0)\Big[13.174\frac{(ft-k)}{ft.}\Big] + (1.3)(1.0)\Big[18.930\frac{(ft-k)}{ft.}\Big]</math>
 +
 
 +
:::''ΣM'' = 41.735 (ft−k)/ft.
 +
 
 +
::e = <math>\frac{\Sigma M}{\Sigma V} = \frac{41.735 (ft-k)}{13.842k}</math> = 3.015 ft.
 +
 
 +
::Moment arm = 3.015 ft. - 1.833 ft. = 1.182 ft.
 +
 
 +
::<math>P_H = \frac{\Sigma V}{A} + \frac{M_c}{I} = \frac{13.842k}{0.250A} + \frac{13.842k (1.182 ft.)(3.667 ft.)}{1.681(A)ft^2}</math>
 +
 
 +
::<math>P_H = 91.059 \frac{k}{pile}\Big(\frac{1}{12 ft.}\Big)</math> = 7.588 k/ft.
 +
 
 +
::<math>M_u = \Big(7.588\frac{k}{ft.}\Big)(3.667 ft.)</math> = 27.825(ft−k)/ft.
 +
 
 +
::<math>R_n = \frac{M_u}{\phi bd^2} = \frac{27.825(ft-k)}{(0.9)(1 ft.)(32 in.)^2}</math> = 0.0301 ksi
 +
 
 +
::<math>\rho = \frac{0.85(3 ksi)}{60ksi}\Bigg[1 - \sqrt{1 - \frac{2(0.0301 ksi)}{0.85(3 ksi)}}\Bigg]</math> = 0.000505
 +
 
 +
::<math>\rho_{min} = 1.7\Big[\frac{36 in.}{32 in.}\Big]^2 \frac{\sqrt{3000 psi}}{60,000 psi}</math> = 0.00196
 +
 
 +
::Use ''ρ'' = 4/3 ''ρ'' = 4/3 (0.000505) = 0.000673
 +
 
 +
::''A<sub>S<sub>Req</sub></sub> = ρbd'' = (0.000673)(12 in.)(32 in.) = 0.258 in<sup>2</sup>/ft.''
 +
 
 +
 
 +
::One #4 bar has A<sub>s</sub> = 0.196 in<sup>2</sup>.
 +
 
 +
::<math>\frac{s}{0.196 in.^2} = \frac{12 in.}{0.258 in.^2}</math>
 +
 
 +
::''s'' = 9.1 in.
 +
 
 +
::<u>Use #4 bars @ 9 in. cts.</u>
 +
 
 +
:::'''Check Shear'''
 +
 
 +
:::The critical section for shear for the toe is at a distance d = 21.75 inches from the face of the stem. The toe pile is 6 inches from the stem face so the toe pile shear does not affect the shear at the critical section. The critical section for shear is at the stem face for the heel so all of the force of the heel pile affects the shear at the critical section. The worst case for shear is Case IV.
 +
 
 +
:::''V<sub>u</sub>'' = 7.588k
 +
 
 +
:::<math>\frac{\nu_u}{\phi} = \frac{V_u}{\phi bd} = {7588 lbs}{0.85(12 in.)(32 in.)}</math> = 23.248 psi ≤ 109.5 psi = ''ν<sub>c</sub>'' <u>o.k.</u>
 +
 
 +
::'''Reinforcement - Shear Key'''
 +
 
 +
::''b'' = 12 in.
 +
 
 +
::''h'' = 12 in.
 +
 
 +
::cover = 3 in.
 +
 
 +
::''d'' = 12 in. - 3 in. - 0.5(0.5 in.) = 8.75 in.
 +
 
 +
:::'''Apply Load Factors'''
 +
 
 +
:::''P<sub>P</sub> = γβ<sub>E</sub>'' (3.845k) = (1.3)(1.3)(3.845k) = 6.498k
 +
 
 +
::''M<sub>u</sub>'' = (0.912 ft.)(6.498k) = 5.926(ft−k)
 +
 
 +
::<math>R_n = \frac{M_u}{\phi bd^2} = \frac{5.926(ft-k)}{(0.9)(1 ft.)(8.75 in.)^2}</math> = 0.0860 ksi
 +
 
 +
::<math>\rho = \frac{0.85(3ksi)}{60ksi}\Bigg[1 - \sqrt{1 - \frac{2(0.0860ksi)}{0.85(3ksi)}}\Bigg]</math> = 0.00146
 +
 
 +
::<math>\rho_{min} = 1.7\Big[\frac{12 in.}{8.75 in}\Big]^2\frac{\sqrt{3000 psi}}{60,000 psi}</math> = 0.00292
 +
 
 +
::Use ''ρ'' = 4/3 ''ρ'' = 4/3(0.00146) = 0.00195
 +
 
 +
::''A<sub>S<sub>Req</sub></sub> = ρbd'' = (0.00195)(12 in.)(8.75 in.) = 0.205 in.<sup>2</sup>/ft.
 +
 
 +
 
 +
::One #4 bar has A<sub>s</sub> = 0.196 in<sup>2</sup>
 +
 
 +
 
 +
::<math>\frac{s}{0.196 in.^2} = \frac{12 in.}{0.205 in.^2}</math>
 +
 
 +
::''s'' = 11.5 in.
 +
 
 +
::<u>Use #4 bars @ 11 in. cts.</u>
 +
 
 +
:::'''Check Shear'''
 +
 
 +
:::<math>\frac{\nu_u}{\phi} = \frac{V_u}{\phi bd} = \frac{6498 lbs}{0.85(12 in.)(8.75 in.)}</math> = 72.807 psi < 109.5 psi = ''ν<Sub>c</sub>''
 +
 
 +
::'''Reinforcement Summary'''
 +
 
 +
[[image:751.24.3.5 summary.jpg|center|350px]]
 +
 
 +
==== 751.40.8.15.8 Dimensions ====
 +
'''Cantilever Walls'''
 +
 +
Each section of wall shall be in increments of 4 ft. with a maximum length of 28'-0".
 +
[[image:751.24.3.6 friction or bearing piles.jpg|center|800px]]
  
  
Notes:
+
Each section of wall shall be in increments of 4 ft. with a maximum length of 28'-0".
 +
[[image:751.24.3.6 pile footing.jpg|center|800px]]
  
No more than 20% of deadman may fall outside of the roadway shoulders.  To prevent more than 20% limit, using a deeper deadman to reduce its length.  If this is not possible, the total passive pressure resistance should be calculated by summing the resistance from the different fill depths.
 
  
When deadman anchors are to be used, design the piles for a factor of safety of 1.0 for sliding and design deadman anchors to resist all horizontal earth forces with a factor of safety of 1.0.  This will result in a factor of safety for sliding of 2.0. For special cases, see the Structural Project Manager.
+
'''Cantilever Walls - L-Shaped'''
 
 
 
 
'''Design Example'''
 
 
 
{|border="0"
 
 
 
|colspan="2"|Assume:
 
|-
 
|width="25"|&nbsp;||Roadway width = 36', Out-Out slab width = 36' + 2 x 16" = 38.67'
 
|-
 
|width="25"|&nbsp;||Skew = <math>\, 15^\circ</math>, Length of Beam = <math>\, (38.67')/(Cos 15^\circ) = 40.03'</math>
 
|-
 
|width="25"|&nbsp;||Beam depth = <math>\, 3^\prime-0^{\prime\prime} </math>, <math>\, \phi = 27^\circ</math>, <math>\, H = 8.20'</math>
 
|-
 
|&nbsp;
 
|-
 
|width="25"|&nbsp;||<math>\, \frac{H}{3} = \frac{8.20'}{3} = 2.73'</math>
 
|-
 
|width="25"|&nbsp;||<math>\, 3^\prime - 2.73^\prime = 0.27^\prime < 9^{\prime\prime}</math>, use <math>\, 9^{\prime\prime}</math>
 
|-
 
|width="25"|&nbsp;||<math>\, h = H - (Beam\ depth) + 9^{\prime\prime} = 8.20^\prime - 3^\prime + 0.75 = 5.95^\prime</math>
 
|-
 
|width="25"|&nbsp;||Assume <math>\, T = 2^\prime-0^{\prime\prime} </math> (Deadman anchor depth)
 
|}
 
  
 +
Each section of wall shall be in increments of 4 ft. with a maximum length of 28'-0".
 +
[[image:751.24.3.6 L shaped.jpg|center|800px]]
  
{|border="0" cellpadding="5"
 
  
|colspan="4"|Determine Earth and Surcharge Forces
+
'''Counterfort Walls'''
|-
+
[[image:751.24.3.6 counterfort part elev.jpg|center|800px|thumb|
|width="25"|&nbsp;||<math>\, K_A</math>||=||<math>\, Tan^2 (45^\circ - \varnothing/2) = Tan^2 (45^\circ - 27^\circ/2) = 0.3755</math>
+
{| style="margin: 1em auto 1em auto style="text-align:left""
|-
 
|width="25"|&nbsp;||<math>\, K_P</math>||=||<math>\, Tan^2 (45^\circ - \varnothing/2) = Tan^2 (45^\circ - 27^\circ/2) = 2.6629</math>
 
|-
 
|width="25"|&nbsp;||<math>\, F_e</math>||=||<math>\, \frac{1}{2} (120 K_AH^2)(Length\,of\,Beam)</math>
 
|-
 
|width="25" colspan="2"|&nbsp;||=||<math>\, (60 lb./cu.ft.)(0.3755)(8.20')^2(40.03')</math>
 
|-
 
|width="25" colspan="2"|&nbsp;||=||<math>\, 60,842 lbs.</math>
 
|-
 
|width="25"|&nbsp;||<math>\, F_s</math>||=||<math>\, (2')(120 K_AH)</math><math>(Length\,of\,Beam)</math>
 
|-
 
|width="25" colspan="2"|&nbsp;||=||<math>\, (240 lb./cu.ft.)(0.3755)(8.20')(40.03')</math>
 
|-
 
|width="25" colspan="2"|&nbsp;||=||<math>\, 297,582 lbs.</math>
 
|-
 
|width="25"|&nbsp;||<math>\, P_A</math>||=||<math>\, 120 K_Ah\;T</math>
 
|-
 
|width="25" colspan="2"|&nbsp;||=||<math>\, (120 lb./cu.ft.)(0.3755)(5.95')(2.0')</math>
 
 
|-
 
|-
|width="25" colspan="2"|&nbsp;||=||<math>\, 536 lbs.\,per\,foot\,of\,Deadman</math>
+
|'''Notes:'''
 
|-
 
|-
|width="25"|&nbsp;||<math>\, P_P</math>||=||<math>\, 120 K_Ph\;T</math>
+
|'''Dimension "A"'''
 
|-
 
|-
|width="25" colspan="2"|&nbsp;||=||<math>\, (120 lb./cu.ft.)(2.6629)(5.95')(2.0')</math>
+
|• Maximum length = 28'-0".
 
|-
 
|-
|width="25" colspan="2"|&nbsp;||=||<math>\, 3,803 lbs.\,per\,foot\,of\,Deadman</math>
+
|• Each section to be in 4'-0" increments.
|}
 
 
 
 
 
{|border="0"
 
 
 
|colspan="2"|Determine number of Tie Rods required
 
 
|-
 
|-
|width="25"|&nbsp;||Try 7/8"Ø Rods: <math>\, F_R = 8.0</math> kips
+
|• (See [[#Rustication Recess|rustication recess details]].)
 
|-
 
|-
|width="25"|&nbsp;||Number of Rods required = <math>\, (F_E + F_S)/F_R = (60,642 + 29,582)/8,000 = 11.29</math>
+
|'''Dimensions "B" & "C"'''
 
|-
 
|-
|width="25"|&nbsp;||Use 12-7/8"Ø Rie Rods.
+
|• As required by the design to balance the negative and positive moments. (See the design assumptions).
|}
+
|}]]
 
 
{|border="0"
 
 
 
|colspan="2"|Determine length of Deadman
 
|-
 
|width="25"|&nbsp;||Length of Deadman required = <math>\, (F_E + F_S)/(P_P - P_A = {(60,642 + 29,582) lbs.}/{(3,803 - 536) lb/ft.} = 27.62'</math>
 
|-
 
|width="25"|&nbsp;||Tie Rod spacing = <math>\, (27.62^\prime - 2.0^\prime )/11 = 2.33^\prime  say 2^\prime-4^{\prime\prime} > 12^{\prime\prime}</math> minimum, ok.
 
|-
 
|width="25"|&nbsp;||Length of Deadman provided = <math>\, (2'-4^{\prime\prime})(11) + 2.0^\prime = 27^\prime-8^{\prime\prime}</math>
 
|}
 
 
 
 
 
<center>[[Image:751.40_Deadman_Anchor_Design_Example_Detail_1.gif]]</center>
 
 
 
 
 
<center><math>\, \phi = 27^\circ</math></center>
 
 
 
 
 
<center><math>\, 45^\circ - \frac{\phi}{2} = 31.5^\circ</math></center>
 
 
 
 
 
{|border="0" cellpadding="5"
 
  
|1)||colspan="2"|Check tie rod skew angle at Fill Face of End Bent
+
[[image:751.24.3.6 counterfort typ section.jpg|center|800px|thumb|
 +
{| style="margin: 1em auto 1em auto style="text-align:left""
 
|-
 
|-
|&nbsp;|| <math>\, (5.5\ spacing)(30.5^{\prime\prime} - 28^{\prime\prime}) = 13.75^{\prime\prime}, tan</math> || <math>\, \phi = 13.75^{\prime\prime}/(24.33 \times 12^{\prime\prime}) = 0.471</math>
+
|'''Notes:'''
 
|-
 
|-
|colspan="2"|&nbsp;||<math>\, \phi = 2.70^\circ < 30^\circ</math>, tie capacity ok.
+
|'''Batter  "D":'''
 
|-
 
|-
|&nbsp;
+
|* As required to maintain 9" minimum at the top of the counterfort and 12" minimum edge distance at the top of the footing, between counterfort and footing edge.
 
|-
 
|-
|colspan="3" align="center"|[[Image:751.40_Deadman_Anchor_Design_Example_Detail_2.gif]]
+
|* Batter to be given an eighth of an inch per foot of counterfort height.
 
|-
 
|-
|&nbsp;
+
|'''Dimension "L":'''
 
|-
 
|-
|2)||colspan="2"|Check criteria for Deadman Anchors extending into Fill Slope
+
|* As required for stability.
 
|-
 
|-
|&nbsp;
+
|* As an estimate, use "L" equal to 1/2 the height of "H".
|-
+
|}]]
|colspan="3" align="center"|[[Image:751.40_Deadman_Anchor_Design_Example_Detail_3.gif]]
 
|}
 
 
 
 
 
:{|border="0"
 
  
|A)||colspan="3"|Extension of Deadman into Fill Slope
+
'''Sign-Board Type Counterfort Walls'''
|-
+
[[image:751.24.3.6 sign board part elev.jpg|center|800px|thumb|
|&nbsp;||colspan="3"|Length of Deadman extending into Fill Slope = <math>\, 1.08^\prime tan 15^\circ +</math>
+
{| style="margin: 1em auto 1em auto style="text-align:left""
|-
 
|&nbsp;||width="10"|&nbsp;||colspan="2"| <math>\, (13.83^\prime - ((15.04^\prime + 3.87^\prime) - 24.33^\prime  tan 15^\circ)) = 1.73^\prime</math>
 
|-
 
|colspan="2"|&nbsp;||colspan="2"|0.2 (Length of Deadman) = <math>\, 0.2 (27.67^\prime) = 5.53^\prime</math>
 
|-
 
|colspan="2"|&nbsp;||width="60"|&nbsp;||<math>\, 1.73^\prime < 5.53^\prime</math>
 
|-
 
|&nbsp;||colspan="3"|Length of Deadman extending into Fill Slope <math>\, < 0.2</math> (Length of Deadman), ok
 
 
|-
 
|-
|&nbsp;
+
|'''Notes:'''
 
|-
 
|-
|colspan="4"|Note: See below for Section A-A details.
+
|'''Dimension "A"'''
 
|-
 
|-
|&nbsp;
+
|* Maximum length = 28'-0".
 
|-
 
|-
|B)||colspan="3"|Cover of Deadman in Fill Slope
+
|* Each section to be in 4'-0" increments.
|-
 
|&nbsp;||colspan="3"|<math>\, 1.44^\prime \times (cos 15^\circ) = 1.39^\prime</math>
 
|}
 
 
 
 
 
<center>[[Image:751.40_Deadman_Anchor_Design_Example_Detail_4.gif]]</center>
 
 
 
<center>'''SECTION A-A<BR/>DETAIL AT FILL SLOPE'''</center>
 
 
 
 
 
Note:
 
 
 
(*) Fill slope shown is for illustration purpose only, see roadway plans.
 
 
 
====751.40.8.13.2 Reinforcement====
 
=====751.40.8.13.2.1 Wide Flange Beams, Plate Girders and Prestressed Girders=====
 
 
 
 
 
'''END BENT WITH EXPANSION DEVICE'''
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|[[Image:751.40_Reinf_End_Bent_With_Exp_Device_Sec_AA.gif]]
 
|rowspan="4"|[[Image:751.40_Reinf_End_Bent_With_Exp_Device_Part_Elevation.gif]]
 
 
|-
 
|-
|'''SECTION A-A'''
+
|* (See [[#Rustication Recess|rustication recess details]].)
 
|-
 
|-
|&nbsp;
+
|'''Dimensions "B" & "C"'''
 
|-
 
|-
|&nbsp;
+
|* As required by the design to balance the negative and positive moments. (See the design assumptions).
 
|-
 
|-
|&nbsp;||'''PART ELEVATION'''
+
|'''Dimension "E"'''
|}
 
 
 
Notes:
 
 
 
(1) See details for reinforcement of end bent backwall.
 
 
 
(2) #6-H bars and #4-H bars in backwall of skewed bridges shall be bent in field if required.
 
 
 
(3) Center #5 bars in backwall.
 
 
 
Epoxy coat all reinforcing in end bents with expansion devices.  See ______ for details of protective coating and sloping top of beam to drain.
 
 
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|rowspan="2"|[[Image:751.40_Reinf_End_Bent_With_Exp_Device_Part_Plan_BB.gif]]
 
|width="250"|[[Image:751.40_Reinf_End_Bent_With_Exp_Device_Detail_of_-5_Shape_19_Bar.gif]]
 
 
|-
 
|-
|'''DETAIL OF #5 BARS<br/>SHAPE 19'''<!--cell 1 occupied by [[Image:751.40_Reinf_End_Bent_With_Exp_Device_Part_Plan_BB.gif]]-->
+
|* (Sign-board type only)
 
|-
 
|-
|'''PART PLAN B-B'''
+
|* As required to maintain footing pressure within the allowable for existing foundation material.  12" minimum.
|}
 
 
 
 
 
'''END BENT WITHOUT EXPANSION DEVICE'''
 
 
 
  
{|border="0" cellpadding="5" align="center" style="text-align:center"
+
|}]]
  
|[[Image:751.40_Reinf_End_Bent_Without_Exp_Device_Sec_AA.gif]]
+
[[image:751.24.3.6 sign board typ section.jpg|center|800px|thumb|
|rowspan="4"|[[Image:751.40_Reinf_End_Bent_Without_Exp_Device_Part_Elevation.gif]]
+
{| style="margin: 1em auto 1em auto style="text-align:left""
 
|-
 
|-
|'''SECTION A-A'''
+
|'''Notes:'''
 
|-
 
|-
|&nbsp;
+
|'''Batter  "D":'''
 
|-
 
|-
|&nbsp;
+
|* As required to maintain 9" minimum at the top of the counterfort and 12" minimum edge distance at the top of the footing, between counterfort and footing edge.
 
|-
 
|-
|&nbsp;||'''PART ELEVATION'''
+
|* Batter to be given an eighth of an inch per foot of counterfort height.
|}
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|[[Image:751.40_Reinf_End_Bent_Without_Exp_Device_Part_Plan_BB.gif]]
 
|valign="top"|
 
{|border="0" cellpadding="3" style="text-align:left"
 
 
 
|valign="top"|(1)||#5 Dowel bars are 2'-6" long and placed parallel to centerline roadway.
 
|-
 
|valign="top"|(2)||#6-H bars and #4-H bars in backwall of skewed bridges shall be bent in field.
 
|-
 
|valign="top"|(3)||For skewed bridges with no expansion device place a #4 bar along skew.
 
 
|-
 
|-
|valign="top"|(4)||See details of end bent backwall for reinforcement.
+
|'''Dimension "L":'''
 
|-
 
|-
|valign="top"|(5)||Seal joint with joint sealant. See special provisions.
+
|* As required for stability.
|-
 
|colspan="2"|Note:  See Structural Project Manager before using this detail.
 
|}
 
 
|-
 
|-
|'''PART PLAN B-B
+
|* As an estimate, use "L" equal to 1/2 the height of "H".
|}
+
|}]]
 
 
 
 
'''END BENT WING'''
 
 
 
  
{|border="0" cellpadding="5" align="center" style="text-align:center"
+
==== 751.40.8.15.9 Reinforcement ====
 
+
'''Cantilever Walls'''
|[[Image:751.40_Reinf_End_Bent_Wing_Sec_AA.gif]]|
+
[[image:751.24.3.7 friction.jpg|center|800px|thumb|
|rowspan="3"|[[Image:751.40_Reinf_End_Bent_Wing_Typ_Elevation.gif]]
+
{| style="margin: 1em auto 1em auto"
 
|-
 
|-
|'''SECTION A-A'''
+
|'''(*)''' Alternate long and short bars at equal spaces.
 
|-
 
|-
|&nbsp;
+
|'''(**)''' If collision forces are assumed, use #4 @ 12" cts. min. and extend at least development length into footing.  (See [[751.5 Structural Detailing Guidelines#751.5.9.2.8.1 Development and Lap Splice General|EPG 751.5.9.2.8.1 Development and Lap Splice General]].)
 
|-
 
|-
|&nbsp;||'''TYPICAL ELEVATION OF WING'''
+
|'''(***)''' Theo. cut-off for bending + development length.  (Wall height over 10' only.)
 
|}
 
|}
 +
]]
  
Note: (1) Development length
+
[[image:751.24.3.7 pile footing.jpg|center|800px|thumb|
 
+
{| style="margin: 1em auto 1em auto"
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|valign="top"|
 
{|border="1" cellpadding="5" align="center" style="text-align:center"
 
 
 
|h||(2)||(3)
 
|-
 
|2' or less||#4 @ 12"||#6 @ 6"
 
|-
 
|Over 2' to 4'||#5 @ 6"||#7 @ 6"
 
|-
 
|Over 4' to 6'||#7 @ 5"||#8 @ 5"
 
|}
 
|[[Image:751.40_Reinf_End_Bent_Wing_Sec_BB.gif]]
 
 
|-
 
|-
|&nbsp;||'''SECTION B-B'''
+
|'''(*)''' Alternate long and short bars at equal spaces.
 
|-
 
|-
|[[Image:751.40_Reinf_End_Bent_Wing_Part_Sec_With_Passive_Pressure.gif]]
+
|'''(**)''' If collision forces are assumed, use #4 @ 12" cts. min. and extend at least development length into footing.  (See [[751.5 Structural Detailing Guidelines#751.5.9.2.8.1 Development and Lap Splice General|EPG 751.5.9.2.8.1 Development and Lap Splice General]].)
|rowspan="2"|[[Image:751.40_Reinf_End_Bent_Wing_Horiz_Sec_Thru_Wing.gif]]
 
 
|-
 
|-
|'''PART SECTION THRU BENTS<br/>WITH PASSIVE PRESSURE'''
+
|'''(***)''' Theo. cut-off for bending + development length.  (Wall height over 10' only.)
 
|-
 
|-
|&nbsp;||'''HORIZONTAL SECTION THRU WING'''<br/>(K bars not shown for clarity)
+
|'''(****)''' Due to site constriction.
 
|}
 
|}
 +
]]
  
 +
'''Cantilever Walls - L-Shaped'''
  
'''END BENT BEAM HEEL'''
+
[[image:751.24.3.7 L shaped.jpg|center|800px|thumb|
 
+
{| style="margin: 1em auto 1em auto"
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Elev_AA.gif]]
 
|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Square.gif]]
 
|-
 
|'''ELEVATION A-A (TYP.)'''||'''PART PLAN OF BEAM (SQUARE)'''
 
|-
 
|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_thru_15_deg.gif]]
 
|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_thru_15_deg_(2).gif]]
 
|-
 
|colspan="2"|'''PART PLAN OF BEAM - SKEWS THRU 15° - LEFT ADVANCE SHOWN'''
 
|}
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|rowspan="2"|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_over_15_deg_(1).gif]]
 
|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_over_15_deg_(Sec_BB).gif]]
 
|rowspan="2"|[[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_over_15_deg_(2).gif]]
 
 
|-
 
|-
|'''SECTION B-B''' <!--column 1 occupied by cell [[Image:751.40_Reinf_End_Bent_Beam_Heel_Part_Plan_-_Skews_over_15_deg_(1).gif]]-->
+
|'''(*)''' Do not splice stress bars in the fill face at top of footing.
 
|-
 
|-
|colspan="3"|'''PART PLAN OF BEAM - SKEWS OVER 15° - LEFT ADVANCE SHOWN'''
+
|'''(**)''' If collision forces are assumed, use #4 @ 12" cts. min. and extend at least development length into footing.  (See [[751.5 Structural Detailing Guidelines#751.5.9.2.8.1 Development and Lap Splice General|EPG 751.5.9.2.8.1 Development and Lap Splice General]].)
 
|}
 
|}
 +
]]
  
 
+
'''Counterfort Walls'''
Note:
+
:'''Wall and Stem'''
 
+
[[image:751.24.3.7 counterfort.jpg|center|800px|thumb|
Vertical spacing for #7 bars shown in Elevation A-A is typical for all types of end bent beams.
+
{| style="margin: 1em auto 1em auto"
 
 
For a long distance between heel pile and bearing beam investigate for use of larger bars; e.g. larger skews where the shear line does not fall within the bearing beam.
 
 
 
 
 
{|border="1" cellpadding=6" cellspacing="1" align="center" style="text-align:center"
 
 
 
|rowspan="2" width="150"|Pile Load Not Greater||rowspan="2" width="150"|(1)<math>*</math> Hair-Pin Stirrups||colspan="4"|(2) Horizontal Rebar around Heel Pile
 
 
|-
 
|-
|width="75"|Skew thru 30° <!--column 1 occupied by cell Pile Load Not Greater--> <!--column 2 occupied by cell (1)* Hair-Pin Stirrups-->||width="75"|Skew 31° thru 45°||width="75"|Skew 46° thru 60°||width="75"|Skew over 60°
+
|<center>(For footing reinforcement, see the "Footing" diagram, below)</center>
 
|-
 
|-
|140 kips||#6 @ 9"||5-#7||5-#7||5-#8||By Design
+
|'''(*)''' Use development length or standard hook in accordance with [[751.5 Structural Detailing Guidelines#751.5.9.2.8.1 Development and Lap Splice General|EPG 751.5.9.2.8.1 Development and Lap Splice General]].
 
|-
 
|-
|194 kips||#6 @ 6"||5-#7||5-#8||By Design||By Design
+
|'''(**)''' See lap splices Class B.  (See [[751.5 Structural Detailing Guidelines#751.5.9.2.8.1 Development and Lap Splice General|EPG 751.5.9.2.8.1 Development and Lap Splice General]].)
 
|}
 
|}
 +
]]
  
 
+
:'''Footing'''
<math>*</math>  Use 21" horizontal leg.
+
[[image:751.24.3.7 footing.jpg|center|800px|thumb|
 
+
{| style="margin: 1em auto 1em auto"
 
 
'''END BENT BACKWALL'''
 
 
 
 
 
<center>[[Image:751.40_Reinf_End_Bent_Backwall_Part_Section.gif]]</center>
 
 
 
<center>'''PART SECTION THRU BACKWALL AND BEAM'''</center>
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
 
 
|colspan="4"|'''V-BAR SIZE AND SPACING'''
 
|-
 
|h<br/>(feet)||t<br/>(inch)||Fill Face<br/>Reinforcement||Front Face<br/>Reinforcement
 
|-
 
|1-6||12||#5 @ 12"||#5 @ 12"
 
|-
 
|7||12||#5 @ 12"||#5 @ 12"
 
 
|-
 
|-
|8||12||#5 @ 12"||#5 @ 12"
+
|'''(*)''' By design for loads and footing pressures on section under consideration.  (#5 @ 12" cts. is the minimum.)
|-
 
|9||12||#6 @ 12"||#5 @ 12"
 
|-
 
|10||12||#6 @ 10"||#5 @ 12"
 
|-
 
|11||15||#6 @ 10"||#5 @ 12"
 
|-
 
|12||15||#6 @ 8"||#5 @ 12"
 
|-
 
|13||18||#6 @ 8"||#5 @ 12"
 
|-
 
|14||18||#6 @ 6"||#5 @ 12"
 
 
|}
 
|}
 +
]]
  
 +
'''Counterfort Walls - Sign-Board Type'''
 +
:'''Wall and Stem'''
 +
:Refer to "Counterfort Walls, Wall and Stem", above.
  
Note:
+
:'''Spread Footing'''
 
+
[[image:751.24.3.7 sign board.jpg|center|800px]]
All reinforcement is grade 60.
 
 
 
Design is based on 45 lbs. per cu. ft. equivalent fluid pressure and 90 lbs. per sq. ft. live load surcharge.
 
 
 
Epoxy coat all reinforcing steel in beam and backwall on non-integral end bents with expansion devices.
 
 
 
=== 751.40.8.14 Concrete Pile Cap Integral End Bents ===
 
  
 +
:If the shear line is within the counterfort projected (longitudinally or transversely), the footing may be considered satisfactory for all conditions.  If outside of the counterfort projected, the footing must be analyzed and reinforced for bending and checked for bond stress and for diagonal tension stress.
  
==== 751.40.8.14.1 Design ====
+
[[image:751.24.3.7 sign board footing.jpg|center|800px]]
  
 +
==== 751.40.8.15.10 Details ====
 +
'''Non-Keyed Joints'''
  
===== 751.40.8.14.1.1 Design Unit Stresses =====
+
Each section of wall shall be in increments of 4 ft. with a maximum length of 28'-0".
 +
[[image:751.24.3.8 nonkeyed.jpg|center|800px]]
 +
<center>See [[751.50 Standard Detailing Notes|EPG 751.50 Standard Detailing Notes]] for appropriate notes.</center>
  
#Reinforced Concrete
+
'''Keyed Joints'''
#*Class B Concrete (Substructure) &nbsp; <math>\, f_c</math> &nbsp; = 1,200 psi, &nbsp; <math>\, f'_c</math> &nbsp; = 3,000 psi
+
[[image:751.24.3.8 keyed.jpg|center|800px]]
#*Reinforcing Steel (Grade 60) &nbsp; &nbsp; &nbsp; &nbsp; <math>\, f_s</math> &nbsp; = 24,000 psi &nbsp; <math>\, f_y</math> &nbsp; = 60,000 psi
+
<center>See [[751.50 Standard Detailing Notes|EPG 751.50 Standard Detailing Notes]] for appropriate notes.</center>
#*<math>\, n</math> &nbsp; = 10
 
#*<math>\, E_c</math> &nbsp; =<math>\, w^{1.5} \times 33 \sqrt{f'_c}</math> &nbsp; (AASHTO Article 8.7.1)(*)
 
#Structural Steel
 
#*Structural Carbon Steel  (ASTM A709 Grade 36) &nbsp; <math>\, f_s</math> &nbsp; = 20,000 psi &nbsp; <math>\, f_y</math> &nbsp; = 36,000 psi
 
#Piling
 
#*See the Design Layout if pile capacity is indicated.
 
#Overstress
 
#*The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for Service Loads design method.
 
  
(*) &nbsp; <math>\, E_c = 57,000 \sqrt {f'_c} for\ W = 145 pcf,\ E_c = 60,625 \sqrt{f'_c} for W = 150 pcf </math>
 
  
===== 751.40.8.14.1.2 Loads =====
+
<div id="Rustication Recess"></div>
 +
'''Rustication Recess'''
 +
[[image:751.24.3.8 rustication.jpg|center|800px]]
  
#Dead Loads
 
#Live Load
 
#*As specified on the Design Layout.
 
#*Impact of 30% is to be used for design of the beam. No impact is to be used for design of any other portion of bent including the piles.
 
#Temperature, Wind and Frictional Loads
 
  
===== 751.40.8.14.1.3 Distribution of Loads =====
+
'''Drains'''
 +
[[image:751.24.3.8 drains.jpg|center|800px]]
 +
<center>Note: French drains shall be used on all retaining walls, unless otherwise specified on the Design Layout.</center>
  
#Dead Loads
+
[[image:751.24.3.8 drop inlet.jpg|center|800px]]
#*Loads from stringers, girders, etc. shall be concentrated loads applied at the intersection of centerline of stringer and centerline of bearing. Loads from concrete slab spans shall be applied as uniformly, distributed loads along the centerline of bearing.
 
#Live Load
 
#*Loads from stringers, girders, etc. shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of bearing.  For concrete slab spans distribute two wheel lines over 10'-0" (normal to centerline of roadway) of substructure beam.  This distribution shall be positioned on the beam on the same basis as used for wheel lines in Traffic Lanes for Substructure Design.
 
#Wing with Detached Wing Wall
 
#*When wing length, L, is greater than 17'-0", use maximum length of 10'-0" rectangular wing wall combined with a detached wing wall.  When detached wing walls are used, no portion of the bridge live load shall be assumed distributed to the detached wing walls.  Design detached wing wall as a retaining wall.  (The weight of Safety Barrier Curb on top of the wall shall be included in Dead Load.)
 
  
===== 751.40.8.14.1.4 Design Examples =====
 
  
Design H-bar and F-bar of an intermediate wing as shown in the figures below (wing length = 12.5', wing thickness = 24", wing height = 8'-4"), a Seismic Force of &nbsp; <math>\, \omega</math> = 12.21 kips/ft. is applied on the wall.
+
'''Construction Joint Keys:
 +
:'''Cantilever Walls'''
 +
[[image:751.24.3.8 cantilever.jpg|center|800px]]
  
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
+
:'''Counterfort Walls'''
|-
+
[[image:751.24.3.8 counterfort.jpg|center|800px]]
|[[Image:751.40 conc pile cap int end bents-section near intermediate wing.gif]]
 
|[[Image:751.40 conc pile cap int end bents-intermediate wing sectin b-b.gif]]
 
|-
 
!Section Near Intermediate Wing
 
!Section B-B
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|rowspan="2"|[[Image:751.40 conc pile cap int end bents-intermediate wing sectin c-c.gif]]
 
|[[Image:751.40 conc pile cap int end bents-interior wing design.gif]]
 
|-
 
!Interior Wing Design
 
|-
 
!Section C-C
 
|}
 
  
  
Solve:   Assume #6 V bar, #8 H bar, #6 F bar
+
::Key length:  Divide the length "A" into an odd number of spaces of equal lengths.  Each space shall not exceed a length of 24 inches.  Use as few spaces as possible with the minimum number of spaces equal to three (or one key).
  
{|
+
::Key width = Counterfort width/3 (to the nearest inch)
|valign="top" rowspan="14"|1.)||Design H-bar for bending
 
|-
 
|<math>\, d = 24in. - 2in. (clr.) - 0.75in. (V\ Bar) - 0.5 \times 1in. (H\ bar) = 20.75in.</math>.
 
|-
 
| <math>\, \ell = 11ft.,</math> &nbsp; <math>\, \omega = 12.21 kips/ft.,</math> &nbsp;  <math>\, b = 8ft. 4in. = 100in. </math>
 
|-
 
|&nbsp;
 
|-
 
|At Section A-A:
 
|-
 
|<math>\, Mu = (1.0)( \omega \ell^2 / 2) = 12.21 \times 11^2/2 = 738.705 kip-ft.</math>
 
|-
 
|<math>\, Ru = Mu/( \phi bd^2) = 738.705 \times 12,000/(0.9 \times 100in. \times (20.75)^2) = 228.85 psi</math>
 
|-
 
|Use <math>\, f-c = 3 kisi,</math> &nbsp; <math>\, fy = 60 ksi</math>
 
|-
 
|<math>\, m = fy/(0.85 f'c) = 60/(0.85 \times 3) = 23.53</math>
 
|-
 
|<math>\, \rho = (1/m)[1 - \sqrt{1 - 2 Rum/fy}] = (1 - \sqrt{1 - 2 \times 228.85 \times 23.53/60000})/23.53 = 0.004003</math>
 
|-
 
|As (Req'd) = <math>\, \rho\ bd = 0.004003 \times 100in. \times 20.75in. = 8.31 sq.\ in.</math>
 
|-
 
|Try No. 8 @ 9", USE &nbsp; <math>\, \frac{100in - 3in. (clr.) - 2in. (clr.) - 1in (No.\ 8\ bar)}{9in} = 10.44\ spacing</math>
 
|-
 
|Say 11 spacings, 12 bars (Each Face)
 
|-
 
|Total Area = <math>\, 12 (0.7854) = 9.42 sq.\ in. > 8.31 sq.\ in.,</math> &nbsp; USE 12-No. 8 H-bar (Each Face)
 
|}
 
  
 +
::Key depth = 2" (nominal)
  
{|
+
:'''Sign-Board Walls'''
|valign="top" rowspan="22"|2.)||Design F-bar for shear
+
[[image:751.24.3.8 sign board.jpg|center|800px]]
|-
 
|<math>\, Vu \le \phi (Vc = Vs),\ \phi = 0.85</math> &nbsp; (AASHTO Article 8.16.6.1.1)
 
|-
 
| &nbsp;
 
|-
 
|At Section A-A:
 
|-
 
|<math>\, Vu = 1.0 \times (\omega \ell) = (12.21 kips/ft.)(11ft.) = 134.11 kips</math>
 
|-
 
|<math>\, Vc = bd(\vartheta c) = bd(2 \sqrt{f'c} = (100in. \times 20.75in.)(2 \times \sqrt{3000})/1000 = 227.30 kips</math>
 
|-
 
|<math>\, \phi\ Vc = 0.85 Vc = 0.85 \times 227.30 kips = 193.20 kips</math>
 
|-
 
|<math>\, \phi\ Vc = 193.20 kips > Vu = 134.11 kips,</math> &nbsp; No &nbsp; <math>\, Vs</math> &nbsp; needed by AASHTO Article 8.16.6.3.1.
 
|-
 
|Minimum shear reinforcement is required by AASHTO Article 8.19.1.1(a).(ACI 318-95 11.5.5.1)
 
|-
 
|&nbsp;
 
|-
 
|F-bar is a single group of parallel bars, all bent up at the same distance from support (no "spacing" along the "L" direction of the wing).
 
|-
 
|Try No. 6 @ 12" F-bar (each face).
 
|-
 
|Try <math>\, (100in. - 3in. - 2in. - 1in. )/12in = 7.83,</math> say 8 spacing, 9 bars (each face).
 
|-
 
| &nbsp;
 
|-
 
|Since seismic force is a cyclic loading, assume one bar works at any instance.  
 
|-
 
|<math>\, Av (provided) = 1 \times 9 \times (0.4418 sq.\ in.) = 3.98 sq.\ in.</math>
 
|-
 
| &nbsp;
 
|-
 
|<math>\, Vs = Av (Fy\ Sin 45^\circ) = (3.98 sq.\ in.)(60 ksi)(Sin 45^\circ) = 168.7 kips</math>
 
|-
 
|Check &nbsp; <math>3 \sqrt{f'c} b_\omega d = 3 \sqrt{3000} \times 100in. \times 20.75in. / 1000 = 341.0 kips</math>
 
|-
 
| &nbsp;
 
|-
 
|<math>\, Vs = Av (fy\ Sin 45^\circ) \le 3 \sqrt{f'c} b_\omega d,</math> &nbsp; O.K. by AASHTO Article 8.16.6.3.4.
 
|-
 
|USE 9 No. 6 F-bars (each face).
 
|}
 
  
==== 751.40.8.14.2 Reinforcement ====
+
::Key length = divide length "A" or "B" into an odd number of spaces of equal lengths. Each space length shall not exceed 24 inches. Use as few spaces as possible with the minimum number of spaces equal to three (or one key).
  
  
===== 751.40.8.14.2.1 Earthquake Loads at End Bent – Intermediate Wing (Seismic Shear Wall) =====
 
  
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|[[Image:751.40 conc pile cap int end bents-section near intermediate wing(seismic).gif]]
 
|[[Image:751.40 conc pile cap int end bents-intermediate wing sectin b-b(seismic).gif]]
 
|-
 
!Section Near Intermediate Wing
 
!Section B-B
 
|-
 
|colspan="2"| &nbsp;
 
|-
 
|[[Image:751.40 conc pile cap int end bents-intermediate wing sectin a-a(seismic).gif]]
 
|&nbsp;
 
|-
 
!Section A-A
 
|&nbsp;
 
|}
 
{|border="0" cellpadding="5" cellspacing="1" align="center" style="text-align:center"
 
|-
 
|valign="top" align="right"|*||align="left" width="400pt"|Use 1.25 x development length for seismic design.
 
|-
 
|valign="top" align="right"|**||align="left" width="400pt"|Additional reinforcing steel by design if required.
 
|-
 
|valign="top" align="right"|Note:||align="left" width="400pt"|Make sure reinforcement does not interfere with girders.
 
|}
 
  
  
 
[[Category:751 LRFD Bridge Design Guidelines]]
 
[[Category:751 LRFD Bridge Design Guidelines]]

Latest revision as of 15:16, 21 November 2024

Contents

751.40.1 General

751.40.1.1 Widening and Repair of Existing Structures

The Federal Highway Administration and the States have established a goal that the LRFD standards be used on all new bridge designs after October 2007. For modification to existing structures and with the approval of the Structural Project Manager or Structural Liaison Engineer, the LRFD Specifications or the specifications which were used for the original design, may be used by the designer.

751.40.2 Deck Treatments

751.40.2.1 Resurfacing

751.40 Resurfacing Plan.gif
PLAN


751.40 Resurfacing Section Thru Roadway.gif
SECTION THRU ROADWAY

Place the following notes on plans.

The existing asphaltic concrete surface shall be removed to a uniform grade line * below the existing control grade line as noted.
Resurface with * Asphaltic Concrete.
* Depth of asphaltic concrete as specified in the Bridge Memorandum.

751.40.2.2 Special Repair Zones

The following order of repair zones shall be used for the deck repair on continuous concrete structures.

Hydro Demolition Projects (Case 1 and 2)

Conventional deck repair required in the areas designated as special repair zones shall be completed before demolition in alphabetical sequence beginning with Zone A. Zones with the same letter designation may be repaired at the same time.

Any deck repair in areas not designated as a special repair zone shall be completed after hydro demolition. Case 1 is primarily monolithic deck repair after hydro demolition. Case 2 is primarily conventional deck repair after hydro demolition.

Note:

- Case 1 shall not be used for polyester polymer and low slump concrete wearing surfaces (too stiff for monolithic repairs).
- Conventional deck repair is required with void tube replacement after hydro demolition with both Case 1 and Case 2.
- If an excessive number of zones are required at any bent, see the Structural Project Manager or Structural Liaison Engineer.
- Consider combining zones if the length of a zone in the longitudinal direction of the bridge is less than 24 inches.
751.40.2.2 hydro part-plan.png
PART PLAN OF SLAB SHOWING REPAIR ZONES (A, B, C and D)
(1) Development Length.
See EPG 751.50 Standard Detailing Notes for appropriate notes.

Non-Hydro Demolition Projects

Any deck repair in areas not designated as a special repair zone shall be completed prior to work in Zone A. Zones with the same letter designation may be repaired at the same time.

Note:

- If an excessive number of zones are required at any bent, see the Structural Project Manager or Structural Liaison Engineer.
- Consider combining zones if the length of a zone in the longitudinal direction of the bridge is less than 24 inches.
751.40.2.2 nonhydro part-plan.png
PART PLAN OF SLAB SHOWING REPAIR ZONES (A, B and C)
(1) Development Length.
See EPG 751.50 Standard Detailing Notes for appropriate notes.

751.40.2.3 Deck Repair and Filled Joints

Bridge Deck, Repair
Report 2002
See also: Research Publications

Bridge Standard Drawings
Rehabilitation, Surfacing & Widening – RHB; Deck Rehab (Deck Repair and Wearing Surface Details)

751.40.2.4 Wearing Surfaces

Replacement of Typical Expansion Joint Systems (Strip Seal Shown, Other Systems Similar)

751.40.3.1 wearing surfaces.jpg

When concrete is removed and armor is replaced, see EPG 751.13 Expansion Joint Systems for the appropriate expansion joint system details and EPG 751.50 H5 for the appropriate notes.

For chip seals and polymer wearing surfaces, see EPG 751.50 I1 for the appropriate notes.

Elastomeric Expansion Joint System

When a thick wearing surface (low slump, latex, silica fume, CSA cement, steel fiber reinforced, asphaltic) is used, the elastomeric joint must be replace by another type of expansion joint system.

751.40.3.1 elastomeric.jpg

Flat Plate Expansion Joint System

751.40.3.1 flat thick.jpg
* When this dimension exceeds 3" and a concrete wearing surface is used, tack weld a one inch bar chair to the plate for each 3" of plate to be covered by the wearing surface.
** Scarify existing slab. See the Bridge Memorandum for the minimum depth of scarification. Scarification not required for asphaltic concrete wearing surface.
Note: See standard plans for Steel Dams at Expansion Joints.


751.40.3.1 flat thin.jpg

751.40.2.5 Edge Treatments

751.40.2.5.1 Epoxy Coating

751.40.3.1 latex section.jpg
TYPICAL SECTION OF EXISTING CURB
OUTLET SHOWING LIMITS OF EPOXY COATING
Note:
* Dimension to edge of girder or stringer ±. For bridges that do not have girders or stringers use 2'-6", except that if with thrie beam rail, then use 4'-0".
Consult with Structural Project Manager or Liaison for making work incidental to another item or use of pay item "Cleaning and Epoxy Coating".


751.40.3.1 latex elevation.jpg
TYPICAL ELEVATION OF EXISTING CURB
OUTLET SHOWING LIMITS OF EPOXY COATING

(Wearing surface not shown for clarity)

751.40.2.5.2 Edge Repair

If slab edge repair is specified on the Bridge Memorandum when the barrier or railing is not removed or when full depth repair is not a pay item, the following detail shall be provided.

751.40 Concrete Wearing Surface Slab Edge Repair (Concrete Edge Repair) no 1.gif
CONCRETE EDGE REPAIR
If the barrier or railing is removed when full depth repair and slab edge repair are pay items, the following detail shall be provided.


751.40 Concrete Wearing Surface Slab Edge Repair (Concrete Edge Repair) no 1.gif
CONCRETE EDGE REPAIR
* If the dimension exceeds 4 inches, the repair extending to the edge of slab will be paid for as Full Depth Repair.

751.40.2.6 Longitudinal Joints

REPLACEMENT OF EXISTING EXPANSION DEVICE

MEDIAN BARRIER

751.40.2.6 section thru barrier.jpg
SECTION THRU BARRIER


751.40.2.6 detail A.jpg
DETAIL A
(1) May be cast vertical and saw cut to slant.
* Latex Concrete Wearing Surface = 1-3/4".
Low Slump Concrete Wearing Surface = 2-1/4".
** Cut minimum 1/2" support notch (rough finish). Remove any existing compression seal.

751.40.2.7 Temporary Traffic Control Device

Show Barrier as per district recommendation. Typically Barrier is shown when structure is on interstate and/or the rail is being removed. Otherwise, show the dimension lines with 2'-0" dimension.

751.40.2.5.jpg
* If this dimension is less than 3 feet, the temporary concrete traffic barrier shall be attached with tie-down straps, with the approval of the Structural Project Manager or Structural Liaison Engineer. Where lateral deflection cannot be tolerated, the temporary concrete traffic barrier shall be attached with the bolt through deck detail (to be used only on existing decks). See EPG 617.1 Temporary Traffic Barriers and EPG 751.1.2.12 Temporary Barriers.
** Where slab removal represents small and discontinuous openings in the deck along the bridge length (e.g. expansion device replacement) use of either a flat steel plate, a 22 ½” temporary traffic control device or a temporary concrete traffic barrier may be more appropriate. Consult with the Structural Project Manager or Structural Liaison Engineer.

751.40.3 Substructure Repair

751.40.3.1 Formed and Unformed Repair Areas

751.40.3.1 elev int bent.png
Elevation of Int. Bent


751.40.3.1 sec through end bent.png
Section through End Bent

751.40.3.2 Bent Cap Shear Strengthening using FRP Wrap

Bridge Standard Drawings
Rehabilitation, Surfacing & Widening; Fiber Reinf. Polymer (FRP) Wrap for Bent Cap Strengthening [RHB08]

Fiber Reinforced Polymer (FRP) wrap may be used for Bent Cap Shear Strengthening.

When to strengthen: When increased shear loading on an existing bent cap is required and a structural analysis shows insufficient bent cap shear resistance, bent cap shear strengthening is an option. An example of when strengthening a bent cap may be required: removing existing girder hinges and making girders continuous will draw significantly more force to the adjacent bent. An example of when strengthening a bent cap is not required: redecking a bridge where analysis shows that the existing bent cap cannot meet capacity for an HS20 truck loading, and the new deck is similar to the old deck and the existing beam is in good shape.

How to strengthen: Using FRP systems for shear strengthening follows from the guidelines set forth in NCHRP Report 678, Design of FRP System for Strengthening Concrete Girders in Shear. The method of strengthening, using either discrete strips or continuous sheets, is made optional for the contractor in accordance with NCHRP Report 678. A Bridge Standard Drawing and Bridge Special Provision have been prepared for including this work on jobs. They can be revised to specify a preferred method of strengthening if desired, strips or continuous sheet.

What condition of existing bent cap required for strengthening: If a cap is in poor shape where replacement should be considered, FRP should not be used. Otherwise, the cap beam can be repaired before applying FRP. Perform a minimum load check using (1.1DL + 0.75(LL+I))* on the existing cap beam to prevent catastrophic failure of the beam if the FRP fails (ACI 440.2R, Guide for the Design and Construction of Externally Bonded FRP, Sections 9.2 and 9.3.3). If the factored shear resistance of the cap beam is insufficient for meeting the factored minimum load check, then FRP strengthening should not be used.

* ACI 440.2R: Guide for the Design and Construction of Externally Bonded FRP

Design force (net shear strength loading): Strengthening a bent cap requires determining the net factored shear loading that the cap beam must carry in excess of its unstrengthened factored shear capacity, or resistance. The FRP system is then designed by the manufacturer to meet this net factored shear load, or design force. The design force for a bent cap strengthening is calculated considering AASHTO LFD where the factored load is the standard Load Factor Group I load case. To determine design force that the FRP must carry alone, the factored strength of the bent cap, which is 0.85 x nominal strength according to LFD design, is subtracted out to give the net factored shear load that the FRP must resist by itself. NCHRP Report 678 is referenced in the special provisions as guidelines for the contractor and the manufacturer to follow. The report and its examples use AAHTO LRFD. Regardless, the load factor case is given and it is left to the manufacturer to provide for a satisfactory factor of safety based on their FRP system.

Other References:

* ACI 201.1R: Guide for Making a Condition Survey of Concrete in Service
* ACI 224.1R: Causes, Evaluation, and Repair of Cracks in Concrete
* ACI 364.1R-94: Guide for Evaluation of Concrete Structures Prior to Rehabilitation
* ACI 440.2R-08: Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures
* ACI 503R: Use of Epoxy Compounds with Concrete
* ACI 546R: Concrete Repair Guide
* International Concrete Repair Institute (ICI) ICI 03730: Guide for Surface Preparation for the Repair of Deteriorated Concrete Resulting from Reinforcing Steel Corrosion
* International Concrete Repair Institute (ICI) ICI 03733: Guide for Selecting and Specifying Materials for Repairs of Concrete Surfaces
* NCHRP Report 609: Recommended Construction Specifications Process Control Manual for Repair and Retrofit of Concrete Structures Using Bonded FRP Composites

751.40.3.3 Steel HP Pile Maintenance and Repair

Maintenance/Repair Guidelines

Piles are primary structural members and are compressively loaded all the time which makes it important to safely inspect, maintain and repair them if necessary. Pile inspection will require an assessment of pile performance by looking for pile deterioration and measuring pile section loss in order to determine the level of pile maintenance/repair required. The following schedule may be used for selecting the level of maintenance/repair required:

Pile Percent Section Loss Method* Level
0% through 25% Clean and recoat existing piles Maintenance
>25% through 40% Encasement of deteriorated section Maintenance
>40% through 75% or holes in any element or local buckling of any element Plating ** of deteriorated section OR replacement *** of section (splicing), AND encasement of the repaired section Repair
>75% Contact the Bridge Division Repair
* Method may also include cleaning and recoating all exposed piles, and cleaning and recoating all remaining exposed pile sections after encasement and/or repair.
** Plating can be for both flanges only, web only or both flanges and web. Overall symmetry of the pile cross-section shall be maintained when plating.
*** Based on additional factors other than just the percent of pile section loss, a replacement pile section (splicing) may be considered. Minimizing or eliminating traffic loading, adding falsework or just having support conditions such as integral bents (where both the pile cap beam and the superstructure concrete diaphragm are connected by more than just dowel bars – see bridge plans) can help to determine the method of repair. A replacement pile section can be coated or galvanized. See Structural Project Manager.

Estimating Pile Percent Section Loss in the Field

Quantifying pile section loss can be inexact. To encourage uniform application of the maintenance/repair guidelines, the following procedure is recommended:

1. Pile section loss should be determined using a thickness meter.
2. Remove deteriorated material and clean pile for measurement.
3. At any point along a pile (cross-section) where there are three elements to be considered independently, e.g. two flanges and a web.
4. Estimate the actual cross-section area of each element at its most deteriorated point along the length of pile. Using the thickness meter, measure the thickness at several points along a horizontal line across the element. From this data, estimate the actual cross-section area of each element.
5. The fraction of section remaining (PSR) is the actual cross-section area of each element at its most deteriorated point along the length of pile divided by the original area of same element.
6. Percent section loss is 100(1 – PSR) for each element.
7. The greatest PSR dictates the maintenance/repair method.
8. Examine continuity at flange/web intersections. Section loss along these intersections along the length of pile of more than 6 linear inches should be repaired using encasement as either the only method or part of plating/replacing repair method regardless of a low percent section loss.
9. Interference from cross bracing at pile sections to be repaired will need special consideration not detailed on the standard drawings.
Bridge Standard Drawings
Rehabilitation, Surfacing & Widening – RHB; Steel HP Pile Maintenance and Repair

Additional types of maintenance and repairs may be considered which include but are not limited to:

  • Zinc tape coating
  • FRP strengthening
  • Corrosion inhibitor

751.40.4 Barriers and Railings

751.40.4.1 End Post Modification for 12-inch Vertical Barrier (Safe & Sound Bridges)

The 12-inch vertical barrier requires modification to allow attachment of the transition for the Midwest Guardrail System.

Bridge Standard Drawings
Barrier End Modifications – BEM & CBO/Barrier End Modification – BEM

751.40.4.2 Replacement of Existing Type B Barrier Using Anchor Systems

NEW BARRIER ON SLAB

751.40 Replacement of Existing Curb (Safety Barrier Curb on Slab) Section Thru Curb.gif
SECTION THRU BARRIER


751.40 Replacement of Existing Curb (Safety Barrier Curb on Slab) Section Thru Curb Optional Anchoring System.gif
SECTION THRU BARRIER
(OPTIONAL ANCHORING SYSTEM)
See EPG 751.50 I2. Resin & Cone Anchors for appropriate notes.


NEW BARRIER ON WING

751.40 Replacement of Existing Curb (Safety Barrier Curb on Wing) Section Thru Curb.gif
SECTION THRU BARRIER(*)


751.40 Replacement of Existing Curb (Safety Barrier Curb on Wing) Section Thru Curb Optional Anchoring System.gif
SECTION THRU BARRIER(*)
(OPTIONAL ANCHORING SYSTEM)
Note: See EPG 751.50 I2. Resin & Cone Anchors for appropriate notes. For details not shown, see EPG 751.12 Barriers, Railings, Curbs and Fences.


REPLACEMENT OF EXISTING BARRIER AT END OF WING USING ANCHOR SYSTEMS

INTEGRAL END BENTS

(*)Extend existing horizontal bars 2'-3" into new concrete.
(**) Fit bar to follow transition face of barrier.
Note: For details of guardrail attachment, see barrier standard drawings.
751.40 Replacement of Existing Curb at End of Wing (Integral End Bents) Part Elevation.gif
751.40 Replacement of Existing Curb at End of Wing (Integral End Bents) Anchor Systems at Section CC.gif
ANCHOR SYSTEMS AT SECTION C-C PART ELEVATION


751.40 Replacement of Existing Curb at End of Wing (Integral End Bents) Section AA.gif 751.40 Replacement of Existing Curb at End of Wing (Integral End Bents) Section BB.gif 751.40 Replacement of Existing Curb at End of Wing (Integral End Bents) Section CC.gif
SECTION A-A SECTION B-B SECTION C-C


REPLACEMENT OF EXISTING BARRIER AT END OF WING USING ANCHOR SYSTEMS

NON-INTEGRAL END BENTS

(*)Extend existing horizontal bars 2'-3" into new concrete.
(**) Fit bar to follow transition face of barrier.
Note: For details of guardrail attachment, see barrier standard drawings.
751.40 Replacement of Existing Curb at End of Wing (Non-Integral End Bents) Part Elevation.gif
751.40 Replacement of Existing Curb at End of Wing (Non-Integral End Bents) Anchor Systems at Section CC.gif
ANCHOR SYSTEMS AT SECTION C-C PART ELEVATION


751.40 Replacement of Existing Curb at End of Wing (Non-Integral End Bents) Section AA.gif 751.40 Replacement of Existing Curb at End of Wing (Non-Integral End Bents) Section BB.gif | 751.40 Replacement of Existing Curb at End of Wing (Non-Integral End Bents) Section CC.gif
SECTION A-A SECTION B-B SECTION C-C


751.40.4.3 Replacement of Existing Rail with Thrie Beam Rail

As a matter of policy, blockouts for thrie beam railings are required while FHWA does show similar systems without blockouts as NCHRP 350 approved. See the Structural Project Manager (SPM) or the Structural Liaison Engineer (SLE), if practical, to omit blockout. A design exception shall be required. Blockouts shall always be required on major routes.

There are four systems for use on state routes. In these four systems the connection design load used is 1.5 times plastic moment capacity (Mp) of W6 x 20 Post. The vertical clearance of System 3 shall be checked due to the obtruding lower connection.

Bridge Standard Drawings
Thrie Beam Rails - THRIE

751.40.4.4 End Treatment Using Thrie Beam Rail

751.40.4.4.jpg


751.40.4.4 clearance.jpg


Guidance for Design:

Adequate clearance to first post off bridge shall be required. (See also Standard Plan 617.10 for new bridges.)

751.40.4.5 Curb Blockouts

See EPG 751.1.3.4 Barrier or Railing Type, Height and Guidelines for Curb Blockouts for usage guidance.

Bridge Standard Drawings
Barrier Modifications – BEM & CBO/Curb Blockouts - CBO

751.40.5 Drainage

751.40.5.1 Structure with Wearing Surface Slab Drains - Details

Two material options may be used for slab drains:

1. Steel Slab Drains and inserts are only shown in the following details.
2. Fiberglass Reinforced Polymer (FRP) drains may be used with the approval of the Structural Project Manager or Structural Liaison Engineer. See EPG 751.10.3.2.1 New Structure Without Wearing Surface Slab Drains - Details for guidance and details of FRP drains on new structures as an aid.
A positive mechanical connection must be used for attaching FRP drains to either existing steel drains or to new FRP inserts since welding cannot be used as is shown in the following details for steel drains. For example, using at least four bolt-through connectors (one per side) from new FRP drains into a new wearing surface or an existing steel drain, or using an epoxy adhesive in conjunction with at least two bolt-through connectors is required. It has been shown that using a more viscous epoxy or anchoring gel is beneficial in order to avoid dripping during placement. Using epoxy adhesive or an anchoring gel by itself is not acceptable.
FRP drain may not fit exactly to the inside or to the outside of existing steel drain. The looseness of fit can be addressed by considering a combination of attachment details like mechanical connectors (to existing slab drain) plus either a viscous epoxy adhesive or a positive attachment to an exterior girder depending on the length of the slab drain extension.

For new wearing surface over new slab, note on plans:

Piece "A" shall be cast in the concrete slab. Prior to placement of wearing surface, piece "B" shall be inserted into piece "A".


FOR STRUCTURE WITH WEARING SURFACE
(GIRDER DEPTH LESS THAN 48")


751.40 Slab Drain Details (Girder Depth Less than 48 in.) Part Elev of Slab at Drain.gif


PART ELEVATION OF SLAB AT DRAIN


751.40 Slab Drain Details (Girder Depth Less than 48 in.) Elev of Drain.gif


ELEVATION OF DRAIN
* Deck thickness minus 1/8" minus the depth of the scarification.
** Do not include the depth of the scarification.

     



751.40 Slab Drain Details (Girder Depth Less than 48 in.) Plan of Drain.gif


PLAN OF DRAIN


FOR STRUCTURE WITH WEARING SURFACE
(GIRDER DEPTH 48" AND OVER)


751.40 Slab Drain Details (Girder Depth 48 in. and over) Part Elevation of Slab at Drain.gif 751.40 Slab Drain Details (Girder Depth 48 in. and over) Elev of Drain.gif
ELEVATION OF DRAIN
751.40 Slab Drain Details (Girder Depth 48 in. and over) Plan of Drain.gif
PART ELEVATION OF SLAB AT DRAIN PLAN OF DRAIN
* If dimension is less than 1", drains shall be placed parallel to roadway. Otherwise, place drains transverse to roadway.
** Do not include the depth of the scarification.
*** Deck thickness minus 1/8" minus the depth of the scarification.


751.40 Slab Drain Details (Girder Depth 48 in. and over) Part Plans Showing Bracket Assembly.gif
DRAIN TRANSVERSE TO ROADWAY DRAIN PARALLEL TO ROADWAY
 
PART PLANS SHOWING BRACKET ASSEMBLY


FOR STRUCTURE WITH WEARING SURFACE
(CONTINUOUS CONCRETE STRUCTURES)


751.40 Slab Drain Details (Continuous Concrete Structures) Part Section Near Drain.gif


PART SECTION NEAR DRAIN


751.40 Slab Drain Details (Continuous Concrete Structures) Elevation of Drain.gif


ELEVATION OF DRAIN


751.40 Slab Drain Details (Continuous Concrete Structures) Plan of Drain.gif


PLAN OF DRAIN


* Deck thickness minus 1/8" minus the depth of the scarification.
** Do not include the depth of scarification.


FOR STRUCTURE WITH WEARING SURFACE
(VARIABLE DEPTH GIRDERS)


751.40 Slab Drain Details (Variable Depth Girders) Part Elevation of Slab at Drain.gif


PART ELEVATION OF SLAB AT DRAIN


Note: For variable depth girders with drains in deeper section, let the deeper section control and use throughout the structure.


751.40 Slab Drain Details (Variable Depth Girders) Typ Section Straight Drain.gif


TYPICAL SECTION STRAIGHT DRAIN

751.40.5.2 Structure with Wearing Surface Round Slab Drains - Details

FOR STRUCTURE WITH WEARING SURFACE
MISCELLANEOUS DETAILS - ROUND DRAINS

FRP round drains may be used optionally unless otherwise specified. See EPG 751.10.3 Bridge Deck Drainage – Slab Drains for guidance and details as an aid. Specify nominal pipe size as needed referencing ASTM D2996. Specify outer diameter based on nominal pipe size necessary for drainage for coring the correct size hole in deck.

Note: See EPG 751.10.3 Bridge Deck Drainage – Slab Drain for slab drain spacing.


751.40.5.2 typical.jpg
751.40.5.2 section.jpg
TYPICAL PART PLAN SECTION SHOWING BRACKET ASSEMBLY


751.40 Slab Drain Details (Misc. Details - Round Drains) Typical Part Plan of Drain.gif


TYPICAL PART PLAN OF DRAIN


Note: See EPG 751.50 Standard Detailing Notes for appropriate notes.


751.40.5.3 Structure with Wearing Surface Raising Slab Drains or Scuppers - Details

FOR STRUCTURE WITH WEARING SURFACE
RAISING SLAB DRAINS


751.40 Slab Drain Details (Raising Standard Slab Drains) Part Section of Drain.gif


PART SECTION OF DRAIN


751.40 Slab Drain Details (Raising Standard Slab Drains) Part Plan of Existing Drain.gif


PART PLAN OF EXISTING DRAIN
Note:
Outside dimensions of drain extension are 7-1/4" x 3-1/4", and drain extension shall be galvanized in accordance with ASTM A123.


FOR STRUCTURE WITH WEARING SURFACE
RAISING SCUPPERS


751.40 Slab Drain Details (Details for Raising Scuppers) Typ Section thru Scupper.gif


TYPICAL SECTION THRU SCUPPER


751.40 Slab Drain Details (Details for Raising Scuppers) Plan of Grate Support and Scupper Extension.gif


PLAN OF GRATE SUPPORT
AND
PLAN OF SCUPPER EXTENSION


* Plate thicknesses should match those of existing scupper and existing grate.

751.40.5.4 Cored Slab Drains

Cored slab drains may be installed in areas where the existing drainage is a concern, but the deck is not in need of replacement. Typically, 4-inch diameter drains are installed vertically to avoid the deck reinforcing steel which is typically spaced at 5-inch centers. If necessary, larger diameter drains or angled drains may be used with approval of the SPM or SLE.

Bridge Standard Drawings
Rehabilitation, Surfacing & Widening - RHB/Cored Slab Drain for Existing Bridge Deck [RHB18]

751.40.6 Closure Pour

Note:

For closure pour on solid slab or voided slab bridges, use expansive concrete.

Release the forms before the closure pour is placed.


751.40 Closure Pour - Part Section Thru Roadway.gif


PART SECTION THRU ROADWAY


751.40.7 Design and Posting Considerations

Existing structures to redecked and/or widened should be evaluated to determine if the superstructure is considered to be structurally adequate. The structural adequacy check should be determined based on load ratings using the Load Factor Method. Strengthening of the superstructure will not be required if the minimum posting values shown below meet or exceed legal load requirements. In addition, there may be cases where the existing bridge posting is acceptable based on the bridge specific site conditions such as AADT, amount of truck traffic, overweight permit route, etc.


1) H20 (one lane with Impact) [Posting Rating] ≥ 23 tons
2) 3S2 (one lane with impact) [Posting Rating] ≥ 40 tons


Posting Rating = 86% of Load Factor Operating Rating (Refer to figures below for H20, 3S2 and MO5 criteria).

If a structure is located within a commercial zone, then the following additional posting condition must be investigated:

3) M05 (two lane with impact) [Operating Rating] ≥ 70 Tons (posting limit)

Any other overstresses or inadequacies (slab, substructure, etc.) shall be reported to the Structural Project Manager.

Deck thickness for redecks shall be determined such that Posting will not be required or the existing posting is not lowered, and it is generally not less than original deck thickness.

Deck thickness for widenings shall be existing thickness unless thicker slab does not create overall deck stiffening irregularities.

See Structural Project Manager if AASHTO minimum deck thickness can not be used on redecks and widenings.


Future Wearing Surface (FWS) Loadings for widenings with concrete wearing surfaces - In addition to weight of wearing surface:

Add FWS of 35 psf to the design of new girders if existing girders are sufficient for the 35 psf FWS
Lower FWS loading to 15 psf if existing girders are not sufficient for FWS loading of 35 psf
If existing girders are not sufficient for any FWS then lower FWS to FWS = 0.
The existing ratings should be reviewed to determine what wearing surface loads were used. When necessary, the rating should be evaluated for acceptability of the proposed changes in the wearing surface loads and geometry. Preliminary ratings that are based on estimated geometry shall be revised when the updated, final geometry is known.


751.40 Posting Rating (H20 Legal Truck).gif


751.40 Posting Rating (3S2 Truck).gif


751.40 Posting Rating (MO5 Truck).gif

751.40.8 Design Information when using AASHTO Standard Specifications for Highway Bridges 17th Edition

751.40.8.1 Loadings

751.40.8.1.1 Live Load

Structures shall be designed to carry the dead load, live load, impact (or dynamic effect of the live load), wind load and other forces, when they are applicable.

Members shall be designed with reference to service loads and allowable stresses as provided in AASHTO (17th edition) Service Load Design Method (Allowable Stress Design) or with reference to factored load and factored strength as provided in AASHTO Strength Design Method (Load Factor Design). Load groups represent various combination of loads and forces to which a structure may be subjected. Group loading combinations for Service Load Design and Load Factor Design are given by AASHTO (17th edition) 3.22.1 and AASHTO (17th edition) Table 3.22.1A.

The live load shall consist of the applied moving load of vehicles and pedestrians. The design live load to be used in the design of bridges for the state system will be as stated on the Bridge Memorandum.

  • The design truck: HS20-44 or HS20-44 Modified
  • The design tandem (Military)
  • The design lane loading


Criteria

  1. All widened or retrofitted bridges on the National Highway System and in commercial zones may be designed for HS20-44 Modified loading. All remaining bridges will be designed for HS20-44 loading.
  2. The Design Tandem loading is to be checked on national highway system or when Alternate Military loading appears on the Bridge Memorandum.
  3. Carrying members of each structure shall be investigated for the appropriate loading.
    • Main carrying members include:
      • Steel or Concrete stringers or girders.
      • Longitudinally reinforced concrete slabs supported on transverse floor beams or substructure units (includes hollow slabs).
      • Transversely reinforced concrete slabs supported by main carrying members parallel to traffic and over 8'-0" center to center. Use the formulas for moment in AASHTO Article 3.24.3.1 Case A.
      • Steel grid floors when the main elements of the grid extend in a direction parallel to traffic, or with main elements transverse to traffic on supports more than 8'-0" apart.
      • Timber floors and orthotropic steel decks.
  4. The reduction in live load for calculating substructure members is based on AASHTO 3.12.1. See Live Load Distribution in the Load Distribution Section.


HS20-44 Truck Loading

The HS20-44 truck is defined below as one 8 kip axle load and two 32 kip axle loads spaced as shown.

751.40 loadings-hs20-44 truck loading(side).gif


Varies = Variable spacing 14’ to 30’ inclusive. Spacing to be used is that which produces the maximum stresses.


751.40 loadings-hs20-44 truck loading(back).gif
HS20-44 Design Truck


(*) In the design of timber floors and orthotropic steel decks (excluding transverse beams) for H-20 Loading, one axle load of 24 kips or two axle loads of 16 kip each, spaced 4 feet apart may be used, whichever produces the greater stress, instead of the 32 kip axle load shown.

(**) For slab design, the center line of wheels shall be assumed to be one foot from face of cur


HS20-44 Modified Truck Loading

The HS20-44 Modified truck is defined below as one 10 kip axle load and two 40 kip axle loads spaced as shown. This is the same as HS20-44 truck modified by a factor of 1.25.

751.40 loadings-hs20-44 modified truck loading(side).gif


Varies = Variable spacing 14’ to 30’ inclusive. Spacing to be used is that which produces the maximum stresses.


751.40 loadings-hs20-44 modified truck loading(back).gif
HS20-44 Modified Design Truck


(*) For slab design, the center line of wheels shall be assumed to be one foot from face of curb.


Design Tandem Loading

The Design Tandem Loading is a two axle load each of 24 kips. These axles are spaced at 4'-0" centers. The transverse spacing of wheels shall be taken as 6'-0".

751.40 loadings-design tandem loading(plan view).gif
Design Tandem Loading - Plan View


Design Lane Loading

  • For HS20-44 Truck, the design lane load shall consist of a load 640 lbs per linear foot, uniformly distributed in the longitudinal direction with a single concentrated load (or two concentrated loads in case of continuous spans for determination of maximum negative moment), so placed on the span as to produce maximum stress. The concentrated load and uniform load shall be considered as uniformly distributed over a 10'-0" width on a line normal to the center line of the lane.
  • For HS20-44 Modified Truck, use the HS20-44 truck modified by a factor of 1.25.


751.40 loadings-design lane loading.gif
Design Lane Loading
  • For the design of continuous structures, an additional concentrated load is placed in another span to create the maximum effect. For positive moments, only one concentrated load is used, combined with as many spans loaded uniformly as are required to produce the maximum moment.


Standard Roadway Width

26'-0" (up to 2 traffic lanes)
28'-0" (up to 2 traffic lanes)
30'-0" (up to 3 traffic lanes)
32'-0" (up to 3 traffic lanes)
36'-0" (up to 3 traffic lanes)
38'-0" (up to 3 traffic lanes)
40'-0" (up to 4 traffic lanes)
44'-0" (up to 4 traffic lanes)

751.40.8.1.2 Impact

Highway live loads shall be increased by a factor given by the following formula:

  in feet

For continuous spans, to be used in this equation for negative moments is the average of two adjacent spans at an intermediate bent or the length of the end span at an end bent. For positive moments, is the span length from center to center of support for the span under consideration.

Impact is never to be more than 30 percent. It is intended that impact be included as part of the loads transferred from superstructure to substructure but not in loads transferred to footings or parts of substructure that are below the ground line. The design of neoprene bearing pads also does not include impact in the design loads.

751.40.8.1.3 Collision Force

Collision forces shall be applied to the barrier or railing in the design of the cantilever slab. A force of 10 kips is to be applied at the top of the standard barrier or railing. This force is distributed through the barrier or railing to the slab.

751.40.8.1.4 Centrifugal Force

Structures on curves shall be designed for a horizontal radial force equal to the following percentage of the live load in all the lanes, without impact.

Where:

= the centrifugal force in percent of the live load
= the design speed in miles per hour
= the radius of the curve in feet

This force shall be applied at 6 feet above the centerline of the roadway with one design truck being placed in each lane in a position to create the maximum effect. Lane loads shall not be used in calculating centrifugal forces.

The effects of superelevation shall be taken into account.

751.40.8.1.5 Lateral Earth Pressure

Structures which retain fills shall be designed for active earth pressures as

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, P_a} = active earth pressure per length (lb/ft)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \gamma} = unit weight of the back fill soil = 120 lb/ft³
= coefficient of active earth pressure as given by Rankine’s formula
= = equivalent fluid pressure (lb/ft³)(*)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, H} = height of the back fill soil (ft)


Rankine's Formula

The coefficient of active earth pressure is:

Where:

= angle of internal friction of the backfill soil (*)
= the angle of incline of the backfill

If the backfill surface is level, angle a is zero and is:

(*) Use the internal friction angle indicated on the Bridge Memorandum. However, if the friction angle is not determined, use the minimum equivalent fluid pressure value, , of 45 lb/ft³ for bridges and retaining walls. For box culverts use a maximum of 60 lb/ft³ and a minimum of 30 lb/ft³ for fluid pressure.


Live Load Surcharge

An additional earth pressure shall be applied to all structures which have live loads within a distance of half the structure height. This additional force shall be equal to adding 2'-0" of fill to that presently being retained by the structure.

751.40.8.1.6 Longitudinal Forces (Braking Forces)

A longitudinal force of 5% of the live load shall be applied to the structure. This load shall be 5% of the lane load plus the concentrated load for moment applied to all lanes and adjusted by the lane reduction factor. Apply this force at 6 feet above the top of slab and to be transmitted to the substructure through the superstructure.

751.40.8.1.7 Wind Load

Wind loads shall be applied to the structure regardless of length.

The pressure generated by wind load is:

Where:

= wind pressure in pounds per square foot
= design wind velocity = 100 miles per hour
= 0.004 for wind load

Basic wind load (pressure) = 0.004 x (100)² = 40 lb/ft²


Wind Load for Superstructure Design

Transverse

A wind load of the following intensity shall be applied horizontally at right angles to the longitudinal axis of the structure.

  • Trusses and Arches = 75 pounds per square foot =
  • Girders and Beams = 50 pounds per square foot (*) = (for plate girder lateral bracing check only)
  • The total force shall not be less than 300 pounds per linear foot in the plane of windward chord and 150 pounds per linear foot in the plane of the leeward chord on truss spans, and not less than 300 pounds per linear foot on girder spans.


Wind Load for Substructure Design

Forces transmitted to the substructure by the superstructure and forces applied directly to the substructure by wind load shall be as follows:


Forces from Superstructure: Wind on Superstructure

Transverse

A wind load of the following intensity shall be applied horizontally at right angles to the longitudinal axis of the structure.

  • Trusses and Arches = 75 pounds per square foot =
  • Girders and Beams = 50 pounds per square foot (*) =


(*) Use Wt = 60 lbs/ft² for design wind force on girders and beams If the column height on a structure is greater than 50 feet, where the height is the average column length from ground line to bottom of beam.

The transverse wind force for a bent will be:

Where:

= length in feet = the average of two adjacent spans for intermediate bents and half of the length of the end span for end bents.
= the total height of the girders, slab, barrier or raling and any superelevation of the roadway, in feet
= wind force per unit area in pounds per square foot

This transverse wind force will be applied at the top of the beam cap for the design of the substructure.


Longitudinal (**)

The standard wind force in the longitudinal direction shall be applied as a percentage of the transverse loading. Use approximately 25%.

Truss and Arch Structures = 75 x 0.25 = approximately 20 lbs/ft²
Girder Structures = 50 x 0.25 = approximately 12 lbs/ft²

The total longitudinal wind force will be:

Where:

= the overall bridge length in feet
= the total height of the girders, slab, barrier or railing and anysuperelevation of the roadway, in feet
= wind force per unit area in pounds per square foot

This longitudinal force is distributed to the bents based on their stiffness. (**)

The longitudinal wind force for the bent will be applied at the top of the beam cap for the design of the substructure.


Forces from Superstructure: Wind on Live Load

A force of 100 pounds per linear foot of the structure shall be applied transversely to the structure along with a force of 40 pounds per linear foot longitudinally. These forces are assumed to act 6 feet above the top of slab. The transverse force is applied at the bents based on the length of the adjacent spans affecting them. The longitudinal force is distributed to the bents based on their stiffness. (**)

(**) See EPG 751.2.4.6 Longitudinal Wind Force Distribution.


Forces Applied Directly to the Substructure

The transverse and longitudinal forces to be applied directly to the substructure elements shall be calculated from an assumed basic wind force of 40 lbs/ft². This wind force per unit area shall be multiplied by the exposed area of each substructure member in elevation (use front view for longitudinal force and side view for transversely force, respectively). These forces are acting at the center of gravity of the exposed portion of the member.

A shape factor of 0.7 shall be used in applying wind forces to round substructure members.

When unusual conditions of terrain or the special nature of a structure indicates, a procedure other than the Standard Specification may be used subject to approval of the Structural Project Manager.

751.40.8.1.8 Temperature Forces

Temperature stresses or movement need to be checked on all structures regardless of length. Generation of longitudinal temperature forces is based on stiffness of the substructure. (*)

Coefficients

Steel: Thermal - 0.0000065 ft/ft/°F
Concrete: Thermal - 0.0000060 ft/ft/°F
  Shrinkage - 0.0002 ft/ft (***)
  Friction - 0.65 for concrete on concrete


Temperature Range From 60° F (**)
  Rise Fall Range
Steel Structures 60°F 80°F 140°F
Concrete Structures 30°F 40°F 70°F


(*) See EPG 751.2.4.7 Longitudinal Temperature Force Distribution.

(**) Temperature Range for expansion bearing design and expansion devices design see EPG 751.11 Bearings and EPG 751.13 Expansion Devices, respectively.

(***) When calculating substructure forces of concrete slab bridges, the forces caused by the shrinkage of the superstructure should be included with forces due to temperature drop. This force can be ignored for most other types of bridges.

751.40.8.1.9 Sidewalk Loading

Sidewalk floors and their immediate support members shall be designed for a live load of 85 pounds per square foot of sidewalk area. Girders, trusses, and other members shall be design for the following sidewalk live load:

Spans 0 to 25 feet 85 lbs/ft²
Spans 26 to 100 feet 60 lbs/ft²
Spans over 100 feet use the following formula

Where:

= live load per square foot, max. 60 lbs/ft²
= loaded length of sidewalk in feet
= width of sidewalk in feet

When sidewalk live loads are applied along with live load and impact, if the structure is to be designed by service loads, the allowable stress in the outside beam or stringer may be increased by 25 percent as long as the member is at least as strong as if it were not designed for the additional sidewalk load using the initial allowable stress. When the combination of sidewalk live load and traffic live load plus impact governs the design under the load factor method, use a b factor of 1.25 instead of 1.67.

Unless a more exact analysis can be performed, distribution of sidewalk live loads to the supporting stringers shall be considered as applied 75 percent to the exterior stringer and 25 percent to the next stringer.

751.40.8.1.10 Other Loads

Stream Pressure

Stream flow pressure shall be considered only in extreme cases. The affect of flowing water on piers shall not be considered except in cases of extreme high water and when the load applied to substructure elements is greater than that which is applied by wind on substructure forces at low water elevations.

The pressure generated by stream flow is:

Where:

= stream pressure in pounds per square foot
= design velocity of water in feet per second
= shape constant for the surface the water is in contact with.
= 1.4 for square-ended piers
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, K} = 0.7 for circular piers
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, K} = 0.5 for angle-ended piers where the angle is 30 degrees or less


Ice Forces

Ice forces on piers shall be applied if they are indicated on the Bridge Memorandum.


Buoyancy

Buoyancy shall be considered when its effects are appreciable.


Fatigue in Structural Steel

Steel structures subjected to continuous reversal of loads are to be designed for fatigue loading.


Prestressing

See EPG 751.22 P/S Concrete I Girders.


Other Loads

Other loads may need to be applied if they are indicated on the Bridge Memorandum. Otherwise see Structural Project Manager before applying any additional loads.

751.40.8.1.11 Group Loads

Group Loading (Service Load Design)

Group loading combinations are:

GP I SL Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = D+L+I} 100%
GP II SL Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = D+W} 125%
GP III SL Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = D+L+I+0.3W+WL+LF} 125%
GP IV SL Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = D+L+I+T} 125%
GP V SL 140%
GP VI SL Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = D+L+I+0.3W+WL+LF+T} 140%

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, D} = dead load
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L} = live load
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, I} = live load impact
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, W} = wind load on structure
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, WL} = wind load on live load
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, T} = temperature force
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, LF} = longitudinal force from live load


Group Loading (Load Factor Design)

Group loading combinations are:

GP I LF Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = 1.3[\beta_d D+1.67 (L+I)]}
GP II LF Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = 1.3[\beta_d D+W]}
GP III LF Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = 1.3[\beta_d D+L+I+0.3W+WL+LF]}
GP IV LF Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = 1.3[\beta_d D+L+I+T]}
GP V LF Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = 1.25[\beta_d D+W+T]}
GP VI LF Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = 1.25[\beta_d D+L+I +0.3W+WL+LF+T]}

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, D} = dead load
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L} = live load
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, I} = live load impact
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, W} = wind load on structure
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, WL} = wind load on live load
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, T} = temperature force
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, LF} = longitudinal force from live load
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \beta_d} = coefficient, see AASHTO Table 3.22.1A


Other group loadings in AASHTO Table 3.22.1A shall be used when they apply.

751.40.8.2 Distribution of Loads

751.40.8.2.1 Distribution of Dead Load

Composite Steel or Prestressed Concrete Structures

The dead load applied to the girders through the slab shall be:


Dead Load 1

Non-composite dead loads should be distributed to girders (stringers) on the basis of continuous spans over simple supports.

Dead Load 2

Composite loads shall be distributed equally to all girders. The following are all Dead Load 2 loads:

Barrier or railing
Future wearing surface on slab
Sidewalks
Fences
Protective coatings and waterproofing on slab


Concrete Slab Bridges

Distribute entire dead load across full width of slab.

For longitudinal design, heavier portions of the slab may be considered as concentrated load for entry into the "Continuous Structure Analysis" computer program.

For transverse bent design, consider the dead load reaction at the bent to be a uniform load across entire length of the transverse beam.

751.40.8.2.2 Distribution of Live Load

Live loading to be distributed shall be the appropriate loading shown on the Bridge Memorandum. Applying Live Load to Structure


Superstructure

For application of live load to superstructure, the lane width is considered 12 feet. Each design vehicle has wheel lines which are 6 feet apart and adjacent design vehicles must be separated by 4 feet.


Substructure

To produce the maximum stresses in the main carrying members of substructure elements, multiple lanes are to be loaded simultaneously. The lane width is 12 feet. Partial lanes are not to be considered. Due to the improbability of coincident maximum loading, a reduction factor is applied to the number of lanes. This reduction however, is not applied in determining the distribution of loads to the stringers.


Distribution of Live Load to Beams and Girders
Number of Lanes Percent
one or two lanes 100
three lanes 90
four lanes or more 75


Moment Distribution

Moments due to live loads shall not be distributed longitudinally. Lateral distribution shall be determined from AASHTO Table 3.23.1 for interior stringers. Outside stringers distribute live load assuming the flooring to act as a simple span, except in the case of a span with a concrete floor supported by four or more stringers, then AASHTO 3.23.2.3.1.5 shall be applied. In no case shall an exterior stringer have less carrying capacity than an interior stringer.


Shear Distribution

As with live load moment, the reactions to the live load are not to be distributed longitudinally. Lateral distribution of live load shall be that produced by assuming the flooring to act as simply supported. Wheel lines shall be spaced on accordance with AASHTO 3.7.6 and shall be placed in a fashion which provides the most contribution to the girder under investigation, regardless of lane configuration. The shear distribution factor at bents shall be used to design bearings and bearing stiffeners.


Deflection Distribution

Deflection due to live loads shall not be distributed longitudinally. Lateral distribution shall be determined by averaging the moment distribution factor and the number of wheel lines divided by the number of girder lines for all girders. The number of wheel lines shall be based on 12 foot lanes. The reduction in load intensity (AASHTO Article 3.12.1) shall not be applied.

Deflection Distribution Factor =   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \cfrac {\big\{ \frac{2n}{N} \big\} + MDF}{2}}

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, n} = number of whole 12 foot lanes on the roadway
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, N} = number of girder lines;
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, MDF} = Moment Distribution Factor.


Example: 38'-0" Roadway (Interior Girder),   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, n=3} ,   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, N=5} ,   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, MDF=1.576}

Deflection Distribution Factor =   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \cfrac {\big\{ \frac{2 \times 3lanes}{5 girders} \big\} + 1.576}{2} = 1.388}


Live Load Distribution Factors for Standard Roadway Widths
Roadway
Width
Number
Girders
Girder
Spacing
Exterior Girder Interior Girder (1)
Mom. Shear Defl. Mom. Shear Defl.
26’-0” 4 7’-6” 1.277 1.133 1.139 1.364 1.667 1.182 1.071
28’-0” 4 8’-2” 1.352 1.204 1.176 1.485 1.776 1.243 1.167
30’-0” 4 8’-8” 1.405 1.308 1.453 1.576 1.846 1.538 1.238
32’-0” 4 9’-2” 1.457 1.400 1.479 1.667 1.909 1.584 1.310
36’-0” 5 8’-2” 1.352 1.184 1.276 1.485 1.776 1.343 1.167
38’-0” 5 8’-8” 1.405 1.231 1.303 1.576 1.846 1.388 1.238
40’-0” 5 9’-0” 1.440 1.333 1.520 1.636 1.889 1.618 1.286
44’-0” 5 9’-9” 1.515 1.487 1.558 1.773 1.974 1.687 1.393
(1) Use when checking interior girder moment cyclical loading Case I Fatigue for one lane loading.


Distribution of Live Load to Substructure

For substructure design the live load wheel lines shall be positioned on the slab to produce maximum moments and shears in the substructure. The wheel lines shall be distributed to the stringers on the basis of simple spans between stringers. The number of wheel lines used for substructure design shall be based on 12 foot lanes and shall not exceed the number of lanes times two with the appropriate percentage reduction for multiple lanes where applicable.

In computing these stresses generated by the lane loading, each 12 foot lane shall be considered a unit. Fractional units shall not be considered.


Distribution of Loads to Slabs

For simple spans, the span length shall be the distance center to center of supports but need not be greater than the clear distance plus the thickness of the slab. Slabs for girder and floor beam structures should be designed as supported on four sides.

For continuous spans on steel stringers or on thin flanged prestressed beams (top flange width to thickness ratios > 4.0), the span length shall be the distance between edges of top flanges plus one quarter of each top flange width. When the top flange width to thickness is < 4.0 the span distance shall be the clear span between edges of the top flanges.

When designing the slab for live load, the wheel line shall be placed 1 foot from the face of the barrier or railing if it produces a greater moment.


Bending Moments in Slab on Girders

The load distributed to the stringers shall be:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \Bigg( \frac {S + 2}{32} \Bigg) }   P20 or P25 = Moment in foot-pounds per-foot width of slab.

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, S} = effective span length between girders in feet
P20 or P25 = wheel line load for HS20 or HS20 Modified design Truck in kips.

For slabs continuous over 3 or more supports, a continuity factor of 0.8 shall be applied.


Main Reinforcement Parallel to Traffic

This distribution may be applied to special structure types when its use is indicated.


Distribution of Live Load to Concrete Slab Bridges

Live load for transverse beam, column and pile cap design shall be applied as concentrated loads of one wheel line. The number of wheel lines used shall not exceed the number of lanes x 2 with the appropriate reduction where applicable.

For slab longitudinal reinforcement design, use live load moment distribution factor of 1/E for a one-foot strip slab with the appropriate percentage reduction.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, E = 4' + 0.06S, E (max.) = 7'}

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, E} = Width of slab in feet over which a wheel is distributed
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, S} = Effective span length in feet.

For slab deflection, use the following deflection factor for a one-foot strip slab without applying percentage reduction.

Deflection Factor = (Total number of wheel line) / (width of the slab)

751.40.8.2.3 Frictional Resistance

The frictional resistance varies with different surfaces making contact. In the design of bearings, this resistance will alter how the longitudinal forces are distributed. The following table lists commonly encountered materials and their coefficients. These coefficients may be used to calculate the frictional resistance at each bent.

Frictional Resistance of Expansion Bearings
Bearing Type Coef. General Data
Type C Bearing 0.14 Coef. of sliding friction
steel to steel = 0.14


Coef. for pin and rocker
type bearing =

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \frac {0.14 (Radius\ of\ pin)}{Radius\ of\ Rocker}}


Frictional Force =
Reaction x Coef.

6” Diameter Roller 0.01
Type D Bearing  
Pin Diameter Rocker Radius  
2” 6.5” 0.0216
2” 7” 0.0200
2” 7.5” 0.0187
2” 8” 0.0175
2” 10.5” 0.0133
PTFE Bearing 0.0600


The design of a bent with one of the above expansion bearings will be based on the maximum amount of load the bearing can resist by static friction. When this static friction is overcome, the longitudinal forces are redistributed to the other bents.

The maximum static frictional force at a bent is equal to the sum of the forces in each of the bearings. The vertical reaction used to calculate this maximum static frictional force shall be Dead Loads only for all loading cases. Since the maximum longitudinal load that can be experienced by any of the above bearings is the maximum static frictional force, the effects of longitudinal wind and temperature can not be cumulative if their sum is greater than this maximum static frictional force.

Two conditions for the bents of the bridge are to be evaluated.

  1. Consider the expansion bents to be fixed and the longitudinal loads distributed to all of the bents.
  2. When the longitudinal loads at the expansion bearings are greater than the static frictional force, then the longitudinal force of the expansion bearings is equal to the dynamic frictional force. It is conservative to assume the dynamic frictional force to be zero causing all longitudinal loads to be distributed to the remaining bents.

751.40.8.3 Unit Stresses

751.40.8.3.1 Fatigue in Structural Steel

Steel structures subjected to continuous reversal of loads are to be designed for fatigue loading.

AADTT, annual average daily truck traffic (one direction), shall be indicated on the Bridge Memorandum. Based on AADTT, the fatigue case and corresponding stress cycles can be obtained from AASHTO Table 10.3.2A.

When Case I fatigue is considered, it is necessary to check fatigue due to truck loading for both the 2,000,000 and over 2,000,000 stress cycles. For the over 2,000,000 stress cycles, the moment distribution factor for all stringers or girders (for fatigue stresses only) will be based on one lane loaded. For truck loading 2,000,000 cycles and lane loading 500,000 cycles, use the moment distribution factor based on two or more traffic lanes (same as for design moment).

The number of cycles to be used in the fatigue design is dependent on the case number and type of load producing maximum stress as indicated in AASHTO Table 10.3.2A. The allowable fatigue stress range based on the fatigue stress cycles can be obtained from AASHTO Table 10.3.1A.

The type of live load used to determine the number of cycles will be the type of loading used to determine the maximum stress at the point under consideration.

In continuous beams, the maximum stresses may be produced by the truck loading at some points, but by lane loading at other points. However, if the lane loading governs, then the longitudinal members should also be checked for truck loading.

Only live loading and impact stresses need to be considered when designing for fatigue.

Fatigue criteria applies only when the stress range is one of tension to tension or reversal. The fatigue criteria does not apply to the stress range from compression to compression.

All fracture critical structures, those which consist of only one or two main carrying members, trusses or single box girders, shall be considered as Non-redundant structures. Use the appropriate table which accompanies these structures.

751.40.8.3.2 Reinforced Concrete

Allowable Stresses of Reinforcing Steel

Tensile stress in reinforcement at service loads, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} :

Concrete
Reinforcing Steel (Grade 40) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 20,000 psi
Reinforcing Steel (Grade 60) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 24,000 psi

For compression stress in beams, see AASHTO Article 8.15.3.5.

For compression stress in columns, see AASHTO Article 8.15.4.

For fatigue stress limit, see AASHTO Article 8.16.8.3.

Fatigue in Reinforcing Steel

For flexural members designed with reference to load factors and strengths by Strength Design Method, stresses at service load shall be limited to satisfy the requirements for fatigue. Reinforcement should be checked for fatigue at all locations of peak service load stress ranges and at bar cut-off locations except for concrete deck slab in multi-girder applications.


Allowable Stress Range: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, fr_{allow}}

The allowable stress range is found using the equation listed below and the minimum stresses from dead load, live load, and impact based on service loads.

The term minimum stress level fmin for this formula indicates the algebraic minimum stress level: tension stress with a positive sign and compression stress with a negative sign.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, fr_{allow} = 21 - 0.33 f_{min} + 8(r/h)}

Where:

= allowable stress range (ksi)
= algebraic minimum stress level ksi):
  positive if tension, negative if compression.
= ratio of base radius to height of rolled-on transverse deformation; if the actual value is not know, 0.3 may be used.
=     when

Fatigue research has shown that increasing minimum tensile stress results in a decrease in fatigue strength for a tension to tension stresses case. The fatigue strength increases with a bigger compressive stress in a tension to compression stresses case.


Actual Stress Range:

The actual stress range, , is found using dead load, live load, and impact from service loads.

=
= greatest tension stress level (ksi), always positive.
  (Not necessary to check compression to compression for fatigue.)
= algebraic least stress level (ksi):
  = positive if the least stress is tension
    (tension to tension stresses)
  = negative if the least stress is compression
    (tension to compression stresses)


Tension and Compression Stress Computation

Tension and compression stress are determined by using the following formulae for double reinforced concrete rectangular beams.

= tensile stress in reinforcement at service loads (ksi)

Tensile stress  

= compressive stress in reinforcement at service loads (ksi)

Compressive stress  

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, j = \cfrac {k^2 \Big( 1 - \frac {k}{c} \Big) + 2 \rho'n \Big( k - \frac {d'}{d} \Big) \Big( 1 - \frac {d'}{d} \Big)}{k^2 + 2 \rho'n \Big( k - \frac {d'}{d} \Big)}}      Eq. 2.2-1


Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, k = \sqrt{2n \Bigg( \rho + \rho' \Bigg( \frac{d'}{d}\Bigg) \Bigg) + n^2 \big( \rho + \rho' \big)^2 - n \big( \rho + \rho' \big)}}      Eq. 2.2-2


Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \rho} = tension reinforcement ratio,   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \rho = \frac{A_s}{bd}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \rho'} = compression reinforcement ratio,   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \rho' = \frac{A'_s}{bd}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, A_s} = area of tension reinforcement (sq. inch)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, A'_s} = area of compression reinforcement (sq. inch)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, b} = width of beam (inch)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, d} = distance from extreme compression fiber to centroid of tension reinforcement (inch)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, d'} = distance from extreme compression fiber to centroid of compression reinforcement (inch)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, jd} = distance from tensile steel to resultant compression (inch)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, kd} = distance from neutral plane to compression surface (inch)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, n} = ratio of modulus of elasticity of steel to that of concrete

751.40.8.4 Standard Details

751.40.8.4.1 Welding Details

All welding shall be detailed in accordance with ANSI / AASHTO / AWS D1.5, Bridge Welding Code.

For ASTM A709, Grade 36 steel (Service Load Design Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_u} = 58,000 psi) the allowable shear stress in fillet welds (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_V} ) is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_V = 0.27 F_u}

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_V} = allowable basic shear stress
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_u} = tensile strength of the electrode classification but not greater than the tensile strength of the connected part


Allowable Shear Loads for Fillet Welds (*)
Size of Fillet Weld
(Inch)
Allowable Shear Loads per Length
(Pound per lineal inch)
1/8” 1,380
3/16” 2,075
1/4" 2,770
5/16” 3,460
3/8” 4,150
1/2" 5,535
5/8” 6,920
3/4" 8,300
7/8” 9,690
1” 11,070


(*) Allowable Shear Load = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (0.27)(58000 psi)(0.707xSize of Weld)(L)}

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L} = Effective Length, in inch
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (0.707xSize of Weld)} = Effective Throat, in inch
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (0.707xSize of Weld)(L)} = Effective weld area in sq. inch

751.40.8.4.2 Development and splicing of Reinforcement

751.40.8.4.2.1 General

Development of Tension Reinforcement

Development lengths for tension reinforcement shall be calculated in accordance with AASHTO Article 8.25. Development length modification factors described in AASHTO Articles 8.25.3.2 and 8.25.3.3 shall only be used in situations where development length without these factors is difficult to attain. All other modification factors shown shall be used.

Development lengths for tension reinforcement have been tabulated on the following pages and include the modification factors except those described above.


Lap Splices of Tension Reinforcement

Lap splices of reinforcement in tension shall be calculated in accordance with AASHTO Article 8.32.1 and 8.32.3. Class C splices are preferred when possible, however it is permissible to use Class A or B when physical space is limited. The designer shall satisfy AASHTO Table 8.32.3.2 when using Class A or B splices. It should be noted that As required is based on the stress encountered at the splice location, which is not necessarily the maximum stress used to design the reinforcement.

Temperature and shrinkage reinforcement is assumed to fully develop the specified yield stresses. Therefore the development length shall not be reduced by (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, A_s} required)/(Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, A_s} supplied).

Splice lengths for tension reinforcement have been tabulated on the following pages and include the development length modifications as described above.


Development of Tension Hooks

Development of tension hooks shall be calculated in accordance with AASHTO Article 8.29. Hook length modification factors described in Articles 8.29.3.3 and 8.29.3.4 shall only be used in situations where hook length without these factors is difficult to attain. All other modification factors shown shall be used.

Development lengths of tension hooks have been tabulated on the following pages and include the modification factors except those described above.


Development of Compression Reinforcement

Development lengths for compression reinforcement shall be calculated in accordance with AASHTO Article 8.26. Development length modification factors described in AASHTO Articles 8.26.2.1 and 8.26.2.2 shall only be used in situations where development length without these factors is difficult to attain. All other modification factors shown shall be used.

Development lengths for compression reinforcement have been tabulated on the following pages and include the modification factors except those described above.


Lap Splices of Compression Reinforcement

Lap splices of reinforcement in compression shall be calculated in accordance with AASHTO Article 8.32.1 and 8.32.4.

Splice lengths for compression reinforcement have been tabulated on the following pages.


Mechanical Bar Splices

Mechanical bar splices may be used in situations where it is not possible or feasible to use lap splices. Mechanical bar splices shall meet the criteria of AASHTO Article 8.32.2. Refer to the manufacturers literature for more information on the design of mechanical bar splices.

751.40.8.4.2.2 Development and Tension Lap Splice Lengths - Top Bars (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_y} = 60 ksi)
751.40 reinforcement- Development and Tension Lap Splice Lengths - Top Bars (Fy = 60 ksi).gif


Top reinforcement is placed so that more than 12” of concrete is cast below the reinforcement.

Class A splice =1.0 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L_d} , Class B splice =1.3 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L_d} , Class C splice =1.7 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L_d}

Use development and tension lap splices of = 4 ksi for concrete strengths greater than 4 ksi.

751.40.8.4.2.3 Development and Tension Lap Splice Lengths - Other Than Top Bars (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_y} = 60 ksi)
751.40 reinforcement- Development and Tension Lap Splice Lengths - Other Than Top Bars (Fy = 60 ksi).gif


Class A splice =1.0 , Class B splice =1.3 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L_d} , Class C splice =1.7 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L_d}

Use development and tension lap splices of = 4 ksi for concrete strengths greater than 4 ksi.

751.40.8.4.2.4 Development and Lap Splice Lengths - Bars in Compression ( = 60 ksi)
751.40 reinforcement- Development and Lap Splice Lengths - Bars in Compression (Fy = 60 ksi).gif


Development length for spirals, , , should be used if reinforcement is enclosed in a spiral of not less than 1/4” diameter and no more than 4” pitch. See AASHTO 8.26 for special conditions.

All values are for splices with the same size bars. For different size bars, see AASHTO 8.32.4.

(*) Lap splices for #14 and #18 bars are not permitted except as column to footing dowels.

751.40.8.4.2.5 Development of Standard Hooks in Tension, Ldh ( = 60 ksi)

The development length, , is measured from the critical section to the outside edge of hook. The tabulated values are valid for both epoxy and uncoated hooks.


751.40 reinforcement- Development of Standard Hooks in Tension, Ldh (Fy = 60 ksi).gif


Case A - For #11 bar and smaller, side cover (normal to plane of hook) less than 2 1/2 inches and for a 90 degree hook with cover on the hook extension less than 2 inches.

Case B - For #11 bar and smaller, side cover (normal to plane of hook) greater than 2 1/2 inches and for a 90-dgree hook with cover on the hook extension 2 inches or greater.

(*) See Structural Project Manager before using #14 or #18 hook.

751.40 reinforcement-DETAIL NEAR FREE EDGE OR CONSTRUCTION JOINT.gif   751.40 reinforcement- HOOKED-BAR DETAILS FOR DEVELOPMENT OF STANDARD HOOKS.gif
(1) = (#3 thru #8)
(1) = (#9, #10 and #11)
(1) = (#14 and #18)
DETAILS NEAR FREE EDGE
OR CONSTRUCTION JOINT
  HOOKED-BAR DETAILS FOR
DEVELOPMENT OF STANDARD HOOKS
751.40.8.4.2.6 Development of Uncoated Grade 40 Deformed Bars in Tension, (AASHTO 8.25)
Bars spaced laterally less than 6 inches on center or less than 3 inches concrete cover in direction of the spacing
Bar = 3 ksi = 4 ksi = 5 ksi
Top bar Top bar Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L_d} Top bar
#3 12 12 12 12 12 12
#4 12 12 12 12 12 12
#5 12 14 12 14 12 14
#6 13 19 12 17 12 17
#7 18 25 16 22 14 20
#8 23 33 20 28 18 25
#9 30 41 26 36 23 32
#10 38 52 33 45 29 41
#11 46 64 40 56 36 50
#14 63 87 54 76 49 68
#18 81 113 70 98 63 88


Bars spaced laterally 6 inches or more on center and at least 3 inches concrete cover in direction of the spacing
Bar = 3 ksi = 4 ksi = 5 ksi
Top bar Top bar Top bar
#3 12 12 12 12 12 12
#4 12 12 12 12 12 12
#5 12 12 12 12 12 12
#6 12 15 12 14 12 14
#7 15 20 13 18 12 16
#8 19 26 16 23 15 20
#9 24 33 21 29 19 26
#10 30 42 26 36 23 33
#11 37 52 32 45 29 40
#14 50 70 44 61 39 54
#18 65 90 56 78 50 70
751.40.8.4.2.7 Minimum lap length for uncoated Grade 40 tension lap splices, (AASHTO 8.32)
Bars spaced less than 6 inches laterally on center and at least 3 inches concrete cover in direction of the spacing
  Other than Top Bars Top Bars
= 3 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'_c} = 4 ksi = 5 ksi = 3 ksi = 4 ksi = 5 ksi
Bar A B C A B C A B C A B C A B C A B C
#3 12 12 12 12 12 12 12 12 12 12 16 21 12 16 21 12 16 21
#4 12 12 14 12 12 14 12 12 14 12 16 21 12 16 21 12 16 21
#5 12 13 17 12 13 17 12 13 17 14 19 24 14 19 24 14 19 24
#6 13 17 22 12 16 21 12 16 21 19 24 31 17 22 29 17 22 29
#7 18 23 30 16 20 26 14 19 24 25 32 42 22 28 37 20 26 34
#8 23 30 40 20 26 34 18 24 31 33 42 55 28 37 48 25 33 43
#9 30 38 50 26 33 43 23 30 39 41 54 70 36 47 61 32 42 54
#10 38 49 63 33 42 55 29 38 49 52 68 89 45 59 77 41 53 69
#11 46 60 78 40 52 68 36 46 61 64 84 109 56 72 95 50 65 85


Bars spaced 6 inches or more laterally on center and at least 3 inches concrete cover in direction of the spacing
  Other than Top Bars Top Bars
= 3 ksi = 4 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'_c} = 5 ksi = 3 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'_c} = 4 ksi = 5 ksi
Bar A B C A B C A B C A B C A B C A B C
#3 12 12 12 12 12 12 12 12 12 12 16 21 12 16 21 12 16 21
#4 12 12 12 12 12 12 12 12 12 12 16 21 12 16 21 12 16 21
#5 12 12 14 12 12 14 12 12 14 12 16 21 12 16 21 12 16 21
#6 12 14 18 12 13 17 12 13 17 15 19 25 14 18 23 14 18 23
#7 15 19 24 13 16 21 12 15 20 20 26 34 18 23 29 16 21 27
#8 19 24 32 16 21 28 15 19 25 26 34 44 23 29 38 20 26 34
#9 24 31 40 21 27 35 19 24 31 33 43 56 29 37 49 26 33 44
#10 30 39 51 26 34 44 23 30 39 42 54 71 36 47 62 33 42 55
#11 37 48 63 32 42 54 29 37 49 52 67 87 45 58 76 40 52 68

751.40.8.4.3 Miscellaneous

Negative Moment Steel over Intermediate Supports

Dimension negative moment steel over intermediate supports as shown.

751.40 reinforcement-Negative Moment Steel over Intermediate Supports.gif
Prestressed Structures:
(1) Bar length by design.
(2) Reinforcement placed between longitudinal temperature reinforcing in top.
Bar size: #5 bars at 7-1/2" cts. (Min.)
  #8 bars at 5" cts. (Max.)
Steel Structures:
(1) Extend into positive moment region beyond "Anchor" Stud shear connectors at least 40 x bar diameter x 1.5 (Epoxy Coated Factor)(*) as shown below. (AASHTO 10.38.4.4 & AASHTO 8.25.2.3)
(2) Use #6 bars at 5" cts. between longitudinal temperature reinforcing in top.
751.40 reinforcement-elevation of girder showning negative moment steel.gif
(*) 40 x bar diameter x 1.5 = 40 x 0.75" x 1.5 = 45” for #6 epoxy coated bar.

751.40.8.5 General Superstructure

751.40.8.5.1 Concrete Slabs

751.40.8.5.1.1 Design Criteria

Slabs on Girders

Stresses:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_c} = 1,600 psi
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'_c} = 4,000 psi
= 8
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 60,000 psi


Moments Over Interior Support (Use for positive moment reinf. also) (Sec. 1.5 E40A)

Dead Load = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, -0.107wS^2} (Continuous over 5 supports)
Dead Load = (Continuous over 4 supports)
Live Load = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (S + 2) \frac {P}{32}}   Continuity Factor = 0.8
      Impact Factor = 1.3
      P = 16 Kips for HS20
      P = 20 Kips for HS20 Modified
 
Design Load:   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, M_u = 1.3 (M_{DL} + 1.67 M_{LL+I})}

Cantilever Moment

Dead Load = Moment due to slab, F.W.S. and S.B.C.

Live Load:

Wheel Load =   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, M_{LL=I} = \frac {Px}{E}}

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, P} = Wheel load (apply impact factor)
= Distance from load to support (ft.)
=


Collision Load =  

Where:

= 10 kips (Collision force)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, y} = Moment arm (Curb ht.+ 1/2 Slab th.)
=


Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, x} = Distance from center of gravity of barrier to support


The "support" is assumed at the 1/4 point of the minimum flange. 751.40.8.5.1.1 slab cantilever.jpg
Wheel loads and collision loads shall not be applied simultaneously.
Use the greater of the two for the Design Load.
Design Load:<br./>Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, M_u = 1.3 (M_{DL} + 1.67 M_{LL+I})}
  Slab Cantilever Section

Design of top reinforcement is based on maximum moment over supports or cantilever moment. Flexural reinforcement shall meet the criteria of AASHTO Art. 8.16.3.

When designing for bottom transverse reinforcement, a 1" wearing surface is removed from the effective depth.

Prestressed panels replace the bottom transverse reinforcement.

Prestressed panels are assumed to carry DL1 stresses. Therefore, the negative moment due to DL1 at interior supports may be neglected.

The maximum P/S panel width (clear span + 6") for HS20 Modified is 9'-6". (Based on 10'-0" girder spacing and 10" flanges) The maximum P/S panel width (clear span + 6") for HS20 is 9'-11".


Distribution of Flexural Reinforcement

Allowable Stress:   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s = \frac {Z}{(d_c \times A)^{1/3}} \le 0.6 f_y}

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Z} = 130 k/in.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, d_c} = Dist. from extreme tension fiber to center of closest bar (concrete cover shalll not be taken greater than 2")
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, A} = Effective tension area of concrete
  = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 2d_c s}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, s} = Bar spacing ctr. to ctr.


Actual Stress:   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s = \frac {M_W}{A_S \times j \times d}}

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, M_W} = Service load moment
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, A_S} = Area of steel
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, j} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 1 - k/3}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, k} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \sqrt {2n\rho + (n \rho)^2 - n \rho}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, n} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, E_S/E_C}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \rho} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, A_S /(b \times d)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, b} = Effective width
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, d} = Effective depth

Distribution of flexural reinforcement does not need to be checked in concrete considered unexposed to weather.


Longitudinal distribution reinforcement:

Top of slab - use #5 bars at 15" cts. for temperature distribution.

Bottom of slab - by design.


Negative moment reinforcement over supports:

Steel structures - add. #6 bars at 5" between #5 bars.

P/S girder structures - by design.

Additional reinforcement over supports shall be a minimum of #5 bars and a maximum of #8 bars at 5" ctrs. When necessary, replace the #5 temperature reinforcement with a larger bar to satisfy negative moment reinforcement requirement, but keep all bars within two bar sizes.

Note: See details of negative moment reinforcement.


751.40 general superstructure-sections thru slab showing negative moment reinforcement.gif
CIP Slab P\S Panel Slab
751.40 circled 1.gif 3" Cl. preferred min., 2 3/4" Cl. preferred min. for P/S panels to accommodate #8 bars over supports and 2 1/2" Cl. absolute min. by AASHTO 8.22.1.

Method of measurement:

The area of the concrete slab shall be measured and computed to the nearest square yard. This area shall be measured transversely from out to out of slab and longitudinally from end to end of bridge slab.


Precast Prestressed Panels

3" Precast prestressed concrete panels with 5-1/2" minimum cast-in-place concrete will be the standard slab used on all girder superstructures except curved steel structures.

Concrete for prestressed panels shall be Class A1 with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'{c}} = 6,000 psi, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'_{ci}} = 3,500 psi. Prestressing tendons shall be uncoated, low-relaxation, seven-wire(7) strands for prestressed concrete conforming to AASHTO M203 Grade 270, with nominal diameter of strand = 3/8" and area = 0.085 sq.in., minimum ultimate strength = 22.95 kips (270 ksi), and strand spacing = 4.5 inches.

Panels shall be set on joint filler or polystyrene bedding material. Filler thickness shall be a Min. of 3/4" and a Max. of 2". Standard filler width is 1 1/2" except at splice plates where 3/4" Min. is allowed to clear splice bolts. Joint filler thickness may be reduced to a minimum of 1/4" over splice plates on steel structures. For prestressed girder structures, joint filler thickness may be varied within these limits to offset girder camber or at the contractor's option a uniform 3/4" (Min.) thickness may be used throughout. The same thickness shall be used under any one edge of any panel and the maximum change in thickness between adjacent panels shall be 1/4 inch for steel spans and 1/2 inch for concrete spans.

Standard roadway cross sections and slab reinforcement for HS20 and HS20 Modified live loads are shown in this section. Reinforcement shown is for a cast-in-place slab or a P/S panel slab with the bottom layer of reinforcement between girders being replaced by the panels. Cantilever reinforcement details for P/S panel slab are shown in this section.

Maximum panel width (clear span + 6") = 9'-6" for HS20 Modified.
Maximum panel width (clear span + 6") = 9'-11" for HS20.

When a barrier or railing is permanently required on the structure, other than at the edge of slab, precast prestressed panels will not be allowed in the bay underneath the barrier or railing. Prestressed panels are not allowed for use as simply supported for live loads, i.e. staging, where only two supports may be provided for live loads.


S.I.P.

Stay-in-place corrugated metal forms with cast-in-place concrete may be used on horizontally curved steel structures with the approval of the Structural Project Manager.

The standard slab reinforcements shown in this section for HS20 live load were designed using S.I.P. Dead Loads. If design is for HS20 Modified, the standard slab reinforcement needs to be checked for S.I.P. forms.

The bottom transverse reinforcement shall maintain a 1" clear distance from the top of forms.


C.I.P.

8 1/2" cast-in-place concrete slab with conventional forming may be used at the contractor's option, on all girder structures. Conventional forming shall also be used between girders with stage construction joints.


Details of Precast Prestressed Panels Prestressed Structure:
751.40 general superstructure-panels - square ends - prestressed structures.gif 751.40 general superstructure-panels - skewed ends - prestressed structures.gif
Panels-Squared Ends Panels-Skewed Ends
PLAN OF PRECAST PRESTRESSED PANELS PLACEMENT
(1) End panels shall be dimensioned 1" min. to 1-1/2"
max. from the inside face of diaphragm.
751.40 general superstructure-panels - section thru const joint.gif
(2) S-Bars shown are bottom steel in slab between
panels and used with squared end panels only.
(3) Extend S-Bars 18 inches beyond the front
face of end bents only.
751.40 general superstructure-panels - section a-a.gif Section Thru Const. Joint
(*) Adjust the permissible construction joint to a clearance of 6
inches minimum from the joints of the panels.

Note: All reinforcement other than prestressing strands shall
be epoxy coated.

Section A-A 751.40 general superstructure-panels - section thru cantilever.gif
(**) 3/4" Min. thru 2" max. thickness and 1 1/2" width of
preformed fiber expansion joint material or Sec 1057
or polystyrene bedding material Sec 1073.
 
 
 
  Section Thru Cantilever


Details of Precast Prestressed Panels Steel Structure:
751.40 general superstructure-panels - square ends - end bent - steel structure.gif 751.40 general superstructure-panels - square ends - int end bent - steel structure.gif 751.40 general superstructure-panels - square ends - int bent - steel structure.gif
End Bent End Bent (Integral) Int. Bent (Exp. Gap)
Panels-Squared Ends
751.40 general superstructure-panels - skewed ends - int bent exp gap - steel structure.gif 751.40 general superstructure-panels - skewed ends - end bent - steel structure.gif 751.40 general superstructure-panels - skewed ends - int end bent - steel structure.gif
Int. Bent (Exp. Gap) End Bent End Bent (Integral)
Panels-Skewed Ends
PLAN OF PRECAST PRESTRESSED PANELS PLACEMENT
(1) End panels shall be dimensioned 1" min. to 1 1/2" max. from the inside face of diaphragm. 751.40 general superstructure-panels - section a-a steel structure.gif
(2) S-Bars shown are bottom steel in slab between panels and used with squared end panels only.
(3) Extend S-bars 18 inches beyond the front face of end bents only. Section A-A
(*) Over splice plates, 3/4" Min. thickness allowed.
(5) S-Bars shown are used with skewed end panels, or square end panels of square structures only. The #5-S Bars will extend the width of slab (30" lap if necessary) or to within 3" of expansion device assemblies. 751.40 general superstructure-panels - section b-b steel structure.gif
Note: All reinforcement other than prestressing strands shall be epoxy coated.
   
    Part Section B-B
751.40 general superstructure-panels - section thru cantilever steel structure.gif
Section Thru Cantilever


Details of Precast Prestressed Panels for all Structures:
751.40 general superstructure-panels - plan of precast prestressed panel.gif 751.40 general superstructure-panels - plan of precast prestressed panel (skewed end-option).gif
Plan of Precast Prestressed Panel Plan of Precast Prestressed Panel
(Skewed End-Optional)
(*) = 3" (Typ.) for steel girder structures 751.40 general superstructure-panels - detail a (precast panels).gif
(*) = 3" (Typ.) for P/S girder structures
(**) Use #3-P3 bars if panel is skewed Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \,45^\circ} or greater.
751.40 general superstructure-panels - section b-b (precast panels).gif Detail "A"
Note: Area of Strand = Astra = 0.085 sq. in./strand
Initial prestressing stress = fsi = (0.75)(270 ksi) = 202.5 ksi
Initial prestressing force = Astra x fsi
= (0.085 sq. in./strand)(202.5 ksi) = 17.2 kips/strand
Section B-B
751.40.8.5.1.2 Details of Concrete Slabs for Structures
751.40 general superstructure-HS20 (26ft0in ROADWAY - 4 GIRDER).gif
HS20 (26'-0" ROADWAY - 4 GIRDER)
 
751.40 general superstructure-HS20 modified (26ft0in ROADWAY - 4 GIRDER).gif
HS20 Modified (26'-0" ROADWAY - 4 GIRDER)
 
751.40 general superstructure-HS20 (28ft0in ROADWAY - 4 GIRDER).gif
HS20 (28'-0" ROADWAY - 4 GIRDER)
 
751.40 general superstructure-HS20 modified (28ft0in ROADWAY - 4 GIRDER).gif
HS20 Modified (28'-0" ROADWAY - 4 GIRDER)
 
751.40 general superstructure-HS20 (30ft0in ROADWAY - 4 GIRDER).gif
HS20 (30'-0" ROADWAY - 4 GIRDER)
 
751.40 general superstructure-HS20 modified (30ft0in ROADWAY - 4 GIRDER).gif
HS20 Modified (30'-0" ROADWAY - 4 GIRDER)
 
751.40 general superstructure-HS20 (32ft0in ROADWAY - 4 GIRDER).gif
HS20 (32'-0" ROADWAY - 4 GIRDER)
 
751.40 general superstructure-HS20 modified (32ft0in ROADWAY - 4 GIRDER).gif
HS20 Modified (32'-0" ROADWAY - 4 GIRDER)
 
751.40 general superstructure-HS20 (36ft0in ROADWAY - 5 GIRDER).gif
HS20 (36'-0" ROADWAY - 5 GIRDER)
 
751.40 general superstructure-HS20 modified (36ft0in ROADWAY - 5 GIRDER).gif
HS20 Modified (36'-0" ROADWAY - 5 GIRDER)
 
751.40 general superstructure-HS20 (38ft0in ROADWAY - 5 GIRDER)(unsymmetrical).gif
HS20 (38'-0" ROADWAY - 5 GIRDER)(Unsymmetrical)
 
751.40 general superstructure-HS20 modified (38ft0in ROADWAY - 5 GIRDER)(unsymmetrical).gif
HS20 Modified (38'-0" ROADWAY - 5 GIRDER)(Unsymmetrical)
 
751.40 general superstructure-HS20 (40ft0in ROADWAY - 5 GIRDER).gif
HS20 (40'-0" ROADWAY - 5 GIRDER)
 
751.40 general superstructure-HS20 modified (40ft0in ROADWAY - 5 GIRDER).gif
HS20 Modified (40'-0" ROADWAY - 5 GIRDER)
 
751.40 general superstructure-HS20 (44ft0in ROADWAY - 5 GIRDER).gif
HS20 (36'-0" ROADWAY - 5 GIRDER)
 
751.40 general superstructure-HS20 modified (44ft0in ROADWAY - 5 GIRDER).gif
HS20 Modified (36'-0" ROADWAY - 5 GIRDER)
 

751.40.8.5.2 Timber Floor

Maximum stringer spacing as determined by strength of timber floor
Stress = 1,200 lbs. per square inch
  H-10 H-15
(*) 3" x 12" Plank 18" + 1/2 Flange Width 16" + 1/2 Flange Width
4" Laminated Floor 2'-11" + 1/2 Flange Width 2'-3" + 1/2 Flange Width
6" Laminated Floor 6'-0" + 1/2 Flange Width 4'-4" + 1/2 Flange Width
Stress = 1,600 lbs. per square inch
  H-10 H-15
3" x 12" Plank 23" + 1/2 Flange Width 21" + 1/2 Flange Width
4" Laminated Floor 3'-9" + 1/2 Flange Width 2'-11 1/2" + 1/2 Flange Width
6" Laminated Floor 7'-10 3/4" + 1/2 Flange Width 5'-9" + 1/2 Flange Width
(*) 3" x 12" Plank without treads.

751.40.8.5.3 Steel Grid Bridge Flooring

In general, the 5" depth (concrete filled to half depth) steel grid bridge flooring shall be specified. Bar spacing may vary as necessary to meet minimum section modulus requirements. Main member spacing shall not exceed 10" and cross bar spacing shall not exceed 4". At present, the manufacturers of the following types have provided data to show they are acceptable:

Greulich 5" Standard
Foster 5" Standard

The section properties Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (n = 8)} and maximum span for HS20 loading have been computed for these types and are as follows:


Company (For Design
Purpose only)
Weight (PSF)
(Steel & Conc.)
Main bar
Spacing
Cross bar
Spacing
Moment of Inertia
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (in^4/Ft.)}
Mid Span Over-Support
Conc. Steel Steel
Greulich 48.0 7 1/2" 3 3/4" 99.41 12.43 9.03
Foster 48.0 8" 4" 128.1 16.01 12.25


Company Section Modulus Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (in^2/ft.)} Maximum Span (*)
Mid-Span Over-Support Simple Span Continuous Spans
Conc.
(Top)
Steel
(Bott.)
Steel
(Top)
Steel
(Bott.)
ASTM
A709
Gr. 36
ASTM
A709
Gr. 50W
ASTM
A709
Gr. 36
ASTM
A709
Gr. 50W
Greulich 59.5 3.53 3.90 3.14 4'-4" 5'-10" 5'-10" 7'-1"
Foster 72.5 4.68 5.25 4.30 5'-9" 7'-5" 7'-2" 9'-4"


The cross-section DETAILS used in computing the section properties are shown on the sketches on the following sheets. Maximum span determination included an allowance for a 35#/sq.ft. future wearing surface and assumed a wheel load to be distributed, normal to the main bars, over a width of 4'-0".

(Place the following note on the Bridge Plans with the Steel Grid Details.

Note: The steel grid deck shall be electrically grounded.

(*) For main beams of grid either parallel or perpendicular to traffic.


751.40 general superstructure-greulich 5in standard.gif
  Composite Section Steel Section Only (net)
y 1.671" 2.317"


Greulich 5" Standard
Note: Dimensions obtained form Greulich plans.


751.40 general superstructure-foster 5in standard.gif
  Composite Section Steel Section Only (net)
y 1.766" 2.338"


Foster 5" Standard
Note: Dimensions obtained form Foster Catalog.

751.40.8.5.4 Longitudinal Diagrams

751.40.8.5.4.1 Hinged Beam Connections

The diagrams of various joints in steel structures are intended to be guides primarily for the determination of horizontal longitudinal dimensions for the plan view on the first sheet of plans.

These diagrams are not to be detailed on the design plans. However, the arrangement of the joints should be useful in detailing the longitudinal diagram for structural steel, particularly for bridges on grades and vertical curves.

Longitudinal dimensions for the plan of structural steel and for the plan of slab shall be horizontal from centerline bearing to centerline bearing.

For proper correlation of details when developing plans for widening or redecking bridges, match the method of dimensioning on the new plans with the method used on the originals.


Hinged Beam Connections
751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves1.gif
Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves
 
751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Flat Grade.gif
Geometrics for Hinged Beam Connections for Bridges on Flat Grade
 
751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Straight, Plus Grades.gif
Geometrics for Hinged Beam Connections for Bridges on Straight, Plus Grades
 
751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves.gif
Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves
 
751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves2.gif
Geometrics for Hinged Beam Connections for Bridges on Sag Vertical Curves
 
751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Symmetrical Vertical Curves.gif
Geometrics for Hinged Beam Connections for Bridges on Symmetrical Vertical Curves
 
751.40 general superstructure-Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves1.gif
Geometrics for Hinged Beam Connections for Bridges on Crown Vertical Curves


Hanger Beam Connections
751.40 general superstructure-Geometrics for Hanger Beam Connections for Bridges on Crown Vertical Curves.gif
Geometrics for Hanger Beam Connections for Bridges on Crown Vertical Curves
 
751.40 general superstructure-Geometrics for Hanger Beam Connections for Bridges on Sag Vertical Curves.gif
Geometrics for Hanger Beam Connections for Bridges on Sag Vertical Curves


Pin Plate Connections
751.40 general superstructure-Geometrics for Pin Plate Connections for Bridges on Crown Vertical Curves.gif
Geometrics for Pin Plate Connections for Bridges on Crown Vertical Curves
 
751.40 general superstructure-Geometrics for Pin Plate Connections for Bridges on Sag Vertical Curves.gif
Geometrics for Pin Plate Connections for Bridges on Sag Vertical Curves
751.40.8.5.4.2 Longitudinal Sections
Expansion Device at End Bent
751.40 general superstructure-longitudinal sections-expansion device at end bent(not on grade).gif
Bearing Stiffener Connection Plate
Structures Not on Grade (Typical)
 
751.40 general superstructure-longitudinal sections-expansion device at end bent(on grade).gif
Structures on Grade (Typical)
(*) Parallel to Girder. All other dimensions shown are normal to backwall.
(**) See EPG 751.13 Expansion Devices for dimension of overhang from end of stringer or girder to face of plate, edge of concrete or face of vertical leg of angle.


No Expansion Device at End Bent
751.40 general superstructure-longitudinal sections-no expansion device at end bent(not on grade) 1.gif
Bearing Stiffener Connection Plate
Structures Not on Grade (Typical)
 
751.40 general superstructure-longitudinal sections-no expansion device at end bent(on grade) 1.gif
Structures on Grade (Typical)
(*) Parallel to Girder. All other dimensions shown are normal to backwall.
(**) 18" min. (Use same dimension as the expansion device end on 3-span continuous, if it is not more than 2" greater.)
(***) 3" min. for type C, D and E bearing, and 2" min. for an elastomeric bearing.



Intermediate Bent
751.40 general superstructure-longitudinal sections-intermediate bent-no expansion device.gif 751.40 general superstructure-longitudinal sections-intermediate bent-expansion device.gif
No Expansion Device Expansion Device
751.40 circled 1.gif 1/2" minimum overhang from end of stringer to face of plate, edge of concrete or face of vertical leg of angle.
751.40 circled 2.gif Gap as required for a particular type of expansion device.
751.40 circled 3.gif Expansion device gap plus 1 1/2" minimum (taken parallel to centerline stringer).
(*) Parallel to Girder. All other dimensions shown are normal to centerline Bent.
Blockout shown is for Elastomeric Expansion Joint Seal. Check
Bridge Memorandum for type of device for a particular structure.



Expansion Device at Any Bent
751.40 general superstructure-longitudinal sections-expansion device at any bent-end(no grade).gif 751.40 general superstructure-longitudinal sections-expansion device at any bent-int(no grade).gif
Structures Not on Grade (Typical)
 
751.40 general superstructure-longitudinal sections-expansion device at any bent-end(on grade).gif
Structures On Grade (Typical)



Point on Rotation of Bearings
751.40 general superstructure-longitudinal sections-point of rotation of bearings-type c bearing.gif 751.40 general superstructure-longitudinal sections-point of rotation of bearings-type c bearing grade 4% and greater.gif
Type "C" Bearing Type "C" Bearing
(Grade 4% and Greater)
 
751.40 general superstructure-longitudinal sections-point of rotation of bearings-type d bearing.gif 751.40 general superstructure-longitudinal sections-point of rotation of bearings-type e bearing.gif
Type "D" Bearing Type "E" Bearing
 
751.40 general superstructure-longitudinal sections-point of rotation of bearings-flat plate bearing.gif 751.40 general superstructure-longitudinal sections-point of rotation of bearings-prestressed structure bearing pad.gif
Flat Plate Bearing
(For Grade 2% and Greater)
Prestressed Structure
Bearing Pad
 
751.40 general superstructure-longitudinal sections-point of rotation of bearings-steel structure bearing pad.gif
Steel Structure
Bearing Pad



Blocking Diagram
751.40 general superstructure-longitudinal sections-blocking diagram.gif
Elevation of Longitudinal Steel Diagram
Note: The typical elevation shown above should be detailed on the plans for all steel structures that are on vertical curve grades.
(1) Longitudinal dimensions are horizontal from centerline Brg. to centerline Brg.
(*) Horizontal dimensions.
BLOCKING DIAGRAM SHOULD NOT BE USED FOR CAMBERED GIRDERS.

751.40.8.5.5 Miscellaneous Bearing Connections

751.40.8.5.5.1 Typical Details of “Hinged Connection"
751.40 general superstructure-misc details-section showing hinged beam conn1.gif
Section Showing Hinged Beam Connection
 
751.40 general superstructure-misc details-detail of web at radius transition.gif 751.40 general superstructure-misc details-plan of brg plate.gif 751.40 general superstructure-misc details-typ welding details for stiffeners.gif
Plan of Brg. Plate
Detail of Web at
Radius Transition
  Typical Welding Details
for Stiff. Plates
 
751.40 general superstructure-misc details-section c-c.gif
"D" Gap as required for expansion (3" Min.)
"J" 5" for bearing with 3" web thickness. Use 6" for all others.
751.40 circled 1.gif Dimension to be 1/3 brg. length (Typ.)
(*) To be used unless greater depth is required by design.
(**) See EPG 751.13 Expansion Devices
Note: Web thickness and size of fillet weld connecting bearing stiffener plate to web as required by design.
  Plans for bridges on a grade or vertical curve shall have the conn. detailed in relation to the slope of the girders and stringers.
Section C-C



751.40 general superstructure-misc details-section showing hinged beam conn2.gif
Section Showing Hinged Beam Connection
 
751.40 general superstructure-misc details-sections d-d & e-e.gif
  Section D-D Section E-E  
 
751.40 general superstructure-misc details-typical welding details for stiffeners.gif
Typical Welding Details
for Stiff. Plates
(*) See below for dimension "G".
(**) See EPG 751.13 Expansion Devices
"F" = Gap as required for expansion (3" Min.).
"H" = 10 3/4" Min. (12" preferred.)
"J" = 5" for bearing with 3" web thickness. Use 6" for all others.
All dimensions shown are minimum, increase, as necessary.


Allowable Dead Load Reactions for Various Depths of "G"
Web
Thickness
Depth
"G"
(*) Allowable
Dead Load
Reactions, Kips
(At 150% Overstress)
  Web
Thickness
Depth
"G"
(*) Allowable
Dead Load
Reactions, Kips
(At 150% Overstress)
5/16" 8" 45.0 7/16" 8" 63.0
5/16" 9" 50.6 7/16" 9" 70.8
5/16" 10" 56.2 7/16" 10" 78.7
5/16" 11" 61.8 7/16" 11" 86.6
5/16" 12" 67.5 7/16" 12" 94.5
5/16" 13" 73.1 7/16" 13" 102.3
5/16" 14" 78.8 7/16" 14" 110.2
5/16" 15" 84.3 7/16" 15" 118.1


3/8" 8" 54.0   1/2" 8" 72.0
3/8" 9" 60.7 1/2" 9" 81.0
3/8" 10" 67.5 1/2" 10" 90.0
3/8" 11" 74.2 1/2" 11" 99.0
3/8" 12" 81.0 1/2" 12" 108.0
3/8" 13" 87.7 1/2" 13" 117.0
3/8" 14" 94.5 1/2" 14" 126.0
3/8" 15" 101.2 1/2" 15" 135.0
(*) No (Live load + impact) excluded.



Typical Details of "Hinged" Connection"
751.40 general superstructure-misc details-section showing hinged beam conn3.gif
Section Showing Hinged Beam Connection


751.40 general superstructure-misc details-section thru plate girders.gif
Plate Girder 42" Thru 46"
Also 48" and Over
Plate Girder 36" Thru 40"


751.40 general superstructure-misc details-detail a.gif 751.40 general superstructure-misc details-detail b.gif
Detail "A" Detail "B"
Note: Modify standard end diaphragm connections as shown above, if clearance problems exist between bearing plate and end diaphragm connection bolts.


751.40.8.6 Composite Design

751.40.8.6.1 General

GENERAL

This portion of the article pertains to structures composed of steel girders with concrete slab connected by shear connectors. The stresses of composite girders and slab shall be computed based on the composite cross-section properties and shall be consistent with the properties of the various materials used. The regions subjected to positive moment are considered as composite and the regions subjected to negative moment are considered as non-composite. For the initial girder design, composite/non-composite regions can be approximately assumed as:

751.40 Widen and Repair Design Assumptions- Initial Girder Design.gif


SECTION PROPERTIES

Cross-section properties of the composite section shall include concrete slab and steel section.

Cross-section properties of the non-composite section shall include steel section only.

Use composite property for positive moment section.

Use non-composite property for negative moment section. The effect of reinforcing steel in the section is not considered.

The ratio of modulus of elasticity of steel to that of concrete, n, shall be assumed to be eight. The effect of creep shall be considered in the design of composite girders which have dead loads acting on the composite section. In such structures, n=24 shall be used.


DESIGN UNIT STRESSES (also see note A1.1 in EPG 751.50 Standard Detailing Notes)

Reinforcement Concrete

Reinforcing Steel (Grade 60) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 24,000 psi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 60,000 psi
Class B-2 Concrete (Substructure) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_c} = 1,600 psi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'_c} = 4,000 psi

Structural Steel

Structural Carbon Steel (ASTM A709 Grade 36) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 20,000 psi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 36,000 psi
Structural Steel (ASTM A709 Grade 50) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 27,000 psi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 50,000 psi
Structural Steel (ASTM A709 Grade 50W) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 27,000 psi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 50,000 psi

751.40.8.6.2 Design

751.40.8.6.2.1 Shear Connector Design

The shear connectors shall be designed for fatigue and checked for ultimate strength (AASHTO Article 10.38.5.1).

Step 1:

Compute Vr, the range of shear in kips, from the structural analysis, due to live loads and impact, for entire span.

At any section, the range of shear shall be taken as the difference in the minimum and maximum shear envelopes (excluding dead loads).


Step 2:

Use the average Vr per span, for the section of the span that is assumed to act compositely (from end of span to point of contraflexure for end spans, or from point of contraflexure to point of contraflexure for int. spans).


Step 3:

Using the average Vr from step 2, compute the range of horizontal shear load per linear inch, Sr in kips per inch, at the junction of the slab and stringer from the following equation:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \ Sr = \frac{VrQ}{I}}

(AASHTO Article 10.38.5.1.1 Eq. 10-58)


where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Q } = static moment of the transformed compressive concrete area about the neutral axis of the composite section, in cubic inches (*);

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, I } = moment of inertia of the transformed composite girder in positive moment regions in inches to the fourth power (*).

(*) In the formula, the compressive concrete area is transformed into an equivalent area of steel by dividing the effective concrete flange width by the modular ratio n=8.


Step 4:

Compute the allowable range of horizontal shear, Zr, in pounds on an individual connector, welded stud, by use of the following formula:

where:


=height of stud in inches;

=diameter of stud in inches;

=13,000 for 100,000 cycles

10,600 for 500,000 cycles
7,850 for 2,000,000 cycles
5,500 for over 2,000,000 cycles.


Step 5:

Compute the number of additional connectors required at point of contraflexure, N , from the following formula:

Pitch =

Where: Pitch = required pitch, in inches;

= the resistance of all connectors at one (1) transverse girder cross-section as a shear connector unit.

Note:

The pitch is to be constant and spaced in the composite section (round to the nearest inch).

Step 6:

Compute the required pitch of the shear connector units, pitch by the following formula:


(AASHTO Article 10.38.5.1.1 Eq. 10-69)

where:

= number of additional connectors required at the point of contraflexure;

= total area of longitudinal slab reinforcing steel for each girder over interior support;

= range of stress due to live load plus impact, in the slab reinforcement over the support (in lieu of more accurate computations, f may be taken as equal to 10,000 psi);

= the allowable range of horizontal shear on an individual connector.


This number of additional connectors, N , shall be placed adjacent to the point of dead load contraflexure within a distance equal to 1/3 of the effective slab width, if it is possible. If it is impossible, use minimum pitch of 6".


Step 7: Check connectors for ultimate strength

The number of connectors provided for fatigue must be checked to ensure that adequate connectors are provided for ultimate strength.

To check for ultimate strength, proceed as follows:

(1) Compute the force in the slab (P), which is defined as: at the point of maximum positive moment, the force in the slab is taken as the smaller value of the following two formulae:


(AASHTO Article 10.38.5.1.2 Eq. 10-62)

or

(AASHTO Article 10.38.5.1.2 Eq. 10-63)


Where:

= total area of the steel section including cover plates (if used);

= specified minimum yield point of the steel being used;

= compressive strength of concrete at age of 28 days;

= effective flange width given in AASHTO Article 10.38.3;

= thickness of concrete slab.


Note:

If it becomes impractical to place the number of shear connectors required by ultimate strength in the specified distance (structures with span ratios greater than 1.5); base the number and spacing of shear connectors on the fatigue analysis only.

Increase the haunch by 1/2"± more than what is required to make one size shear connector work for C.I.P. or S.I.P. option.

751.40.8.6.2.2 Shear Connector Spacing

If it becomes impractical to place the number of shear connectors required by ultimate strength in the specified distance (structures with span ratios greater than 1.5); base the number and spacing of shear connectors on the fatigue analysis only.

For a typical 3-spans bridge, the shear connector units can be approximately arranged as below:

751.40 Widen and Repair Design Assumptions- Shear Connectors Spacing 2 2 1.gif

751.40.8.6.3 Details

751.40.8.6.3.1 Shear Connector Details

Use precast prestressed panels on all tangent steel structures. Evaluate the viability of the use of P/S panels on curved structures on a case by case basis and use or include as an option to a CIP slab where deemed appropriate.

Whenever panels are used, the minimum top flange width shall be 12" for Plate Girders and 10" for Wide Flange Beams.

Steel girders shall be cambered when using P/S Panels. Minimum joint filler thickness is 3/4", except over splice plates, in which case use 1/4" minimum. Maximum joint filler thickness is 2".

Shear connectors shall have a minimum height equal to the top of panel.

Shear connectors shall be spaced by units and shear connectors in each unit shall be placed along of girder. On wide flange widths, two lines of connectors may be used if spacings and clearances allow.

Additional shear connectors, Nc, at point of contraflexure may be placed in units normal to girder as space allows or in a single row along girder as shown below:

751.40 Widen and Repair Design Assumptions- PCP on Steel Shear Connector.gif

P/S strands shall extend 3" minimum and 6" maximum past edge of precast prestressed panel and not closer than 1" to the adjacent panels.

Panel end at splices shall be notched to avoid bolt heads as shown below:

751.40 Widen and Repair Design Assumptions- PCP on Steel Shear Connector- B.gif

751.40 circled 1.gif 3/4" min. wide bearing edge for panel at splice, typ. (*)

751.40 circled 2.gif 1-1/4" min. (Typ.)

751.40 circled 3.gif 4 x (Stud diameter) preferred minimum, may be reduced if necessary for a more economical design; 2-1/4" absolute minimum.


(*) In order to meet 751.40 circled 1.gif and 751.40 circled 2.gif above, it is necessary to have an edge bolt distance of 2" or greater for splice plate. For unusual cases, which would require field splices for flange widths 14" or 15" for P/S precast panel option, it will be necessary to change the top flange width to either 13" or 16" of equal area to maintain the 3/4" minimum panel bearing edge on the splice plates.

Minimum joint filler thickness is 3/4" except over splice plates in which case use 1/4" minimum. When joint filler is less than 1/2" thick over splice plate, make the width of joint filler at splice the same width as panel on splice (maximum 1-1/2" wide).

Maximum difference in top of flange thickness should be checked so that joint filler thickness does not exceed 2".

751.40.8.6.3.2 Deflection

Allowable Live Load Deflection

1. Composite Design: Defl. = 1/1000 of span;
2. Non-composite Design: Defl. = 1/800 of span


Where:
Defl. = allowable deflection due to service live load plus impact.


Dead Load Deflection Compute at 1/4 point for bridge with spans less than 75’, at 1/10 points for spans 75’ and over.

751.40.8.7 Wide Flange Beam Spans

751.40.8.7.1 Design

751.40.8.7.1.1 Design Data

Slabs

Reinforcing Steel = 60,000 psi
Concrete = 1,600 psi   = 4,000 psi
  = 8


Simple Design Span

Design Span = Center to Center of Bearings.


Dead Load


Live Load Distribution Factors

See EPG 751.40.8.2.2 Distribution of Live Load


Live Load Deflection Allowable

Composite
Non-Composite


Live Load Reaction

Live Load Wheel Line is the Live Load Reaction per Wheel Line, no distribution, no impact; Maximim Live Load Impact is the Live Load Reaction x Distribution Factor = Impact.


751.40 wf bm spans-truck loading.gif
Truck Loading
(Governs thru 33' simple spans for H20 and all simple spans for HS20)


751.40 wf bm spans-lane loading1.gif
Lane Loading
(Governs for simple soabs 35' and over for H20)


Typical Continuous Steel Structures - Integral End Bents:

751.40 wf bm spans-structure length.gif
(*) Maximum length for End Bent to end Bent - 500 feet.
751.40.8.7.1.2 Stringer Design

Stresses:

Steel: AASHTO - Article 10.2, 10.32
  ASTM A709 Grade 36 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 36,000 psi ( Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 20,000 psi)
  ASTM A709 Grade 50 & Grade 50W Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 50,000 psi ( Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 27,000 psi)


Superstructure Concrete: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_c} = 1,600 psi
  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'_c} = 4,000 psi
  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, n} = 8


Reinforcing Steel: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 60,000 psi


Physical Properties of Spans

Composite Design - See Widening and Repair - Composite Design.
Non-Composite Design - Use "Constant I" analysis.

When the neutral axis of a composite section falls in the concrete fange, the section shall be designed as Non-Composite (21" Wide Flange is the smallest beam generaly made conposite).


Deflection

Live Load Deflection: AASHTO - Article 10.6
  Composite - Allowable Deflection L/1000
  Non-Composite - Allowable Deflection l/800
Dead Load Deflection: Compute at 1/4 points for bridges with spans less than 75', at 1/10 points for spans 75' and over. Give percentage of deflection due to weight of structural steel.


Fatigue Stress

AASHTO - Article 10.3 Case I, Case II or Case III (as specified on Bridge Memorandum generally within the following limitations).

Case I: Bridges with the TRUCK traffic count of 2500 or more vehicles per day (one direction).
Case II: Bridges with traffic count of 750 or more vehicles per day, and less than 2500 TRUCK traffic count (one direction) per day.
Case III: Bridges with traffic count of less than 750 vehicles per day, except when Live Loading is H20 or greater.
No Fatigue: Bridges with traffic of less than 75 vehicles per day.


Economic Comparison

When comparing cost of low-alloy steels (A-572, Gr.-50, and A-588) to the cost of A-36 steel, the low-alloy steels shall be figured a t 3 1/2 cents for A-572, Gr.-50 and 5 1/4 cents for A-588 per pound more than A-36 steel. Cost comparisions will be based on current average bid prices that may be obtained from the CHIEF DESIGNER, for comparable bridges.

No overstressed will be permitted in the design.


Total Capacity of Exterior Griders (Dead Load and Live Load)

In no case shall an exterior stringer have less carrying capacity than an interior stringer.

751.40.8.7.1.3 Flange Plate Lengths
751.40 wf bm spans-flange plates-details of flange plates at int bents1.gif
Top Flange Bottom Flange
Details of Flange Plates at Intermediate Bents
 
751.40 wf bm spans-flange plates-details of flange plates at int bents2.gif
Details of Flange Plates at Intermediate Bents
(Top and Bottom Flanges)

Allowable flange plate sizes are as shown with the section properties. Different plate sizes may be used on adjacent stringers.

Lengths to be shown on the bridge plans are those required as follows:

Lengths each side of the bearing shall be the larger of:
  1. Theoretical End + Terminal Distance (***) or
  2. Point where the stress range (tension or reversal) in the beam flange is equal to or less than allowable fatigue stess range (Cat. E or E') or where the beam flange is in compression, whichever is smaller.
    • Use Cat. E when the flange is less than or equal to 0.8 inch thick.
    • Use Cat. E' when the flange is greater than 0.8 inch thick.

(***) Where the theoretical end = the point where the flange stress without cover plate less than or equal to base allowable stress. Terminal distance = 1 1/2 times nominal cover plate width.

The total length of the cover plate greater than or equal to (2D + 3'-0"). Where "D" = Depth of beam in feet.

When required lengths of plates vary by 12" or less on adjacent stringers or on each side of the centerline stiffener plate, use greater length for all such positions.

Plate lengths taken form the computer programs should be rouned up to at least the nearest 6".


751.40.8.8 Welded Plate Girders

751.40.8.8.1 Design

751.40.8.8.1.1 Design Assumptions & Procedures

Design Unit Stresses

Reinforcement Concrete
Reinforcing Steel (Grade 60) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 24,000 psi, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 60,000 psi
Class B2 Concrete (Superstructure) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_c} = 1,600 psi, = 4,000 psi


Structural Steel:
Structural Carbon Steel (ASTM A709 Grade 36) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 20,000 psi, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 36,000 psi
Structural Steel (ASTM A709 Grade 50) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 27,000 psi, = 50,000 psi
Structural Steel (ASTM A709 Grade 50W) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = 27,000 psi, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y} = 50,000 psi


Design Procedure:

Moments and shears by "Variable I" analysis:

use computer program.

Trial sections from "Preliminary analysis":

Combination of web depth, flanges and length of plates used shall be the most economical section available with depths compatible with vertical clearance requirements. Web depths in 6" increments are preferred, however other increments may be used when required by the Bridge Memorandum. (See Structural Project Manager)


Flanges:

Minimum flange dimensions = 3/4" x 12" (*).

Increments:

Thickness 1/8"
Width 1"

Maximum flange dimensions:

Reference AASHTO - Table 10.32.1A)
maximum thickness = 4"

Note: It is preferred office practice to maintain the same flange thickness at as many locations as practical. This can be accomplished by varying the flange width.

(*) For shipping and erection purposes, minimum width of both compression and tension flanges shall not be less than L/85 where L is the shipping length of the girder. This limitation is for preventing out-of-plane distortion of the girder.


Webs:

Web dimensions:

(Reference AASHTO - Article 10.34 & 10.48)
ASTM A709 Grade 36 = 3/8" minimum thickness for curved girders and for continuous straight girders.
ASTM A709 Grade 50W = 3/8" minimum thickness.
AASHTO - Article 10.3 Case I, Case II or Case III.
Case I
Bridges with the truck traffic count of 2500 or more vehicles per day. (One direction)
Case II
Bridges with traffic count of 750 or more vehicles per day, and less than 2500 truck traffic count (One direction) per day.
Case III
Bridges with traffic count of less than 750 vehicles per day, except when live loading is H20 or greater.
No Fatigue:
Bridges with traffic count of less than 75 vehicles per day.


Total Capacity of Exterior Girders:

(Dead Load and Live Load)

In no case shall an exterior girder have less carrying capacity than an interior girder.

Horizontal Curved Girders Design Procedures (*)

Curved plate girders are to be designed using load factor design criteria. The 1980 AASHTO Guide Specifications for Horizontally Curved Highway Bridges as revised by Interim Specifications for Bridges 1981, 1982, 1984, 1985 and 1986 is to be applied with the USS Highway Structure Design Handbook (\) V-Load method to be used as a working example.

The following procedure may be followed to determine the required cross-section for any system of curved girders with skews less than 46°.

1. Determine the primary moments by the same procedures as for a system of straight girders, using the developed lengths of the curved girders.

2. From primary moments, compute shear loads, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, V} , using the formula:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, V = \frac{\sum M}{Coeff. * K}} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, V} = Shear loads.
M = Primary moments.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, K = \frac{RD}{d}} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, R} = Radius of curvature (outside girder).
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, D} = Radial distance between inside and outside girders.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, d} = Distance between diaphragms measured along axis of outside girder.

The following coefficients may be applied to "Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, K} " for the various multiple-girder systems with equal spacing between girders.


SYSTEM COEFFICIENT
FRACTION
COEFFICIENT
DECIMAL
2 girders 1 1.00
3 girders 1 1.00
4 girders 10/9 1.11
5 girders 5/4 1.25
6 girders 7/5 1.40
7 girders 14/9 1.56
8 girders 12/7 1.72
9 girders 15/8 1.88
10 girders 165/81 2.04

3. Compute Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, V-Load} moments


  • Reference: USS "Highway Structures Design Handbook" 1965 Edition. (Updated 1986 Volume II Section 6) developed by Richardson, Gordon and Associates in cooperation with Dr. John Scalzi is to be used as a working example.


4. Compute lateral bending moments using the approximate formula:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, M_L = \frac{Hd}{10} = \frac{Md^2}{10Rh}}   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, ML } = Lateral bending moment
    Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, H } = The Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, H} values are approximately equal to the reactions at the supports.
    Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, h } = Depth of girder between centers of gravity of flanges.
    Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, M } = Primary moment + Secondary moment.

751.40 Widen and Repair Design Assumptions- Horizontally Curved Girders Design Procedure.gif

5. Determine cross-section required to provide for vertical and lateral forces computed under Items 1 to 4 inclusive. As with any statically indeterminate system it is necessary to make an initial assumption of the required cross-sections and to repeat the calculations one or more times to obtain reasonable agreement between the assumed and required sections.


6. The non-compact section requirement that Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_y > (f_b + f_w)} is to be applied to all sections with the tension flange Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_y > (f_b + f_w)} and the compression flange as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_y (1-3 \lambda^2) > (f_b + f_w)} to ensure conservative design.

In computing Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \lambda} , use Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ell} to be actual diaphragm spacing for compression and tension stresses.

The value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_w} is to be selected as plus or minus in the equations for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, P_w} to give the worst possible case.


Design and Detail Guides

1. Economic Arrangement of Spans and Depth-to-Spans Ratios

Where there is flexibility in span arrangement, the same guides that apply to economic arrangement of straight girders are equally applicable to curved girders. Similarly the rules used to establish depth-to-span ratios for straight girders usually will apply to curved girders.


2. Spacing of Girders

Spacing depends on the arrangements of diaphragms and bracing. In general, however, it will be found that the most economical arrangement for straight girders will accord very well with the best arrangement for a system of curved girders. The effect of curvature increases in proportion to the square of the span length and decreases in proportion to the radius of curvature and the spacing of girders.


3. Arrangement and Spacing of Diaphragms

The diaphragms shall be placed radially, with a maximum spacing of 15'-0". In order to minimize lateral bending of the girder flanges, the flanges should be as wide as practical.


Sway frame bracing is selected for curved girder system, by same methods as for straight girders.


4. Effect of Lateral Bracing

made in a similar manner as for straight bridges. If lateral Provision for lateral loading on curved girders may be bracing is used in a system of curved girders, the forces resulting from the radial components of flange stress may be carried partially or entirely by the bracing system; when both diaphragms and lateral bracing are used, radial reaction components may be divided between the two systems.


5. Approximate Estimate of Curvature

The following formula may be used in making preliminary approximations of the effect of curvature:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, P = 10.5 \times \frac{(1+r)(L')^2}{R_2D}} Note: For "r" refer to paragraph No. 7
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, r = \frac{(R_1)^2}{(R_2)^2} \times \bigg( \frac {Inside \ girder \ loading)}{Outside \ girder \ loading} \bigg)} (*)


(*) May be omiteed if supports are on radial lines.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, P } % increase in positive moment due to effect of curvature.
Radius of inside girder.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, R_1} Radius of outside girder.
Distance between points of contraflexure in any pisitive moment area.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, D } Spacing between inside and outside girders.


In the above form, the formula applies to a two-girder system, but it may be modified by reference to the table of coefficients for multiple-girder systems shown in Item #2. From primary moments, compute shear loads.

The formula applies particularly to positive moment, but for preliminary approximation it may be assumed that the curvature effect on negative moments will be about the same.


6. Design of Diaphragms and Connections

Where the degree of curvature is equal to or under 1° - 30' and when spans are equal to or under 75'-0" in length, the diaphragm and connections shall be the same as for Bridges with straight girders. Where the degree of curvature is over 1°- 30' to 3° or with a span length of more than 75'-0", the diaphragm must be attached to the tension flange. Where the degree of curvature is over 3°, a special design will be required for connection of intermediate diaphragms to flanges.

The maximum allowable diaphragm spacing is 15'-0", regardless of the amount of curvature, or span lengths.


The following applies to those bridges where the special design is to be considered:


Since diaphragm moments due to effect of curvature are a function of the radial component of flange stress, they are directly proportional to the vertical bending moment in the girders.


For exterior girders the moment in the diaphragm equals Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, M \times d/R} , in which Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, M} = vertical bending moment in girder for any particular condition of loading; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, d} = diaphragm spacing; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, R} = Radius of curvature of girder.


For negative moment over the support, the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, M} value used in this equation should be the average moment between a point at the support and a point at the first adjacent diaphragm.


Diaphragm connections may be made directly to the flanges of the girders or through stiffeners, provided details are arranged to adequately transfer radial components of flange stress into the diaphragms.


7. Supports positioned other than on radial lines.

If field conditions permit, the most orderly arrangement for curved girders will be attained by placing the supports on radial lines.


It may be necessary to treat each line of girders independently, first finding the direct loading moments and then correcting for curvature by applying the separate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, V-loads} .


8. Transverse stiffeners


The maximum transverse stiffener spacing for curved plate girders is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, D} , the web height.


Transverse stiffeners should be placed along the girder length only as far as required by design.

The maximum spacing of the first transverse stiffener at the simple support end of a curved plate girder is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, D/2} .


Reference:

AASHTO - Article 10.5
Limit radius of heat curved girders according to AASHTO Article 10.15.

Where the distance between field splices of curved girders exceeds that given by the following formula, a special note shall be placed on the plans.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \sqrt{\frac{0.667 \ x \ f_s \ x \ SM}{W}}} (*)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L} = Allowable distance between field splices, in feet.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_s} = Allowable fs of flange steel, in psi. e.g. use 20,000 psi for Grade 36 steel.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, W} = Weight of girder (flanges and web), in pounds per foot.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, SM} = Section Modulus of girder about x-x axis as shown, in inches cubed.


751.40 Design Assumptions- Heat Curved Girders- Section Modulus.gif


Note:

If flanges are of different sizes, use smaller Section Modulus.

See Structural Project Manager for allowable overstress.


(*) Derivation

Positive moment at centerline, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Mom. = \frac{WL^2}{8} \times 12}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, fs = \frac{Mom.}{SM}}
Substitute mom. in fs equation.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, fs = \frac{WL^2 \times 12}{8 \times SM}}
solve for L
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L = \sqrt{\frac{8 f_s \times SM}{12W}}}

Design Example

ASTM A709 Grade 36 Steel

751.40 Design Assumptions- Heat Curved Girders- Design Example Plan View.gif

  751.40 Design Assumptions- Heat Curved Girders- Design Example Section 2.gif
751.40 Design Assumptions- Heat Curved Girders- Design Example Section A-A.gif
Shape Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, I_{xx}}
PL 13" x 3/4" Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \frac{0.75 \times (13)^3}{12} = 137.31}
PL 70" x 3/8" Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \frac{70 \times (0.375)^3}{12} = 0.31}
PL 12" x 3/4"
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle = 245.62 \ In.^4}
SECTION A-A
 
Weight per Foot of Girder
PL 12" x 3/4" = 30.6 lbs./ft.
PL 70" x 3/8" = 89.3 lbs./ft.
PL 13" x 3/4" = 33.2 lbs./ft.
Total = 153.1 lbs./ft.

  From Formula:   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L = \sqrt{\frac{0.667 \times fs \times SM}{W}} = \sqrt{\frac{0.667 \times 20,000 \times 37.79}{153.1}} = 57.38'} (Use 57.5')


57'-6" < 60'-0". Therefore, Special Note required.

Special Note:

Heat curving of girders (Identify) (*) will not be allowed shile in the horizontal position.

(*)Complete underlined portion as required.


Maximum Plate Lengths:

80 feet. See Structural Project Manager for use of longer lengths up to 85' for ASTM A709 Grade 50 or ASTM A709 Grade 50W and 100' for ASTM A709 Grade 36.

Minimum Plate Lengths:

10 feet. Shop flange splices should be eliminated and extra plate material used when :economy indicates and span lengths permit.

Preliminary Analysis:

(1) Compute moments from influence lines on basis of "Constant I" analysis and apply the following percentage increase or decrease to non-composite dead load moments.

References may be used in lieu of the above.

751.40 Design Assumptions- Preliminary Analysis-Moments Diagram.gif

= 1.2 to 1.5 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, n} = 1.2 to 1.5
-5%
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, -M_2} +15%
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, +M_3} -15%
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, +M_1} -5%
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, -M_2} +15%
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, +M_3} -15%
+15%

(2) Determine trial sections and plot a rough moment curve to determine location of flange plate cutoffs, if any.

(3) Complete analysis by using computer programs to obtain actual moments and stresses.

Design Stress investigation for Positive Moment Area of Plate Girder Structure

The design stresses are to be checked at the top of flange (steel) and the top of concrete slab in the composible area of Plate Girder Structures to ensure that they are within the allowable stresses.

751.40 Design Assumptions- Design Stress Investigation- Plate Girder.gif

SECTION A-A


Structure Length


Typical Continuous Steel Structures- Integral End Bents:


751.40 Design Assumptions- Structure Length- Maximum Length for Continuous Steel.gif


Estimated Girder Depth Based on Three Spans With Ratio N = 1.3±

Continuous Plate Girders HS20 Loading Load Factor
(ASTM A709 Grade 50 or ASTM A709 Grade 50W)

Initial Estimate
(Feet)
Girder Depths (*)
(Inches)
Structure Depth (**)
(Feet)
85 to 104 42 4.50
105 to 124 48 5.00
125 to 134 54 5.50
135 to 144 60 6.00
145 to 159 66 6.50
160 to 174 72 7.00
175 to 184 78 7.50
185 to 194 84 8.00
195 to 204 90 8.50


Trial steel plate girder depths use program BR109 to check designs and deflections. Web depths may be adjusted by two inch increments.

(*) Bethlehem steel economic study (N = 1.3±). Bethlehem steel provided an economic study of multiple steel girder depths. The study indicated that cheaper designs are obtained by reducing the plate girder depths and reducing the number of stiffeners. The recommended initial estimates above are based on these designs.


(**) Structure depth includes slab and haunch.

A general rule of thumb is to determine the minimum web thickness without stiffeners; then, use a web thickness of one-sixteenth inch less. Match MoDOT requirements for web increments of one-sixteenth inch only.


If two-span structures are used, a deeper web is required. A good estimate is to use six inches additional depth than the above tables for two-span structures.

751.40.8.8.2 Details

751.40.8.8.2.1 Field Flange Splice – Bolted

General

Splices shall be designed using the Service Load Design Method and in accordance with AASHTO Articles 10.18, 10.24 and 10.32 except as noted.

Splices shall be designed to develop 100% of the flange strength by the flange splice plate strength. When the flange section or steel grade changes at a splice, the smaller flange strength shall be used to design the splice. Splice plates shall then match the lower grade used in the flanges.


Minimum Yield Strength and Minimum Tensile Strength Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (Fu)}

ASTM A709 Grade 36 = 36 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_u} = 58 ksi
ASTM A709 Grade 50 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_y} = 50 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_u} = 65 ksi
ASTM A709 Grade 50W Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_y} = 50 ksi = 70 ksi


Allowable Steel Stresses Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (F_t)}

Allowable stresses are determined by AASHTO Table 10.32.1A.

Allowable tensile stress Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_t = 0.55 \times F_y}


ASTM A709 Grade 36 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_t} = 20 ksi
ASTM A709 Grade 50 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_t} = 27 ksi
ASTM A709 Grade 50W Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_t} = 27 ksi


Allowable Bolt Stresses

Splices shall be designed as slip critical connections with Class B surface preparation and oversized holes. Although standard holes are used in the fabrication of flange splices, designing the splices for oversize holes allows for some fabrication and erection tolerances. All splice bolts shall be 7/8" diameter ASTM F3125 Grade A325.

AASHTO Table 10.32.3C specifies Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_s} = 19 ksi for a class B slip-critical connection. Tables shown in this article are based on 19 ksi that should also be used to design splices not listed in the table.


Although slip-critical connections are theoretically not subject to shear and bearing, they must be capable of resisting these stresses in the event of an overload that causes slip to occur. The allowable shear stress per bolt Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (Fv)} for bearing is 19 ksi with the threads included and ksi for threads not included.


Flange Strength

The flange strength shall be determined by multiplying the allowable stress of the flange by the area of the flange. The area of the flange shall be taken as the gross area of the flange, except that if more than 15 percent of each flange area is removed, that amount removed in excess of 15 percent shall be deducted from the gross area. Bolt holes are considered to be 1" diameter for the purpose of determining flange area.


Splice Plate Strength

The splice plate strength shall be determined by multiplying the allowable stress of the splice plates by the area of the splice plates. The area of the splice plates shall be taken as the gross area of the splice plates, except that if more than 15 percent of the splice plate area is removed, that amount in excess of 15 percent shall be deducted from the gross area.


Two Row Splices

Splices with two rows of bolts are used with flanges 12 to 13 inches wide. The inner and outer plates may either be the same length or the inner plate may be shorter. This is the case if the end bolts in the splice are only needed to be in single shear. All other bolts will be in double shear. (See Figure 3.42.2.2-1)

751.40 Widen and Repair- Field Flange Splice- Bolted.gif

Figure 3.42.2.2-1


Four Row Splices

When the width of the flange being spliced is 14 inches or greater, four longitudinal rows of bolts are used. Three variations of the end bolts positioning may be used. In each of these variations, the last two bolts shall be located in the outer rows closest to the edge of the splice plate.

751.40 Widen and Repair- Field Flange Splice- Bolted Four Row Splice.gif

Figure 3.42.2.2-2


Flange Width Transitions

When the width of the flanges being spliced differs by more than 2", the larger flange shall be beveled as shown in Figure 3.42.2.2-3

751.40 Widen and Repair- Field Flange Splice- Bolted- Flange Width Transition.gif


Figure 3.42.2.2-3


Weight of Splice

When calculating the weight of splice, the following simplified weights shall be used.

Weight of High-Strength bolts (diameter 7/8") = 0.95 lbs/bolt

Unit weight of Structural Steel = 490 lbs/ft3

751.40.8.8.2.2 Field Web Splice – Bolted

General

Splices shall be designed using the Service Load Design Method and in accordance with AASHTO Articles 10.18, 10.24 and 10.32 except as noted.

The web splice consists of 2-Plates:

Thickness = 5/16" minimum.
Width = 12-1/2" (18-1/2" if 3 rows of bolts are required).

When the web section or steel grade changes at a splice, the smaller web strength should be used to design the splice.


Minimum Yield Strength and Minimum Tensile Strength Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (F_u)}

ASTM A709 Grade 36 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_y} = 36 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_u} = 58 ksi
ASTM A709 Grade 50 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_y} = 50 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_u} = 65 ksi
ASTM A709 Grade 50W Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_y} = 50 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_u} = 70 ksi


Allowable Steel Stresses Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (F_b, F_w)}

Allowable stresses are determined by AASHTO Table 10.32.1A.

Allowable bending stress Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_b = 0.55 \times F_y}
Allowable shear stress Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_v = 0.33 \times F_y}


ASTM A709 Grade 36 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_b} = 20 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_v} = 12 ksi
ASTM A709 Grade 50 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_b} = 27 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_v} = 17 ksi
ASTM A709 Grade 50W Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_b} = 27 ksi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_v} = 17 ksi


Allowable Bolt Stresses

Although standard holes are used in the fabrication of web splices, designing the splices for oversize holes allows for some fabrication and erection tolerances. Web splices required to resist shear between their connected parts are designated as slip-critical connections. Shear connections subjected to stress reversal, or where slippage would be undesirable, shall be slip-critical connections. Potential slip of joints should be investigated at intermediate load stages especially those joints located in composite regions. The resultant force shall be less than the allowable bolt shear force. All splice bolts shall be ASTM F3125 Grade A325 7/8" diameter High Strength Bolts.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, F_v} = 19 ksi


Bolt Arrangement

The minimum distance from the center of any fastener in a standard hole to a sheared or thermally cut edge shall be 1-1/2 inches for 7/8" diameter fasteners. The minimum distance between centers of fasteners in standard holes shall be three times the diameter of the fastener, but shall not be less than 3 inches for 7/8" diameter fasteners.


Splice Plate Strength

The strength of the splice plates shall be determined by multiplying the allowable stress of the splice plates by the net area of all splice plates. The splice plates net area shall be taken as the gross area of the splice plates minus the bolt holes. Bolt holes are considered to be 1 inch diameter for the purpose of determining splice plate net area. Web splices are designed to develop 75% of net section of the web.


Web Strength

The strength of the web should be determined from the allowable web stress at the "top of web" to account for hybrid sections. Otherwise, the allowable web stress is based on a linear distribution of stress from outside face of flange to "top of web".


Weight of Splice

When calculating the weight of splice, the following simplified weights shall be used.

Weight of High-Strength bolts (diameter 7/8") = 0.95 lbs/bolt

Unit weight of Structural Steel = 490 lbs/ft3

751.40.8.9 Continuous Concrete Slab Bridges

751.40.8.9.1 Slabs

751.40.8.9.1.1 Design Assumptions
Stresses - FC = 1600 psi N = 8 (Slab, Integral Column)
  FC = 1200 psi N = 10 (Open Bent, Footing)
  FY = 60,000 psi reinforcing steel

Use "Variable I" analysis for all structures except solid slabs without drop panels.
Use "Constant I" analysis for solid slabs without drop panels.


751.40 Slabs Design Assumptions Diagram.gif


"L" = Design Span
"H" = Design Height
"I" = Gross moment of inertia of the full cross-section (Slab minus voids - integral wearing surface not included) ("I1", "IA", etc. suggested I's to be considered.)
"S" = The effective span length for the use in determining minimum slab thickness under load factor design (AASHTO 8.9).

Use the same column diameter and spacing for all Intermediate Bents.
Use the same slab thickness for all spans.


DEGREE OF RESTRAINT - LONGITUDINAL
  Column Type Footing Type Top Column Bottom Column
INT. BENTS Integral Column Spread or Pile Integral (**)
Integral Column Pedestal Pile Integral (**)
END BENTS Pinned Column any Pinned (**)
Integral Pile   (*) Pinned  
Open Bent with Column any Simple
INT. BENTS Open Bent with Pile   Simple


(*)   See EPG 751.40.8.9.2.5 Design Assumptions for Integral Piles.
(**)   Use "Pinned" for Seismic Performance Category A and "Fixed for Seismic Performance Categories B, C & D. (See Structural Project Manager or Liaison)
751.40.8.9.1.2 Slab Design and Drop Panel

The Slab Depth is based on the following limitations:


1.   Vertical Clearance Requirements: see the Bridge Memorandum.
2.   Allowable Depths:
  A. Positive Moments -
  see table of "Available Slab Depths and Void Data", in EPG 751.40.8.9.1.4 Slab Cross Section and Section Properties.
  B. Slab Depth controlled by the minimum thickness formula -
  (Integral wearing surface is included with the total depth provided.)
  Continuous Spans - AASHTO 8.9 = (S + 10)/30
  "S" may be used as the clear distance between drop panels.
  Bridges may have two adjacent spans averaged if S2/S1 < 1.5
  Simple Spans - AASHTO 8.9 = 1.2 (S + 10)/30
  C. Negative Moments -


  DROP PANEL DEPTHS
  MIN. MAX.
Bents in median of dual roadway 0" or 3" 13"
Other Bents 0" or 3" 9"
INCREMENTS OF 1"


  APPROXIMATE DROP PANEL WIDTH (FEET)
(PARALLEL TO THE CENTERLINE OF ROADWAY)
  Bents Drop Panel Depth
4" 6" 7" 8" 9" 12"
3 Span Bridge 2 & 3 6' 6' 10' 8' 6'
4 Span Bridge 2 & 4 6' 6' 10' 8' 6'
3 8' 10' 12' 12' 12' 12'
THESE WIDTHS ARE SUGGESTED ONLY AS TRIAL DIMENSIONS FOR
DESIGN AND ARE NOT TO BE USED AS LIMITS FOR THE FINAL DESIGN.


3.   Reinforcing Steel:
  A. Positive Moments = Maximum #11 @ 5" cts.
  B. Negative Moments = Maximum #11 @ 5" cts., except #14s @ 6" cts., may be used for long spans.
4.   Live Load Deflection - AASHTO 10.6
  The deflection due to service live load plus impact shall not exceed 1/800 of the span, except on bridges in urban areas used in part by pedestrains whereon the ratio preferably shall not exceed 1/1000.
751.40.8.9.1.3 Slab Longitudinal Sections

HOLLOW SLABS


751.40 Slabs - Hollow End Spans.gif
END SPANS


751.40 Slabs - Hollow Intermediate Spans.gif
INTERMEDIATE SPANS


751.40 Slabs - Hollow Part Plan Skewed Detail.gif (*)Increase to maintain 6" minimum on skews (see detail)
(**) By Design (6" increments measured normal to the centerline of bent) (The minimum is equal to the column diameter + 2'-6")
Note:
All longitudinal dimensions shown are horizontal (Bridges on grades and vertical curves, included).
For Sections A-A and B-B see EPG 751.40.8.9.1.4 Slab Cross Section and Section Properties.


 


SOLID SLABS


751.40 Slabs - Solid End Spans.gif
END SPANS


751.40 Slabs - Solid Intermediate Spans.gif
INTERMEDIATE SPANS


(*) By Design (6" increments measured normal to the centerline of Bent) (The minimum is equal to the column diameter + 2'-6")


Note:
All longitudinal dimensions shown are horizontal (Bridges on grades and vertical curves, included).

751.40.8.9.1.4 Slab Cross Section and Section Properties
751.40 Slab Cross Section AA & BB.gif


HALF SECTION A-A
CENTER OF SPAN
HALF SECTION B-B
NEAR INTERMEDIATE BENT


AVAILABLE SLAB DEPTHS
AND VOID DATA
Truck Loading
T (*)   "D" "E" "F"
17" and less - no voids
18"   9" 15" 21"
19" (***) 10" 16" 22"
21"   12" 18" 24"
23"   14" 20" 26"
25"   15.7" 22" 28"
26"   16.7" 23" 29"
28"   18.7" 25" 31"
30"   20.85" 27" 33"
Pedestrian Overpasses  
T (*)   "D" "E"
15" and less - no voids
16"   8" 14"
17"   9" 15"
18"   10" 16"
20"   12" 18"
751.40 Slab Cross Section Thru Void.gif
PART SECTION THRU VOID
751.40 Slab Cross Section - Detail C.gif
DETAIL "C"


Notes:
(*) Increase the Dimension "T" by 1/2" for #14 bars placed in the top or bottom of the slab.
  Increase the Dimension "T" by 1" for #14 bars placed in the top and bottom of the slab.
  ("T" and "D" are based on 3" clearance which includes the integral wearing surface to the top of the longitudinal bar.)
 
(**) For Roadways with slab drains, use 10" minimum. For Roadways that require additional reinforcement for resisting moment of the edge beam 20" minimum, refer to EPG 751.40.5.1 Structure with Wearing Surface Slab Drains - Details.
 
(***) Preferred minimum (Consult the Structural Project Manager prior to the use of a thinner slab.)


Voided Slab Spans


Void Dia.
(in.)
Area
(sq.ft.)
Area
(sq.in.)
Moment
of Inertia
(ft.4)
Moment
of Inertia
(in.4)
Weight
(lb./ft.)
8.00 0.3490 50.2656 0.0096 201.0624 52.35
9.00 0.4417 63.6174 0.0155 322.0630 66.26
10.00 0.5454 78.5400 0.0236 490.8750 81.81
12.00 0.7854 113.0976 0.0490 1017.8784 117.81
14.00 1.0690 153.9384 0.0909 1885.7454 160.35
15.70 1.3443 193.5932 0.1438 2982.4242 201.66
16.70 1.5211 219.0402 0.1841 3818.0075 228.17
18.70 1.9072 274.6465 0.2894 6002.5789 286.09
20.85 2.3710 341.4310 0.4473 9276.7336 355.65
751.40.8.9.1.5 Slab Reinforcement

 

HOLLOW SLABS


751.40 Slab Reinf - Positive Moment.gif


DETAIL "A"
(POSITIVE MOMENT)


751.40 Slab Reinf - Negative Moment.gif


DETAIL "B"
(NEGATIVE MOMENT)


Longitudinal Reinforcement
(Largest Bar)
"G"
#8 3-5/8"
#9 3-3/4"
#10 3-7/8"
#11 4"
#14 4-3/8"


Moment Curves

1. Determine reinforcing steel from the sum of the dead loads and the live loads + impact (working stress design) or design in accordance with AASHTO Article 8.16 and 8.9 (load factor design).
2. Determine the cut-off points for the stress bars in sets of 2 or 3.
Maximum length = 60'-0", see AASHTO Article 8.24 for extension of reinforcement.
3. Determine the drop panel width:
  Minimum width = Column diameter plus 2~6".
Maximum width = (Parallel to the centerline of roadway) as determined by deign).
  In general, the width of the drop panel normal to centerline bent should be adjusted to 6" increments.


SOLID SLABS (BOTTOM)

Use AASHTO 3.24.10 Distribution Reinforcement shall be a percentage of positive moment reinforcement (% = 100/√S, with a maximum of 50%).


EDGE BEAM

Positive Moment:
The bridge curb is not to be used in determining the resisting moment of the edge beam.
Dead Load: Use the same distribution as for the slab design.
Use for simple spans 0.1 PS.
Live Load + I: AASHTO Article 3.24.8
  Use for negative moment on continuous spans 0.1 PS.
Use for positive moment on continuous spans 0.08 PS.
  Where P = Wheel load in pounds, see EPG 751.40.8.5.1.1 Cantilever Moment.
    S = Span in feet


751.40 Slab Reinf - Edge Beam Detail.gif
751.40.8.9.1.6 Shear

Shear Loads

The shear in the Hollow Slab should be computed for all loadings H20 and over.


Distribution of Loads

Use the same distribution for the dead and live load as was used for the moment.


Unit Shear Stress

Load Factor:
  Shear Stress = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Vu = \frac{Vu}{\phi(Bd - voids~area)}}
Working Stress:
  Shear Stress =
Where "d" = effective depth, = 0.85 for shear


751.40 Slab Shear Stress Elevation.gif


Allowable Shear Stress

Load Factor:
 
  Where Vc = shear strength provided by concrete
 
Working Stress:
 
 
  Where Vc = Allowable shear stress carried by concrete


If shear stress (load) exceeds the allowable shear use one or more of the following solutions.

  1. Eliminate some voids and replace remainder.
  2. Shorten alternate voids
  3. Use shear reinforcing in the critical zone.


751.40 Slab Shear Stress Diagram.gif


Note:
Consider a voided slab the same as a regular slab as it pertains to the minimum stirrups (AASHTO - Article 8.19).
i.e. The minimum stirrups are not required if the shear stress is less than allowable.

751.40.8.9.1.7 Camber Deflection

Ultimate Deflection:

Compute the "ultimate deflection" at 0.2 points of the spans for the dead loads without the 35# future wearing surface.

Ultimate deflection (long term) = elastic deflection x 3

Ec (Elastic Modulus) = psi (districts 1 and 4)
  psi (remainder of districts)

The modulus of elasticity for the use in a continuous structure analysis computer program should be determined as follows:

=
= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Coeff./E_c}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \Delta_{ULT}} =
 
Where:
= deflection.
= Ultimate deflection
= Elastic deflection


Example No. 1

(Assume bridge is in District 8)

= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 6 \times 10^6 psi}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \Delta_{ULT}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Coeff. / (6/3) = Coeff./2}

Therefore, use 2 \times 106 psi for modulus of elasticity in the structure analysis computer program to get ultimate deflection. (*)


Example No. 2

(Assume bridge is in District 1)

=
=

Therefore, use psi for modulus of elasticity in the structure analysis computer program to get ultimate deflection. (*)


(*) Gives long term deflection as output.

751.40.8.9.1.8 Slab Construction Joint Details
751.40 Slab Const Jt Key (Slab Depth 17 in or more).gif


DETAILS OF SLAB CONSTRUCTION JOINT KEY
(FOR SLAB DEPTHS 17" OR MORE)


751.40 Slab Const Jt Key (Slab Depth 16.5 in or less).gif


DETAILS OF SLAB CONSTRUCTION JOINT KEY
(FOR SLAB DEPTHS 16½" OR LESS)


751.40 Slab Const Jt Void Spacing.gif


VOID SPACING AT LONGITUDINAL CONSTRUCTION JOINT


751.40.8.9.2 End Bents

751.40.8.9.2.1 Pile Cap Bents
751.40 End Bent (Pile Cap Sections).gif
* See Bridge Memorandum for maximum slope of spill fill.
SECTION THRU WING SECTION A-A


751.40 End Bent (Pile Cap Elevation).gif


ELEVATION


751.40 End Bent (Pile Cap Plan (SQ)).gif


PLAN (SQUARE)


(1) Wing brace details. 751.40 End Bent (Pile Cap Detail B).gif


751.40 End Bent (Pile Cap Plan (Skewed)).gif


PLAN (SKEWED)
(*) Use the same Dimension (centerline Curb Joint) as the opposite side when the wings are the same length.
751.40.8.9.2.2 Integral Column Bents

SEISMIC PERFORMANCE CATEGORY A
(PINNED COLUMN AT TOP AND BOTTOM)


751.40 End Bent (Integral Column Part Section).gif
PART SECTION


751.40 End Bent (Integral Column Pinned Column).gif 751.40 End Bent (Integral Column Section AA).gif
SECTION A-A
751.40 End Bent (Integral Column Section BB).gif
PINNED COLUMN SECTION B-B


Note: If the columns at an end bent have excessive moments due to shortness of the Column or length of the span, they should be detailed as "pinned" and designed for vertical reactions only.


SEISMIC PERFORMANCE CATEGORIES B, C & D
(PINNED COLUMN AT TOP, FIXED COLUMN AT BOTTOM)

For pinned column conditions at the top, see the above details.
For fixed column conditions at the bottom and column reinforcement details.

Note: For details not shown, see integral pile cap details.

751.40.8.9.2.3 Reinforcement - Pile Cap Bents
751.40 Reinforcement - Pile Cap Section 1 (Slab Depth less than 16 in).gif
SECTION THRU END BENT
(Slab depth less than 16")


751.40 Reinforcement - Pile Cap Section 2 (Slab Depth 16 in or more).gif
SECTION THRU END BENT
(Slab depth 16" or more)


(**) Development length for top bar minimum.

751.40.8.9.2.4 Reinforcement - Wing
751.40 Reinforcement - Wing (Elevation & Part Section).gif
ELEVATION OF WING PART SECTION THRU WING
(*) Clip K bars as required to maintain
minimum clearance at bottom of wing.


   


751.40 Reinforcement - Wing (Section AA & Part Section Thru End).gif
SECTION A-A
(K-bars not shown for clarity)
PART SECTION THRU
END OF WING

 

 

Note: See _____ for barrier railing details and spacing of K-bars.

751.40.8.9.2.5 Design Assumptions for Integral Piles

Seismic Performance Category A

Piles may be considered as "pinned" (for superstructure) at the pile cap and designed for vertical loads only unless they fall under the following general conditions in which case they should be checked for the loadings as specified for columns.

1. Height from centerline of slab to "pin" is less than 15'.
  The location of the pinned joint is arbitratily taken as about 1/3 of the length of long piles or at a point about 10' below the natural ground line.
2. Piles having a large gross moment of inertia (cast-in-place concrete) gross I of steel BP = I x n.
3. The number of piles used on a fairly long structure is small.


Seismic Performance Categories B, C & D

Piles shall be checked for combined axial and bending stresses for seismic loading conditions. For AASHTO group loads I thru VI as applicable, follow criteria noted above for seismic performance category A.


751.40.8.9.3 Intermediate Bents

751.40.8.9.3.1 Integral Bents
751.40 Intermediate Bents (Integral Bents Half Section).gif


HALF SECTION


(*) 25'-0" is the max. column spacing allowed. However, the footing pressure may be the controlling factor for the column spacing. It is suggested that a rough check be made of the footing pressure before the spacing is definitely established.

In congested areas, when it is desired to keep the number of columns to a min., larger column spacings may be desirable. (consult the Structural Project Manager).

In general, use two 2'-6" columns for Roadways thru 44'-0" and additional 2'-6" columns for wider Roadways.


SEISMIC PERFORMANCE CATEGORY A


751.40 Intermediate Bents (Integral Bents Category A Half Section).gif


HALF SECTION


751.40 Intermediate Bents (Integral Bents Category A Part Section AA).gif


PART SECTION A-A
751.40.8.9.3.2 Integral Column Bent with Drop Panel
751.40 Intermediate Bents - Integral Column Bents with Drop Panel (Part Section).gif ATTENTION DETAILER:
When detailing Int. Bents on SPS the Section thru drop panel shall be drawn to appropriate grade.
PART SECTION


751.40 Intermediate Bents - Integral Column Bents with Drop Panel (Part Sections AA).gif


PART SECTION A-A
(FLAT)
PART SECTION A-A
(GRADE OR V.C.)

D = Diameter of Column


751.40 Intermediate Bents - Integral Column Bents with Drop Panel (Part Plans Square & Skewed).gif


PART PLAN - SQUARE PART PLAN - SKEWED


751.40 Intermediate Bents - Integral Column Bents with Drop Panel (Section Thru Drop Panel).gif


SECTION THRU DROP PANEL


Largest
Longitudinal
Slab Bar
"a"
#8 1-13/16"
#9, #10 & #11 2-1/16"
#14 2-9/16"
Symbol.gif For Reference Only
 
Largest
Longitudinal
Slab Bar
"a" (*)
#8 & #9 2-5/8"
#10 & #11 2-7/8"
#14 3-3/8"


(*) Based on 3" clearance and #6 stirrups, (includes Integral W.S.) to top longitudinal bar.

(1) Standard 90° Hook.

(2) Const. joint key D/3 x D/3 x 2", D = Diameter of Column

751.40.8.9.3.3 Integral Pile Cap Bents with Drop Panel
751.40 Intermediate Bents - Integral Pile Cap Bents with Drop Panel (Part Section & Flat).gif
PART SECTION PART SECTION A-A
(FLAT)


Bottom or drop panel to be parallel to top of slab both transversely and longitudinally. 751.40 Intermediate Bents - Integral Pile Cap Bents with Drop Panel (Part Section Grade or VC).gif
(1)Horizontal except for superelevated structures.
(2) Use 3" Min. clip on beam for skews above 35°.
 
 
  PART SECTION A-A
(GRADE OR V.C.)


751.40 Intermediate Bents - Integral Pile Cap Bents with Drop Panel (Part Plans Square & Skewed).gif
PART PLAN - SQUARE PART PLAN - SKEWED


REINFORCEMENT


751.40 Intermediate Bents - Integral Pile Cap Bents with Drop Panel - Reinforcement (Half Section).gif


HALF SECTION


751.40 Intermediate Bents - Integral Pile Cap Bents with Drop Panel - Reinforcement (Section Thru Drop Panel).gif


SECTION THRU DROP PANEL


(1) Use 5 1/4" for computing length of stirrup bar. Do not detail on plans.

(2) Standard 90° hook.

(3) Optional Const. Joint Key 10" x 2"

751.40.8.9.3.4 Integral Pile Cap Bents without Drop Panel

REINFORCEMENT


751.40 Intermediate Bents - Integral Pile Cap Bents without Drop Panel - Reinforcement (Half Section).gif


HALF SECTION


751.40 Intermediate Bents - Integral Pile Cap Bents without Drop Panel - Reinforcement (Section Thru Bent).gif


SECTION THRU BENT


(1) Use 5 1/4" for computing length of stirrup bar. Do not detail on plans.

(2) Horizontal except for superelevated structures.

(3) Standard 90° hook.

751.40.8.9.3.5 Pile Footing Design and Details

(1) GENERAL

Number, size and spacing of piling shall be determined by computing the pile loads and applying the proper allowable overstresses.

Cases of Loading (AASHTO Article 3.22)

Group I maximum vertical loads.

Group IV temperature and shrinkage moments with applicable vertical loads.

1983 AASHTO guide specifications for seismic design of highway bridges. (See chapter 4 for earthquake loads combined with applicable vertical loads.) (*) (See Structural Project Manager or Liaison)

Internal stresses including the position of the shear line shall then be computed.

Long narrow footings are not desirable and care should be taken to avoid the use of an extremely long footing 6~0" wide when a shorter footing 8'-3" or 9'-0" wide could be used.

When using the load factor design method for footings, design the number of piles needed based on the working stress design method.


ASSUMPTIONS (Bents with 2 or more columns)


SEISMIC PERFORMANCE CATEGORY A

  1. Dead and live load moments will be 25% of the moments used for slab and top of Column design.
  2. Temperature moments shall be 50% of the moment at top of Column.
  3. Column reinforcement to be same as that required at top of Column. Footing dowel's to be #5 bars, same number as column bars.
  4. Footings to be proportioned for conditions as specified. Do not use ratio of bent height as specified for Intermediate Bents for longitudinal footings dimensions.


SEISMIC PERFORMANCE CATEGORIES B, C & D

  1. For Seismic Performance categories B, C & D, the connection between the bottom of Column and the footing is a fixed connection.
  2. Footing design is based on (Seismic Design of Beam-Column Joint).

(*) The design of all bridges in seismic performance B, C & D are to be designed by earthquake criteria in accordance with EPG 751.9 Bridge Seismic Design.


(2) PILE LOADS

P = N/n ± M/S
P = Pile Loads
N = Vertical Loads
n = number of piles
M = overturning moment
if minimum eccentricity controls the moment in both directions, it is necessary to use the moment in one direction (direction with less section modulus of Pile group) only for the footing check.
S = Section Modulus of pile group


AASHTO GROUP I AND IV LOADS

Maximum P = Pile Capacity Minimum P = 0

Tension on a pile will not be allowed for any combination of forces.

Overstress reduction will not be used for loading minimums.


EARTHQUAKE LOADS

POINT BEARING PILES

(**) Maximum P = Pile capacity x 2

(I.E. for HP 10 x 42 piles, maximum P = 56 x 2 = 112 tons/pile).

Minimum P = Use allowable uplift force specified for piles in EPG 751.39 Seal Course.

(**) Two (2) is our normal factor of safety. Under earthquake loadings only the point bearing pile and rock capacities are their ultimate capacities.


FRICTION PILES

Maximum P = Pile capacity


(3) INTERNAL STRESSES

A) Shear Line
B) Bending
C) Distribution of Reinforcement
D) Shear
751.40.8.9.3.6 Pedestal Pile

GENERAL

No concrete bell shall be used without approval of Structural Project Manager or Liaison.


SEISMIC PERFORMANCE CATEGORY A

  1. Assume column to be "pinned" for belled footing sitting on rock. All loads will be axial.
  2. Assume column to be fixed for pedestal pile embedded in rock.
  3. All earth loads within the diameter of belled footing, or pedestal pile if there is no bell, above ground line shall be included in footing design.


751.40 Intermediate Bents - Pedestal Pile General (Category A) Elevation.gif


SEISMIC PERFORMANCE CATEGORY B, C & D

See (Seismic Design).


DETAILS

SEISMIC PERFORMANCE CATEGORY A


751.40 Intermediate Bents - Pedestal Pile Details (Category A) Elevation & Section AA.gif


Diameter
of Shaft
Minimum
Bell Diameter
Maximum
Bell Diameter
Minimum
(*) Reinf.
Cubic Yards
Concrete per ft.
2'-0" 2'-4" 6'-0" 8-#7 0.1164
2'-6" 2'-10" 7'-6" 8-#9 0.1818
3'-0" 3'-6" 9'-0" 11-#9 0.2618
3'-6" 4'-0" 10'-6" 14-#9 0.3563
4'-0" 4'-6" 12'-0" 19-#9 0.4654
4'-6" 5'-0" 13'-0" 24-#9 0.5890
5'-0" 5'-6" 14'-0" 29-#9 0.7272
5'-6" 6'-0" 15'-0" 35-#9 0.8799
6'-0" 6'-6" 16'-0" 41-#9 1.0472


Concrete Quantities shown in table are per linear foot of shaft only. Bell Quantities are not included.

(*) Amount of reinforcing may be increased from that shown to meet the individual job requirements.

Minimum reinforcement meets AASHTO Spec. 8.18 for reinforcement of compression members.


DETAILS

SEISMIC PERFORMANCE CATEGORY B, C & D


751.40 Intermediate Bents - Pedestal Pile Details (Category B C & D) Elevation & Section AA.gif


Diameter
of Shaft
Minimum
(*) Reinf.
Cubic Yards
Concrete per ft.
2'-0" 8-#7 0.1164
2'-6" 8-#9 0.1818
3'-0" 11-#9 0.2618
3'-6" 14-#9 0.3563
4'-0" 19-#9 0.4654
4'-6" 24-#9 0.5890
5'-0" 29-#9 0.7272
5'-6" 35-#9 0.8799


Concrete Quantities shown in table are per linear foot of shaft only.

(*) Amount of reinforcing may be increased from that shown to meet the individual job requirements.

Minimum reinforcement meets AASHTO Spec. 8.18 for reinforcement of compression members.

(**) Stay in place casing may be used in place of spirals for column diameters greater than 4 foot.

751.40.8.10 Prestressed Concrete I-Girders

751.40.8.10.1 Design

751.40.8.10.1.1 Girder Design

Geometric Dimensions

Girder Analysis (Continuous Span Series)

Stresses due to dead load weight of slab, girder, diaphragms, haunch and forms will be based on simple spans from centerline to centerline of bearings.

Stresses due to dead load weight of curbs, parapet, rails, future wearing surface and outlets will be based on continuous composite spans with loads equally distributed to all girders. The span lengths used in these computations will be based on the distance from the centerline of the bearing at the End Bent to the centerline of the Int. Bent, and from centerline of Int. Bent to centerline of Int. Bent.

Stresses due to live load plus impact will be based on continuous composite spans whose lengths are described above for curbs, etc.

The analysis will be made on the basis of transformed areas of all steel (both strands and bars) in the section using concrete with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, n} = 6.

In composite design, allowances shall be made for the difference in modulus of elasticity of slab and girder by using the effective slab area as specified for concrete T-Beams as given in the current AASHTO Specifications, multiplied by the factor Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (E_{slab}/E_{girder})} . The area shall include the transformed area of all longitudinal reinforcing bars within the effective width. The 1" integral wearing surface shall not be used in the effective slab depth.


Effective Flange Width

The effective flange width for Beam Types 2,3,4 & 6 should be calculated using AASHTO 8.10.1. For Beam Type 7, the effective flange width should be calculated using AASHTO 9.8.3.


Continuity at Intermediate Supports

Continuity will be obtained at intermediate supports by pouring a concrete diaphragm monolithic with the deck slab and encasing the prestressed girders. Reinforcing bars will tie the slab, diaphragms and girders together.

Reinforcing bars, = 60,000 psi, will be placed in the deck slab for tensile steel.

The ultimate negative moments should be 2.17 times the maximum live load moments including impact and 1.3 times moments for future wearing surface and dead load of barrier or railing.

The area of longitudinal reinforcing steel at the centerline of the intermediate bent should be determined on the basis of a cracked section. This area of reinforcing bars is to be provided by adding additional bars between the normal longitudinal bars at the top of the slab. #8 maximum bar size for additional bars over bents.

These special negative moment reinforcing bars should be ended by one of the following criteria (whichever is greater):

  1. Where the stress on the normal longitudinal reinforcing bars does not exceed 24,000 psi. as based on a cracked section, plus 15 bar diameters or development length.
  2. Not closer to the centerline of the intermediate bent than 1/10 of the span. (8' min.)

The concrete stress at the bottom of the girder should be checked at a point 70 strand diameters plus 9 inches from the centerline of the intermediate bent to see that the total compressive stress due to prestress and negative moment does not exceed 3,000 psi. (AASHTO. 9.7.2)

The positive moment at the intermediate bent should be provided for by extending the top two rows of the top strands (both straight or deflected) and if available, the number of bottom strands indicated in tables below bent to form a right angle hook.


Design of Negative Moment Reinforcement

Since most of the dead load moments are carried by the beam acting as a simple span, the negative design moment over piers is the live load plus impact moment. In most designs, the dead load applied after continuity is achieved should also be considered in the negative design moment. The effect of initial precompression due to prestress in the precast girders may be neglected in the negative moment computation of ultimate strength if the maximum precompression stress is less than and the continuity reinforcement is less than 1.5 percent.

It will usually be found that the depth of the compression block will be less than the thickness of the bottom flange of the precast girder. For this reason, the negative moment reinforcement required can be determined by assuming the beam to be a rectangular section with a width equal to the bottom flange width of the girder. Due to the lateral restraint of the diaphragm concrete, ultimate negative compression failure in the PCA tests always occurred in the girders, even though the diaphragm concrete strength was about 1000 psi less than that of the girder concrete for this reason, it is recommended that the negative moment reinforce-ment be designed using the compressive strength of the girder concrete.


751.40 prestressed concrete i-girders-rectangular beam curves.gif
Rectangular Beam Curves



Web
Thickness
(Inches)
Number of Bottom Strands for Positive Moment
Connection (C) for Closed Diaphragms
Beam Type 2
or Modified
Beam Type 3
or Modified
Beam Type 4
or Modified
Beam Type 6
or Modified
Beam Type 7
or Modified
6 6 8 10 -- 18
6 1/2 -- -- -- 14 --
7 (A) 8 10 10 -- --
7 1/2 (B) -- -- -- 16 --
8 (A) 8 10 12 -- --
8 1/2 (B) -- -- -- 16 --


Web
Thickness
(Inches)
Number of Bottom Strands for Positive Moment Connection (C) for
Open Intermediate Diaphragms with Continuous Superstruecture
Beam Type 2
or Modified
Beam Type 3
or Modified
Beam Type 4
or Modified
Beam Type 6
or Modified
Beam Type 7
or Modified
6 12 16 16 -- 22
6 1/2 -- -- -- 22 --
7 (A) 12 16 16 -- --
7 1/2 (B) -- -- -- 22 --
8 (A) 12 16 16 -- --
8 1/2 (B) -- -- -- 22 --


(A) Modified Beam Type 2, 3 or 4.
(B) Modified Beam Type 6.
(C) If available, otherwise bend all bottom strands.


Negative Moment Bar Cut-Off (Working Stress Controlling)

Area of slab bars required and stress in the slab bars are printed in program BR200.

Determine stress of the area of slab bars input into program at a point where the area required is larger than that input.

Interpolate along a straight line to where the stress is 24,000 psi.

Note: Negative moment bar computations use a cracked section analysis to determine stresses.

751.40.8.10.1.2 Allowable Concrete Stresses

The following criteria is shown for clarity and is in accordance with AASHTO 9.15.

= 5,000 psi,   = 4,000 psi


A. Temporary stresses before losses except as noted:

  • Compression... (*)
  • Tension
    • Precompressed tensile zone ....................
      • No temporary allowable stresses are specified. See paragraph "B" below.
      • In tension areas with no bonded reinforcement...
      • Where the calculated tensile stress exceeds this value, bonded reinforcement shall be provided to resist the total tension force in the concrete computed on the assumption of an uncracked section. The maximum tensile stress shall not exceed...Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 7.5 \sqrt{f'_{ci}} = 7.5 \sqrt{4,000} = 475 psi}


B. Stresses at service loads after losses:

  • Compression...Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 0.4 f'_c = 0.4 \times 5,000 = 2,000 psi}
  • Tension in the precompressed tensile zone...
    • (a) For members with bonded reinf. (**)...Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 6 \sqrt {f'_c} = 6 \sqrt{5,000} = 425 psi}
    • (b) For members without bonded reinf...Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, = Zero}
  • Tension in other areas
    • Tension in other area is limited by the allowable temporary stresses specified in "A" above.


C. Cracking stress:

  • Modulus of rupture from tests or (for normal weight concrete)...Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 7.5 \sqrt{f'_c} = 7.5 \sqrt {5,000} = 530 psi}


D. Negative moment stresses in girders made continuous after deadload of slab is in place:

  • Tension in negative moment reinforcement... = 60,000 psi,   = 24,000 psi
  • Compression in concrete at bottom of girder... = 5,000 psi,  

(*) BR200 allows 2% overstress

(**)Strands qualify if not debonded at ends.

751.40.8.10.1.3 Prestress Loss and Prestress Camber


Reduce to:     Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, SH} = Shrinkage
= Elastic Strain
= Concrete Creep
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, CR_s} = Steel Creep


Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, CR_c} =
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, CR_c} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 12 fc - 7/2 fc = 8.5 fc}  (Approximate Estimate)
=      (Approximate Estimate)
= Concrete stress at centroid of P/S steel at point considered due to P/S and dead load at release.
= (Assume )
= (Estimate average)
= Concrete stress at centroid of P/S Steel (due to dead load)(Assume fcds = 1/2 fc)
= Initial stress in P/S steel
=
=
= (AASHTO 9.16.2.1)
=




Total loss due to all causes, except friction, is 34.22 ksi. (Friction losses are applied to post-tensioned girder only.) Use 8.84% for initial loss and 8.84% for final loss for design.


= initial loss

= final loss

= total loss


In the above design example, if tension exceeds AASHTO Specifications, (425 psi for 5,000 psi concrete) the girder will have to be modified to limit stress to 425 psi.


= 6,000 psi
= 4,500 psi
Grade 270 low relaxation strands
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, fc} = (Estimated average)
=
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \frac{Es}{Ec}} =
AASHTO 9.16.2.1.3: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, CRc = 12fc - 7/2fc = 8.5fc} (approximate estimate)



Reduce to:  


= (estimated average)
=

= Initial stress in low relaxation strands stressed to 75% of ultimate (*)

= 270,000 psi \times 75% = 202,500 psi


Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \frac {10,700 + (0.9 \times 6.89 + 8.08) \times 1,800}{202,500} = 18.0%}


Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 202.50 ksi \times 18.0% = 36.45 ksi} = total loss except friction

Use 9.44% for initial loss and 9.44% for final loss.

= initial loss

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 183.38 ksi \times 9.44% = 17.31 ksi} = final loss

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 19.12 + 17.31 = 36.43 ksi \approx 36.45 ksi = 202.5 ksi \times 18.0%} = total loss


P/s force initial =

P/s force final =


(*) Suggested by FHWA: when using 3/8" round strands, max. , whichever is smaller. Larger initial stresses will cause debonding.


Prestress Concrete Girder Formula for Stress Calculation

(-) Tension;   (+) Compression


Temp. Stress

Allow Top tension for
Bottom compression for
Temp. Top =


Temp. Bottom =


Design Load Stress

Allow Top compression for
Bottom tension for
Top final =


Bottom final =


0.153 sq. in. = Area of one 1/2 inch strand
270 ksi = f's = Ult, Str. P/S Strand
202.5 ksi = 0.75 (270) = Initial steel stress


0.0884 = 8.84% Initial loss - low relaxation
0.0884 = 8.84% Final loss - low relaxation
4 Str. 2 Draped
202.5 (0.153) = 30.98 kips/Str. P/s force
6 Strands (30.98) = 185.90 P/s force


= Area Composite
= Area Girder
= Eccentricity of prestress force of composite section
= Eccentricity of prestress force of non-composite section
= Composite dead load moment
= Girder dead load moment
= Live load + impact moment
= Slab + diaphragm moment
= Prestress forces in girder
= Composite section modulus at bottom of girder
= Non-composite section modulus at bottom of girder
= Composite section modulus at top of girder
= Non-composite section modulus at top of girder


Prestress Camber

Reference: Computer Program BR139B

751.40 prestressed concrete i-girders-camber diagram.gif


  Used to resist uplift before beam is set on bent.


  Used after beam is in place.


Mult. factor  
  Mult. Factor
= 5,000psi = 6,000psi
Beam Type 3 1.780 1.773
Beam Type 4 1.772 1.765
Beam Type 4 1.775 1.768
Beam Type 6 1.761 1.754
= 1.77
=2.718
= \varepsilon\ creep \times E_{28\ days}
= (See page 3 PCA design of precast prestressed concrete girders. Use 40% factor based on creep at erection for 28 days.)


The following formulas are used to determine:

  • Camber due initial strand stress (inch),
  • deflection due beam weight (inch),
  • camber due strands, beam weight and 28 day creep (inch),
  • camber L/4 due strands, beam weight and 28 day creep (inch),
  • deflection due to slab weight (inch),
  • camber centerline due strands, beam weight, 28 day creep, slab and diaphragm (inch), and
  • camber quarterpoint due strands, beam weight, 28 day creep, slab and diaphragm (inch).


Formulas used:

Positive deflect up

Negative deflect down



Beam weight camber


Slab weight camber


Force straight strands (1/2" low relaxation strands)


Force draped strands ( 1/2 " low relaxation strands)



= dist. centroid beam to centroid straight strand (in.)
= dist. centroid beam to low centroid draped at center of beam (in.)
= dist. centroid beam to up centroid draped at end of beam (in.)
= length (ft.) (cneterline bearing to centerline bearing).
= moment of inertia (in.2) non-transformed.
= moment of inertia (in.2) transformed.
= concentrated loads due to variable slab thickness on each end.
= dist. from centerline brg. to Ps.
= concentrated load due to diaphragm at center of span (kips)
= uniform beam load (kips/ft.)
= uniform slab load (kips/ft.)
= factor for 28 day creep
= modulus of elasticity corresponding to initial girder concrete strength
= modulus of elasticity corresponding to final girder concrete strength



Note: Compute and show on plans camber at 1/4 points for bridges with spans less than 75', 1/10 points for spans 75' and over.

751.40.8.10.1.4 Superstructure Design

Live Load Distribution

The live load distribution to girders may be assumed to be the same as the AASHTO distribution for concrete floors on steel I-Beam stringers. These factors may be found in EPG 751.40.8.2 Distribution of Loads.


Ultimate Load Capacity

The ultimate load capacity shall be not less than 1.3 times (the weight of the girder plus the weight of the slab and diaphragms plus the weight of the future wearing surface) plus 2.17 times the design live load plus impact.


Ultimate Strength

The ultimate moment on a prestressed girder as determined in accordance with the ultimate load capacity indicated above, shall not be greater than the ultimate strength determined as follows:


Where     Where  
751.40 prestressed concrete i-girders-ultimate strength diagram-1.gif   751.40 prestressed concrete i-girders-ultimate strength diagram-2.gif

or
Use the lesser
in each case

or


Where:

= Area of p/s strands in bottom flange
, , & = as shown above
= Ultimate strength of p/s strands
= Ultimate strength of slab concrete = 4,000 psi


Maximum Prestressing Steel Area

  When  


  When  


In lieu of the above, AASHTO - Article 9.17 & 9.18 may be used. (This is the method used by computer program BR200)

751.40.8.10.1.5 Web Reinforcement

(5" Min. - 21" Max. bar spacing for #4 bars) (5" Min. - 24" Max. bar spacing for #5 bars)


751.40 prestressed concrete i-girders-web reinforcement diagram.gif


(*) Prestressed concrete members shall be reinforced for diagonal tension stresses. Shear reinforcement shall be placed perpendicular to the axis of the member. The formula to be used to compute areas of web reinforcement is as follows:

  Where     but not more than
But shall not be less than   .


(**) Since large moments and large shears occur in the same area of the girder near the interior supports, the AASHTO formula (AASHTO - 9.20 -Shear) for computing the area of web reinforcement has been modified. The formula to be used to compute areas of web reinforcement near interior supports is as follows:

The value "jd" is the distance from the slab reinforcement to the center-of-gravity of the compression area under ultimate loads.

Use #4 shear reinforcement when possible. Alternate B1 bar will not work with #5.


Anchorage Zone Reinforcement - AASHTO Article 9.21.3

The following detail meets the criteria for anchorage zone reinforcement for pretensioned girders (AASHTO Article 9.21.3) for all MoDOT standard girder shapes.


Standard P/S Girder End Section
751.40 prestressed concrete i-girders-standard girder end-end section.gif 751.40 prestressed concrete i-girders-standard girder end-end elevation.gif
* 2 3/4" (Type 2, 3 & 4)
5 1/4" (Type 6)
** 15 1/2" (Type 2, 3 & 4)
22 1/2" (Type 6)


Sole Plate Anchor Studs

The standard 1/2" sole plate will be anchored with four 1/2" x 4" studs.

Studs shall be designed to meet the criteria of AASHTO Div. I-A in Seismic Performance Category C or D.

Stud capacity is determined as follows:

Where:

= no. of studs
= area of stud
= yield strength of stud (50 ksi)
= Allowable Shear in Pins AASHTO Table 10.32.1A
= seismic overload factor

If required, increase the number of 1/2" studs to six and space between open B2 bars. If this is still not adequate, 5/8" studs may be used. The following table may be used as a guide to upper limits of dead load reactions:

The minimum 3/16" fillet weld between the
1/2" bearing plate and 1 1/2" sole plate is
adequate for all cases.
Seismic Bearing Plate Anchor Design
No. of
Studs
Stud
Dia.
Max. Allowable D.L. Reaction (Kips)
A = 0.30 A = 0.36
4 1/2" 78 65
6 1/2" 117 98
4 5/8" 122 102
6 5/8" 184 153
751.40.8.10.1.6 Strands – Miscellaneous

Detensioning

In all detensioning operations the prestressing forces must be kept symmetrical about the vertical axis of the member and must be applied in such a manner as to prevent any sudden or shock loading.


General Information

Splicing:

One approved splice per pretensioning strand will be permitted provided the splices are so positioned that none occur within a member. Strands which are being spliced shall have the same "Twist" or "Lay". Allowance shall be made for slippage of the splice in computing strand elongation.

Wire failure:

Failure of one wire in a seven wire pretensioning strand may be accepted, provided that, it is not more than two percent of the total area of the strands.

Sand Blasting:

On structures where it is questionable as to the clarity of areas to be sandblasted: show limits of sandblasted area in a plan view of details on girder ends (bent sheet). However, generally, sandblasting is covered by Missouri Standard Specification 705.4.14.

751.40.8.10.2 Length

751.40.8.10.2.1 Structure Length
751.40 prestressed concrete i-girders-structure length-integral end bents.gif
(*) Maximum length for End Bent to End Bent = 600 feet.
Typical Continuous Prestressed Structure
(Integral End Bents)


751.40 prestressed concrete i-girders-structure length-non integral end bents.gif
(**) Maximum length for End Bent to End Bent = 800 feet.
Typical Continuous Prestressed Structure
(Non-Integral End Bents)

751.40.8.10.3 Miscellaneous Details

751.40.8.10.3.1 Shear Blocks

A minimum of two Shear Blocks 12" wide x 751.40 circled 1.gif high by width of diaphragm, will be detailed at effective locations on open diaphragm bent caps when adequate structural restraint cannot be provided for with anchor bolts.


751.40 prestressed concrete i-girders-miscellaneous details-shear block.gif


751.40 circled 1.gif Height of shear block shall extend a minimum of 1" above the top of the sole plate.
751.40.8.10.3.2 Anchor Bolts

Simple Spans

751.40 prestressed concrete i-girders-miscellaneous details-anchor bolts.gif
Expansion Fixed
Part Elevation
Note: It is permissible for the reinforcing bars and or the strands to come in contact with the materials used in forming A.B. holes.
  If A.B. holes are formed with galvanized sheet metal, the forms may be left in place.
  Hole (1 1/2" round) to be grouted with approved non-shirk grout.
751.40.8.10.3.3 Dowel Bars
751.40 prestressed concrete i-girders-miscellaneous details-dowel bars part elevation.gif 751.40 prestressed concrete i-girders-miscellaneous details-dowel bars section a-a.gif
Part Elevation
(Fixed Bent) (*)
Section A-A (*)
(*) Details shown are for SPC A and B only.

Dowel bars shall be used for all fixed intermediate bents under prestressed superstructures.


Seismic Performance Category A:

Use #6 Bars @ 18" Cts. for dowel bars.


Seismic Performance Category B:

Dowel bars shall be determined by design. (#6 Bars @ 18" Cts. minimum)
Design dowel bars for shear using service load design.
Allowable stresses are permitted to increase by 33.3% for earthquake loads.


Seismic Performance Categories C & D:

See Structural Project Manager.
751.40.8.10.3.4 Expansion Device Support Slots
751.40 prestressed concrete i-girders-miscellaneous details-exp device support holes part plan.gif
Part Plan of P/S Concrete I-Girder @ Expansion Device End
 
751.40 prestressed concrete i-girders-miscellaneous details-exp device support holes part elevation.gif
Part Elevation of P/S Concrete I-Girder @ Expansion Device End
(*) Show these dimensions on the P/S concrete girder sheet.

751.40.8.11 Open Concrete Intermediate Bents and Piers

751.40.8.11.1 Design

751.40.8.11.1.1 General and Unit Stresses

GENERAL

Use Load Factor design method, except for footing pressure and pile capacity where the Service Load design method shall be used.

In some cases, Service Load design method may be permitted on widening projects, see Structural Project Manager.

The terms, Intermediate Bents and Piers, are to be considered interchangeable for EPG 751.40.8.11 Open Concrete Intermediate Bents and Piers.


DESIGN UNIT STRESSES


(1) Reinforced Concrete

Class B Concrete (Substructure) = 1,200 psi = 3,000 psi
Reinforcing Steel (Grade 60) = 24,000 psi = 60,000 psi
n = 10  
(AASHTO Article 8.7.1) (*)


(2) Reinforced Concrete (**)

Class B-1 Concrete (Substructure) = 1,600 psi = 4,000 psi
Reinforcing Steel (Grade 60) = 24,000 psi = 60,000 psi
= 8  
(AASHTO Article 8.7.1) (*)


(3) Structural Steel

Structural Carbon Steel (ASTM A709 Grade 36)
= 20,000 psi,   = 36,000 psi


(4) Overstress

The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for Service Load design method.


(*) Use

(**) May be used for special cases, see Structural Project Manager.

751.40.8.11.1.2 Loads

(1) Dead Loads


(2) Live Loads

As specified on the Bridge Memorandum.
Impact of 30% is to be used for the design of beam, web supporting beam and top of columns. No impact is to be used for bottom of column, tie beam or footing design.


(3) Wind and Frictional Forces


(4) Temperature and Shrinkage

The effect of normal and parallel components to the bent shall be considered. When bearings with high friction coefficients are used or for long bridge lengths, the columns and footings are to be analyzed for moments normal to the bent due to the horizontal deflection of the top of the bent.


(5) Buoyancy

If specified by the Structural Project Manager, or by the Bridge Memorandum.


(6) Earth Pressure

Bents are to be analyzed for moments due to equivalent fluid pressure on columns and web where the ground line at time of construction, or potential changes in the ground line, indicate.


(7) Earthquake

See Structural Project Manager or Liaison.


(8) Special Stability Situations

When indicated by the Bridge Memorandum or by the Structural Project Manager, piers must be analyzed for special loadings as directed (i.e., differential settlement).


(9) Collision

Where the possibility of collision exists from railroad traffic, the appropriate protection system, for example Collision Wall, shall be provided (See the Bridge Memorandum).


(10) Collision Walls

Collision walls are to be designed for the unequal horizontal forces from the earth pressure, if the condition exists (See the Bridge Memorandum). The vertical force on the collision wall is the dead load weight of the wall (*). If a bent has three or more columns, design the steel in the top of the wall for negative moment.


(*) For footing design, the eccentricity dead load moment due to an unsymmetrical collision wall shall be considered.

751.40.8.11.1.3 Distribution of Loads

(1) Dead Loads

Loads from stringers, girders, etc. shall be concentrated loads applied at the centerline of bearing. Loads from superstructure, such as concrete slab spans, shall be applied as uniformly distributed loads.


(2) Live Loads

Loads from stringers, girders, etc., shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of bent.


(3) Wind and Frictional Forces


(4) Temperature

Apply at the top of the substructure beam.


(5) Earth Loads

(a) Vertical
Vertical earth loads on tie beams shall be applied as uniform loads for a column of earth equal to 3 times the width of the beam. The weight of earth for footing design shall be that directly above the footing, excluding that occupied by the column.


The earth above the seal courses shall be considered in computing pile loads. Refer to the Design and Dimension of the Pile Footings portion of EPG 751.40.8.13 Concrete Pile Cap Non-Integral End Bents or EPG 751.36 Driven Piles.


(b) Horizontal

751.40 Open Concrete Int Bents and Piers- Distribution Loads.gif

(*) A factor of 2.0 is applied to the moment to allow for the possibility of the column esisting earth pressure caused by the earth behind the column twice the column width.


(6) Earthquake Loads

See Structural Project Manager or Liaison.


(7) Seal Course

The weight of the seal course shall not be considered as contributing to the pile loads, except for unusual cases.
751.40.8.11.1.4 Types of Design

TYPES OF DESIGN

Rigid frame design is to be used for the design of Intermediate Bents and Piers.


The joint between the beam and column, and web or tie beam and column, is assumed to be integral for all phases of design and must be analyzed for reinforcement requirements as a "Rigid Frame".


The joint between the column and footing is assumed to be "fixed", unless foundation fexibility needs to be considered (consult Structural Project Manager for this assessment).


If the distance from the ground line to the footing is large (*), consideration shall be given to assuming the column to be "fixed" at a point below the ground line.


(*) When the distance from the ground line to the top of footing is 10' or more, the unsupported height and the fixed point may be measured from the bottom of the beam to the ground line plus 1/2 of the distance from the ground line to the top of the footing.


UNSUPPORTED HEIGHT

Unsupported height is the distance from the bottom of the beam to the top of the footing.


SINGLE COLUMN

Use rigid frame design with the column considered "fixed" at the bottom for all of the conditions.


COLUMN DIAMETER CHANGE

Use a change in column diameter as required by the Bridge Memorandum or column design.


COLUMN SPACING (TRIAL)

(Except Web Supporting Beam type)

Estimate centerline-centerline column spacing for a two column bent as 72% of the distance from the centerline of the outside girder to the centerline of the outside girder.

A three column bent spacing estimation is 44% of the centerline-centerline outside girder spacing.

751.40.8.11.2 Reinforcement

751.40.8.11.2.1 Hammer Head Type
751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Part Plan.gif 751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Section A-A.gif
PART PLAN SECTION A-A
751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Part Elev.gif Note:
When an expansion device in the slab is used at an intermediate bent, all reinforcement located entirely within the beam shall be epoxy coated. See details of protective coating and sloping top of beam to drain.
751.40 Open Concrete Int Bents and Piers- Hammer Head Type- Part Section B-B.gif
PART ELEVATION PART SECTION B-B

(*) Add hooked reinforcement as required by design.

(**) See AASHTO Article 8.18.2.3.4 for tie requirements.


751.40 circled 1.gif All stirrups in beam to be the same size bar. (Use a min. spacing of 5" (6" for double stirrups), minimum stirrups are #4 at 12" cts., and maximum stirrups are #6 at 6" cts.)

Locate #4 bars (┌─┐) under bearings if required. (Not required for P/S Double-Tee Girders.)


751.40 circled 2.gif See development length (Other than top bars) or standard hooks in tension, Ldh.


751.40 circled 3.gif See lap splice class C.

751.40.8.11.3 Pile Footings

751.40.8.11.3.1 Design and Dimensions

GENERAL

Number, size and spacing of piling shall be determined by computing the pile loads and applying the proper allowable overstresses.
Cases of Loading: (AASHTO Article 3.22)
Group I and Group II maximum vertical loads (refer to distribution of loads, this Section).
Group III thru VI wind and/or temperature moments with applicable vertical loads.
Internal stresses including the position of the shear line shall then be computed.
Long narrow footings are not desirable and care should be taken to avoid the use of an extremely long footing 6~0" wide when a shorter footing 8'-3" or 9'-0" wide could be used.
Footings are to be designed for the greater of the minimum moment requirements at the bottom of the column, or the moments at the bottom of the footing.
When using the load factor design method for footings, design the number of piles needed based on the working stress design method.


PILE LOADS

- Pile Loads
- Vertical Loads
- Number of Piles
- Overturning Moment
  If minimum eccentricity controls the moment in both directions,
  It is necessary to use the moment in one direction (direction with
  less section modulus of pile group) only for the footing check.
- Section Modulus of Pile Group


(A) AASHTO Group I thru VI Loads as applicable
Maximum = Pile Capacity
Minimum (zero)
Tension on a pile will not be allowed for any combination of forces.
Pile design force shall be calculated with consideration of AASHTO percentage overstress factors.


(B) Earthquake Loads

See Structural Project Manager or Liaison before using the following seismic information.

Point Bearing Pile
Maximum (**)
(i.e., for HP 10 X 42 piles, Max. tons/pile)
Minimum = Allowable uplift force specified for piles in this
Section under Seal Course Design.
(**) Two "2" is our normal factor of safety. Under earthquake loadings only the point bearing pile and rock capacities are their ultimate capacities.
Friction Piles
Maximum = Pile Capacity
Minimum = Allowable uplift force specified for piles in this
Section under Seal Course Design.
See combined axial & bending stresses in Cast-In-Place friction piles in liquefaction areas.


(1) Shear Line

If the shear line is within the column projected, the footing may be considered satisfactory for all conditions and standard #6 hairpin bars shall be used.


If the shear line is outside of the column projected, the footing must be analyzed and reinforced for bending and checked for shear stress (see (4) Shear, below).


Footing depths may be increased, in lieu of reinforcement, if an increase would be more economical. (6'-0" Maximum depth, with 3" increments.)

751.40 Open Concrete Int Bents and Piers- Pile Footings- Internal Stresses.gif


(2) Bending

The critical section for bending shall be taken at the face of the columns (concentric square of equivalent area for round columns).

The reinforcement shall be as indicated for reinforced footings, except that the standard #6 hairpin bars may be used for small footings if they provide sufficient steel area.


(3) Distribution of Reinforcement

Reinforcement in Bottom of Footing

751.40 Open Concrete Int Bents and Piers- Pile Footings- Distribution of Reinforcement.gif

Reinforcement shall be distributed uniformly across the entire width of footing in the long direction. In the short direction, the portion of the total reinforcement given by AASHTO Equation 4.4.11.2.2-1 shall be distributed uniformly over a band width equal to the length of the short side of the footing, .

Band Width Reinforcement =
where

The remainder of the reinforcement required in the short direction shall be distributed uniformly outside the center band width of footing.


Reinforcement in Top of Footing

Reinforcement in the top of the footing shall be provided based on a seismic analysis for Seismic Performance Categories B, C and D. This reinforcement shall be at least the equivalent area as the bottom steel in both directions. The top steel shall be placed uniformly outside the column.


(4) Shear

(AASHTO Article 8.15.5 or 8.16.6)

The shear capacity of footing in the vicinity of concentrated loads shall be governed by the more severe of the following two conditions.


(i) Beam shear

Critical Section at "d" distance from face of column.

b = Footing Width Service Load 751.40 Open Concrete Int Bents and Piers- Pile Footings- Internal Stresses- Part Plan of Footing- Beam Shear.gif
Service Load
Load Factor
PART PLAN OF FOOTING


(ii)Peripheral Shear


Critical Section at "d/2" distance from face of column.

Service Load 751.40 Open Concrete Int Bents and Piers- Pile Footings- Internal Stresses- Part Plan of Footing- Peripheral Shear.gif
Load Factor
PART PLAN OF FOOTING


If shear stress is excessive, increase footing depth.

751.40 circled 1.gif Piles to be considered for shear. (Center of piles are at or outside the critical section.)


751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Side Elev.gif 751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Front Elev.gif
SIDE ELEVATION FRONT ELEVATION


751.40 circled 1.gif Min. = 1/8 x (Distance from top of beam to bottom of footing.)
751.40 circled 2.gif 3'-0" (Min.) & 6'-0" (Max.) for steel HP piles, 14" CIP piles. AASHTO Article 4.5.6.4 shall be considered if piles are situated in cohesive soils.
  3D (Min.) and 6D (Max.) for 20" and 24" CIP piles. (D = pile diameter)
751.40 circled 3.gif Indicates column diameter, or column length or width on a hammer head pier.
751.40 circled 4.gif Min. = 2'-6" or column diameter (*) (Or width) for friction piles for SPC A.
  Min. = 3'-0" or column diameter (*) (Or width) for steel piles for SPC A.
  Min. = 3'-0" or column diameter (*) (Or width) for friction piles for SPC B,C,& D.
  Min. = 3'-6" or column diameter (*) (Or width) for steel piles for SPC B, C & D.
751.40 circled 5.gif 12" for seismic performance category A and 18" for SPC B, C, & D.
(*) For column diameters 4'-0" and greater use a 4'-0" min. footing thickness.
(**) Use 18" for steel HP piles, 14" CIP piles, prescase and prestress piles.

751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Typ Plan of 3 Pile Footing.gif

TYPICAL PLAN OF
3 PILE FOOTINGS

(minimum pile spacings)

NOTES:

Use 3- piles on exterior foorings only.

Use only HP 10 x 42 or friction piles on three pile footings.

751.40 Open Concrete Int Bents and Piers- Pile Footings- Design and Dims- Typ Plan of Staggered Pile.gif

TYPICAL PLAN
STAGGERED PILE

(7 Pile footings shall not be used.)

751.40 circled 1.gif If horizontal thrust requires pile batter- consult the Structural Project Manager.

(*) The maximum pile spacing is 4'-0".

751.40.8.11.3.2 Reinforcement

Unreinforced Footing - Use only in Seismic Performance Category A

751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Elev 3 Pile Footing.gif 751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Elev 4 Pile Footing.gif
Elevation
(3 Pile Footing)
Elevation
(4 Pile Footing
 
751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Plan 3 Pile Footing.gif 751.40 Open Concrete Int Bents and Piers- Pile Footing- Reinforcement- Plan 4 Pile Footing.gif
Plan
(3 Pile Footing)
Plan
(4 Pile Footing
(*) See lap splice class C (Other than top bars).
Notes: Reiforcement not required by design. Hairpins are sufficient for renforcing requirements.
  The minimum percentage of reinforcement, "P" , is not required to be met, unless scour is anticipated.
  Use for all types of piling, except timber.


Reinforced Footing - Seismic Performance Category A

751.40 seismic performance category a footing reinforcement front elevation.gif 751.40 seismic performance category a footing reinforcement side elevation.gif
Front Elevation Side Elevation
 
  751.40 Open Concrete Int Bents and Piers-reinforcement-seismic performance category a footing reinforcement plan.gif
  Plan
(*) See lap splice class C (Other than top bars).
Note: The maximum size of stress steel allowed is #8 bars.


Reinforced Footing - Seismic Performance Categorys B, C & D

See Structural Project Manager or Liaison before using the following seismic details.


751.40 seismic performance category b c & d footing reinforcement front elevation.gif 751.40 seismic performance category b c & d footing reinforcement side elevation.gif
Front Elevation Side Elevation
 
751.40 Open Concrete Int Bents and Piers- Pile Footings- typical detail pile channel shear connector.gif 751.40 seismic performance category b c & d footing reinforcement plan of top reinforcement.gif
Typical Detail
Pile Channel
Shear Connector
  Plan Showing Top Reinforcement
 
  751.40 seismic performance category b c & d footing reinforcement plan of bottom reinforcement.gif
  Plan Showing Bottom reinforcement
(*) For reinforcement in top of the footing, see lap splice class C (Top bars).
(**) Place the top reinforcement uniformly outside the column.
(***) Use same area of steel in the top of the footing as is required for the bottom.
Notes: For reinforcement in bottom of the footing, see lap splice Class C (Other than top bars).
  The maximum size of stress steel allowed is #8 bars.
  Unreinforced footings shall not be used in seismic performance categories B, C & D.

751.40.8.11.4 Spread Footings

751.40.8.11.4.1 Design and Dimensions
751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-side elevation.gif 751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-front elevation.gif
Side Elevation Front Elevation
d = column diameter
L = footing length
b = footing depth
B = footing width
A = edge distance from column


The calculated bearing pressure shall be less than the ultimate capacity of the foundation soil. The ultimate capacity of the foundation soil can be conservatively estimated as 2.0 times the allowable bearing pressure given on the Bridge Memorandum. The analysis method of calculating bearing pressures is outlined in the following information.


Dimensional Requirements

L - Minimum of 1/6 x distance from top of beam to bottom of footing (3" increments);
B - Minimum footing width is column diameter + 2A, (3" increments);
A - Minimum of 12";
b - Minimum of 30" or column diameter, Maximum of 72" at 3" increments; (for column diameters 48" and greater use a 48" minimum footing depth.)


Size

The size of footing shall be determined by computing the location of the resultant force and by calculating the bearing pressure.

Long, narrow footings are to be avoided, especially on foundation material of low capacity. In general, the length to width ratio should not exceed 2.0, except on structures where the ratio of the longitudinal to transverse loads or some other consideration makes the use of such a ratio limit impractical.


Location of Resultant Force


The location of the resultant force shall be determined by the following equations.

The Middle 1/3 is defined as:

The Middle 1/2 is defined as: and

The Middle 2/3 is defined as: and

The following table specifies requirements for the location of the resultant force.


Soil Type Resultant Location Group I - VI Resultant Location Earthquake Loads Categories B, C and D
Clay, clay and boulders, cemented gravel, soft shale with allowable bearing values less than 6 tons, etc. middle 1/3 middle 1/2
Rock, hard shale with allowable bearing values of 6 tons or more. middle 1/2 middle 2/3


Bearing Pressure

The bearing pressure for Group I thru VI loads shall be calculated using service loads and the allowable overstress reduction factors as specified in AASHTO Table 3.21.1A. The calculated bearing pressure shall be less than the allowable pressure given on the Bridge Memorandum.

The bearing pressure for Earthquake Loads in Categories B, C, and D shall be calculated from loads specified in AASHTO Division I-A Seismic Design, Sections 6.2.2, 7.2.1, and 7.2.2. The seismic design moment shall be the elastic seismic moment (EQ) divided by the modified response modification factor R'. The modified seismic moment shall then be combined independently with moments from other loads:

Group Load =

Where:

= dead load
= buoyancy
= stream flow pressure
= elastic seismic moment
= earth pressure
= R/2 for category B
  = 1 for categories C and D
 
= Response Modification Factor
  = 5 for multi-column bent
  = 3 for single-column bent


The calculated bearing pressure shall be less than the ultimate capacity of the foundation soil. The ultimate capacity of the foundation soil can be conservatively estimated as 2.0 times the allowable bearing pressure given on the Bridge Memorandum. The analysis method of calculating bearing pressures is outlined in the following information.


See AASHTO 4.4.2 for explanation of notations.


751.40 sketch of dimensions for footings subjected to eccentric loading.gif
Sketch of Dimensions for Footings Subjected to Eccentric Loading


For   For  
 
 
 
751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-plan view 1.gif 751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-plan view 2.gif
Plan View Plan View
 
751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure 1.gif 751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure 2.gif
Bearing Pressure Bearing Pressure
Bearing Pressure for Footing Loaded Eccentrically About One Axis



CASE 1 CASE 2
751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 1 plan view.gif 751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 2 plan view.gif
  k, x and y from AASHTO chart
CASE 1 Plan View CASE 2 Plan View
 
CASE 3 CASE 4
751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 3 plan view.gif 751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-bearing pressure case 4 plan view.gif
 
CASE 3 Plan View CASE 4 Plan View
Bearing Pressure for Footing Loaded Eccentrically About Two Axes


Loading Cases

Loads for Groups I thru VI shall be calculated for all bridges.

Earthquake loads shall be calculated when the bridge is in Seismic Zones B, C, and D.

Loads for other group loadings shall be used on a case by case basis.


Reinforcement

The footing is to be designed so that the shear strength of the concrete is adequate to handle the shear stress without the additional help of reinforcement. If the shear stress is too great, the footing depth should be increased.


Shear

The shear capacity of the footings in the vicinity of concentrated loads shall be governed by the more severe of the following two conditions.


Critical section at "d" distance from face of column:

751.40 critical section at d dist from face of column.gif
Load Factor
= footing width


Critical section at "d/2" distance from face of column:

751.40 critical section at d divided by 2 dist from face of column.gif
Load Factor
If shear stress is excessive, increase footing depth.


Bending

If the shear line is within the projected equivalent square column, the footing may be considered satisfactory for all conditions. (minimum reinforcement required)

If the shear line is outside of the projected column, the footing must be analyzed and reinforced for bending and checked for shear stress.

751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-shear line diagrams.gif

The critical section for bending shall be taken at the face of the equivalent square column. The equivalent square column is the theoretical square column which has a cross sectional area equal to the round section of the actual column and placed concentrically.


Reinforcement in Bottom of Footing

The bearing pressure used to design bending reinforcement for Group I thru VI loads shall be calculated using Load Factor Loads.

The bearing pressure used to design bending reinforcement for Earthquake Loads in Categories B, C, and D shall be calculated from the same loads as specified in AASHTO Division 1-A Seismic Design for ultimate bearing pressure.

The bottom reinforcement shall be designed using ultimate strength design.


Distribution of Reinforcement

751.40 Open Concrete Int Bents and Piers- spread footings-design and dimensions-distribution of reinforcement.gif
L = Footing Length
B = Footing Width

Reinforcement shall be distributed uniformly across the entire width of footing in the long direction. In the short direction, the portion of the total reinforcement given by AASHTO Equation 4.4.11.2.2-1 shall be distributed uniformly over a band width equal to the length of the short side of the footing, B.


Reinforcement in Top of Footing

Reinforcement in the top of the footing shall be provided for Seismic Performance Categories B, C, and D. This reinforcement shall be the equivalent area as the bottom steel in both directions. The top steel shall be placed uniformly outside the column.


Reinforcement Details - Seismic Performance Category A
751.40 Open Concrete Int Bents and Piers- spread footings-SPC A reinforcement details-front elevation.gif 751.40 Open Concrete Int Bents and Piers- spread footings-SPC A reinforcement details-side elevation.gif
Front Elevation Side Elevation


Reinforcement Details - Seismic Performance Categorys B, C & D
751.40 Open Concrete Int Bents and Piers- spread footings-SPC b c & d reinforcement details-front elevation.gif 751.40 Open Concrete Int Bents and Piers- spread footings-SPC b c & d reinforcement details-side elevation.gif
Front Elevation Side Elevation
(*) Use same area of steel in the top of the footing as is required for the bottom.

751.40.8.12 Concrete Pile Cap Intermediate Bents

751.40.8.12.1 Design

751.40.8.12.1.1 Unit Stresses
(1) Reinforced Concrete
  Class B Concrete (Substructure) = 1,200 psi = 3,000 psi
  Reinforcing Steel (Grade 60 = 24,000 psi = 60,000 psi
  = 10
 
 
(2) Structural Steel
  Structural Carbon Steel (ASTM A709 Grade 36) = 20,000 psi = 36,000 psi
 
(3) Piling
 
(4) Overstress
  The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for service loads.
751.40.8.12.1.2 Loads
(1) Dead Loads
 
(2) Live Load
  As specified on Bridge Memorandum.
  Impact of 30% is to be used for design of the beam. No impact is to be used for design of any other portion of bent including the piles.
 
(3) Temperature, Wind and Frictional Loads
751.40.8.12.1.3 Distribution of Loads
(1) Dead Loads
  Loads from stringers, girders, etc. shall be concentrated loads applied at the intersection of centerline of stringer and centerline of bearing. Loads from concrete slab spans shall be applied as uniformly, distributed loads along the centerline of bearing.
 
(2) Live Load
  Loads from stringers, girders, etc. shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of bearing. For concrete slab spans distribute two wheel lines over 10'-0" (normal to centerline of roadway) of substructure beam. This distribution shall be positioned on the beam on the same basis as used for wheel lines in Traffic Lanes for Substructure Design.
 
(3) Temperature, Wind and Frictional Loads
751.40.8.12.1.4 Design Assumptions

LOADINGS

(1) Beam
  The beam shall be assumed continuous over supports at centerline of piles.
  Intermediate bent beam caps shall be designed so that service dead load moments do not exceed the cracking moment of the beam cap (AASHTO Article 8.13.3, Eq. 8-2).
 
(2) Piles
  (a) Bending
  Stresses in the piles due to bending need not be considered in design calculations for Seismic Performance Category A.
  (b) Dead Loads, etc.
  Dead load of superstructure and substructure will be distributed equally to all piles which are under the main portion of the bent.

751.40.8.12.2 Reinforcement

751.40.8.12.2.1 General

PRESTRESS DOUBLE-TEE STRUCTURES


751.40 Conc Pile Cap Int Bents PS Dbl Tee (Bents with 3 thru 6 in crown).gif
BENTS WITH 3" THRU 6" CROWN


751.40 Conc Pile Cap Int Bents PS Dbl Tee (Section AA).gif 751.40 Conc Pile Cap Int Bents PS Dbl Tee (Section BB).gif
SECTION A-A SECTION B-B


(*) Channel shear connectors are to be used in Seismic Performance Categories B, C & D. For details not shown, see EPG 751.9 Bridge Seismic Design.
(**) 2'-6" Min. for Seismic Performance Category A.
2'-9" Min. for Seismic Performance Categories, B, C & D.
Note: Use square ends on Prestress Double-Tee Structures.


751.40 Conc Pile Cap Int Bents PS Dbl Tee (Bents with crown over 6 in).gif
BENTS WITH CROWN OVER 6"


751.40 Conc Pile Cap Int Bents PS Dbl Tee (Bents with crown over 6 in) (Section AA).gif 751.40 Conc Pile Cap Int Bents PS Dbl Tee (Bents with crown over 6 in) (Section BB).gif
SECTION A-A SECTION B-B


(*) Channel shear connectors are to be used in Seismic Performance Categories B, C & D.
(**) 2'-6" Min. for Seismic Performance Category A.
2'-9" Min. for Seismic Performance Categories, B, C & D.
Note: Use square ends on Prestress Double-Tee Structures.
751.40.8.12.2.2 Anchorage of Piles for Seismic Performance Categories B, C & D

STEEL PILE


751.40 Conc Pile Cap Int Bents Reinf Steel Pile (Part Elevation).gif 751.40 Conc Pile Cap Int Bents Reinf Steel Pile (Sec thru beam).gif
PART ELEVATION SECTION THRU BEAM
751.40 Conc Pile Cap Int Bents Reinf Steel Pile (Part Plan).gif
PART PLAN


CAST-IN-PLACE PILE


751.40 Conc Pile Cap Int Bents Reinf CIP Pile (Part Elevation).gif 751.40 Conc Pile Cap Int Bents Reinf CIP Pile (Sec thru beam).gif
PART ELEVATION SECTION THRU BEAM
751.40 Conc Pile Cap Int Bents Reinf CIP Pile (Part Plan).gif
PART PLAN
751.40.8.12.2.3 Beam Reinforcement Special Cases

SPECIAL CASE I


If centerline bearing is 12" or less on either side of centerline piles, for all piles (as shown above), use 4-#6 top and bottom and #4 at 12" cts. (stirrups), regardless of pile size.


751.40 Conc Pile Cap Int Bents Beam Reinf (Special Case I).gif


SPECIAL CASE II


When beam reinforcement is to be designed assuming piles to take equal force, design for negative moment in the beam over the interior piles.


751.40 Conc Pile Cap Int Bents Beam Reinf (Special Case II).gif


(*) Dimensions shown are for illustration purposes only.

751.40.8.12.3 Details

751.40.8.12.3.1 Sway Bracing

Refer to EPG 751.32.3.2.1 Sway Bracing.

751.40.8.12.3.2 Miscellaneous Details for Prestressed Girder

PRESTRESSED GIRDERS (INTEGRAL INT. BENT)


751.40 Conc Pile Cap Int Bents Misc Details PS Girders (Integral Int Bent) Jt Filler Detail.gif


DETAIL OF JOINT FILLER AT INT. BENTS
(Continuous Spans - No Longitudinal Beam Steps)


(*) ¼ Joint Filler for a P/S Double Tee Structure
  ½ Joint Filler for a P/S I-Girder Structure


PRESTRESSED GIRDERS (NON-INTEGRAL INT. BENT)


751.40 Conc Pile Cap Int Bents Misc Details PS Girders (Non Integral Int Bent) Jt Filler Detail.gif


DETAIL OF JOINT FILLER AT INT. BENTS
Longitudinal Beam Step and Shear Blocks shown)


DETAILS OF CONST. JOINT KEY

751.40 Conc Pile Cap Int Bents Misc Details Const Jt Key (Part Elevation).gif 751.40 Conc Pile Cap Int Bents Misc Details Const Jt Key (Part Section PS I Girders).gif 751.40 Conc Pile Cap Int Bents Misc Details Const Jt Key (Part Section Dbl Tee Girders).gif
PART ELEVATION PART SECTION THRU KEYS
(P/S I-GIRDERS)
PART SECTION THRU KEYS
(P/S DOUBLE TEE GIRDERS)


751.40.8.13 Concrete Pile Cap Non-Integral End Bents

751.40.8.13.1 Design

751.40.8.13.1.1 Unit Stresses
(1) Reinforced Concrete
  Class B Concrete (Substructure) = 1,200 psi = 3,000 psi
  Reinforcing Steel (Grade 60) = 24,000 psi = 60,000 psi
  = 10
  AASHTO Article 8.7.1) (*)
 
(2) Structural Steel
  Structural Carbon Steel (ASTM A709 Grade 36) = 20,000 psi = 36,000 psi
 
(3) Piling
 
(4) Overstress
  The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for Service Loads design method.
(*) = 145 pcf., for = 150 pcf.
751.40.8.13.1.2 Loads
(1) Dead Loads
 
(2) Live Load
  As specified on the Bridge Memorandum
  Impact of 30% is to be used for design of the beam. No impact is to be used for design of any other portion of bent including the piles.
 
(3) Temperature, Wind and Frictional Loads
  Wind and temperature forces can be calculated based on longitudinal force distribution.
751.40.8.13.1.3 Distribution of Loads
(1) Dead Loads
  Loads from stringers, girders, etc. shall be concentrated loads applied at the intersection of centerline of stringer and centerline of bearing.
 
(2) Live Load
  Loads from stringers, girders, etc. shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of earing.
 
(3) Temperature
  The force due to expansion or contraction applied at bearing pads are not used for stability or pile bearing computations. However, the movement due to temperature should be considered in the bearing pad design and expansion device design.
 
(4) Wing with Detached Wing Wall
751.40 Detached Wing Wall Section AA.gif
SECTION A-A


751.40 Detached Wing Wall Detail B.gif
DETAIL B


(*) Detached wing wall shown is for illustration purpose only. Design detached wing wall as a retaining wall.
(**) See retaining wall design.
751.40.8.13.1.4 Design Assumptions - Loadings
1) Piles
  a. Stresses in the piles due to bending need not be considered in design calculations except for seismic design in categories B, C and D.
  b. The following four loading cases should be considered.
   
Case Vertical Loads Horizontal Loads Special Consideration
I DL + E + SUR EP + SUR -
II DL + LL + E + SUR EP + SUR -
III DL + LL + E EP -
IV DL + LL + E None Allow 25% Overstress
    Where,
    LL = live load
    DL = dead load of superstructure, substructure and one half of the apporach slab
    SUR = two feet of live load surcharge
    E = dead load of earth fill
    EP = equivalent fluid pressure of earth
    Maximum pile pressure = pile capacity
    Minimum pile pressure = 0 (tension on a pile will not be allowed for any combination of forces exept as noted)
 
2) Analysis Procedure
  a. Find the lateral stiffness of a pile, :
    With fixed pile-head (i.e., only translation movement is allowed but no rotation allowed): The lateral stiffness of a pile can be estimated using Figures 1 and 3 or 2 and 3 for pile in cohesionless or cohesive soil, respectively. The method of using Figures 1, 2, and 3 to find lateral stiffness is called Linear Subgrade Modulus Method. Usually the significant soil-pile interaction zone for pile subjected to lateral movement is confined to a depth at the upper 5 to 10 pile diameters. Therefore, simplified single layer stiffness chart shown in Figure 3 is appropriate for lateral loading. The coefficient in Figures 1 and 2 is used to define the subgrade modulus at depth “z” representing the soil stiffness per unit pile length. For the purpose of selecting an appropriate value, the soil condition at the upper 5 pile diameters should be used. Since soil property, friction angle , or cohesion c, is needed when Figure 1 or 2 is used, determine soil properties based on available soil boring data. If soil boring data is not available, one can conservatively use value of 0.1 in Figure 3. Designer may also use soil properties to convert SPT N value to friction angle , or cohesion c, for granular or cohesive soil, respectively. Figures 1 and 2 were based on test data for smaller-diameter (12 inches) piles, but can be used for piles up to about 24 inches in diameter. In Figure 2, the solid line (by Lam et al. 1991) shall be used in design.
  b. Find the axial stiffness of a pile, :
    For friction pile, may be determined based on a secant stiffness approach as described in EPG 751.9 Bridge Seismic Design or by the in-house computer program “SPREAD” where is calculated as:
      Equation (1)
    Where:
    = cross sectional area of pile
    = elastic modulus of pile
    = total length of pile
    = secant stiffness due to ultimate friction capacity of the pile as described in EPG 751.9.2.6.3 Pile Axial Stiffness
    = secant stiffness due to ultimate bearing capacity of the pile as described in EPG 751.9.2.6.3 Pile Axial Stiffness
  For HP bearing pile on rock shall be calculated as:
      Equation (2)
    Or Conservatively, may be determined as:
      Equation (3)
 
751.40 Subgrade Modulus with Depth for Sand.gif
 
Recommended Coefficient of Variation in Subgrade Modulus with Depth for Sand
 
751.40 Subgrade Modulus with Depth for Clay.gif
 
Recommended Coefficient of Variation in Subgrade Modulus with Depth for Clay
 
751.40 Lateral Embedded Pile-Head Stiffness.gif
PILE HEAD AT
GRADE LEVEL
  EMBEDDED PILE HEAD
 
Lateral Embedded Pile-Head Stiffness
 
  c. Find the equivalent cantilever pile length,
    For the structural model used in the structural analyses of loading cases I through IV. As shown in figure below, length L can be calculated as:
      Equation (4)
 
751.40 Structural Model.gif
 
Structural Model
 
  d. Find the equivalent pile area,  :
    Once the equivalent cantilever pile length has been determined from step (c) above, the equivalent axial rigidity of the pile, , can be calculated as . Then, the equivalent pile area, , is equal to
      Equation (5)
 
  e. Perform structural analyses for loading cases I through IV.
    Use computer programs STRUCT3D, SAP2000 or any other program capable of running static analysis.
 
  f. Check abutment movement at the top of backwall and at the bottom of beam cap
    Maximum movement away from the backfill shall not be greater than 1/8". Maximum movement toward the backfill shall not be greater than 1/4".
 
  g. Check pile axial loads from the analysis with the allowable pile axial load capacity.
 
  h. Check overturning of bent
    Conservatively, use the same equivalent cantilever pile length, . Check overturning of bent at the bottom of toe pile for loading cases I and II(Figure of Structural model).
   
Case I Point of
Investigation
Vertical Loads Horizontal Loads Factor of Safety (**)
I Toe Pile DL + E EP + SUR 1.2
II Toe Pile DL + LL + E EP + SUR 1.5
 
5) Deadman Anchorage System
  Deadman anchorage can be used when the abutment movement exceeds the allowable movement.
  The size and location of deadman anchorage shall be designed appropriately to maintain the stability of the abutment.
  The deadman forces may be used to resist overturning with the approval of the Structural Project Manager.
 
6) Passive Pressure Shear Key (if applicable)
  Passive pressure shear key may be used when the abutment movement exceeds the allowable movement.
  The passive resistance of soil to the lateral force at shear keys may be used with the approval of structural project manager.
751.40.8.13.1.5 Deadman Anchors

Design Assumptions


751.40 Deadman Anchor Design Assumption Detail.gif


  Length of Deadman =
  Number of tie rods required =
  = Active earth pressure on deadman, in lb./ft. = (120 pcf)
(**) = Passive earth pressure on deadman, in lb./ft. = (120 pcf)
  = Earth pressure on end bent, in lb. = 0.5(120 pcf) (length of beam)
  = Surcharge on end bent, in lb. =
 
 
(***) = 8.0 kips for 7/8" Ø tie rod and 10.50 kips for 1" Ø tie rods
(Capacity of the tie rods based on a maximum skew of 30°.)
 
* If the number of 7/8" Ø tie rods causes too long of a deadman, then try 1" Ø tie rods.
** For seismic loads only, use = 4 kips/sq.ft. as the ultimate capacity of compacted fill.
*** For seismic loads only, the allowable stress in the tie rod may be taken as the yield stress of the rod.


Notes:

No more than 20% of deadman may fall outside of the roadway shoulders. To prevent more than 20% limit, using a deeper deadman to reduce its length. If this is not possible, the total passive pressure resistance should be calculated by summing the resistance from the different fill depths.

When deadman anchors are to be used, design the piles for a factor of safety of 1.0 for sliding and design deadman anchors to resist all horizontal earth forces with a factor of safety of 1.0. This will result in a factor of safety for sliding of 2.0. For special cases, see the Structural Project Manager.


Design Example

Assume:
  Roadway width = 36', Out-Out slab width = 36' + 2 x 16" = 38.67'
  Skew = , Length of Beam =
  Beam depth = , ,
 
 
  , use
 
  Assume (Deadman anchor depth)


Determine Earth and Surcharge Forces
  =
  =
  =
  =
  =
  =
  =
  =
  =
  =
  =
  =
  =
  =


Determine number of Tie Rods required
  Try 7/8"Ø Rods: kips
  Number of Rods required =
  Use 12-7/8"Ø Rie Rods.
Determine length of Deadman
  Length of Deadman required =
  Tie Rod spacing = minimum, ok.
  Length of Deadman provided =


751.40 Deadman Anchor Design Example Detail 1.gif




1) Check tie rod skew angle at Fill Face of End Bent
 
  , tie capacity ok.
 
751.40 Deadman Anchor Design Example Detail 2.gif
 
2) Check criteria for Deadman Anchors extending into Fill Slope
 
751.40 Deadman Anchor Design Example Detail 3.gif


A) Extension of Deadman into Fill Slope
  Length of Deadman extending into Fill Slope =
   
  0.2 (Length of Deadman) =
   
  Length of Deadman extending into Fill Slope (Length of Deadman), ok
 
Note: See below for Section A-A details.
 
B) Cover of Deadman in Fill Slope
 


751.40 Deadman Anchor Design Example Detail 4.gif
SECTION A-A
DETAIL AT FILL SLOPE


Note:

(*) Fill slope shown is for illustration purpose only, see roadway plans.

751.40.8.13.2 Reinforcement

751.40.8.13.2.1 Wide Flange Beams, Plate Girders and Prestressed Girders

END BENT WITH EXPANSION DEVICE


751.40 Reinf End Bent With Exp Device Sec AA.gif 751.40 Reinf End Bent With Exp Device Part Elevation.gif
SECTION A-A
 
 
  PART ELEVATION

Notes:

(1) See details for reinforcement of end bent backwall.

(2) #6-H bars and #4-H bars in backwall of skewed bridges shall be bent in field if required.

(3) Center #5 bars in backwall.

Epoxy coat all reinforcing in end bents with expansion devices. See ______ for details of protective coating and sloping top of beam to drain.


751.40 Reinf End Bent With Exp Device Part Plan BB.gif 751.40 Reinf End Bent With Exp Device Detail of -5 Shape 19 Bar.gif
DETAIL OF #5 BARS
SHAPE 19
PART PLAN B-B


END BENT WITHOUT EXPANSION DEVICE


751.40 Reinf End Bent Without Exp Device Sec AA.gif 751.40 Reinf End Bent Without Exp Device Part Elevation.gif
SECTION A-A
 
 
  PART ELEVATION


751.40 Reinf End Bent Without Exp Device Part Plan BB.gif
(1) #5 Dowel bars are 2'-6" long and placed parallel to centerline roadway.
(2) #6-H bars and #4-H bars in backwall of skewed bridges shall be bent in field.
(3) For skewed bridges with no expansion device place a #4 bar along skew.
(4) See details of end bent backwall for reinforcement.
(5) Seal joint with joint sealant. See special provisions.
Note: See Structural Project Manager before using this detail.
PART PLAN B-B


END BENT WING


751.40 Reinf End Bent Wing Sec AA.gif| 751.40 Reinf End Bent Wing Typ Elevation.gif
SECTION A-A
 
  TYPICAL ELEVATION OF WING

Note: (1) Development length


h (2) (3)
2' or less #4 @ 12" #6 @ 6"
Over 2' to 4' #5 @ 6" #7 @ 6"
Over 4' to 6' #7 @ 5" #8 @ 5"
751.40 Reinf End Bent Wing Sec BB.gif
  SECTION B-B
751.40 Reinf End Bent Wing Part Sec With Passive Pressure.gif 751.40 Reinf End Bent Wing Horiz Sec Thru Wing.gif
PART SECTION THRU BENTS
WITH PASSIVE PRESSURE
  HORIZONTAL SECTION THRU WING
(K bars not shown for clarity)


END BENT BEAM HEEL


751.40 Reinf End Bent Beam Heel Elev AA.gif 751.40 Reinf End Bent Beam Heel Part Plan - Square.gif
ELEVATION A-A (TYP.) PART PLAN OF BEAM (SQUARE)
751.40 Reinf End Bent Beam Heel Part Plan - Skews thru 15 deg.gif 751.40 Reinf End Bent Beam Heel Part Plan - Skews thru 15 deg (2).gif
PART PLAN OF BEAM - SKEWS THRU 15° - LEFT ADVANCE SHOWN


751.40 Reinf End Bent Beam Heel Part Plan - Skews over 15 deg (1).gif 751.40 Reinf End Bent Beam Heel Part Plan - Skews over 15 deg (Sec BB).gif 751.40 Reinf End Bent Beam Heel Part Plan - Skews over 15 deg (2).gif
SECTION B-B
PART PLAN OF BEAM - SKEWS OVER 15° - LEFT ADVANCE SHOWN


Note:

Vertical spacing for #7 bars shown in Elevation A-A is typical for all types of end bent beams.

For a long distance between heel pile and bearing beam investigate for use of larger bars; e.g. larger skews where the shear line does not fall within the bearing beam.


Pile Load Not Greater (1) Hair-Pin Stirrups (2) Horizontal Rebar around Heel Pile
Skew thru 30° Skew 31° thru 45° Skew 46° thru 60° Skew over 60°
140 kips #6 @ 9" 5-#7 5-#7 5-#8 By Design
194 kips #6 @ 6" 5-#7 5-#8 By Design By Design


Use 21" horizontal leg.


END BENT BACKWALL


751.40 Reinf End Bent Backwall Part Section.gif
PART SECTION THRU BACKWALL AND BEAM


V-BAR SIZE AND SPACING
h
(feet)
t
(inch)
Fill Face
Reinforcement
Front Face
Reinforcement
1-6 12 #5 @ 12" #5 @ 12"
7 12 #5 @ 12" #5 @ 12"
8 12 #5 @ 12" #5 @ 12"
9 12 #6 @ 12" #5 @ 12"
10 12 #6 @ 10" #5 @ 12"
11 15 #6 @ 10" #5 @ 12"
12 15 #6 @ 8" #5 @ 12"
13 18 #6 @ 8" #5 @ 12"
14 18 #6 @ 6" #5 @ 12"


Note:

All reinforcement is grade 60.

Design is based on 45 lbs. per cu. ft. equivalent fluid pressure and 90 lbs. per sq. ft. live load surcharge.

Epoxy coat all reinforcing steel in beam and backwall on non-integral end bents with expansion devices.

751.40.8.14 Concrete Pile Cap Integral End Bents

751.40.8.14.1 Design

751.40.8.14.1.1 Design Unit Stresses
  1. Reinforced Concrete
    • Class B Concrete (Substructure)     = 1,200 psi,     = 3,000 psi
    • Reinforcing Steel (Grade 60)           = 24,000 psi     = 60,000 psi
    •   = 10
    •   =   (AASHTO Article 8.7.1)(*)
  2. Structural Steel
    • Structural Carbon Steel (ASTM A709 Grade 36)     = 20,000 psi     = 36,000 psi
  3. Piling
    • See the Bridge Memorandum if pile capacity is indicated.
  4. Overstress
    • The allowable overstresses as specified in AASHTO Article 3.22 shall be used where applicable for Service Loads design method.

(*)  

751.40.8.14.1.2 Loads
  1. Dead Loads
  2. Live Load
    • As specified on the Bridge Memorandum.
    • Impact of 30% is to be used for design of the beam. No impact is to be used for design of any other portion of bent including the piles.
  3. Temperature, Wind and Frictional Loads
751.40.8.14.1.3 Distribution of Loads
  1. Dead Loads
    • Loads from stringers, girders, etc. shall be concentrated loads applied at the intersection of centerline of stringer and centerline of bearing. Loads from concrete slab spans shall be applied as uniformly, distributed loads along the centerline of bearing.
  2. Live Load
    • Loads from stringers, girders, etc. shall be applied as concentrated loads at the intersection of centerline of stringer and centerline of bearing. For concrete slab spans distribute two wheel lines over 10'-0" (normal to centerline of roadway) of substructure beam. This distribution shall be positioned on the beam on the same basis as used for wheel lines in Traffic Lanes for Substructure Design.
  3. Wing with Detached Wing Wall
    • When wing length, L, is greater than 17 feet, use maximum length of 10 feet rectangular wing wall combined with a detached wing wall. When detached wing walls are used, no portion of the bridge live load shall be assumed distributed to the detached wing walls. Design detached wing wall as a retaining wall. (The weight of barrier or railing on top of the wall shall be included in Dead Load.)
751.40.8.14.1.4 Design Examples

Design H-bar and F-bar of an intermediate wing as shown in the figures below (wing length = 12.5', wing thickness = 24", wing height = 8'-4"), a Seismic Force of   = 12.21 kips/ft. is applied on the wall.


751.40 conc pile cap int end bents-section near intermediate wing.gif 751.40 conc pile cap int end bents-intermediate wing sectin b-b.gif
Section Near Intermediate Wing Section B-B
 
751.40 conc pile cap int end bents-intermediate wing sectin c-c.gif 751.40 conc pile cap int end bents-interior wing design.gif
Interior Wing Design
Section C-C


Solve: Assume #6 V bar, #8 H bar, #6 F bar

1.) Design H-bar for bending
.
   
 
At Section A-A:
Use  
As (Req'd) =
Try No. 8 @ 9", USE  
Say 11 spacings, 12 bars (Each Face)
Total Area =   USE 12-No. 8 H-bar (Each Face)


2.) Design F-bar for shear
  (AASHTO Article 8.16.6.1.1)
 
At Section A-A:
  No     needed by AASHTO Article 8.16.6.3.1.
Minimum shear reinforcement is required by AASHTO Article 8.19.1.1(a).(ACI 318-95 11.5.5.1)
 
F-bar is a single group of parallel bars, all bent up at the same distance from support (no "spacing" along the "L" direction of the wing).
Try No. 6 @ 12" F-bar (each face).
Try say 8 spacing, 9 bars (each face).
 
Since seismic force is a cyclic loading, assume one bar works at any instance.
 
Check  
 
  O.K. by AASHTO Article 8.16.6.3.4.
USE 9 No. 6 F-bars (each face).

751.40.8.14.2 Reinforcement

751.40.8.14.2.1 Earthquake Loads at End Bent – Intermediate Wing (Seismic Shear Wall)
751.40 conc pile cap int end bents-section near intermediate wing(seismic).gif 751.40 conc pile cap int end bents-intermediate wing sectin b-b(seismic).gif
Section Near Intermediate Wing Section B-B
 
751.40 conc pile cap int end bents-intermediate wing sectin a-a(seismic).gif  
Section A-A  
* Use 1.25 x development length for seismic design.
** Additional reinforcing steel by design if required.
Note: Make sure reinforcement does not interfere with girders.

751.40.8.15 Cast-In-Place Concrete Retaining Walls

751.40.8.15.1 Loads

Dead Loads

Dead loads shall be determined from the unit weights in EPG 751.2.1.1 Dead Load.

Equivalent Fluid Pressure (Earth Pressures)

Additional Information
AASHTO 3.20.1

For determining equivalent earth pressures for Group Loadings I through VI the Rankine Formula for Active Earth Pressure shall be used.

Rankine Formula: where:

Ca = = coefficient of active earth pressure
Pa = equivalent active earth pressure
H = height of the soil face at the vertical plane of interest
= unit weight of soil
= slope of fill in degrees
= angle of internal friction of soil in degrees
751.24.1.2.jpg

Example

Given:

δ = 3:1 (H:V) slope
ϕ = 25°
γs = 0.120 kcf
H = 10 ft

δ = arctan = 18.4°

Ca = = 0.515

Pa = (1/2)(0.515)(0.120 kips/ft3)(10 ft)2 = 3.090 kips per foot of wall length

The ϕ angle shall be determined by the Materials Division from soil tests. If the ϕ angle cannot be provided by the Construction and Materials Division a ϕ angle of 27 degrees shall be used.

Drainage shall be provided to relieve water pressure from behind all cast-in-place concrete retaining walls. If adequate drainage can not be provided then walls shall be designed to resist the maximum anticipated water pressure.

Surcharge Due to Point, Line and Strip Loads

Surcharge due to point and line loads on the soil being retained shall be included as dead load surcharge. The effect of these loads on the wall may be calculated using Figure 5.5.2B from AASHTO.

Surcharge due to strip loads on the soil being retained shall be included as a dead load surcharge load. The following procedure as described in Principles of Foundation Engineering by Braja M. Das (1995) shall be applied to calculate these loads when strip loads are applicable. An example of this application is when a retaining wall is used in front of an abutment so that the wall is retaining the soil from behind the abutment as a strip load on the soil being retained by the wall.

Retaining Wall in front of an Abutment

The portion of soil that is in the active wedge must be determined because the surcharge pressure only affects the wall if it acts on the active wedge. The actual failure surface in the backfill for the active state can be represented by ABC shown in the figure below. An approximation to the failure surface based on Rankine's active state is shown by dashed line AD. This approximation is slightly unconservative because it neglects friction at the pseudo-wall to soil interface.

The following variables are shown in the figure below:

β = slope of the active failure plane in degrees
δ = slope of fill in degrees
H = height of the pseudo-wall (fom the bottom of the footing).
L1 = distance from back of stem to back of footing heel
L2 = distance from footing heel to intersection of failure plane with ground surface
Determination of Active Wedges

In order to determine β, the following equation which has been derived from Rankine's active earth pressure theory must be solved by iteration:

ϕ = angle of internal friction of soil in degrees

A good estimate for the first iteration is to let β = 45° + (ϕ/2). In lieu of iterating the above equation a conservative estimate for β is 45°. Once β has been established, an estimate of L1 is needed to determine L2. From the geometry of the variables shown in the above figure:

The resultant pressure due to the strip load surcharge and its location are then determined. The following variables are shown in the figure below:

q = load per unit area
Ps = resultant pressure on wall due only to surcharge earth pressure
= location of Ps measured from the bottom of the footing
L3 = distance from back of stem to where surcharge pressure begins
Surcharge Pressure on Retaining Wall

From the figure:

Ps = where
where

When applicable, Ps is applied to the wall in addition to other earth pressures. The wall is then designed as usual.

Live Load Surcharge

Additional Information
AASHTO 3.20.3 & 5.5.2

Live load surcharge pressure of not less than two feet of earth shall be applied to the structure when highway traffic can come within a horizontal distance equal to one-half of the wall height, measured from the plane where earth pressure is applied.

751.24.1.2 live load1.jpg
Live Load Surcharge
PLLS = (2 ft.) γs Ca H = pressure due to live load surcharge only
γs = unit weight of soil (Note: AASHTO 5.5.2 specifies a minimum of 125 pcf for live load surcharge, MoDOT policy allows 120 pcf as given from the unit weights in EPG 751.2.1.1 Dead Load.)
Ca = coefficient of active earth pressure
H = height of the soil face at the vertical plane of interest

The vertical live load surcharge pressure should only be considered when checking footing bearing pressures, when designing footing reinforcement, and when collision loads are present.

Live Load Wheel Lines

Live load wheel lines shall be applied to the footing when the footing is used as a riding or parking surface.

Additional Information
AASHTO 3.24.5.1.1 & 5.5.6.1

Distribute a LLWL equal to 16 kips as a strip load on the footing in the following manner.


P = LLWL/E
where E = 0.8X + 3.75
X = distance in ft. from the load to the front face of the wall
Additional Information
AASHTO 3.24.2 & 3.30

Two separate placements of wheel lines shall be considered, one foot from the barrier or wall and one foot from the toe of the footing.

751.24.1.2 wheel.jpg

Collision Forces

Additional Information
AASHTO Figure 2.7.4B

Collision forces shall be applied to a wall that can be hit by traffic. Apply a point load of 10 kips to the wall at a point 3 ft. above the finished ground line.

Section

Distribute the force to the wall in the following manner:

Force per ft of wall = (10 kips)/2L
Profile

When considering collision loads, a 25% overstress is allowed for bearing pressures and a factor of safety of 1.2 shall be used for sliding and overturning.

Wind and Temperature Forces

These forces shall be disregarded except for special cases, consult the Structural Project Manager.

When walls are longer than 84 ft., an expansion joint shall be provided.

Contraction joint spacing shall not exceed 28 feet.

Seismic Loads

Retaining walls in Seismic Performance Category A (SPC A) and SPC B that are located adjacent to roadways may be designed in accordance with AASHTO specifications for SPC A. Retaining walls in SPC B which are located under a bridge abutment or in a location where failure of the wall may affect the structural integrity of a bridge shall be designed to AASHTO specifications for SPC B. All retaining walls located in SPC C and SPC D shall be designed in accordance to AASHTO specifications for the corresponding SPC.

In seismic category B, C and D determine equivalent fluid pressure from Mononobe-Okabe static method.

Additional Information
1992 AASHTO Div. IA Eqns. C6-3 and C6-4

PAE = equivalent active earth pressure during an earthquake

PAE = 0.5 γsH2(1 - kv)KAE where

KAE = seismic active pressure coefficient


γs = unit weight of soil

Additional Information
AASHTO 5.2.2.3 & Div. IA 6.4.3

kv = vertical acceleration coefficient

kh = horizontal acceleration coefficient which is equal to 0.5A for all walls,

but 1.5A for walls with battered piles where
A = seismic acceleration coefficient

The following variables are shown in the figure below:

ϕ = angle of internal friction of soil

θ =

β = slope of soil face

δ = angle of friction between soil and wall in degrees

i = backfill slope angle in degrees

H = distance from the bottom of the part of the wall to which the pressure is applied to the top of the fill at the location where the earth pressure is to be found.

Active Soil Wedge

Group Loads

For SPC A and B (if wall does not support an abutment), apply AASHTO Group I Loads only. Bearing capacity, stability and sliding shall be calculated using working stress loads. Reinforced concrete design shall be calculated using load factor design loads.

Additional Information
AASHTO Table 3.22.1A

AASHTO Group I Load Factors for Load Factor Design of concrete: γ = 1.3

βD = 1.0 for concrete weight

βD = 1.0 for flexural member

βE = 1.3 for lateral earth pressure for retaining walls

βE = 1.0 for vertical earth pressure

βLL = 1.67 for live load wheel lines

βLL = 1.67 for collision forces

Additional Information
AASHTO 5.14.2

βE = 1.67 for vertical earth pressure resulting from live load surcharge

βE = 1.3 for horizontal earth pressure resulting from live load surcharge

For SPC B (if wall supports an abutment), C, and D apply AASHTO Group I Loads and seismic loads in accordance with AASHTO Division IA - Seismic Design Specifications.

Additional Information
AASHTO Div. IA 4.7.3

When seismic loads are considered, load factor for all loads = 1.0.

751.40.8.15.3 Unit Stresses

Concrete Concrete for retaining walls shall be Class B Concrete (f'c = 3000 psi) unless the footing is used as a riding surface in which case Class B-1 Concrete (f'c = 4000 psi) shall be used.

Reinforcing Steel

Reinforcing Steel shall be Grade 60 (fy = 60,000 psi).

Pile Footing

For steel piling material requirements, see the unit stresses in EPG 751.50 Standard Detailing Notes.

Spread Footing

For foundation material capacity, see Foundation Investigation Geotechnical Report.

751.40.8.15.4 Design

For epoxy coated reinforcement requirements, see EPG 751.5.9.2.2 Epoxy Coated Reinforcement Requirements.

If the height of the wall or fill is a variable dimension, then base the structural design of the wall, toe, and heel on the high quarter point between expansion joints.

Fig. 40.8.15.4.1
Additional Information
AASHTO 5.5.5
751.40.8.15.4.1 Spread Footings

Location of Resultant

The resultant of the footing pressure must be within the section of the footing specified in the following table.

When Retaining Wall is Built on: AASHTO Group Loads I-VI For Seismic Loads
Soila Middle 1/3 Middle 1/2 b
Rockc Middle 1/2 Middle 2/3
a Soil is defined as clay, clay and boulders, cemented gravel, soft shale, etc. with allowable bearing values less than 6 tons/sq. ft.
b MoDOT is more conservative than AASHTO in this requirement.
c Rock is defined as rock or hard shale with allowable bearing values of 6 tons/sq. ft. or more.

Note: The location of the resultant is not critical when considering collision loads.

Factor of Safety Against Overturning

Additional Information
AASHTO 5.5.5

AASHTO Group Loads I - VI:

  • F.S. for overturning ≥ 2.0 for footings on soil.
  • F.S. for overturning ≥ 1.5 for footings on rock.

For seismic loading, F.S. for overturning may be reduced to 75% of the value for AASHTO Group Loads I - VI. For seismic loading:

  • F.S. for overturning ≥ (0.75)(2.0) = 1.5 for footings on soil.
  • F.S. for overturning ≥ (0.75)(1.5) = 1.125 for footings on rock.

For collision forces:

  • F.S. for overturning ≥ 1.2.

Factor of Safety Against Sliding

Additional Information
AASHTO 5.5.5

Only spread footings on soil need be checked for sliding because spread footings on rock or shale are embedded into the rock.

  • F.S. for sliding ≥ 1.5 for AASHTO Group Loads I - VI.
  • F.S. for sliding ≥ (0.75)(1.5) = 1.125 for seismic loads.
  • F.S. for sliding ≥ 1.2 for collision forces.

The resistance to sliding may be increased by:

  • adding a shear key that projects into the soil below the footing.
  • widening the footing to increase the weight and therefore increase the frictional resistance to sliding.

Passive Resistance of Soil to Lateral Load

The Rankine formula for passive pressure can be used to determine the passive resistance of soil to the lateral force on the wall. This passive pressure is developed at shear keys in retaining walls and at end abutments.

Additional Information
AASHTO 5.5.5A

The passive pressure against the front face of the wall and the footing of a retaining wall is loosely compacted and should be neglected when considering sliding.

Rankine Formula: where thefollowing variables are defined in the figure below

Cp =
y1 =
Pp = passive force at shear key in pounds per foot of wall length
Cp = coefficient of passive earth pressure
= unit weight of soil
H = height of the front face fill less than 1 ft. min. for erosion
H1 = H minus depth of shear key
y1 = location of Pp from bottom of footing
= angle of internal friction of soil
751.24.3.2.1 passive.jpg
Additional Information
AASHTO 5.5.2

The resistance due to passive pressure in front of the shear key shall be neglected unless the key extends below the depth of frost penetration.

Additional Information
MoDOT Materials Division

Frost line is set at 36 in. at the north border of Missouri and at 18 in. at the south border.

Passive Pressure During Seismic Loading

During an earthquake, the passive resistance of soil to lateral loads is slightly decreased. The Mononobe-Okabe static method is used to determine the equivalent fluid pressure.

PPE = equivalent passive earth pressure during an earthquake
Additional Information
1992 AASHTO Div. IA Eqns. C6-5 and C6-6
where:
KPE = seismic passive pressure coefficient
= unit weight of soil
H = height of soil at the location where the earth pressure is to be found
kV = vertical acceleration coefficient
= angle of internal friction of soil
kH = horizontal acceleration coefficient
= slope of soil face in degrees
i = backfill slope angle in degrees
= angle of friction between soil and wall

Special Soil Conditions

Due to creep, some soft clay soils have no passive resistance under a continuing load. Removal of undesirable material and replacement with suitable material such as sand or crushed stone is necessary in such cases. Generally, this condition is indicated by a void ratio above 0.9, an angle of internal friction () less than 22°, or a soil shear less than 0.8 ksf. Soil shear is determined from a standard penetration test.

Soil Shear

Friction

In the absence of tests, the total shearing resistance to lateral loads between the footing and a soil that derives most of its strength from internal friction may be taken as the normal force times a coefficient of friction. If the plane at which frictional resistance is evaluated is not below the frost line then this resistance must be neglected.

When A Shear Key Is Not Used
Additional Information
AASHTO 5.5.2B

Sliding is resisted by the friction force developed at the interface between the soil and the concrete footing along the failure plane. The coefficient of friction for soil against concrete can be taken from the table below. If soil data is not readily available or is inconsistent, the friction factor (f) can be taken as

f = where is the angle of internal friction of the soil (Civil Engineering Reference Manual by Michael R. Lindeburg, 6th ed., 1992).
Coefficient of Friction Values for Soil Against Concrete
Soil Typea Coefficient of Friction
coarse-grained soil without silt 0.55
coarse-grained soil with silt 0.45
silt (only) 0.35
clay 0.30b
a It is not necessary to check rock or shale for sliding due to embedment.
b Caution should be used with soils with < 22° or soil shear < 0.8 k/sq.ft. (soft clay soils). Removal and replacement of such soil with suitable material should be considered.
When A Shear Key Is Used

When a shear key is used, the failure plane is located at the bottom of the shear key in the front half of the footing. The friction force resisting sliding in front of the shear key is provided at the interface between the stationary layer of soil and the moving layer of soil, thus the friction angle is the internal angle of friction of the soil (soil against soil). The friction force resisting sliding on the rest of the footing is of that between the concrete and soil. Theoretically the bearing pressure distribution should be used to determine how much normal load exists on each surface, however it is reasonable to assume a constant distribution. Thus the normal load to each surface can be divided out between the two surfaces based on the fractional length of each and the total frictional force will be the sum of the normal load on each surface multiplied by the corresponding friction factor.

Bearing Pressure

Additional Information
AASHTO 4.4.7.1.2 & 4.4.8.1.3
Group Loads I - VI
The bearing capacity failure factor of safety for Group Loads I - VI must be greater than or equal to 3.0. This factor of safety is figured into the allowable bearing pressure given on the "Design Layout Sheet".
The bearing pressure on the supporting soil shall not be greater than the allowable bearing pressure given on the "Design Layout Sheet".
Seismic Loads
Additional Information
AASHTO Div. IA 6.3.1(B) and AASHTO 5.5.6.2
When seismic loads are considered, AASHTO allows the ultimate bearing capacity to be used. The ultimate capacity of the foundation soil can be conservatively estimated as 2.0 times the allowable bearing pressure given on the "Design Layout".
Stem Design
The vertical stem (the wall portion) of a cantilever retaining wall shall be designed as a cantilever supported at the base.
Footing Design
Additional Information
AASHTO 5.5.6.1
Toe
The toe of the base slab of a cantilever wall shall be designed as a cantilever supported by the wall. The critical section for bending moments shall be taken at the front face of the stem. The critical section for shear shall be taken at a distance d (d = effective depth) from the front face of the stem.
Heel
The rear projection (heel) of the base slab shall be designed to support the entire weight of the superimposed materials, unless a more exact method is used. The heel shall be designed as a cantilever supported by the wall. The critical section for bending moments and shear shall be taken at the back face of the stem.
Shear Key Design
The shear key shall be designed as a cantilever supported at the bottom of the footing.
751.40.8.15.4.2 Pile Footings

Footings shall be cast on piles when specified on the "Design Layout Sheet". If the horizontal force against the retaining wall cannot otherwise be resisted, some of the piles shall be driven on a batter.

Pile Arrangement
For retaining walls subject to moderate horizontal loads (walls 15 to 20 ft. tall), the following layout is suggested.
Section
Plan
For higher walls and more extreme conditions of loading, it may be necessary to:
  • use the same number of piles along all rows
  • use three rows of piles
  • provide batter piles in more than one row
Loading Combinations for Stability and Bearing
The following table gives the loading combinations to be checked for stability and pile loads. These abbreviations are used in the table:
DL = dead load weight of the wall elements
SUR = two feet of live load surcharge
E = earth weight
EP = equivalent fluid earth pressure
COL = collision force
EQ = earthquake inertial force of failure wedge
Loading Case Vertical Loads Horizontal Loads Overturning Factor of Safety Sliding Factor of Safety
Battered Toe Piles Vertical Toe Piles
Ia DL+SUR+E EP+SUR 1.5 1.5 2.0
II DL+SUR+E EP+SUR+COL 1.2 1.2 1.2
III DL+E EP 1.5 1.5 2.0
IVb DL+E None - - -
Vc DL+E EP+EQ 1.125 1.125 1.5
a Load Case I should be checked with and without the vertical surcharge.
b A 25% overstress is allowed on the heel pile in Load Case IV.
c The factors of safety for earthquake loading are 75% of that used in Load Case III. Battered piles are not recommended for use in seismic performance categories B, C, and D. Seismic design of retaining walls is not required in SPC A and B. Retaining walls in SPC B located under a bridge abutment shall be designed to AASHTO Specifications for SPC B.
Pile Properties and Capacities
For Load Cases I-IV in the table above, the allowable compressive pile force may be taken from the pile capacity table in the Piling Section of the Bridge Manual which is based in part on AASHTO 4.5.7.3. Alternatively, the allowable compressive pile capacity of a friction pile may be determined from the ultimate frictional and bearing capacity between the soil and pile divided by a safety factor of 3.5 (AASHTO Table 4.5.6.2.A). The maximum amount of tension allowed on a heel pile is 3 tons.
For Load Case V in the table above, the allowable compressive pile force may be taken from the pile capacity table in the Piling Section of the Bridge Manual multiplied by the appropriate factor (2.0 for steel bearing piles, 1.5 for friction piles). Alternatively, the allowable compressive pile capacity of a friction pile may be determined from the ultimate frictional and bearing capacity between the soil and pile divided by a safety factor of 2.0. The allowable tension force on a bearing or friction pile will be equal to the ultimate friction capacity between the soil and pile divided by a safety factor of 2.0.
To calculate the ultimate compressive or tensile capacity between the soil and pile requires the boring data which includes the SPT blow counts, the friction angle, the water level, and the soil layer descriptions.
Assume the vertical load carried by battered piles is the same as it would be if the pile were vertical. The properties of piles may be found in the Piling Section of the Bridge Manual.
Neutral Axis of Pile Group
Locate the neutral axis of the pile group in the repetitive strip from the toe of the footing at the bottom of the footing.
Moment of Inertia of Pile Group
The moment of inertia of the pile group in the repetitive strip about the neutral axis of the section may be determined using the parallel axis theorem:
I = Σ(IA) + Σ(Ad2) where :
IA = moment of inertia of a pile about its neutral axis
A = area of a pile
d = distance from a pile's neutral axis to pile group's neutral axis
IA may be neglected so the equation reduces to:
I = Σ(Ad2)
Resistance To Sliding
Any frictional resistance to sliding shall be ignored, such as would occur between the bottom of the footing and the soil on a spread footing.
Friction or Bearing Piles With Batter (Case 1)
Retaining walls using friction or bearing piles with batter should develop lateral strength (resistance to sliding) first from the batter component of the pile and second from the passive pressure against the shear key and the piles.
Friction or Bearing Piles Without Batter (Case 2)
Retaining walls using friction or bearing piles without batter due to site constrictions should develop lateral strength first from the passive pressure against the shear key and second from the passive pressure against the pile below the bottom of footing. In this case, the shear key shall be placed at the front face of the footing.
Concrete Pedestal Piles or Drilled Shafts (Case 3)
Retaining walls using concrete pedestal piles should develop lateral strength first from passive pressure against the shear key and second from passive pressure against the pile below the bottom of the footing. In this case, the shear key shall be placed at the front of the footing. Do not batter concrete pedestal piles.
751.24.3.2.2 cases.jpg
Resistance Due to Passive Pressure Against Pile
The procedure below may be used to determine the passive pressure resistance developed in the soil against the piles. The procedure assumes that the piles develop a local failure plane.
F = the lateral force due to passive pressure on pile
, where:
= unit weight of soil
H = depth of pile considered for lateral resistance (Hmax= 6B)
CP = coefficient of active earth pressure
B = width of pile
= angle of internal friction of soil
751.24.3.2.2 resistance passive.jpg
Resistance Due to Pile Batter
Use the horizontal component (due to pile batter) of the allowable pile load as the lateral resistance of the battered pile. (This presupposes that sufficient lateral movement of the wall can take place before failure to develop the ultimate strength of both elements.)
751.24.3.2.2 12.jpg
b = the amount of batter per 12 inches.
(# of battered piles) where:
PHBatter = the horizontal force due to the battered piles
PT = the allowable pile load
Maximum batter is 4" per 12".
Resistance Due to Shear Keys
A shear key may be needed if the passive pressure against the piles and the horizontal force due to batter is not sufficient to attain the factor of safety against sliding. The passive pressure against the shear key on a pile footing is found in the same manner as for spread footings.
Resistance to Overturning
The resisting and overturning moments shall be computed at the centerline of the toe pile at a distance of 6B (where B is the width of the pile) below the bottom of the footing. A maximum of 3 tons of tension on each heel pile may be assumed to resist overturning. Any effects of passive pressure, either on the shear key or on the piles, which resist overturning, shall be ignored.
751.24.3.2.2 resistance overturning.jpg
Pile Properties
Location of Resultant
The location of the resultant shall be evaluated at the bottom of the footing and can be determined by the equation below:
where:
e = the distance between the resultant and the neutral axis of the pile group
ΣM = the sum of the moments taken about the neutral axis of the pile group at the bottom of the footing
ΣV = the sum of the vertical loads used in calculating the moment
Pile Loads
The loads on the pile can be determined as follows:
where:
P = the force on the pile
A = the areas of all the piles being considered
M = the moment of the resultant about the neutral axis
c = distance from the neutral axis to the centerline of the pile being investigated
I = the moment of inertia of the pile group
Additional Information
AASHTO 5.5.6.2
Stem Design
The vertical stem (the wall portion) of a cantilever retaining wall shall be designed as a cantilever supported at the base.
Footing Design
Toe
Additional Information
AASHTO 5.5.6.1
The toe of the base slab of a cantilever wall shall be designed as a cantilever supported by the wall. The critical section for bending moments shall be taken at the front face of the stem. The critical section for shear shall be taken at a distance d (d = effective depth) from the front face of the stem.
Heel
The top reinforcement in the rear projection (heel) of the base slab shall be designed to support the entire weight of the superimposed materials plus any tension load in the heel piles (neglect compression loads in the pile), unless a more exact method is used. The bottom reinforcement in the heel of the base slab shall be designed to support the maximum compression load in the pile neglecting the weight of the superimposed materials. The heel shall be designed as a cantilever supported by the wall. The critical sections for bending moments and shear shall be taken at the back face of the stem.
Shear Key Design
The shear key shall be designed as a cantilever supported at the bottom of the footing.
751.40.8.15.4.3 Counterfort Walls

Assumptions:

(1) Stability The external stability of a counterfort retaining wall shall be determined in the same manner as described for cantilever retaining walls. Therefore refer to previous pages for the criteria for location of resultant, factor of safety for sliding and bearing pressures.

(2) Stem

751.24.3.2.3 counterfort.jpg
where:
Ca = coefficient of active earth pressure
= unit weigt of soil

Design the wall to support horizontal load from the earth pressure and the liveload surcharge (if applicable) as outlined on the previous pages and as designated in AASHTD Section 3.20, except that maximum horizontal loads shall be the calculated equivalent fluid pressure at 3/4 height of wall [(0.75 H)P] which shall be considered applied uniformly from the lower quarter point to the bottom of wall.

In addition, vertical steel In the fill face of the bottom quarter of the wall shall be that required by the vertical cantilever wall with the equivalent fluid pressure of that (0.25 H) height.

Maximum concrete stress shall be assumed as the greater of the two thus obtained.

The application of these horizontal pressures shall be as follows:

Counterfort Wall Section
Moments are to be determined by analysis as a continuous beam. The counterforts are to be spaced so as to produce approximately equal positive and negative moments.

(3) Counterfort Counterforts shall be designed as T-beams, of which the wall is the flange and the counterfort is the stem. For this reason the concrete stresses ane normally low and will not control.

For the design of reinforcing steel in the back of the counterfort, the effective d shall be the perpendicular distance from the front face of the wall (at point that moment is considered), to center of reinforcing steel.

751.24.3.2.3 moment.jpg

(4) Footing

The footing of the counterfort walls shall be designed as a continuous beam of spans equal to the distance between the counterforts.

The rear projection or heel shall be designed to support the entire weight of the superimposed materials, unless a more exact method is used. Refer to AASHTD Section 5.5.6.

Divide footing (transversely) into four (4) equal sections for design footing pressures.

Counterfort walls on pile are very rare and are to be treated as special cases. See Structural Project Manager.

(5) Sign-Board type walls

The Sign-Board type of retaining walls are a special case of the counterfort retaining walls. This type of wall is used where the soiI conditions are such that the footings must be placed a great distance below the finished ground line. For this situation, the wall is discontinued approximately 12 in. below the finished ground line or below the frost line.

Due to the large depth of the counterforts, it may be more economical to use a smaller number of counterforts than would otherwise be used.

All design assumptions that apply to counterfort walls will apply to sign-board walls with the exception of the application of horizontal forces for the stem (or wall design), and the footing design which shall be as follows:

Wall
751.24.3.2.3 load.jpg
Footing
The individual footings shall be designed transversely as cantilevers supported by the wall. Refer to AASHTO Section 5.

751.40.8.15.5 Example 1: Spread Footing Cantilever Wall

Typical Section thru Wall
(Spread Footing)
f'c = 3,000 psi
fy = 60,000 psi
φ = 24 in.
γs = 120 pcf (unit wgt of soil)
Allowable soil pressure = 2 tsf
γc = 150 pcf (unit wgt of concr.)
Retaining wall is located in Seismic Performance Category (SPC) B.
A = 0.1 (A = seismic acceleration coefficient)

Assumptions

  • Retaining wall is under an abutment or in a location where failure of the wall may affect the structural integrity of a bridge. Therefore, it must be designed for SPC B.
  • Design is for a unit length (1 ft.) of wall.
  • Sum moments about the toe at the bottom of the footing for overturning.
  • For Group Loads I-VI loading:
  • F.S. for overturning ≥ 2.0 for footings on soil.
  • F.S. for sliding ≥ 1.5.
  • Resultant to be within middle 1/3 of footing.
  • For earthquake loading:
  • F.S. for overturning ≥ 0.75(2.0) = 1.5.
  • F.S. for sliding ≥ 0.75(1.5) = 1.125.
  • Resultant to be within middle 1/2 of footing.
  • Base of footing is below the frost line.
  • Neglect top one foot of fill over toe when determining passive pressure and soil weight.
  • Use of a shear key shifts the failure plane to "B" where resistance to sliding is provided by passive pressure against the shear key, friction of soil along failure plane "B" in front of the key, and friction between soil and concrete along the footing behind the key.
  • Soil cohesion along failure plane is neglected.
  • Footings are designed as cantilevers supported by the wall.
  • Critical sections for bending are at the front and back faces of the wall.
  • Critical sections for shear are at the back face of the wall for the heel and at a distance d (effective depth) from the front face for the toe.
  • Neglect soil weight above toe of footing in design of the toe.
  • The wall is designed as a cantilever supported by the footing.
  • Load factors for AASHTO Groups I - VI for design of concrete:
  • γ = 1.3.
  • βE = 1.3 for horizontal earth pressure on retaining walls.
  • βE = 1.0 for vertical earth pressure.
  • Load factor for earthquake loads = 1.0.

Lateral Pressures Without Earthquake

Ca =
Ca = = 0.546
Load Area (ft2) Force (k) = (Unit Wgt.)(Area) Arm (ft.) Moment (ft-k)
(1) (0.5)(6.667ft)(2.222ft) = 7.407 0.889 7.278 6.469
(2) (6.667ft)(6.944ft) = 46.296 5.556 6.167 34.259
(3) (0.833ft)(8.000ft) + (0.5)(0.083ft)(8.000ft) = 7.000 1.050 2.396 2.515
(4) (1.500ft)(9.500ft) = 14.250 2.138 4.750 10.153
(5) (2.500ft)(1.000ft) = 2.500 0.375 2.500 0.938
(6) (1.000ft)(1.917ft)+(0.5)(0.010ft)(1.000ft) = 1.922 0.231 0.961 0.222
Σ - ΣV = 10.239 - ΣMR = 54.556
PAV - 1.178 9.500 11.192
Σ resisting - ΣV = 11.417 - ΣMR = 65.748
PAH - 3.534 3.556 12.567
PP - 2.668 1.3891 -
1 The passive capacity at the shear key is ignored in overturning checks,since this capacity is considered in the factor of safety against sliding. It is assumed that a sliding and overturning failure will not occur simultaneously. The passive capacity at the shear key is developed only if the wall does slide.
751.24.3.3 passive.jpg

= 1.389 ft.

Overturning
F.S. = o.k.
where: MOT = overturning moment; MR = resisting moment
Resultant Eccentricity
= 4.658 ft.
o.k.
Sliding
Check if shear key is required for Group Loads I-VI:
F.S. = = 0.896 no good - shear key req'd
where: φs-c = angle of friction between soil and concrete = (2/3)φs-s
F.S. =
where: φs-s = angle of internal friction of soil
F.S. = = 1.789 ≥ 1.5 o.k.
Footing Pressure
PH = pressure at heel = 1.132 k/ft2
PT = pressure at toe = 1.272 k/ft2
Allowable pressure = 2 tons/ft2 = 4 k/ft2 ≥ 1.272 k/ft2 o.k.

Lateral Pressures With Earthquake

kh = 0.5A = 0.5 (0.1) = 0.05

kv = 0

Active Pressure on Psuedo-Wall
δ = φ = 24° (δ is the angle of friction between the soil and the wall. In this case, δ = φ = because the soil wedge considered is next to the soil above the footing.)
i = 18.435°
β = 0°
KAE = 0.674
PAE = ½γsH2(1 − kv)KAE
PAE = ½[0.120 k/ft3](10.667 ft)2(1 ft.)(1 - 0)(0.674) = 4.602k
PAEV = PAE(sinδ) = 4.602k(sin24°) = 1.872k
PAEH = PAE(cosδ) = 4.602k(cos 24°) = 4.204k
P'AH = PAEH − PAH = 4.204k − 3.534k = 0.670k
P'AV = PAEV − PAV = 1.872k − 1.178k = 0.694k
where: P'AH and P'AV are the seismic components of the active force.
Passive Pressure on Shear Key
δ = φ = 24° (δ = φ because the soil wedge considered is assumed to form in front of the footing.)
i = 0
β = 0
KPE = 0.976
PPE = ½γsH2(1 − kv)KPE
PPE = ½[0.120 k/ft3][(5.0 ft)2 - (2.5 ft2)](1 ft.)(1 - 0)(0.976) = 1.098k
Load Force (k) Arm (ft) Moment (ft-k)
Σ (1) thru (6) 10.239 - 54.556
PAV 1.178 9.500 11.192
P'AV 0.694 9.500 6.593
Σresisting ΣV = 12.111 - ΣMR = 72.341
PAH 3.534 3.556 12.567
P'AH 0.670 6.400a 4.288
PPEV 0.447b 0.000 0.000
PPEH 1.003b 1.389c 0.000
- - - ΣMOT = 16.855
a P'AH acts at 0.6H of the wedge face (1992 AASHTO Div. IA Commentary).
b PPEH and PPEH are the components of PPE with respect to δ (the friction angle). PPE does not contribute to overturning.
c The line of action of PPEH can be located as was done for PP.
Overturning
o.k.
Resultant Eccentricity
o.k.


Sliding
o.k.


Footing Pressure
for e ≤ L/6:
= 1.139 k/ft2
= 1.411 k/ft2
Allowable soil pressure for earthquake = 2 (allowable soil pressure)
(2)[4 k/ft2] = 8 k/ft2 > 1.411 k/ft2 o.k.

Reinforcement-Stem

751.24.3.3 reinforcement stem.jpg

d = 11" - 2" - (1/2)(0.5") = 8.75"

b = 12"

f'c = 3,000 psi

Without Earthquake
PAH = ½ [0.120 k/ft3](0.546)(6.944 ft.)2(1 ft.)(cos 18.435°) = 1.499k
γ = 1.3
βE = 1.3 (active lateral earth pressure)
Mu = (1.3)(1.3)(1.499k)(2.315ft) = 5.865 (ft-k)
With Earthquake
kh = 0.05
kv = 0
Additional Information
1992 AASHTO Div. IA Commentary
θ = 2.862°
δ = φ/2 = 24°/2 = 12° for angle of friction between soil and wall. This criteria is used only for seismic loading if the angle of friction is not known.
φ = 24°
i = 18.435°
β = 0°
KAE = 0.654
PAEH = 1/2 γsKAEH2cosδ
PAEH = 1/2 [0.120k/ft](0.654)(6.944 ft.)2(1 ft.) cos(12°) = 1.851k
Mu = (1.499k)(2.315 ft.) + (1.851k − 1.499k)(0.6(6.944 ft.)) = 4.936(ft−k)
The moment without earthquake controls:
= 85.116 psi
ρ =
ρ = = 0.00144
Additional Information
AASHTO 8.17.1.1 & 8.15.2.1.1
ρmin = = 0.00245
Use ρ = 4/3 ρ = 4/3 (0.00144) = 0.00192
ASReq = ρbd = 0.00192 (12 in.)(8.75 in.) = 0.202 in.2/ft
One #4 bar has AS = 0.196 in2
s = 11.64 in.
Use #4's @ 10" cts.
Check Shear
Vuφ Vn
Without Earthquake
Vu, = (1.3)(1.3)(1.499k) = 2.533k
With Earthquake
Vu = 1.851k
The shear force without earthquake controls.
= 28.4 psi
= 109.5 psi > 28.4 psi o.k.

Reinforcement-Footing-Heel

751.24.3.3 heel.jpg

Note: Earthquake will not control and will not be checked.

βE = 1.0 (vertical earth pressure)

d = 18" - 3" - (1/2)(0.750") = 14.625"

b = 12"

f'c = 3,000 psi

Mu = 1.3 [(5.556k + 1.500k)(3.333ft) + 0.889k(4.444ft) + 1.178k(6.667ft)]

Mu = 45.919(ft−k)

= 238.5 psi

ρ = = 0.00418

ρmin = = 0.00235

ASReq = 0.00418 (12 in.) (14.625 in.) = 0.734 in2/ft.


Use #6's @ 7" cts.

Check Shear
Shear shall be checked at back face of stem.
Vu = 1.3 (5.556k + 1.500k + 0.889k + 1.178k) = 11.860k
= 109.5 psi o.k.

Reinforcement-Footing-Toe

751.24.3.3. toe.jpg

d = 18" - 4" = 14"

b = 12"

Without Earthquake
Apply Load Factors
load 4 (weight) = 0.431k(1.3)(1.0) = 0.560k
βE = 1.3 for lateral earth pressure for retaining walls.
βE = 1.0 for vertical earth pressure.
ΣMOT = 12.567(ft−k)(1.3)(1.3) = 21.238(ft−k)
ΣMR = [54.556(ft−k) + 11.192(ft−k)](1.3)(1.0) = 85.472(ft−k)
ΣV = 11.417k(1.3)(1.0) = 14.842k
= 4.328 ft.
e = (9.5 ft./2) − 4.328 ft. = 0.422 ft.
= 1.146k/ft2
= 1.979k/ft2
= 1.811k/ft.
Mu = 2.997(ft−k)
With Earthquake
PH = 1.139 k/ft
PT = 1.411 k/ft
= 1.356 k/ft
Mu = 2.146(ft−k)
The moment without earthquake controls.
= 16.990 psi
ρ = = 0.000284
ρmin = = 0.00257
Use ρ = 4/3 ρ = = 0.000379
ASReq = 0.000379 (12 in.)(14.0 in.) = 0.064 in.2/ft.


s = 36.8 in.
Minimum is # 4 bars at 12 inches. These will be the same bars that are in the back of the stem. Use the smaller of the two spacings.
Use # 4's @ 10" cts.
Check Shear
Shear shall be checked at a distance "d" from the face of the stem.
Without Earthquake
= 1.913k/ft.
= 1.240k
With Earthquake
= 1390k/ft.
= 0.788k
Shear without earthquake controls.
= 109.5 psi o.k.

Reinforcement-Shear Key

751.24.3.3 shear key.jpg

The passive pressure is higher without earthquake loads.

γ = 1.3

βE = 1.3 (lateral earth pressure)

d = 12"-3"-(1/2)(0.5") = 8.75"

b = 12"

Mu = (3.379k)(1.360 ft.)(1.3)(1.3) = 7.764(ft−k)

= 112.677 psi

ρ = = 0.00192

ρmin = = 0.00292

Use ρ = 4/3 ρ = 4/3 (0.00192) = 0.00256

ASReq = 0.00256(12 in.)(8.75 in.) = 0.269 in.2/ft.


Use # 4 @ 8.5 in cts.

Check Shear

= 109.5 psi o.k.

Reinforcement Summary

751.24.3.3 summary.jpg

751.40.8.15.6 Example 2: L-Shaped Cantilever Wall

Typical Section thru Wall
(Spread Footing)

f'c = 4000 psi

fy = 60,000 psi

φ = 29°

γs = 120 pcf

Allowable soil pressure = 1.5 tsf = 3.0 ksf

Retaining wall is located in Seismic Performance Category (SPC) A.

= 21.801°

= 0.462

= 2.882

PA = 1/2 γs CaH2 = 1/2 (0.120 k/ft3)(0.462)(4.958 ft.)2 = 0.681k

For sliding, PP is assumed to act only on the portion of key below the frost line that is set at an 18 in. depth on the southern border.

PP = 1/2 (0.120 k/ft3)(2.882)[(2.458 ft.)2 − (1.500 ft.)2] = 0.656k

Assumptions

  • Design is for a unit length (1 ft.) of wall.
  • Sum moments about the toe at the bottom of the footing for overturning.
  • F.S. for overturning ≥ 2.0 for footings on soil.
  • F.S. for sliding ≥ 1.5 for footings on soil.
  • Resultant of dead load and earth pressure to be in back half of the middle third of the footing if subjected to frost heave.
  • For all loading combinations the resultant must be in the middle third of the footing except for collision loads.
  • The top 12 in. of the soil is not neglected in determining the passive pressure because the soil there will be maintained.
  • Frost line is set at 18 in. at the south border for Missouri.
  • Portions of shear key which are above the frost line are assumed not to resist sliding by passive pressure.
  • Use of a shear key shifts the failure plane to "B" where resistance to sliding is also provided by friction of soil along the failure plane in front of the shear key. Friction between the soil and concrete behind the shear key will be neglected.
  • Soil cohesion along the failure plane is neglected.
  • Live loads can move to within 1 ft. of the stem face and 1 ft. from the toe.
  • The wall is designed as a cantilever supported by the footing.
  • Footing is designed as a cantilever supported by the wall. Critical sections for bending and shear will be taken at the face of the wall.
  • Load factors for AASHTO Groups I-VI for design of concrete are:
  • γ = 1.3.
  • βE = 1.3 for horizontal earth pressure on retaining walls.
  • βE = 1.0 for vertical earth pressure.
  • βLL = 1.67 for live loads and collision loads.

Dead Load and Earth Pressure - Stabilty and Pressure Checks

Dead Load and Earth Pressure - Stabilty and Pressure Checks
Load Force (k) Arm (in.) Moment (ft-k)
(1) (0.833 ft.)(5.167 ft.)(0.150k/ft3) = 0.646 5.333 3.444
(2) (0.958ft)(5.750ft)(0.150k/ft3) = 0.827 2.875 2.376
(3) (1.000ft)(1.500ft)(0.150k/ft3) = 0.22534.259 4.250 0.956
ΣV = 1.698 ΣMR = 6.776
PAV 0.253 5.750 1.455
ΣV = 1.951 ΣMR = 8.231
PAH 0.633 1.653 1.045
PP 0.656 1.061 -
ΣMOT = 1.045
1 The passive pressure at the shear key is ignored in overturning checks.
Overturning
= 7.877 ≥ 2.0 o.k.
Location of Resultant
MoDOT policy is that the resultant must be in the back half of the middle third of the footing when considering dead and earth loads:
= 3.683 ft. o.k.
Sliding
where:
φs-s = angle of internal friction of soil
φs-c = angle of friction between soil and concrete = (2/3)φs-s
= 2.339 ≥ 1.5 o.k.
Footing Pressure
= 0.808 ft.
Heel: = 0.625 ksf < 3.0 ksf o.k.
Toe: = 0.053 ksf < 3.0 ksf o.k.

Dead Load, Earth Pressure, and Live Load - Stability and Pressure Checks

Stability is not an issue because the live load resists overturning and increases the sliding friction force.

751.24.3.4 checks.jpg

The live load will be distributed as:

where E = 0.8X + 3.75
X = distance in feet from the load to the front face of wall

The live load will be positioned as shown by the dashed lines above. The bearing pressure and resultant location will be determined for these two positions.

Live Load 1 ft From Stem Face
Resultant Eccentricity
X = 1 ft.
E = 0.8(1 ft.) + 3.75 = 4.55 ft.
= 3.516k
= 3.834 ft.
= 5.75 ft. o.k.
Footing Pressure
Allowable Pressure = 3.0 ksf
Heel: = 1.902 ksf
Toe: = 0.000ksf
Live Load 1 ft From Toe
Resultant Eccentricity
X = 3.917 ft.
E = 0.8(3.917 ft.) + 3.75 = 6.883 ft.
= 2.324k
= 2.225 ft.
= 0.958 ft. o.k.
Footing Pressure
Allowable Pressure = 3.0ksf
Heel: = 0.239ksf o.k.
Toe: = 1.248ksf o.k.

Dead Load, Earth Pressure, Collision Load, and Live Load - Stability and Pressure Checks

During a collision, the live load will be close to the wall so check this combination when the live load is one foot from the face of the stem. Sliding (in either direction) will not be an issue. Stability about the heel should be checked although it is unlikely to be a problem. There are no criteria for the location of the resultant, so long as the footing pressure does not exceed 125% of the allowable. It is assumed that the distributed collision force will develop an equal and opposite force on the fillface of the back wall unless it exceeds the passive pressure that can be developed by soil behind the wall.

FLL = 3.516k

751.24.3.4 collision.jpg

FCOLL = = 1.667k

= 1.867

PPH = 2.556k > FCOLL Thus the soil will develop an equal but opp. force.

Overturning About the Heel
F.S. =
F.S. = = 1.847 ≥ 1.2 o.k.
Footing Pressure
= 1.022 ft. from heel
e = = 1.853 ft.
Allowable Pressure = (1.25)(3.0ksf) = 3.75ksf
Heel: = 3.566ksf o.k.

Stem Design-Steel in Rear Face

751.24.3.4 steel in rear face.jpg

γ = 1.3

βE = 1.3 (active lateral earth pressure)

d = 10 in. − 2 in. − (0.5 in./2) = 7.75 in.

PAH = 0.412k

Mu = (1.333 ft.)(0.412k)(1.3)(1.3) = 0.928(ft−k)

= 17.160psi

= 0.000287

= 0.00298

Use ρ = (4/3)ρ = (4/3)(0.000287) = 0.000382

One #4 bar has AS = 0.196 in2, so the required minimum of one #4 bar every 12 in. controls.

Use #4's @ 12 in. (min)

(These bars are also the bars in the bottom of the footing so the smaller of the two required spacings will be used.)

Check Shear
= 8.8 psi
= 126.5 psi > 8.8 psi o.k.

Stem Design-Steel in Front Face (Collision Loads)

751.24.3.4 steel in front face.jpg


The soil pressure on the back of the stem becomes passive soil pressure during a collision, however this pressure is ignored for reinforcement design.

γ = 1.3

βLL = 1.67

= 7.75 in.

= 1.667 k/ft.

Mu = 1.667k/ft. (1 ft.)(3 ft.)(1.3)(1.67) = 10.855(ft−k)

= 200.809 psi

= 0.00345

= 0.00298

One #4 bar has AS = 0.196 in2.

s = 7.3 in.

Use #4's @ 7 in.

Check Shear
= 45.8 psi < 126.5 psi o.k.

Footing Design - Bottom Steel

It is not considered necessary to design footing reinforcement based upon a load case which includes collision loads.

Dead Load and Earth Pressure Only
751.24.3.4 dead load.jpg
Footing wt. = = 0.707k
βE = 1.3 (lateral earth pressure)
γ = 1.3
Apply Load Factors:
ΣV = 1.951k (1.3) = 2.536k
ΣMR = 8.231(ft−k)(1.3) = 10.700(ft−k)
ΣMOT = 1.045(ft−k)(1.3)(1.3) = 1.766(ft−k)
Footing wt. = 0.707k (1.3) = 0.919k
= 3.523 ft.
= 0.648 ft.
= 0.739 ksf
= 0.143ksf
= 0.653 ksf
Moment at Wall Face:
= 1.524(ft−k)
Dead Load, Earth Pressure, and Live Load
Live Load 1 ft. From Stem Face
751.24.3.4 live load.jpg
βE = 1.3 (lateral earth pressure)
βLL = 1.67
γ = 1.3
Apply Load Factors:
FLL = 3.516k(1.3)(1.67) = 7.633k
ΣV = 7.633k + 1.951k(1.3) = 10.169k
ΣMOT = 1.045(ft−k)(1.3)(1.3) = 1.766(ft−k)
ΣMR = 8.231(ft−k)(1.3) + 3.917 ft.(7.633k) = 40.599(ft−k)
= 3.819 ft.
e = 3.819 ft. − (5.75 ft./2) = 0.944 ft.
= 0.026 ksf
= 3.511 ksf
= 3.006 ksf
= 2.400 ksf
Footing wt. from face of wall to toe:
Footing wt. = = 0.919k
Footing wt. from LLWL to toe:
Footing wt. = = 0.732k
Moment at Wall Face:
MW =
MW = 2.430(ft−k)
Moment at LLWL:
MLL = = 4.837(ft−k)
Live Load 1 ft. From Toe
751.24.3.4 toe.jpg
Apply Load Factors:
FLL = 2.324k(1.3)(1.67) = 5.045k
ΣV = 5.045k + 1.951k(1.3) = 7.581k
ΣMOT = 1.045(ft−k)(1.3)(1.3) = 1.766(ft−k)
ΣMR = 8.231(ft−k)(1.3) + 5.045k(1ft.) = 15.745(ft−k)
= 1.844 ft.
= 1.031 ft.
PH = 0 ksf
= 2.741 ksf
L1 = 3[(L/2)− e]
L1 = 3[(5.75 ft./2)− 1.031 ft.] = 5.532 ft.
= 0.305 ksf
= 2.196 ksf
Moment at Wall Face:
MW = = 1.298(ft−k)
Moment at LLWL:
MLL = = 1.186(ft−k)
Design Flexural Steel in Bottom of Footing
d = 11.5 in. − 4 in. = 7.500 in.
Mu = 4.837(ft−k) (controlling moment)
= 0.096 ksi
= 0.00162
= 0.00421
Use ρ = (4/3)ρ = (4/3)(0.00162) = 0.00216
ASReq = 0.00216(12 in.)(7.5 in.) = 0.194 in2/ft.


s = 12.1 in.
Use #4's @ 12 in. cts. (Also use this spacing in the back of the stem.)
Check Shear
Dead Load and Earth Pressure Only
VW = 1.038k
Live Load 1 ft. From Stem Face
Shear at the wall can be neglected for this loading case.
VLL = 4.019k
Live Load 1 ft. From Toe
VW = 1.525k
VLL = 2.282k
Use VU = 4.019k
= 126.5 psi

Shear Key Design

751.24.3.4 shear key.jpg

For concrete cast against and permanently exposed to earth, minimum cover for reinforcement is 3 inches.

= 8.75 in.

= 0.331 k/ft.

= 0.850 k/ft.

Mu = 1.287(ft−k)

= 0.0187 ksi

= 0.000312

= 0.00337

Use ρ = (4/3)ρ = (4/3)(0.000312) = 0.000416

ASReq = 0.000416 (12 in.)(8.75 in.) = 0.0437 in2/ft.


s = 53.8 in.

Use #4's @ 18 in. cts. (min)

Check Shear
V = 0.886k
= 16.8 psi < 126.5 psi o.k.

Reinforcement Summary

751.24.3.4 summary.jpg

751.40.8.15.7 Example 3: Pile Footing Cantilever Wall

751.24.3.5.jpg

f’c = 3,000 psi

fy = 60,000 psi

φ = 27°

γs = 120 pcf

Pile type: HP 10 x 42

Allowable pile bearing = 56 tons

Pile width = 10 inches

Toe pile batter = 1:3

See EPG 751.12 Barriers, Railings, Curbs and Fences for weight and centroid of barrier.

Assumptions

  • Retaining wall is located such that traffic can come within half of the wall height to the plane where earth pressure is applied.
  • Reinforcement design is for one foot of wall length.
  • Sum moments about the centerline of the toe pile at a distance of 6B (where B is the pile width) below the bottom of the footing for overturning.
  • Neglect top one foot of fill over toe in determining soil weight and passive pressure on shear key.
  • Neglect all fill over toe in designing stem reinforcement.
  • The wall is designed as a cantilever supported by the footing.
  • Footing is designed as a cantilever supported by the wall.
  • Critical sections for bending are at the front and back faces of the wall.
  • Critical sections for shear are at the back face of the wall for the heel and at a distance d (effective depth) from the front face for the toe.

δ = 0, ϕ = 27° so CA reduces to:

= 0.376

= 2.663

Table 751.24.3.5.1 is for stability check (moments taken about C.L. of toe pile at a depth of 6B below the bottom of the footing).

Table 751.24.3.5.1
Load Force (kips/ft) Arm about C.L. of toe pile at 6B below footing (ft.) Moment (ft-kips) per foot of wall length
Dead Load (1) 0.340 2.542 0.864
(2) (1.333 ft.)(7.000 ft.)(0.150k/ft3) = 1.400 2.833 3.966
(3) (3.000 ft.)(8.500 ft.)(0.150k/ft3) = 3.825 4.417 16.895
(4) (1.000 ft.)(1.750 ft.)(0.150k/ft3) = 0.263 4.417 1.162
Σ ΣV = 5.828 - ΣMR = 22.887
Earth Load (5) (7.000 ft.)(5.167 ft.)(0.120k/ft3) = 4.340 6.083 26.400
(6) (2.000 ft.)(2.000 ft.)(0.120k/ft3) = 0.480 1.167 0.560
Σ ΣV = 4.820 - ΣMR = 26.960
Live Load Surcharge PSV (2.000 ft.)(5.167 ft.)(0.120k/ft3) = 1.240 6.083 MR = 7.543
PSH (2.000 ft.)(0.376)(10.000 ft.)(0.120k/ft3) = 0.902 10.000 MOT = 9.020
Earth Pressure PA 2.2561 8.333 MOT = 18.799
PP 3.2852 - -
Collision Force (FCOL) (10.000k)/[2(7.000 ft.)] = 0.714 18.000 MOT = 12.852
Heel Pile Tension (PHV) (3.000 tons)(2 k/ton)(1 pile)/(12.000 ft.) = 0.500 7.167 MR = 3.584
Toe Pile Batter (PBH) 5.9033 - -
Passive Pile Pressure (Ppp) 0.8324 - -
1
2
3
4


Table 751.24.3.5.2 is for bearing pressure checks (moments taken about C.L of toe pile at the bottom of the footing).

Table 751.24.3.5.2
Load Force (kips/ft) Arm about C.L. of toe pile at 6B below footing (ft.) Moment (ft-kips) per foot of wall length
Dead Load (1) 0.340 0.875 0.298
(2) (1.333 ft.)(7.000 ft.)(0.150k/ft3) = 1.400 1.167 1.634
(3) (3.000 ft.)(8.500 ft.)(0.150k/ft3) = 3.825 2.750 10.519
(4) (1.000 ft.)(1.750 ft.)(0.150k/ft3) = 0.263 2.750 0.723
Σ ΣV = 5.828 - ΣMR = 13.174
Earth Load (5) (7.000 ft.)(5.167 ft.)(0.120k/ft3) = 4.340 4.417 19.170
(6) (2.000 ft.)(2.000 ft.)(0.120k/ft3) = 0.480 -0.500 -0.240
Σ ΣV = 4.820 - ΣMR = 18.930
Live Load Surcharge PSV (2.000 ft.)(5.167 ft.)(0.120k/ft3) = 1.240 4.417 MR = 5.477
PSH (2.000 ft.)(0.376)(10.000 ft.)(0.120k/ft3) = 0.902 5.000 MOT = 4.510
Earth Pressure PA 2.256 3.333 MOT = 7.519
PP 3.285 - -
Collision Force (FCOL) (10.000k)/[2(7.000 ft.)] = 0.714 13.000 MOT = 9.282
Heel Pile Tension (PHV) (3.000 tons)(2 k/ton)(1 pile)/(12.000 ft.) = 0.500 5.500 MR = 2.750
Toe Pile Batter (PBH) 5.903 - -
Passive Pile Pressure (Ppp) 0.832 - -

Investigate a representative 12 ft. strip. This will include one heel pile and two toe piles. The assumption is made that the stiffness of a batter pile in the vertical direction is the same as that of a vertical pile.

Neutral Axis Location = [2piles(1.5 ft.) + 1pile(7 ft.)] / (3 piles) = 3.333 ft. from the toe.

751.24.3.5 neutral axis.jpg

I = Ad2

For repetitive 12 ft. strip:

Total pile area = 3A
I = 2A(1.833 ft.)2 + A(3.667 ft.)2 = 20.167(A)ft.2

For a 1 ft. unit strip:

Total pile area = (3A/12 ft.) = 0.250A
Case I
F.S. for overturning ≥ 1.5
F.S. for sliding ≥ 1.5
Check Overturning
Neglect resisting moment due to PSV for this check.
ΣMR = 22.887(ft−k) + 26.960(ft−k) + 3.584(ft−k)
ΣMR = 53.431(ft−k)
ΣMOT = 9.020(ft−k) + 18.799(ft−k) = 27.819(ft−k)
F.S.OT = = 1.921 > 1.5 o.k.
Check Pile Bearing
Without PSV :
ΣV = 5.828k + 4.820k = 10.648k
e = = 1.885 ft.
Moment arm = 1.885 ft. - 1.833 ft. = 0.052 ft.
Allowable pile load = 56 tons/pile. Each pile has area A, so:
o.k.
o.k.
With PSV:
ΣV = 5.828k + 4.820k + 1.240k = 11.888k
= 2.149 ft.
Moment arm = 2.149 ft. - 1.833 ft. = 0.316 ft.
o.k.
o.k.
Check Sliding
= 3.173 ≥ 1.5 o.k.
Case II
F.S. for overturning ≥ 1.2
F.S. for sliding ≥ 1.2
Check Overturning
ΣMR = (22.887 + 26.960 + 7.543 + 3.584)(ft−k) = 60.974(ft−k)
ΣMOT = (9.020 + 18.799 + 12.852)(ft−k) = 40.671(ft−k)
= 1.499 ≥ 1.2 o.k.
Check Pile Bearing
= 1.369 ft.
Moment arm = 1.833 ft. - 1.369 ft. = 0.464 ft.
o.k.
= 35.519k
o.k.
Check Sliding
= 2.588 ≥ 1.2 o.k.
Case III
F.S. for overturning ≥ 1.5
F.S. for sliding ≥ 1.5
Check Overturning
ΣMR = (22.887 + 26.960 + 3.584)(ft−k) = 53.431(ft−k)
ΣMOT = 18.799(ft−k)
= 2.842 ≥ 1.5 o.k.
Check Pile Bearing
= 2.309 ft.
Moment arm = 2.309 ft. - 1.833 ft. = 0.476 ft.
= 37.065k
o.k.
= 53.649k
o.k.
Check Sliding
= 4.441 ≥ 1.5 o.k.
Case IV
Check Pile Bearing
= 3.015 ft.
Moment arm = 3.015 ft. - 1.833 ft. = 1.182 ft.
25% overstress is allowed on the heel pile:
o.k.
= 28.868k
o.k.
Reinforcement - Stem
751.24.3.5 reinforcement stem.jpg
b = 12 in.
cover = 2 in.
h = 16 in.
d = 16 in. - 2 in. - 0.5(0.625 in.) = 13.688 in.
FCollision = 0.714k/ft
Apply Load Factors
FCol. = γβLL(0.714k) = (1.3)(1.67)(0.714k) = 1.550k
PLL = γβE (0.632k) = (1.3)(1.67)(0.632k) = 1.372k
PAStem = γβE (1.105k) = (1.3)(1.3)(1.105k) = 1.867k
Mu = (10.00 ft.)(1.550k) + (3.500 ft.)(1.372k) + (2.333 ft.)(1.867k)
Mu = 24.658(ft−k)
= 0.146ksi
= 0.00251
= 0.00212
ρ = 0.00251
One #5 bar has AS = 0.307 in2
s = 8.9 in.
Use # 5 bars @ 8.5 in. cts.
Check Shear
VuφVn
Vu = FCollision + PLL + PAStem = 1.550k + 1.372k + 1.867k = 4.789k


= 34.301 psi
= 109.5 psi > 34.3 psi o.k.
Reinforcement - Footing - Top Steel
751.24.3.5 footing.jpg
b = 12 in.
cover = 3 in.
h = 36 in.
d = 36 in. - 3 in. - 0.5(0.5 in.) = 32.750 in.
Design the heel to support the entire weight of the superimposed materials.
Soil(1) = 4.340k/ft.
LLs = 1.240k/ft.
= 2.325k/ft.
Apply Load Factors
Soil(1) = γβE(4.340k) = (1.3)(1.0)(4.340k) = 5.642k
LLs = γβE(1.240k) = (1.3)(1.67)(1.240k) = 2.692k
Slab wt. = γβD(2.325k) = (1.3)(1.0)(2.325k) = 3.023k
Mu = (2.583 ft.)(5.642k + 2.692k + 3.023k) = 29.335(ft−k)
= 0.0304 ksi
= 0.000510
= 0.00188
Use ρ = 4/3 ρ = 4/3 (0.000510) = 0.000680
One #4 bar has As = 0.196 in.2
s = 8.8 in.
Use #4 bars @ 8.5 in. cts.
Check Shear
= 33.998 psi ≤ 109.5 psi = νc o.k.
Reinforcement - Footing - Bottom Steel
Design the flexural steel in the bottom of the footing to resist the largest moment that the heel pile could exert on the footing. The largest heel pile bearing force was in Case IV. The heel pile will cause a larger moment about the stem face than the toe pile (even though there are two toe piles for every one heel pile) because it has a much longer moment arm about the stem face.
751.24.3.5 heel pile.jpg
Pile is embedded into footing 12 inches.
b = 12 in.
h = 36 in.
d = 36 in. - 4 in. = 32 in.
Apply Load Factors to Case IV Loads
ΣV = 13.842 k/ft.
ΣM = 41.735 (ft−k)/ft.
e = = 3.015 ft.
Moment arm = 3.015 ft. - 1.833 ft. = 1.182 ft.
= 7.588 k/ft.
= 27.825(ft−k)/ft.
= 0.0301 ksi
= 0.000505
= 0.00196
Use ρ = 4/3 ρ = 4/3 (0.000505) = 0.000673
ASReq = ρbd = (0.000673)(12 in.)(32 in.) = 0.258 in2/ft.


One #4 bar has As = 0.196 in2.
s = 9.1 in.
Use #4 bars @ 9 in. cts.
Check Shear
The critical section for shear for the toe is at a distance d = 21.75 inches from the face of the stem. The toe pile is 6 inches from the stem face so the toe pile shear does not affect the shear at the critical section. The critical section for shear is at the stem face for the heel so all of the force of the heel pile affects the shear at the critical section. The worst case for shear is Case IV.
Vu = 7.588k
= 23.248 psi ≤ 109.5 psi = νc o.k.
Reinforcement - Shear Key
b = 12 in.
h = 12 in.
cover = 3 in.
d = 12 in. - 3 in. - 0.5(0.5 in.) = 8.75 in.
Apply Load Factors
PP = γβE (3.845k) = (1.3)(1.3)(3.845k) = 6.498k
Mu = (0.912 ft.)(6.498k) = 5.926(ft−k)
= 0.0860 ksi
= 0.00146
= 0.00292
Use ρ = 4/3 ρ = 4/3(0.00146) = 0.00195
ASReq = ρbd = (0.00195)(12 in.)(8.75 in.) = 0.205 in.2/ft.


One #4 bar has As = 0.196 in2


s = 11.5 in.
Use #4 bars @ 11 in. cts.
Check Shear
= 72.807 psi < 109.5 psi = νc
Reinforcement Summary
751.24.3.5 summary.jpg

751.40.8.15.8 Dimensions

Cantilever Walls

Each section of wall shall be in increments of 4 ft. with a maximum length of 28'-0".

751.24.3.6 friction or bearing piles.jpg


Each section of wall shall be in increments of 4 ft. with a maximum length of 28'-0".

751.24.3.6 pile footing.jpg


Cantilever Walls - L-Shaped

Each section of wall shall be in increments of 4 ft. with a maximum length of 28'-0".

751.24.3.6 L shaped.jpg


Counterfort Walls

Notes:
Dimension "A"
• Maximum length = 28'-0".
• Each section to be in 4'-0" increments.
• (See rustication recess details.)
Dimensions "B" & "C"
• As required by the design to balance the negative and positive moments. (See the design assumptions).
Notes:
Batter "D":
* As required to maintain 9" minimum at the top of the counterfort and 12" minimum edge distance at the top of the footing, between counterfort and footing edge.
* Batter to be given an eighth of an inch per foot of counterfort height.
Dimension "L":
* As required for stability.
* As an estimate, use "L" equal to 1/2 the height of "H".

Sign-Board Type Counterfort Walls

Notes:
Dimension "A"
* Maximum length = 28'-0".
* Each section to be in 4'-0" increments.
* (See rustication recess details.)
Dimensions "B" & "C"
* As required by the design to balance the negative and positive moments. (See the design assumptions).
Dimension "E"
* (Sign-board type only)
* As required to maintain footing pressure within the allowable for existing foundation material. 12" minimum.
Notes:
Batter "D":
* As required to maintain 9" minimum at the top of the counterfort and 12" minimum edge distance at the top of the footing, between counterfort and footing edge.
* Batter to be given an eighth of an inch per foot of counterfort height.
Dimension "L":
* As required for stability.
* As an estimate, use "L" equal to 1/2 the height of "H".

751.40.8.15.9 Reinforcement

Cantilever Walls

(*) Alternate long and short bars at equal spaces.
(**) If collision forces are assumed, use #4 @ 12" cts. min. and extend at least development length into footing. (See EPG 751.5.9.2.8.1 Development and Lap Splice General.)
(***) Theo. cut-off for bending + development length. (Wall height over 10' only.)
(*) Alternate long and short bars at equal spaces.
(**) If collision forces are assumed, use #4 @ 12" cts. min. and extend at least development length into footing. (See EPG 751.5.9.2.8.1 Development and Lap Splice General.)
(***) Theo. cut-off for bending + development length. (Wall height over 10' only.)
(****) Due to site constriction.

Cantilever Walls - L-Shaped

(*) Do not splice stress bars in the fill face at top of footing.
(**) If collision forces are assumed, use #4 @ 12" cts. min. and extend at least development length into footing. (See EPG 751.5.9.2.8.1 Development and Lap Splice General.)

Counterfort Walls

Wall and Stem
(For footing reinforcement, see the "Footing" diagram, below)
(*) Use development length or standard hook in accordance with EPG 751.5.9.2.8.1 Development and Lap Splice General.
(**) See lap splices Class B. (See EPG 751.5.9.2.8.1 Development and Lap Splice General.)
Footing
(*) By design for loads and footing pressures on section under consideration. (#5 @ 12" cts. is the minimum.)

Counterfort Walls - Sign-Board Type

Wall and Stem
Refer to "Counterfort Walls, Wall and Stem", above.
Spread Footing
751.24.3.7 sign board.jpg
If the shear line is within the counterfort projected (longitudinally or transversely), the footing may be considered satisfactory for all conditions. If outside of the counterfort projected, the footing must be analyzed and reinforced for bending and checked for bond stress and for diagonal tension stress.
751.24.3.7 sign board footing.jpg

751.40.8.15.10 Details

Non-Keyed Joints

Each section of wall shall be in increments of 4 ft. with a maximum length of 28'-0".

751.24.3.8 nonkeyed.jpg
See EPG 751.50 Standard Detailing Notes for appropriate notes.

Keyed Joints

751.24.3.8 keyed.jpg
See EPG 751.50 Standard Detailing Notes for appropriate notes.


Rustication Recess

751.24.3.8 rustication.jpg


Drains

751.24.3.8 drains.jpg
Note: French drains shall be used on all retaining walls, unless otherwise specified on the Design Layout.
751.24.3.8 drop inlet.jpg


Construction Joint Keys:

Cantilever Walls
751.24.3.8 cantilever.jpg


Counterfort Walls
751.24.3.8 counterfort.jpg


Key length: Divide the length "A" into an odd number of spaces of equal lengths. Each space shall not exceed a length of 24 inches. Use as few spaces as possible with the minimum number of spaces equal to three (or one key).
Key width = Counterfort width/3 (to the nearest inch)
Key depth = 2" (nominal)
Sign-Board Walls
751.24.3.8 sign board.jpg
Key length = divide length "A" or "B" into an odd number of spaces of equal lengths. Each space length shall not exceed 24 inches. Use as few spaces as possible with the minimum number of spaces equal to three (or one key).