Difference between revisions of "751.22 Prestressed Concrete I Girders"

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m (→‎751.22.1.4 Span and Structure Lengths: Per Bridge, clarified usage of plain and laminated bearing pads. Added bearing pad length requirements for P/S NU girders and P/S Spread Box Beams.)
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==751.22.1 General==
 
==751.22.1 General==
 +
EPG 751.22 illustrates the general design procedure for prestressed concrete I girders (Type 2, 3, 4 and 6), bulb-tee girders (Type 7 and 8) and NU girders (NU 35, 43, 53, 63, 70 and 78) using AASHTO LRFD Bridge Design Specifications except as noted.
 
===751.22.1.1 Material Properties===
 
===751.22.1.1 Material Properties===
 +
[[image:751.22.1.1.jpg|right|275px]]
  
 +
'''Increasing Girder Capacity'''
  
'''Concrete'''
+
The following allowable modification of material properties listed in order of increasing costs may be considered if required by design.
 +
:1. Increase concrete strength up to 8.0 ksi (''f′<sub>c</sub>'' = 6.5 ksi) (readily producible by fabricator)
 +
:2. Increase concrete strength greater than 8.0 ksi (readily producible by fabricator)
 +
:3. Modify geometric properties (in order of increasing costs)
 +
::a. Increase top flange height (and overall height accordingly)
 +
::b. Use modified Type 2, 3, 4 and 6 girders (most costly and inconvenient due to required forming bed modifications)
  
Conventional concrete strength for P/S I-Girder shall be the following:
+
'''Class A-1 Concrete '''
  
:'''For MoDOT Standard Girders:'''
+
Conventional concrete with the following compression strengths shall be used as required for I girders and bulb-tee girders.
  
::<math>\, f'_{ci} = 4.5 ksi</math>, <math>\, f'_c = 6.0 ksi</math>
+
<center>''f′<sub>c</sub>'' = 6.0 ksi (''f′<sub>ci</sub>'' = 4.5 ksi) →  ''f′<sub>c</sub>'' = 7.0 ksi (''f′<sub>ci</sub>'' = 5.0 ksi) →  ''f′<sub>c</sub>'' = 8.0 ksi (''f′<sub>ci</sub>'' = 6.5 ksi)</center>
  
::Optional higher concrete strength shall be:
+
The lowest concrete strength satisfying the demand shall be used.
  
::<math>\, f'_{ci} = 5.0 ksi</math>, <math>\, f'_c = 7.0 ksi</math>
+
The NU girders shall use conventional concrete with the following compression strength.
  
::'''OR'''
+
<center>''f′<sub>c</sub>'' = 8.0 ksi (''f′<sub>ci</sub>'' = 6.5 ksi)</center>
  
::With the approval of the Structural Project Manager or Liaison:
+
High strength concrete with compressive strengths up to ''f′<sub>c</sub>'' =10 ksi (''f′<sub>ci</sub>'' = 7.0 ksi) may be used with the permission of the Structural Project Manager or Structural Liaison Engineer. High strength concrete may increase costs due to production modifications necessary to obtain the required strength.
  
::<math>\,f'_{ci} = 6.5 ksi</math>, <math>\,f'_c = 8.0 ksi</math>
+
Modulus of Elasticity
  
:'''For NU Standard Girder:'''
+
::''E<sub>c</sub>'' = 33,000''K<sub>1</sub>w<sub>c</sub><sup>1.5</sup>'''√'''f′<sub>c</sub> ''  (''f′<sub>c</sub> ''in ksi)
  
::<math>\,f'_{ci} = 6.5 ksi</math>, <math>\,f'_c = 8.0 ksi</math>
+
::where:
 +
:::''K<sub>1</sub>'' = correction factor for source of aggregate = 1.0 unless determined by physical testing
 +
:::''w<sub>c</sub>'' = 0.140 + 0.001''f′<sub>c</sub>''    (''f′<sub>c</sub>'' in ksi)
  
::Strengths greater than 8 ksi shall require high performance concrete (HPC) and may increase costs due to production modifications necessary to obtain the required strength.
+
Prestressing Strands
  
::::::::::::Modulus of Elasticity, <math>\, E_c = 33,000\ K_1 \ (w_c^{1.5}) \sqrt{f^'_c}</math>
+
Prestressing strands shall be Grade 270 uncoated, low relaxation, seven-wire strands in accordance with AASHTO M 203 with the following design properties.
 
+
{| style="margin: 1em auto 1em auto"
::::::::::::Where,
 
 
 
::::::::::::f'<sub>c</sub> in ksi
 
 
 
::::::::::::K<sub>1</sub> = correction factor for source of aggregate
 
:::::::::::::= 1.0 unless determined by physical testing
 
 
 
::::::::::::<math>w_c = 0.145 kcf\ \mbox{for}\ f'_c\le 5.0 ksi</math>
 
 
 
::::::::::::'''<math>w_c = 0.140 + 0.001 f'_c\ \mbox{for}\ f'_c>5.0 ksi </math>'''
 
 
 
{| border="0" cellpadding="4" cellspacing="0" align="center" style="textalign:left"
 
|-
 
|&nbsp;
 
|-
 
!colspan="3" align="left"|Prestressing strand
 
|-
 
|colspan="3"|Type of strand:
 
|-
 
|colspan="3"|AASHTO M203 (ASTM A416) Grade 270
 
|-
 
|colspan="3"|Uncoated, seven-wire, low-relaxation strand
 
|-
 
|colspan="2"|Ultimate tensile strength,
 
|align="right"|<math>\,f_{pu} = 270 ksi</math>
 
|-
 
|colspan="2"|Yield strength,
 
|align="right"|<math>\,f_{py} = 0.9 f_{pu} ksi</math>
 
 
|-
 
|-
|colspan="2"|Strand modulus of elasticity,
+
|Ultimate tensile strength, ''f<sub>pu</sub>''  = 270 ksi||width="75"| ||1/2-inch strand: diameter, ''d<sub>ps</sub>''  = 0.5 in. and area, ''A<sub>ps</sub>''  = 0.153 in.<sup>2</sup>
|align="right"|<math>\,E_p = 28500 ksi</math>
 
 
|-
 
|-
|colspan="3"|For standard concrete:
+
|Yield strength, ''f<sub>py</sub>''  = 0.9''f<sub>pu</sub>'' = 243 ksi|| ||0.6-inch strand: diameter, ''d<sub>ps</sub>'' = 0.6 in. and area, ''A<sub>ps</sub>'' = 0.217 in.<sup>2</sup>
 
|-
 
|-
|&nbsp;
+
|Maximum allowed force per strand,<br/>&nbsp;&nbsp;&nbsp;&nbsp;''f<sub>pbt</sub>'' ''A<sub>ps</sub>'' = 30.98 kips (1/2-inch strands)<br/>&nbsp;&nbsp;&nbsp;&nbsp;''f<sub>pbt</sub>'' ''A<sub>ps</sub>'' = 43.94 kips (0.6-inch strands)  || || Modulus of elasticity, ''E<sub>p</sub>'' = 28,500 ksi<br/>Maximum allowed stress prior to transfer,<br/>&nbsp;&nbsp;&nbsp;&nbsp;''f<sub>pbt</sub>'' = 0.75''f<sub>pu</sub>'' = 202.5 ksi
|Strand diameter,
 
|align="right"|<math>\,d_{ps} = 0.5 in</math>
 
|-
 
|&nbsp;
 
|Strand area,
 
|align="right"|<math>\,A_{ps} = 0.153 in^2</math>
 
|-
 
|colspan="3"|For optional concrete:
 
|-
 
|&nbsp;
 
|Strand diameter,
 
|align="right"|<math>\,d_{ps} = 0.6 in</math>
 
|-
 
|&nbsp;
 
|Strand area,
 
|align="right"|<math>\,A_{ps} = 0.217 in^2</math>
 
|-
 
|colspan="3"|&nbsp;
 
|-
 
!colspan="3" align="left"|Mild reinforcing steel
 
|-
 
|colspan="2"|Minimum yield strength,
 
|align="right"|<math>\,f_y = 60.0 ksi</math>
 
|-
 
|colspan="2"|Steel modulus of elasticity,
 
|align="right"|<math>\,E_s = 29000 ksi</math>
 
|-
 
|colspan="3"|&nbsp;
 
|-
 
!colspan="3" align="left"|Welded Wire Reinforcement
 
|-
 
|colspan="2"|Minimum yield strength,
 
|align="right"|<math>\,f_y = 70.0 ksi</math>
 
|-
 
|colspan="2"|Steel modulus of elasticity,
 
|align="right"|<math>\,E_s = 29000 ksi</math>
 
 
|}
 
|}
 +
 +
Total initial prestress force equals the number of strands multiplied by the required initial prestress force per strand.
  
===751.22.1.2 Geometric Dimensions===
+
Typically, the required initial prestress force per strand is the maximum allowed force per strand.
  
 +
Report on the plans the required number of strands by design and the total initial prestress force using [[751.50 Standard Detailing Notes#(H2c1.3)|EPG 751.50 Standard Detailing Notes H2c1.3]].
  
The ratio of the depth of girder to span length will in general be not less than 1/18.
+
'''Reinforcing Steel'''
  
The cross sectional dimensions of the girder shall be one of the following:
+
Deformed bars shall be Grade 60 in accordance with AASHTO M 31 with the following design properties.
 +
{| style="margin: 1em auto 1em auto"
 +
|-
 +
|Yield strength, ''f<sub>y</sub>'' = 60.0 ksi||width="75"| || Modulus of elasticity, ''E<sub>s</sub>'' = 29,000 ksi
 +
|}
  
:'''MoDOT Standard Girders:'''
+
Welded wire reinforcement shall be in accordance with AASHTO M 336 with the following design properties.
<center>[[Image:751.22_dim_beam_types_2_thru_6.gif]]</center>
+
{| style="margin: 1em auto 1em auto"
 
+
|-
{|border="0" cellpadding="5" align="center" textalign="center" width="600"
+
|Yield strength, ''f<sub>y</sub>'' = 70.0 ksi||width="75"| || Modulus of elasticity, ''E<sub>s</sub>'' = 29,000 ksi
 
 
|align="center"|'''BEAM TYPE 2'''
 
|align="center"|'''BEAM TYPE 3'''
 
|align="center"|'''BEAM TYPE 4'''
 
|align="center"|'''BEAM TYPE 6'''
 
 
|}
 
|}
  
 +
All bars extending into slab shall be epoxy coated. Welded wired reinforcement shall not be epoxy coated.
  
<center>[[Image:751.22_dim_beam_types_7_8.gif]]</center>
+
===751.22.1.2 Geometric Properties===
  
 +
The following sections, except those specified as modified, shall be preferred because of their familiarity to local precast plants. These sections have been entered into the beam section libraries of in-house design software. The top flange height and overall height may be increased if required but any deviation from the standard sections shown shall be discussed with Structural Project Manager or Structural Liaison Engineer. The use of the modified girders shall be discussed with Structural Project Manager or Structural Liaison Engineer.
  
{|border="0" cellpadding="5" align="center" textalign="center" width="600"
+
:'''I Girders:'''
 +
:[[image:751.22.1.2 type 2 2022.jpg|center|850px]]
  
|align="center"|'''BEAM TYPE 7'''
 
|align="center"|'''BEAM TYPE 8'''
 
|}
 
  
 +
:[[image:751.22.1.2 type 3 2022.jpg|center|850px]]
  
<math>*</math> If the web is required to be increased, then the top and bottom flanges are to be increased by the same amount. (1" increments 2" max.).
 
  
 +
:[[image:751.22.1.2 type 4 2022.jpg|center|850px]]
  
  
See Structural Project Manager before using NU Sections.
+
:[[image:751.22.1.2 type 6 2022.jpg|center|850px]]
  
:'''NU Standard Girders:'''
 
[[Image:751.22 NU 35 Apr 2011.jpg|thumb|center|400px|<center>'''BEAM NU 35'''</center>
 
<center>''A'' = 639.79 in.<sup>2</sup></center>
 
<center>''Y<sub>b</sub>'' = 15.96 in.</center>
 
<center>''Y<sub>t</sub>'' = 19.48 in.</center>
 
<center>''I<sub>xx</sub>'' = 108,498 in.<sup>4</sup></center>
 
<center>''I<sub>yy</sub>'' = 60,086 in.<sup>4</sup></center>
 
<center>''V/S'' = 3.067 in.</center>]]
 
  
 +
:'''Bulb-Tee Girders:'''
 +
:[[image:751.22.1.2 type 7 2022.jpg|center|850px]]
  
{| style="margin: 1em auto 1em auto text-align:center" align="center"
 
  
|-
+
<div id="NU Standard Girders"></div>
|colspan="2"|[[Image:751.22_dim_NU_girders_43 53 Apr 2011.jpg|620px]]
+
:'''NU Girders:'''
|-
+
[[Image:751.22.1.2 NU 35 43 53 2022.jpg|center|850px]]
|align="center"|'''BEAM NU 43'''||align="center"|'''BEAM NU 53'''
 
|-
 
|align="center"|''A'' = 686.05 in.<sup>2</sup>||align="center"|''A'' = 743.88 in.<sup>2</sup>
 
|-
 
|align="center"|''Y<sub>b</sub>'' = 19.36 in.||align="center"| ''Y<sub>b</sub>'' = 23.71 in.
 
|-
 
|align="center"|''Y<sub>t</sub>'' = 23.95 in.||align="center"|''Y<sub>t</sub>'' = 29.44 in.
 
|-
 
|align="center"|''I<sub>xx</sub>'' = 179,343 in.<sup>4</sup>||align="center"|''I<sub>xx</sub>'' = 297,512 in.<sup>4</sup>
 
|-
 
|align="center"|''I<sub>yy</sub>'' = 60,219 in.<sup>4</sup>||align="center"|''I<sub>yy</sub>'' = 60,385 in.<sup>4</sup>
 
|-
 
|align="center"|''V/S'' = 3.058 in.||align="center"|''V/S'' = 3.048 in.
 
|}
 
  
  
{| style="margin: 1em auto 1em auto text-align:center" align="center"
+
[[Image:751.22.1.2 NU 63 70 78 2022.jpg|center|850px]]
|-
 
|colspan="2"|[[Image:751.22_dim_NU_girders_63 70 Apr 2011.jpg|620px]]
 
|-
 
|align="center"|'''BEAM NU 63'''||align="center"|'''BEAM NU 70'''
 
|-
 
|align="center"|''A'' = 801.72 in.<sup>2</sup>||align="center"|''A'' = 847.98 in.<sup>2</sup>
 
|-
 
|align="center"|''Y<sub>b</sub>'' = 28.14 in.||align="center"| ''Y<sub>b</sub>'' = 31.74 in.
 
|-
 
|align="center"|''Y<sub>t</sub>'' = 34.86 in.||align="center"|''Y<sub>t</sub>'' = 39.14 in.
 
|-
 
|align="center"|''I<sub>xx</sub>'' = 451,306 in.<sup>4</sup>||align="center"|''I<sub>xx</sub>'' = 601,931 in.<sup>4</sup>
 
|-
 
|align="center"|''I<sub>yy</sub>'' = 60,551 in.<sup>4</sup>||align="center"|''I<sub>yy</sub>'' = 60,684 in.<sup>4</sup>
 
|-
 
|align="center"|''V/S'' = 3.040 in.||align="center"|''V/S'' = 3.034 in.
 
|}
 
 
 
  
 
===751.22.1.3 Typical Span Ranges===
 
===751.22.1.3 Typical Span Ranges===
  
The following charts provide span ranges (limits) for P/S I-girders based on girder spacing and standard roadway widths.  
+
The following charts provide a general baseline for the maximum span lengths of prestressed I-girders and NU girders based off single span designs in accordance with LRFD, 9th Edition. The designs used for these charts use the maximum practical girder spacing (9’-6” for Type 2, 3 and 4 girders, approximately 11 feet to 11’-6” for all other girders shown). The charts were developed using designs that used standard materials and shapes and no debonding. Increased span lengths are possible with modification to the materials, shapes, and/or girder spacings used. Increased span lengths are also likely for continuous span bridges. See Increasing Girder Capacity section above for more information. These charts shall be used for preliminary design only.
  
 
'''Limitations of the Charts:'''
 
'''Limitations of the Charts:'''
  
:A. Standard Concrete Charts Only
+
These charts only contain data on designs with a concrete compressive strength equal to 8.0ksi, this is due to a lack of sufficient data for designs using a concrete compressive strength of 6.0ksi or 7.0ksi.  
  
::Criteria used in determining maximum span lengths for lower conventional concrete strength:
+
<center><b><big>Prestressed I-Girder Single Span Ranges</big></b></center>
::1) Low-relaxation strand with 0.5” strand diameter
+
[[image:751.22.1.3_PSI_8ksi_07-23.png|700px|center]]
 +
{| style="margin: auto;"
 +
| <b>Note: </b> || Type 7 I-Girder was not included due to there being insufficient data to report a justified range of span lengths.
 +
|}
  
::2) Concrete strengths, <math>\, f'_{ci}</math> = 4.5 ksi and <math>\, f'_c</math> = 6.0 ksi
 
  
::3) 3-span bridge consisting of 3 equal length girders made continuous and composite
+
<center><b><big>Prestressed NU Girder Single Span Ranges</big></b></center>
 +
[[image:751.22.1.3_PSNU_8ksi_07-23.png|700px|center]]
 +
{| style="margin: auto;"
 +
| style=vertical-align:top | <b>Note: </b> || Nu 78 Girders were excluded from this chart due to there being insufficient data to report an accurate</br>range of span lengths.
 +
|}
  
:B. Optional Concrete Charts Only
+
===751.22.1.4 Span and Structure Lengths===
  
::Criteria used in determining maximum span lengths for greater  conventional concrete strength:
+
====751.22.1.4.1 Limits====
 +
'''Span Lengths'''
  
::1) Low-relaxation strand with 0.6” strand diameter
+
Designs using MoDOT standard Type 6 girders shall be limited to 105 feet maximum length to ensure stability during fabrication, shipping and erection.
  
::2) Concrete strengths, <math>\, f'_{ci}</math> = 5.0 ksi and <math>\, f'_c</math> = 7.0 ksi
+
No limits are set for other types of prestressed girders however the Structural Project Manager or Structural Liaison Engineer shall be consulted prior to the design of any unusually long prestressed girder.
  
::3) 3-span bridge consisting of 3 equal length girders made continuous and composite
+
'''Continuous Structure Lengths'''
 +
[[image:751.22.1.4.1.jpg|center|675px]]
  
:C.  Both Standard Concrete and Optional Concrete Charts
 
  
::Criteria used in determining span ranges for both Standard and Optional Concrete conventional strengths.
+
====751.22.1.4.2 Girder Length and Geometric Layout====
 +
<div id="Tangent Bridges"></div>
 +
:'''Tangent Bridges'''
 +
:Girder lengths of exterior spans (i.e., end spans) and interior spans shall be computed using the requirements shown below.
  
::1) Minimum span lengths were determined by the positive moment capacity of the smallest strand arrangement per beam shape. Shorter span lengths are possible.  
+
[[image:751.22.1.4.2 2021.jpg|center|775px]]
  
::2) Based on 10 ft. design lanes. (Current design practice meets AASHTO LRFD and uses 12 ft. design lanes.)
 
  
::3) Based on unrefined prestress loss equations. (Current design practice  meets AASHTO LRFD and uses refined losses.)
+
::The layout length for single span shall be measured from centerline of bearing to centerline of bearing. If the difference between layout length of the end span and interior span is within one foot, then layout length should be adjusted if possible so the girder lengths are equal for end span and interior span.
 
+
'''Recommended Adjustments for Using the Charts:'''
+
::(1) Minimum dimension from edge of bearing pad to end of girder equals one inch.
 
+
Because the span limit charts were developed using older design criteria as noted above, increased span lengths are probable.
+
::(2) Design layout lengths are horizontal lengths.  Girder lengths should be adjusted according to grade and shall be specified to the nearest 1/8 inch.
 
+
   
:1) Span limits given in all charts should be increased 10 percent to account for current design practice. Ten percent can safely be used without a preliminary girder analysis.
+
::(3) For large skews, end bent beam caps may need to be larger to provide edge distance.
 
+
   
:2) Span limits given in all charts shall be increased when a preliminary girder analysis based on actual design conditions is performed which shall be noted on the Design Layout.   
+
::(4) Horizontal distance along certerline of girder.
 
 
 
 
{|style="padding: 0.3em; margin-left:1px; border:2px solid #a9a9a9; text-align:center; font-size: 95%; background:#f5f5f5" width="480px" align="center"
 
|-
 
|'''Span range charts are planned for future replacement. Use the recommended adjustments until implemented.'''
 
|}
 
 
 
 
 
<center>'''Standard Concrete (<math>\, f'_c</math> = 6 ksi) P/S I Beam Span Ranges for<br/>Given Roadway Widths and Girder Spacing'''</center>
 
 
 
<center>[[Image:751.22_standard_conc_PSI_span_ranges.gif]]</center>
 
  
 
+
::(5) = 1ʺ (minimum) + ½ bearing pad length which equals:
 
+
:::: 5ʺ (minimum) for I-girders and squared-end adjacent beams,
<center>'''Optional Concrete (<math>\, f'_c</math> = 7 ksi) P/S I Beam Span Ranges for<br/>Given Roadway Widths and Girder Spacing'''</center>
+
:::: 3 ½ʺ (minimum) for NU girders and spread beams with squared ends,
 
+
:::: 3⅝ʺ (minimum) for skewed-end spread beams, 3½ʺSEC(15°).
<center>[[Image:751.22_optional_conc_PSI_span_ranges.gif]]</center>
 
 
 
===751.22.1.4 Span and Structure Lengths===
 
 
 
'''Girder Length and Geometric Layout'''
 
 
 
:'''Tangent Bridges'''
 
:Girder lengths of exterior spans (i.e., end spans) shall be computed using the requirements shown below. 
 
:Girder lengths of interior spans shall be computed using the requirements shown below.
 
  
 
:'''Curved Bridges'''
 
:'''Curved Bridges'''
Line 270: Line 168:
 
:#A second tie point may be required if the skew is not measured to the CL of roadway at the bridge tie point.  If this is the case, establish the tie point at the specified station and plot the skew line at the required angle.
 
:#A second tie point may be required if the skew is not measured to the CL of roadway at the bridge tie point.  If this is the case, establish the tie point at the specified station and plot the skew line at the required angle.
 
:#Next, on the centerline of structure or baseline curve, locate the station of the CL of bent for each intermediate bent and the fill face for the end bents.  Once these points are located, plot lines through these stations parallel to skew line.  Normally the layout file will specify that all bents are parallel to the skew line; however, there may be times when the bents are radial or have varying skews.
 
:#Next, on the centerline of structure or baseline curve, locate the station of the CL of bent for each intermediate bent and the fill face for the end bents.  Once these points are located, plot lines through these stations parallel to skew line.  Normally the layout file will specify that all bents are parallel to the skew line; however, there may be times when the bents are radial or have varying skews.
:#When locating the stations in the preceding step, the distance between CL of intermediate bents are exactly the layout lengths specified on the file.  However, the end spans need to follow the procedure for calculating length set forth in this section.   
+
:#When locating the stations in the preceding step, the distance between CL of intermediate bents are exactly the layout lengths specified on the file.  However, the end spans need to follow the procedure for calculating length set forth in [[#Tangent Bridges|Tangent Bridges]].   
:#When the CL of the intermediate bents and the fill face lines have been added, chords should be drawn connecting these points sequentially.  For example, if you have a three span bridge, chords should be drawn from the fill face of bent 1 to CL of bent 2, CL bent 2 to CL bent 3, and CL bent 3 to fill face bent 4.
+
:#When the CL of the intermediate bents and the fill face lines have been added, chords should be drawn connecting these points sequentially.  For example, if you have a three-span bridge, chords should be drawn from the fill face of bent 1 to CL of bent 2, CL bent 2 to CL bent 3, and CL bent 3 to fill face bent 4.
 
:#When all the chords are in, offset each girder in each span  parallel to this chord.  The perpendicular distance between  girders will be the same for all spans, but the skew distance  between girders along the bent will vary from bent to bent  depending on the skew to the CL at that point.  The designer  needs to be aware of the fact that at an intermediate bent the distance between bearings on the approaching and leaving span sides will be different distances.  These bearings will not line up  across the bent and will actually diverge more the farther away  they are from the CL of the survey.
 
:#When all the chords are in, offset each girder in each span  parallel to this chord.  The perpendicular distance between  girders will be the same for all spans, but the skew distance  between girders along the bent will vary from bent to bent  depending on the skew to the CL at that point.  The designer  needs to be aware of the fact that at an intermediate bent the distance between bearings on the approaching and leaving span sides will be different distances.  These bearings will not line up  across the bent and will actually diverge more the farther away  they are from the CL of the survey.
 
:#When establishing the CL of bearing points, the designer needs to allow for a minimum of seven (7) inches between ends of girders at the bents while keeping in mind that the girders will be offset and at different skews.  If the offset is greater than half the girder bottom flange width, see Structural Project Manager.  The distance from the end of girder to CL of bearing point should be half of the bearing length plus one inch minimum clearance. Once the distance for CL bent to CL of bearing is calculated, the  designer should offset lines by that dimension on either side of  the CL of bent.  These lines will then be intersected with each of the girder lines to create the bearing points on each bent.
 
:#When establishing the CL of bearing points, the designer needs to allow for a minimum of seven (7) inches between ends of girders at the bents while keeping in mind that the girders will be offset and at different skews.  If the offset is greater than half the girder bottom flange width, see Structural Project Manager.  The distance from the end of girder to CL of bearing point should be half of the bearing length plus one inch minimum clearance. Once the distance for CL bent to CL of bearing is calculated, the  designer should offset lines by that dimension on either side of  the CL of bent.  These lines will then be intersected with each of the girder lines to create the bearing points on each bent.
 
:#Between the bearing points at the ends of the girders, quarter points or tenth points need to be established, depending on the girder span.  These points will be used in calculating the haunch and bottom of slab elevations for the bridge deck.
 
:#Between the bearing points at the ends of the girders, quarter points or tenth points need to be established, depending on the girder span.  These points will be used in calculating the haunch and bottom of slab elevations for the bridge deck.
:#The bridge deck and barrier curbs can be laid in by offsetting the CL of roadway to each side by the proper distance. Curves should be laid in to designate both the inside and outside edges of the barrier curb. These will later be useful in laying in the wings and end bents.
+
:#The bridge deck and barrier or railing can be laid in by offsetting the centerline of roadway to each side by the proper distance. Curves should be laid in to designate both the inside and outside edges of the barrier or railing. These will later be useful in laying in the wings and end bents.
:#After the outside edge of slab curves are plotted, the curve offsets need to be found. The intersection point of the outside edge of slab and the CL of each bent or fill face can be connected with chords. The distance between these chords and their partner curves need to be calculated at five foot intervals beginning at the center point of each chord.  
+
:#After the outside edge of slab curves are plotted, the curve offsets need to be found. The intersection points of the outside edge of slab and the centerline of each bent or fill face can be connected with chords. The distance between these chords and their partner curves need to be calculated at five-foot intervals beginning at the center point of each chord.  
:#Joints are placed in the barrier curb at each bent. These joints are placed perpendicular to the CL of the roadway through the intersection point of the CL bent and the inside of barrier curb.
+
:#Joints are placed in the barrier or railing at each bent. These joints are placed perpendicular to the centerline of the roadway through the intersection point of the centerline bent and the inside edge of barrier or railing.
:#Wing layout length is given on the profile sheets in the layout file. An arc should be struck so as to intersect the inside of barrier curb the specified length from a point at the intersection of the fill face and the inside of barrier curb. This point will mark the end of the wing which is perpendicular to the CL of the roadway.
+
:#Wing layout length is given on the profile sheets in the layout file. An arc should be struck so as to intersect the inside edge of barrier or railing the specified length from a point at the intersection of the fill face and the inside edge of barrier or railing. This point will mark the end of the wing which is perpendicular to the centerline of the roadway.
  
 
:The vertical curve information needs to be added so a program can calculate the elevations at the desired stations.  After this is done, the designer can request any of the following information which will be needed:
 
:The vertical curve information needs to be added so a program can calculate the elevations at the desired stations.  After this is done, the designer can request any of the following information which will be needed:
Line 287: Line 185:
 
::*Angles between girders and each bent
 
::*Angles between girders and each bent
 
::*Lengths of bents
 
::*Lengths of bents
::*Lengths of barrier curbs between joints
+
::*Lengths of barrier or railing between joints
::*Minimum vertical clearance
+
::*Minimum vertical clearance.
  
 +
====751.22.1.4.3 Coping of Girder Ends====
  
<div id="psi layout length"></div>
+
Non-Integral end bents with skews greater than 40 degrees shall always have girder ends coped.  Skews less than 40 degrees shall have girder ends coped on case by case basis.  It is preferable to not cope across the web.
<center>[[Image:751.22.1.4 Integral end bents.jpg|750px]]</center>
 
  
<center>'''INTEGRAL END BENTS'''</center>
+
Check clearance from fill face of integral end bents to bottom flanges of NU girders.  Maintain 3-inch minimum clearance.  Coping may be permitted with approval of the Structural Project Manager or Structural Liaison Engineer.
  
 +
<center>[[Image:751.22.1.4 coping_detail.jpg|center|775px]]</center>
  
<center>[[Image:751.22.1.4 Non-integral end bents.jpg|750px]]</center>
+
<center>'''PART PLAN SHOWING COPING DETAIL'''</center>
 +
<center>'''(I Girder shown; Bulb-Tee and NU Girder similar)'''</center>
  
<center>'''NON-INTEGRAL END BENTS'''</center>
+
===751.22.1.5 Constant and Varied Joint Filler Loads===
  
 +
'''Varied joint filler load'''
  
::Note: Layout length for single span shall be measured from centerline of bearing to centerline of bearing. If the difference between layout length of the end span and interior span is within 1 ft., then layout length should be adjusted if possible so the girder lengths are equal for end span and interior span.
+
Girders shall be first designed assuming that the contractor will vary the joint filler supporting the panels on the girder flange. This assumption will maintain the minimum slab/panel combination thickness of 8 1/2 inches, and will eliminate the possibility of increased load due to varying slab thickness.
 
::(*) Minimum dimension from edge of bearing pad to end of girder equals one inch.
 
 
::(**) Design layout lengths are horizontal lengths.  Girder lengths should be adjusted according to grade and shall be specified to the nearest 1/8 inch.
 
 
::(***) For large skews, end bent beam caps may need to be larger to provide edge distance.
 
 
::(****) Horizontal distance along certerline of girder.
 
  
::(*****) = 1” (minimum) + ½ bearing pad length which equals:
 
:::: 5” (minimum) for MoDOT Standard Girders and Adjacent P/S Box Beams,
 
:::: 3 ½” (minimum) for NU Girders and P/S Spread Box Beams.
 
  
 
+
'''Constant joint filler load'''
<center>[[Image:751.22.1.4 coping_detail.jpg]]</center>
 
 
 
<center>'''PART PLAN SHOWING COPING DETAIL'''</center>
 
<center>'''(MoDOT Standard Girders and NU Girders)'''</center>
 
 
 
Note: Non-Integral end bents with skews greater than 40° shall always have girder ends coped.  Skews less than 40° shall have girder ends coped on case by case basis.  It is preferable to not cope across the web.
 
 
 
Check clearance from fill face of integral end bents to bottom flanges of NU standard girders.  Maintain 3” (min.) clearance.  Coping may be permitted with approval of the Structural Project Manager or Structural Liaison Engineer.
 
 
 
<center>[[Image:751.22_typ_continuous_PS_structure_Integral_End_Bents.gif]]</center>
 
 
 
<center>(*) Maximum length from End Bent to End Bent = 600 feet.</center>
 
<center>'''TYPICAL CONTINUOUS PRESTRESS STRUCTURE<br/>(INTEGRAL END BENTS)'''</center>
 
 
 
 
 
<center>[[Image:751.22_typ_continuous_PS_structure_Non_Integral_End_Bents.gif]]</center>
 
 
 
<center>(**) Maximum length from End Bent to End Bent = 800 feet.</center>
 
<center>'''TYPICAL CONTINUOUS PRESTRESS STRUCTURE<br/>(NON-INTEGRAL END BENTS)'''</center>
 
 
 
===751.22.1.5 Constant and Varied Joint Filler Loads===
 
 
 
'''Varied joint filler load'''
 
 
 
The prestressed I-girder should first be designed assuming that the contractor will vary the joint filler supporting the panels on the girder flange.  This assumption will maintain the minimum slab/panel combination thickness of 8 1/2”, and will eliminate the possibility of increased load due to varying slab thickness.
 
 
 
 
 
'''Constant joint filler load'''
 
  
 
With the girder designed and the camber and haunching dimensions calculated, the girder should be checked assuming the contractor will use a constant 1” joint filler.  This will cause the slab thickness to vary due to camber of the girder, increasing load.  This additional load shall be placed as a concentrated load at 1/8 point from each end of the girder.   
 
With the girder designed and the camber and haunching dimensions calculated, the girder should be checked assuming the contractor will use a constant 1” joint filler.  This will cause the slab thickness to vary due to camber of the girder, increasing load.  This additional load shall be placed as a concentrated load at 1/8 point from each end of the girder.   
Line 400: Line 262:
  
 
;Resistance factors, <math>\,\phi</math>
 
;Resistance factors, <math>\,\phi</math>
STRENGTH limit states, see LRFD Article 6.5.4.2 & 5.5.4.2.1<br/>
+
STRENGTH limit states, see LRFD Article 6.5.4.2 & 5.5.4.2<br/>
 
For all other limit states, <math>\,\phi</math> = 1.00
 
For all other limit states, <math>\,\phi</math> = 1.00
  
Line 450: Line 312:
 
'''Prestress Losses'''
 
'''Prestress Losses'''
  
Refined estimates of time-dependent losses are used, based on AASHTO LRFD Article 5.9.5.4, as opposed to approximate lump sum estimate of losses in AASHTO LRFD Article 5.9.5.3.   
+
Refined estimates of time-dependent losses are used, based on AASHTO LRFD Article 5.9.3.4, as opposed to approximate lump sum estimate of losses in AASHTO LRFD Article 5.9.3.3.   
  
 
The prestress losses shall be calculated to investigate concrete stresses at two different stages.  
 
The prestress losses shall be calculated to investigate concrete stresses at two different stages.  
Line 459: Line 321:
 
SERVICE I and SERVICE III Limit states shall be investigated at each stage.   
 
SERVICE I and SERVICE III Limit states shall be investigated at each stage.   
  
 
+
<div id="Harped Strands"></div>
 
'''Harped Strands'''
 
'''Harped Strands'''
  
 
Harped strands, although they add to the shear strength of the girder, are primarily used to keep the girder stresses (both top and bottom) within allowable limits while developing the full capacity of the girder at midspan.
 
Harped strands, although they add to the shear strength of the girder, are primarily used to keep the girder stresses (both top and bottom) within allowable limits while developing the full capacity of the girder at midspan.
  
Harped strands should be held down at points of 0.4 of the distance from each end of the girder.
+
Harped strands should be held down at points of 0.4 of the distance from each end of the girder. Distances along girder to hold-down devices and between hold-down devices should be reported on the plans to the nearest inch. Per [http://www.modot.org/business/standards_and_specs/SpecbookEPG.pdf#page=13 Sec 1029], precaster may position hold-down devices +/- 6 in. longitudinally from position shown on the plans.
 
 
  
 
<center>[[Image:751.22_harped_strand_layout.gif]]</center>
 
<center>[[Image:751.22_harped_strand_layout.gif]]</center>
Line 494: Line 355:
 
'''Strand Arrangement Optimizing'''
 
'''Strand Arrangement Optimizing'''
  
Using all straight strands for girder lengths less than 70 ft. should be investigated for MoDOT Standard Girder Types 6, 7, 8 and all NU Standard Girders in order to reduce risk of strand or hold-down breakage, increase safety by reducing risk of injury during fabrication and reduce cost.
+
Using all straight strands for girder lengths less than 70 feet shall be investigated for Type 6, 7 and 8 girders and all NU girders in order to reduce risk of strand or hold-down breakage, increase safety by reducing risk of injury during fabrication and reduce cost.  
  
 
Consider using the same section for all spans.  This permits the use of shorter girders in the casting bed with longer girders, even if straight strands are needed, in the top flanges of the girders.  They can be placed at either end of the bed and still optimize the usage of the bed.
 
Consider using the same section for all spans.  This permits the use of shorter girders in the casting bed with longer girders, even if straight strands are needed, in the top flanges of the girders.  They can be placed at either end of the bed and still optimize the usage of the bed.
 
    
 
    
 
Consider using the same number of draped strands for all spans and debond where needed.  Strand patterns should be similar between long and short spans.  For example, the designer should not use a single column of draped strands on the short spans and two columns of draped strands on the long spans.  This will prevent optimization of the bed.
 
Consider using the same number of draped strands for all spans and debond where needed.  Strand patterns should be similar between long and short spans.  For example, the designer should not use a single column of draped strands on the short spans and two columns of draped strands on the long spans.  This will prevent optimization of the bed.
 +
<div id="When using straight strands"></div>
 +
When using straight strands in the top flange of NU Girders and harped strands, lower (drop) the harped strand end locations and vertically align straight strands directly over harped strands to facilitate top flange blockout fabrication by removing interference created between straight strands placed to the outside of the harped strands and the flange blockout forms. If for any reason this is not possible, then place straight strands to the outside of the harped strands.
  
 
'''Debonding Strands'''
 
'''Debonding Strands'''
 +
 +
Debonding at girder ends may be used to reduce concrete compressive forces and shall be used if required to reduce the prestress force at transfer to meet bursting/splitting requirements. Debonding strands shall be avoided at girder ends located underneath expansion joints.
  
 
In all debonding operations the prestressing forces must be in such a manner as to prevent any sudden or shock loading.
 
In all debonding operations the prestressing forces must be in such a manner as to prevent any sudden or shock loading.
Line 508: Line 373:
 
===751.22.2.3 Flexure===
 
===751.22.2.3 Flexure===
  
Flexure capacity of prestressed I-girders shall be determined as the following.
+
Flexure capacity of girders shall be determined as the following.
  
 
'''Flexural resistance at strength limit state'''<br/>
 
'''Flexural resistance at strength limit state'''<br/>
Line 540: Line 405:
  
 
An effective slab thickness shall be used for design by deducting from the actual slab thickness a 1” integral, sacrificial wearing surface.  
 
An effective slab thickness shall be used for design by deducting from the actual slab thickness a 1” integral, sacrificial wearing surface.  
 +
  
 
<div id="Design A1 reinforcement in the top flange"></div>
 
<div id="Design A1 reinforcement in the top flange"></div>
Line 545: Line 411:
 
'''Design A1 reinforcement in the top flange '''
 
'''Design A1 reinforcement in the top flange '''
  
The A1 reinforcement shall resist the tensile force in a cracked section computed on the basis of an uncracked section. For MoDOT girders, A1 reinforcement shall consist of deformed bars. For NU girders, A1 reinforcement shall consist of strands for reinforcement support (4 – 3/8” Strands, Typ.) and WWR (6 – W8, Typ.) with deformed bars added only as needed.  
+
The A1 reinforcement shall resist the tensile force in a cracked section computed on the basis of an uncracked section.  
 +
 
 +
For I girders and bulb-tee girders, A1 reinforcement shall consist of deformed bars (minimum #5 for Type 2, 3 and 4 and minimum #6 for Type 6, 7 and 8).
 +
 
 +
For NU girders, A1 reinforcement shall consist of the four 3/8-inch diameter reinforcement support strands with deformed bars added only as needed. The WWR in the top flange shall not be used for A1 reinforcement because there is insufficient clearance to splice the WWR.
 +
 
 +
Reinforcement shall be designed and spliced using f’<sub>ci</sub> in accordance with [[751.5 Structural Detailing Guidelines#751.5.9.2.8 Development and Lap Splices|EPG 751.5.9.2.8 Development and Lap Splices]].
 +
 
  
 
Required steel area is equal to:
 
Required steel area is equal to:
Line 565: Line 438:
 
The following criteria shall be considered only at composite stage.
 
The following criteria shall be considered only at composite stage.
  
Minimum amount of prestressed and non-prestressed tensile reinforcement shall be such that the factored flexural resistance, ''M<sub>r''</sub>, is at least equal to the lesser of:<br/>
+
Minimum amount of prestressed and non-prestressed tensile reinforcement shall be so that the factored flexural resistance, ''M<sub>r''</sub>, is at least equal to the lesser of:<br/>
  
::*<math>1.2M_{cr}</math>, or
+
::1) M<sub>cr</sub> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; LRFD Eq. 5.6.3.3-1
::*<math>1.33M_u</math>
+
::2) 1.33M<sub>u</sub>
  
 
Where:
 
Where:
 
{|border="0" cellpadding="5"  
 
{|border="0" cellpadding="5"  
 
|-
 
|-
|<math>M_{cr}</math>||=||Cracking moment, (kip-in.)
+
|M<sub>cr</sub>||=||Cracking moment, (kip-in.)
 
|-
 
|-
|<math>M_u</math>||=||Total factored moment from Strength I load combination,  (kip-in.)
+
|M<sub>u</sub> ||=||Total factored moment from Strength I load combination,  (kip-in.)
 
|}
 
|}
  
Line 581: Line 454:
  
  
Shear capacity of P/S I-girder should be checked along girder length and girder-slab interface.
+
Shear capacity of girders shall be checked along girder length and girder-slab interface.
  
  
Line 700: Line 573:
  
  
'''Maximum reinforcement'''
+
'''Maximum spacing'''
  
 
Maximum spacing of shear reinforcement shall be determined as:<br/>
 
Maximum spacing of shear reinforcement shall be determined as:<br/>
Line 759: Line 632:
 
'''Girder-Slab Interface'''
 
'''Girder-Slab Interface'''
  
The horizontal shear between the girder and slab shall be determined as specified in LRFD 5.8.4.3.  The nominal horizontal shear resistance of the interface plane shall be taken as specified in LRFD 5.8.4.1.  Minimum interface shear reinforcement shall be provided as specified in LRFD 5.8.4.4.  The parameters used in determining the nominal horizontal shear resistance shall be taken as specified for a “cast-in-place concrete slab on clean concrete girder surfaces, free of laitance with surface roughened to an amplitude of 0.25 inch.”   
+
The horizontal shear between the girder and slab shall be determined as specified in LRFD 5.7.4.4.  The nominal horizontal shear resistance of the interface plane shall be taken as specified in LRFD 5.7.4.3.  Minimum interface shear reinforcement shall be provided as specified in LRFD 5.7.4.2.  The parameters used in determining the nominal horizontal shear resistance shall be taken as specified for a “cast-in-place concrete slab on clean concrete girder surfaces, free of laitance with surface roughened to an amplitude of 0.25 inch.”   
  
The interface shear shall be resisted by extending and anchoring the vertical shear reinforcement into the slab. If the resistance provided by extending the vertical shear reinforcement is inadequate then additional U-bars may be provided as shown for a MoDOT Standard Girder Type 7 in [[#751.22.3.6 Girder Reinforcement|EPG 751.22.3.6 Girder Reinforcement]].
+
The interface shear shall be resisted by extending and anchoring the vertical shear reinforcement into the slab. If the resistance provided by extending the vertical shear reinforcement is inadequate then, in lieu of increasing shear reinforcement, additional U bars may be provided as shown for a Type 7 girder in [[#751.22.3.4 Girder Reinforcement|EPG 751.22.3.4 Girder Reinforcement]].
 +
<div id="For NU girders and spread beams"></div>
 +
For NU girders and spread beams the top flange shall be debonded at the edges using a smooth finish and an applied bond breaker to help aid with future deck removal and minimize stress concerns with the thin flange of the NU girders. The debonded regions shall not be included when determining the nominal horizontal shear resistance. The minimum debonded width shown below may be increased in lieu of adding additional U bars in order to reduce the minimum interface shear reinforcement.
 +
 +
[[image:751.22.2.4 Minimum Debonded Width Oct 2021.jpg|450px|center]]
 +
[[image:751.22.2.4 footnote.jpg|397px|center]]
  
For NU Girders the edges of the top of girder flange are intentionally debonded (see figure below) and shall not be included when determining the nominal horizontal shear resistance. See [[751.50 Standard Detailing Notes#(H2c2.10)|EPG 751.50 Standard Detailing Notes H2c2.10]] for specifics about the debonded width for NU Girders. Similarly, for all other prestressed girders, the joint filler width supporting precast panels shall be considered debonded and excluded when determining the interface resistance.
+
The debonding regions shall be indicated on the plans by specifying the required smooth finish and applied bond breaker in the dimensions detail on the beam or girder sheet. Omit underlined portion of footnote (1) if prestressed panels are not used.  
 +
 
 +
Similarly, for all other prestressed girders and beams, the joint filler width supporting precast panels shall be considered debonded and excluded when determining the interface resistance.
  
[[image:751.22.2.4 NU Girder Debonding Limits.jpg|300px|center|thumb|<center>'''NU Girder Debonding Limits'''</center>]]
+
<div id="Pretensioned anchorage zones"></div>
  
'''Pretensioned anchorage zones'''
+
===751.22.2.5 Pretensioned Anchorage Zones===
  
The bursting resistance of anchorage zones provided by vertical reinforcement (i.e., B2 bars, WWF, G402 bars) in the ends of prestressed girders at the service limit state shall be taken as:
+
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp;(LRFD 5.9.4.4)
  
  
<math>\, P_r = f_s A_s \ge 0.04F_{po}</math>
+
'''Bursting Resistance''' (AASHTO Splitting Resistance)
  
 +
The bursting resistance of anchorage zones provided by vertical reinforcement (i.e., B2 bars and the D31 wires of WWR6) in the ends of prestressed girders at the service limit state shall be taken as:
  
Where:
+
 
 +
::<math>\, P_r = f_s A_s \ge 0.04f_{pbt}</math>
 +
 
 +
The required vertical reinforcement shall be provided within the following end regions:
 +
::'''I Girders, NU 35, 43 & 53 Girders:'''
 +
::::- Within h/3, ''in accordance with research by Davis, Buckner and Ozyildirimon (Dunkman et al. 2009). ''
 +
::'''Bulb-Tee Girders and NU 63, 70 & 78 Girders:'''
 +
::::- Within h/4
 +
 
 +
 
 +
Where:
 
{|border="0" cellpadding="5"
 
{|border="0" cellpadding="5"
 
|<math>\, f_s</math>||=||Stress in mild steel not exceeding 20 ksi
 
|<math>\, f_s</math>||=||Stress in mild steel not exceeding 20 ksi
 
|-
 
|-
|<math>\, A_s</math>||=||Total area of vertical reinforcement located within a minimum distance of h/4 from the end of the girder where h is overall depth of precast member as shown below.
+
|valign="top"|<math>\, A_s</math>||valign="top"|=||Total area of vertical reinforcement located within the specified minimum distance from the end of the girder where h equals the overall depth of precast member as shown below.
 
|-
 
|-
|<math>\, F_{po}</math>||=||Prestressing force at transfer
+
|<math>\, f_{pbt}</math>||=||Prestressing force immediately prior to transfer
 
|}
 
|}
  
  
[[Image:751.22.2.4.jpg|center|thumb|550px|<center>'''MoDOT Standard Girder</center>
+
[[Image:751.22.2.5 2022.jpg|center|550px]]
<center>'''Anchorage Zone and Confinement Reinforcement'''</center>]]
+
<center>'''Anchorage Zone (Bursting and Confinement) for I Girders'''<br/>(Bursting zone or reinforcement may differ for other girder types)</center>
 +
 
 +
The number of strands bonded in the anchorage zone is limited by the standard bursting reinforcement of [[#751.22.3.4.3 Anchorage Zone Reinforcement|EPG 751.22.3.4.3 Anchorage Zone Reinforcement]] and the 20 ksi resistance stress limit.
 +
 
 +
<center>'''Maximum Number of Bonded Strands at Girder Ends, N<sub>s</sub>'''
 +
{| border="1" class="wikitable" style="margin: 1em auto 1em auto" style="text-align:center"
 +
|+
 +
! style="background:#BEBEBE" colspan="6"|I Girders & Bulb-Tee Girders<sup>a</sup> !!width="50"  rowspan="10"| !!style="background:#BEBEBE" colspan="6"|NU Girders
 +
|-
 +
! style="background:#BEBEBE" rowspan="2"| Type!! style="background:#BEBEBE"  rowspan="2"|h/3 or<br/>h/4 (in.) !! style="background:#BEBEBE"  rowspan="2"|#6-B2<br/>Pairs !! style="background:#BEBEBE"  rowspan="2"|A<sub>s</sub><br/>(in.<sup>2</sup>) !! style="background:#BEBEBE" colspan="2"|N<sub>s</sub>  !! style="background:#BEBEBE"  rowspan="2"|Type !! style="background:#BEBEBE"  rowspan="2"|h/3 or<br/>h/4 (in.)  !! style="background:#BEBEBE"  rowspan="2"| D31<br/>Pairs!! style="background:#BEBEBE"  rowspan="2"| A<sub>s</sub><br/>(in.<sup>2</sup>)!! style="background:#BEBEBE" colspan="2"|N<sub>s</sub>
 +
|-
 +
!style="background:#BEBEBE"|(0.5") !! style="background:#BEBEBE"| (0.6")!!style="background:#BEBEBE"| (0.5")!! style="background:#BEBEBE"|(0.6")
 +
|-
 +
|Type 2 ||10.67||3.0 ||2.65 ||20 ||20 ||NU 35 ||11.81 ||5.5 ||3.41 ||54||38
 +
|-
 +
|Type 3 ||13.00 ||4.0 ||3.53 ||24 ||24 ||NU 43 ||14.44 ||7.0 ||4.34 ||62<sup>a</sup>||48
 +
|-
 +
|Type 4 ||15.00 ||4.0 ||3.53 ||32 ||32 ||NU 53 ||17.72 ||8.5 ||5.27 ||62<sup>a</sup>||52<sup>b</sup>
 +
|-
 +
|Type 6||18.00 ||4.0 ||3.53 ||38 ||38 ||NU 63 ||15.75 ||7.5 ||4.65 ||62<sup>a</sup>||52
 +
|-
 +
|Type 7 ||18.13||4.0 ||3.53 ||40 ||40 ||NU 70 ||17.72 ||8.5 ||5.27 ||62<sup>a</sup>||58
 +
|-
 +
|Type 8 ||15.88 ||4.0 ||3.53 ||40 ||40 ||NU 78 ||19.69 ||9.0 ||5.58 ||62<sup>a</sup>||62<sup>a</sup>
 +
|-
 +
|colspan="6"|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Area of one #6-B2 bar = 0.4418 in.<sup>2</sup>||colspan="6"|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Area of one D31 wire = 0.31 in.<sup>2</sup>
 +
|-
 +
|align="left" colspan=13"|'''<sup>a</sup>''' Maximum number capped by strand arrangements shown in this article and on the Bridge Standard Drawings.
 +
|-
 +
|align="left" colspan=13"|'''<sup>b</sup>''' Maximum number capped not to exceed the maximum allowed for the NU 63 girder.
 +
|}
 +
</center>
 +
 
 +
:::''N<sub>s</sub> ≤ A<sub>s</sub> /A<sub>s</sub>(req)'' (Rounded down to nearest even number for the purpose of symmetry.)
 +
 
 +
:Where:
 +
:::A<sub>s</sub>(req) = Required bursting reinforcement for one prestressing strand.
 +
:::::= 0.04''f<sub>pbt</sub>A<sub>ps</sub> /f<sub>s</sub>''
 +
:::::= (0.04)(202.5 ksi)(0.153 in.<sup>2</sup>)/(20 ksi) = 0.0620 in.<sup>2</sup>&nbsp;&nbsp;&nbsp; (1/2-inch strand)
 +
:::::= (0.04)(202.5 ksi)(0.217 in.<sup>2</sup>)/(20 ksi) = 0.0879 in.<sup>2</sup>&nbsp;&nbsp;&nbsp; (0.6-inch strand)
  
  
 
'''Confinement reinforcement'''
 
'''Confinement reinforcement'''
  
Reinforcement (i.e., D1 bars or G301 bars, not shown) shown in the figure above shall be placed to confine the prestressing strands in the bottom flange for a minimum distance of 1.5''d'' from the end of beam.
+
Confinement reinforcement (i.e., D1 bars or G1 bars spaced with WWR4) shown in the figure above shall be placed to confine the prestressing strands in the bottom flange for a minimum distance of 1.5''d'' from the end of beam.
  
 
The reinforcement shall not be less than #3 deformed bar, with spacing not exceeding 6.0 inches and shaped to enclose the strands.
 
The reinforcement shall not be less than #3 deformed bar, with spacing not exceeding 6.0 inches and shaped to enclose the strands.
  
MoDOT extends the use of D1 and G301 bars for the full length of girders.
+
The use of D1 bars shall be extended for the full length of I girders, bulb-tee girders and alternate bar-reinforced NU girders.
 +
 
 +
The use of G1 bars at 6-inch spacing shall be extended for the first 10 feet and then at 12-inch spacing for the remaining length of welded wire-reinforced NU girders.
  
===751.22.2.5 Deformations===
+
===751.22.2.6 Deformations===
  
  
Line 804: Line 736:
 
For investigating maximum absolute deflection, all design lanes shall be loaded, and all supporting components should be assumed to deflect equally.
 
For investigating maximum absolute deflection, all design lanes shall be loaded, and all supporting components should be assumed to deflect equally.
  
For composite design, the design cross-section should include the entire width of the roadway and the structurally continuous portions of railings, sidewalks, and median barriers. Note that safety barrier curbs are usually discontinuous over the bents. For skewed bridges, a right cross-section may be used.
+
For composite design, the design cross-section should include the entire width of the roadway and the structurally continuous portions of railings, sidewalks, and median barriers. Note that barrier and railing  are usually discontinuous over the bents. For skewed bridges, a right cross-section may be used.  
  
 
Service I load combination shall be used.  Dynamic load allowance shall be applied.  
 
Service I load combination shall be used.  Dynamic load allowance shall be applied.  
Line 857: Line 789:
 
|}
 
|}
  
Note: Camber is calculated 7 days after strand release to allow sufficient time for inspection. See [http://epg.modot.org/index.php?title=Category:1029_Fabricating_Prestressed_Concrete_Members_for_Bridges#1029.2.13_Inspection_of_Completed_Members EPG 1029 Fabricating Prestressed Concrete Members for Bridges].
+
Note: Camber is calculated 7 days after strand release to allow sufficient time for inspection. See [https://epg.modot.org/index.php?title=Category:1029_Fabricating_Prestressed_Concrete_Members_for_Bridges#1029.2.13_Inspection_of_Completed_Members EPG 1029 Fabricating Prestressed Concrete Members for Bridges].
  
 
'''Camber at midspan after erection (Estimated at 90 days)'''
 
'''Camber at midspan after erection (Estimated at 90 days)'''
 +
 +
Theoretical camber of prestressed girders after erection are estimated at 90 days for typical projects. While some projects may require prestressed girders to be erected in less than 90 days in order to meet fast construction timelines or emergency repair requirements, using less than 90 days (i.e, 45 or 60) would potentially result in lower camber estimates and higher beam seat elevations. The cost risk is believed to be greater for underestimating the camber since it may require an increase in final grade. Due to the risk in underestimating camber and the multitude of variables that affect the actual camber (variability in predicting concrete modulus of elasticity, coarse aggregate effect on initial concrete modulus of elasticity, actual concrete strength, differential temperature at strand release, etc…) the 90 day estimate should be adequate for most projects.
  
 
Theoretical camber of girder after erection due to self-weight of girder and prestressing forces shall be determined at 90 days as:
 
Theoretical camber of girder after erection due to self-weight of girder and prestressing forces shall be determined at 90 days as:
Line 883: Line 817:
 
Where:
 
Where:
 
{|
 
{|
|<math>\, \sum \Delta_{FC}</math>||=||Final camber after slab is poured
+
|<math>\, \Delta_{FC}</math>||=||Final camber after slab is poured
 +
|-
 +
|<math>\, \Delta_s</math>||=||Deflection due to weight of slab
 
|-
 
|-
 
|<math>\, \sum \Delta_c</math>||=||Deflection due to concentrated loads (haunch, diaphragms, etc.)
 
|<math>\, \sum \Delta_c</math>||=||Deflection due to concentrated loads (haunch, diaphragms, etc.)
|-
 
|<math>\, \Delta_s</math>||=||Deflection due to weight of slab
 
 
|}
 
|}
  
Line 909: Line 843:
 
|}
 
|}
  
 +
<div id="Calculation of camber (upward)"></div>
 +
'''Calculation of camber (upward) using transformed properties'''
  
'''Calculation of camber (upward)'''
+
Camber at midspan due to strand forces is determined by the following:
  
Camber at midspan due to strand forces is determined as the following:
+
For straight strands (groups determined by debonding lengths),  
For straight strands,
 
  
  
Line 919: Line 854:
  
  
Where: &nbsp; <math>\, \Delta_{ss-j} = \frac{F_{1-j} e_1 L^2}{8 E_{ci} I_{tri}}</math> &nbsp; &nbsp; <math>\, \Delta_{ss-l} = \frac{F_{1-l} e_1 L^2}{8 E_c I_{tr}}</math>
+
Where: &nbsp; <math>\, \Delta_{ss-j} = \sum \frac{F_{1-j} e_1}{8 E_{ci} I_{tri}} (L^2 - 4l_0^2)</math>  
 +
 
 +
 
 +
:::<math>\, \Delta_{ss-l} = \Delta_{ss-j} \frac{Initial \ Loss}{f_{Pj}}</math>
  
 
   
 
   
 
Where:
 
Where:
 
{|
 
{|
|valign="top"|<math>\, F_{1-j}</math>||= Total prestressing force of straight strands at transfer (including losses due to elastic shortening), (kips)
+
|valign="top"|<math>\, F_{1-j}</math>||= Total prestressing force of straight strand group just prior to transfer, (kips)  
 
|-
 
|-
|valign="top"|<math>\, F_{1-l}</math>||= Total prestressing force in straight strands due to time-dependent losses prior to slab placement (kips).  Opposite in sign to <math>\, F_{1-j}</math>, typically.
+
|<math>\, L</math>||= Distance between centerlines of bearing pads, (in.)
 
|-
 
|-
|<math>\, L</math>||= Distance between centerlines of bearing pads, (in.)
+
|<math>\, l_0</math>||= Debond length of straight strand group from end of girder, (in.)  
 
|-
 
|-
 
|<math>\, E_{ci}</math>||= Initial concrete modulus of elasticity based on <math>\, f'_{ci}</math>, (ksi)
 
|<math>\, E_{ci}</math>||= Initial concrete modulus of elasticity based on <math>\, f'_{ci}</math>, (ksi)
 
|-
 
|-
|<math>\, E_c</math>||= Final concrete modulus of elasticity based on <math>\, f'_c</math> (ksi)
+
|<math>\, I_{tri}</math>||= Moment of inertia of transformed non-composite section computed based on <math>\, E_{ci}</math>, (in.<sup>4</sup>)
 
|-
 
|-
|<math>\, I_{tri}</math>||= Moment of inertia of transformed non-composite section computed based on <math>\, E_{ci}</math>, (in.<sup>4</sup>)
+
|<math>\, e_1</math>||= Eccentricity between centroid of straight strand group (CSS) and center of gravity of transformed non-composite section (CGB) as shown in Figure below, (in.)
 
|-
 
|-
|<math>\, I_{tr}</math>||= Moment of inertia of transformed non-composite section based on <math>\, E_c</math>, (in.<sup>4</sup>)
+
|<math>\, f_{Pj}</math>||= Prestressing force in the strand just prior to transfer, (ksi)
 
|-
 
|-
|<math>\, e_1</math>||= Eccentricity between centroid of straight strands (CSS) and center of gravity of transformed non-composite section (CGB) as shown in Figure below, (in.)
+
|valign="top"|<math>\, Initial \ Loss</math>||= Summation of the time dependent losses (7 or 90 day).  Losses include relaxation, creep and shrinkage, but exclude elastic shortening.
 
|}
 
|}
  
 +
 +
Gross properties may be used to calculate losses and is consistent with AASHTO LRFD 5.9.3.4.
  
 
For two-point harped strands,
 
For two-point harped strands,
Line 948: Line 888:
  
  
Where: &nbsp; <math>\, \Delta_{HS-j} = \frac {F_{2-j} e_2 L^2}{8 E_{ci} I_{tri}} - \frac {F_{2-j}(e_2 + e_3) a^2}{6 E_{ci} I_{tri}}</math> &nbsp; &nbsp; <math>\, \Delta_{HS-l} = \frac {F_{2-l} e_2 L^2}{8 E_c I_{tr}} - \frac {F_{2-l}(e_2 + e_3) a^2}{6 E_c I_{tr}}</math>
+
Where: &nbsp; <math>\, \Delta_{HS-j} = \frac {F_{2-j} e_2 L^2}{8 E_{ci} I_{tri}} - \frac {F_{2-j}(e_2 + e_3) a^2}{6 E_{ci} I_{tri}}</math>  
 +
 
 +
:::<math>\, \Delta_{HS-l} = \frac {F_{2-l} e_2 L^2}{8 E_c I_{tr}} - \frac {F_{2-l}(e_2 + e_3) a^2}{6 E_c I_{tr}}</math>
  
 +
:::<math>\, \Delta_{HS-l} = \Delta_{HS-j} \frac{Initial \ Loss}{f_{Pj}}</math>
 
   
 
   
<math>a = (L - b)/2</math>
+
:::<math>a = (L - b)/2</math>
  
  
 
Where:
 
Where:
 
{|
 
{|
|valign="top"| <math>\, F_{2-j}</math>||= Total prestressing force of harped strands at transfer (including loss due to elastic shortening), (kips)
+
|valign="top"| <math>\, F_{2-j}</math>||= Total prestressing force of harped strands just prior to transfer, (kips)  
|-
 
|valign="top"| <math>\, F_{2-l}</math>||= Total prestressing force of harped strands due to time-dependent losses prior to slab placement (kips)
 
 
|-
 
|-
 
|valign="top"| <math>\, b</math>||= Length between harped points, (in.)
 
|valign="top"| <math>\, b</math>||= Length between harped points, (in.)
Line 984: Line 925:
 
   
 
   
 
Where:
 
Where:
{|
+
 
|<math>W_g</math>||=||Uniform load due to self-weight of girder, (kip/in.)
+
:<math>W_g</math> = Uniform load due to self-weight of girder, (kip/in.)
|}
 
  
  
Line 992: Line 932:
  
  
<math>\, \Delta_s = \frac {5 W_s L^4}{384 E_{c} I'_{tr}}</math>
+
:<math>\, \Delta_s = \frac {5 W_s L^4}{384 E_{c} I'_{tr}}</math>
  
 
   
 
   
 
Where:
 
Where:
{|
+
 
|<math>\, W_s</math>||=||Uniform load due to self-weight of slab, (kip/in.)
+
:<math>\, W_s</math> = Uniform load due to self-weight of slab, (kip/in.)
|}
+
 
 +
:<math>\, E_c</math> = Final concrete modulus of elasticity based on ''f'<sub>c</sub>'', (ksi)
 +
 +
:<math>\, I'_{tr}</math> = Moment of inertia of transformed non-composite section based on ''E<sub>c</sub>'', (in.<sup>4</sup>)
 +
 
 +
 
  
 
Weight of additional slab haunch may be treated as uniform or concentrated load as appropriate.  Diaphragm weight should be treated as concentrated load.
 
Weight of additional slab haunch may be treated as uniform or concentrated load as appropriate.  Diaphragm weight should be treated as concentrated load.
Line 1,021: Line 966:
 
|}
 
|}
  
'''Creep coefficient'''
+
 
 +
{|
 +
|align="left"|'''Creep coefficient'''||width="650"| ||'''LRFD 5.4.2.3.2'''
 +
|}
  
 
Research has indicated that high strength concrete (HSC) undergoes less ultimate creep and shrinkage than conventional concrete.
 
Research has indicated that high strength concrete (HSC) undergoes less ultimate creep and shrinkage than conventional concrete.
Line 1,036: Line 984:
 
|<math>\, k_f</math>||= <math>\, 5/(1+f'_{ci})</math>
 
|<math>\, k_f</math>||= <math>\, 5/(1+f'_{ci})</math>
 
|-
 
|-
|<math>\, k_{td}</math>||= <math>\, t/(61 - 4f'_{ci} + t)</math>
+
|<math>\, k_{td}</math>||= <math>\, t/\Big[ \frac {12 \ (100 - 4f'_{ci})}{f'_{ci} + 20} + t\Big]</math>
 
|}
 
|}
  
Line 1,058: Line 1,006:
  
  
<math>\, \Delta_{CR} = \frac{(m_g - F_{1-j} e_1 - F_{2-j} e_2) \Psi L^2}{8 E_{ci} I_{tri}}</math>
+
<math>\, \Delta_{CR} = ( \Delta_{SS-j} + \Delta_{HS-j} + \Delta_g)\Psi + ( \Delta_{SS-I} + \Delta_{HS-I})0.7\Psi</math>
 +
 
 +
===751.22.2.7 Dowel Bars===
  
Where:
 
{|
 
|<math>\, M_g</math>||= Moment due to girder weight at mid span.
 
|}
 
  
==751.22.3 Details==
+
[[Image:751.22.3.15.jpg|center|650px]]
===751.22.3.1 Reinforcement Criteria===
 
  
  
'''Minimum Concrete Cover'''
+
{|border="0" cellpadding="5" align="center" style="text-align:center"
::*2.0" (Min.) to centerline of strands
 
::*1.0" for stirrups
 
  
 +
|width="540"|'''PART ELEVATION<br/>(FIXED BENT)'''
 +
|width="240" align="left"|'''SECTION A-A'''
  
'''Minimum Radius of Bar Bend in Stirrups'''
+
|}
#3 through #5 bars = 4.0 x Bar Diameter.
 
  
  
'''Minimum Spacing of Reinforcement Bars'''
+
::::Dowel bars shall be used for all fixed intermediate bents under prestressed superstructures. Generally, for typical bridges that require seismic details only (strength limit states), shear resistance from shear key is not considered.
For precast concrete, the clear distance between parallel bars in a layer shall not be lesser than:
 
::*Nominal Diameter of bar
 
::*1.33 x Maximum Aggregate Size
 
::*1.0"
 
  
  
'''Minimum Spacing of Prestressing Strands'''
+
Dowel bars connect standard concrete diaphragms and beams on concrete girder bridges (standard fixed diaphragms are those with beam stirrups NOT extending up into the diaphragm). For a calculated seismic vertical reaction or an anticipated foundation settlement resulting in a net tensile reaction, use the development length of dowel bars into beam and into diaphragm based on dowel bar size. If the dowel bars are not exposed to net tension a 15-inch embedment shall be used regardless of bar size. Dowel bars size and spacing shall be determined by shear design of the bars. (Minimum #6 Bars @ 12" cts.). Dowel bars should be designed for a minimum horizontal force equal to 25% of the maximum dead load applied to the bearing. Live load is ignored in horizontal force computation.
Spacing between each pretressing strand shall not be less than the larger of:
 
::*A clear distance of 1.33 x Maximum Aggregate Size
 
::*Center-to-center spacing of 2" for 0.6" strand diameter
 
::*Center-to-center spacing of 1.75" for 0.5" strand diameter
 
  
===751.22.3.2 MoDOT Standard Girders===
+
:The number of dowels must also fit into the space available on the key:
====751.22.3.2.1 Beam Type 2 Dimensions/Strand Arrangements====
+
::min. bar size = #6; max. bar size = #11
 +
::min. spacing = 6"; max. spacing = 12"
 +
::min. end distance = 3"; max. end distance = 6" (≤ half the spacing)
  
 +
'''For seismic details only (strength limit states)'''
  
<center>[[Image:751.22 Beam Type 2 dim & Girders 2A & 2B.gif]]</center>
+
Horizontal factored shear force, <math>F_H = \sqrt {(F_T)^2 + (F_L)^2}</math> in kips
  
 +
For expansion bearings, transverse F<sub>T</sub> = 0.25(DL) & longitudinal F<sub>L</sub> = 0.
 +
:Where DL = unfactored dead load reaction at the bent, kips
  
{|border="0" cellpadding="5" align="center" textalign="center" width="500"
+
For fixed bearings, Transverse F<sub>T</sub> = 0.25(DL) and Longitudinal F<sub>L</sub> = (0.25)(segment weight) at bent.
 +
:Segment weight includes the full width of superstructure and should be distributed appropriately among fixed bents.
  
|align="center" |'''GIRDERS 2A THRU 2C'''
 
<math>A</math> '''= 310.9 SQ. IN.'''<br/>
 
<math>Y_b</math> '''= 14.08 IN.'''<br/>
 
<math>I</math> '''= 33,974 IN.<sup>4</sup>'''
 
|align="center" width="200"|'''GIRDER 2A'''
 
'''(11 STRANDS)'''
 
|align="center"|'''GIRDER 2B'''
 
'''(12 STRANDS)'''
 
|}
 
  
 +
'''For complete seismic analysis '''
  
 +
Dowel bar designs must meet requirements for strength limit states from above as well as seismic force demand from seismic analysis.
  
{|border="0" cellpadding="5" align="center" textalign="center"
+
:''At Intermediate bent,''
 +
::<math>F_H = \sqrt {\sum (V_L)^2 + \sum (V_T)^2}</math>
  
|align="center" |[[Image:751.22_Beam_Type_2_Girder_2C.gif]]<br/>
+
:where:
'''GIRDERS 2C'''<br/>'''(14 STRANDS)'''
 
|align="center"|[[Image:751.22_Beam_Type_2_Girders_Sequence_No_2A_thru_2C_Table.gif]]
 
{|border="0"
 
|align="left" width="425pt"|&nbsp;<br/>NOTE: Investigate the possibility of using all straight strands when strength check of a hold-down device exceeds allowable.<br/><u>All strand arrangements shown on this page have straight strands only.</u>
 
  
Strand arrangements other than those shown may be investigated by the designer.
+
:F<sub>H</sub> = horizontal seismic force per bent, kips
|}
+
:::If columns are designed for plastic hinging, use the plastic hinging shear.
|}
+
:∑V<sub>L</sub> = summation of top of column longitudinal shears at the bent
 +
:∑V<sub>T</sub> = summation of top of column transverse shears at the bent
  
 +
::<math>P_u = \frac{F_H}{n_d}</math>
 +
 +
:P<sub>u</sub> = Horizontal factored shear force per dowel bar, kips
 +
:n<sub>d</sub> = number of dowel bars
  
<center>[[Image:751.22_Beam_Type_2_Girders_dim_&_Group_I.jpg|700px]]</center>
 
  
 +
'''Shear Resistance'''
  
{|border="0" cellpadding="5" align="center" textalign="center" width="600"
+
Factored shear force shall be less than or equal to the nominal shear resistance.
  
|align="center" width="300"|<math>A</math> '''= 310.9 SQ. IN.'''<br/>
+
::''P<sub>u</sub> ≤ ∅<sub>s</sub> x R<sub>n</sub>''
<math>Y_b</math> '''= 14.08 IN.'''<br/>
 
<math>I</math> '''= 33,974 IN.<sup>4</sup>'''
 
|align="center" width="300"|'''GROUP I'''
 
|}
 
  
 +
:where:
 +
:∅<sub>s</sub> = 0.75 resistance for seismic details only (strength limit states) and 1.0 for complete seismic analysis
  
{|border="0" cellpadding="5" align="center" textalign="center"
+
:Nominal shear resistance of the dowel bar, R<sub>n</sub> = 0.625 A<sub>b</sub>F<sub>ub</sub>, kips
 +
::Note: Since there is no reduced areas as seen in bolts and there is no reduction for bolted connection length, use 0.625 instead of 0.5.
  
|align="center"|[[Image:751.22_Beam_Type_2_Girders_Group_II.jpg|325px]]<br/>&nbsp;<br/>'''GROUP II'''
+
:A<sub>b</sub> = <math>\frac {\pi D^3}{4}</math> = area of the dowel bar, square inches
|width="300"|Numbers shown on girders<br/>relate to strand locations.
+
:F<sub>ub</sub> = minimum tensile strength of the dowel bar, ksi
|}
+
:F<sub>ub</sub> = 80 ksi for Grade 60
 +
:D = diameter of the dowel bar, inch
  
  
ATTENTION:  Location of harped strands shown in top flange are at end of girder and harped strands in bottom flange are at centerline.
+
'''Tensile Resistance'''
  
 +
Factored tensile force shall be less than or equal to the nominal tensile resistance.
  
If the web thickness is required to be increased, then the top and bottom flanges are to be increased by the same amount. (1" increments, 2"&nbsp;max.)
+
:T = the maximum seismic tensile (uplift) force (DL ± EQ) from the seismic analysis, kips. If (DL+EQ) and (DL-EQ) are both compressive, then there is no need to design the dowel for tensile force.
  
====751.22.3.2.2 Beam Type 3 Dimensions/Strand Arrangements====
+
::<math>\frac{T}{n_d} \le {\empty_t} T_n</math>
  
 +
:where:
 +
:∅<sub>t</sub>= 0.8 resistance factor for seismic details only (strength limit states) and 1.0 for complete seismic analysis
 +
:n<sub>d</sub> = the number of dowel bars
  
<center>[[Image:751.22_Beam_Type_3_Girders_3A_thru_3B.gif]]</center>
+
:Nominal tensile resistance of the dowel bar, T<sub>n</sub> = A<sub>b</sub>F<sub>ub</sub> Kips
 +
::Note: Since there is no pretension or reduced areas as seen for bolts, the 0.76 factor is not warranted.
  
 +
:A<sub>b</sub> = area of the dowel bar, square inches
 +
:F<sub>ub</sub> = minimum tensile strength of the dowel bar, ksi
 +
:F<sub>ub</sub> = 80 ksi for Grade 60
  
{|border="0" cellpadding="5" align="center" textalign="center" width="600"
 
  
|align="center"|'''GIRDERS 3A THRU 3B'''
+
'''Combined Tension and Shear Resistance'''
<math>A</math> '''= 381.9 SQ. IN.'''<br/>
 
<math>Y_b</math> '''= 17.08 IN.'''<br/>
 
<math>I</math> '''= 61,841 IN.<sup>4</sup>'''
 
|align="center" width="200"|'''GIRDER 3A'''
 
'''(11 STRANDS)'''
 
|align="center"|'''GIRDER 3B'''
 
'''(12 STRANDS)'''
 
|}
 
  
 +
The resistance of dowel bars for combined tension and shear force shall be determined in accordance with LRFD 6.13.2.11.
 +
:Note: Since there is no pretension or reduced areas as seen for bolts, the 0.76 factor is not warranted.
  
  
<center>[[Image:751.22_Beam_Type_3_Girders_Sequence_No_3A_thru_3B_Table.gif]]</center>
+
:If <math>\frac{P_u}{R_n} \le 0.33</math>, then T<sub>n</sub> = A<sub>b</sub>F<sub>ub</sub>
 +
::Otherwise
 +
:::<math>T_n = A_b F_{ub} \Big[ 1- \Big(\frac{p_u}{\empty_s R_n} \Big)^2 \Big]^{0.5}</math>
  
  
{|border="0" cellpadding="5" align="center"
+
==751.22.3 Details==
|align="left" width="425"|Note: Investigate the possibility of using all straight strands when strength check of a hold-down device exceeds allowable.<br/><u>All strand arrangements shown on this page have straight strands only.</u><br/>
+
===751.22.3.1 Reinforcement Criteria===
Strand arrangements other than those shown may be investigated by the designer.
 
|}
 
  
  
<center>[[Image:751.22_Beam_Type_3_Girders_dim_&_Group_I.gif]]</center>
+
'''Minimum Concrete Cover'''
 +
::*2.0" (Min.) to centerline of strands
 +
::*1.0" for stirrups
  
  
{|border="0" cellpadding="5" align="center" textalign="center" width="600"
+
'''Minimum Bend Diameter for Stirrups'''
 +
::* #3 through #5 bars = 4.0 x Nominal Bar Diameter.
 +
::*Deformed wire larger than D6 = 4.0 x Nominal Wire Diameter
  
|align="center" width="300"|<math>A</math> '''= 381.9 SQ. IN.'''<br/>
 
<math>Y_b</math> '''= 17.08 IN.'''<br/>
 
<math>I</math> '''= 61,841 IN.<sup>4</sup>'''
 
|align="center" width="300"|'''GROUP I'''
 
|}
 
  
{|border="0" cellpadding="5" align="center" textalign="center"
+
'''Minimum Spacing of Reinforcement Bars and Wires'''
 +
For precast concrete, the clear distance between parallel bars in a layer shall not be lesser than:
 +
::* Nominal Bar Diameter or Nominal Wire Diameter
 +
::* 1.33 x Maximum Aggregate Size
 +
::* 1.0"
  
|align="center"|[[Image:751.22_Beam_Type_3_Girders_Group_II.gif]]<br/>&nbsp;<br/>'''GROUP II'''
 
|width="300"|Numbers shown on girders<br/>relate to strand locations.
 
|}
 
  
 +
'''Minimum Spacing of Prestressing Strands'''
 +
Spacing between each pretressing strand shall not be less than the larger of:
 +
::* A clear distance of 1.33 x Maximum Aggregate Size
 +
::* Center-to-center spacing of 2" for 0.6" strand diameter
 +
::* Center-to-center spacing of 1.75" for 0.5" strand diameter
  
ATTENTION: Location of harped strands shown in top flange are at end of girder and harped strands in bottom flange are at centerline.
+
===751.22.3.2 Strand Arrangements===
 +
Designers shall first attempt to use one of the strand arrangements specified in EPG 751.22.3.2.1 through EPG 751.22.3.2.5. The strand arrangement number shall be specified in the design. Bridge standard drawings for prestressed I-girders include strand details for each of these arrangements, by number, in the reference files for quick insertion by the technician.
 +
   
 +
For Group 1 arrangements, all strands in the center two columns are harped. For Group 2 arrangements, the bottom two center strands are straight (two less draped strands). Group 2 arrangements are not provided in diagrams below for Type 6, 7 and 8 girders, but may be derived similarly to how specified for the smaller girders.
  
If the web thickness is required to be increased, then the top and bottom flanges are to be increased by the same amount.  (1" increments, 2"&nbsp;max.)
+
Designers shall include an equivalent detail in the design computations when strand arrangements other than those shown are required.
  
====751.22.3.2.3 Beam Type 4 Dimensions/Strand Arrangements====
+
The use of all straight strands (none harped) may be considered when strength check of a hold-down device exceeds allowable.
  
 +
'''How Strand Arrangements are Detailed from Tables'''
  
 +
:1. For strand locations at mid-span (centerline of girder): Find the “#” designation that corresponds with the number of total strands (T) needed. The strands are to be placed at locations labeled up to and including that number. Example: For 14 total strands, the strands will be placed at all locations labeled 8 thru 14 and are designated as arrangement #14. (See Fig. 751.22.3.2.)
  
<center>[[Image:751.22_Beam_Type_4_Girders_4A_&_4B.gif]]</center>
+
:2. For harped strand locations at end of girder: Harped strands will be placed at locations labeled up to and including the number in the “H” column. Example: For 6 harped strands, the strands will be placed at all locations labeled 2 thru 6. (See Fig. 751.22.3.2.)
 
+
{| style="margin: 1em auto 1em auto"
 
+
|-
{|border="0" cellpadding="5" align="center" textalign="center" width="500"
+
|rowspan="2"|[[image:751.22.3.2.jpg|center|400px]]<br/><center>'''Fig. 751.22.3.2'''</center>||Where:
 
+
|-
|align="center" |'''GIRDERS 4A THRU 4C'''
+
|valign="top"|# = Strand Arrangement Number<br/>T = Total Number of Strands<br/>H = Number of Harped Strands<br/>S = Number of Straight Strands
<math>A</math> '''= 428.9 SQ. IN.'''<br/>
 
<math>Y_b</math> '''= 19.54 IN.'''<br/>
 
<math>I</math> '''= 92,450 IN.<sup>4</sup>'''
 
|align="center" width="200"|'''GIRDER 4A'''
 
'''(10 STRANDS)'''
 
|align="center"|'''GIRDER 4B'''
 
'''(11 STRANDS)'''
 
 
|}
 
|}
  
  
 +
====751.22.3.2.1 Type 2 Girder====
  
{|border="0" cellpadding="5" align="center" textalign="center"
+
[[Image:751.22.3.2.1_2022.jpg|center|850px]]
 +
See [[#751.22.3.2.6 NU Girders|EPG 751.3.2.6]] for guidance notes (1) and (2).
  
|align="center" |[[Image:751.22_Beam_Type_4_Girders_4C.gif]]<br/>
 
'''GIRDERS 4C'''<br/>'''(13 STRANDS)'''
 
|align="center"|[[Image:751.22_Beam_Type_4_Girders_Sequence_No_4A_thru_4C_Table.gif]]
 
{|border="0"
 
|align="left" width="425pt"|&nbsp;<br/>NOTE: Investigate the possibility of using all straight strands when strength check of a hold-down device exceeds allowable.<br/><u>All strand arrangements shown on this page have straight strands only.</u>
 
  
Strand arrangements other than those shown may be investigated by the designer.
+
====751.22.3.2.2 Type 3 Girder====
|}
 
|}
 
  
 +
[[Image:751.22.3.2.2_2022.jpg|center|850px]]
 +
See [[#751.22.3.2.6 NU Girders|EPG 751.3.2.6]] for guidance notes (1) and (2).
  
<center>[[Image:751.22_Beam_Type_4_Girders_dim_&_Group_I.gif]]</center>
 
  
 +
====751.22.3.2.3 Type 4 Girder====
  
{|border="0" cellpadding="5" align="center" textalign="center" width="600"
+
[[Image:751.22.3.2.3_2022.jpg|center|850px]]
 +
See [[#751.22.3.2.6 NU Girders|EPG 751.3.2.6]] for guidance notes (1) and (2).
  
|align="center" width="300"|<math>A</math> '''= 428.9 SQ. IN.'''<br/>
 
<math>Y_b</math> '''= 19.54 IN.'''<br/>
 
<math>I</math> '''= 92,450 IN.<sup>4</sup>'''
 
|align="center" width="300"|'''GROUP I'''
 
|}
 
  
 +
====751.22.3.2.4 Type 6 Girder====
  
{|border="0" cellpadding="5" align="center" textalign="center"
+
[[Image:751.22.3.2.4_2022.jpg|center|550px]]
 +
See [[#751.22.3.2.6 NU Girders|EPG 751.3.2.6]] for guidance notes (1) and (2).
  
|align="center"|[[Image:751.22_Beam_Type_4_Girders_Group_II.gif]]<br/>&nbsp;<br/>'''GROUP II'''
 
|width="300"|Numbers shown on girders<br/>relate to strand locations.
 
|}
 
  
 +
====751.22.3.2.5 Type 7 and 8 (Bulb-Tee) Girders====
  
ATTENTION:  Location of harped strands shown in top flange are at end of girder and harped strands in bottom flange are at centerline.
 
  
 +
[[Image:751.22.3.2.5_2022.jpg|center|600px]]
 +
See [[#751.22.3.2.6 NU Girders|EPG 751.3.2.6]] for guidance notes (1) and (2).
  
If the web thickness is required to be increased, then the top and bottom flanges are to be increased by the same amount. (1" increments, 2"&nbsp;max.)
+
====751.22.3.2.6 NU Girders====
  
====751.22.3.2.4 Beam Type 6 Dimensions/Strand Arrangements====
+
[[image:751.22.3.2.6_2022.jpg|center|310px]]
 
+
Strand arrangements shall start at the bottom row and then move up for the most efficient design.
 
+
{| style="margin: 1em auto 1em auto"
{|border="0" cellpadding="5" align="center"
 
|[[Image:751.22_Beam_Type_6_dimensions.gif]]
 
|&nbsp;
 
{|border="0" cellpadding="5" align="right" width="150"
 
|align="center"|<math>\, A</math>||=||643.6 Sq. In.
 
 
|-
 
|-
|align="center"|<math>\, Y_b</math>||=||25.92 In.
+
|<font color = "grass">'''(1)'''</font color = "grass"> ||Strands shall be placed on outer edge to help place confinement steel.
 
|-
 
|-
|align="center"|<math>\, I</math>||=||235,735 In.<sup>4</sup>
+
|valign="top"|<font color = "grass">'''(2)'''</font color = "grass"> ||If possible, strands shall not be placed at the specified location due to the conflict with B1 and B2 bars. Harped strands at this location are less problematic since this conflict only occurs between the hold-down devices where the B1 bars are spaced farther apart. If straight strands are required below the harped strands the designer shall first attempt to locate these straight strands in the second row. The use of the strands at the specified location shall be discussed with Structural Project Manager or Structural Liaison Engineer.
|}
 
 
|}
 
|}
  
 
+
===751.22.3.3 Top Flange Blockout for NU Girders===
{|border="0" cellpadding="5" align="center"
+
<center>
|align="center"|[[Image:751.22_Beam_Type_6_Group_I.gif]]<br/>&nbsp;<br/>
+
{| border="1" class="wikitable" style="margin: 1em auto 1em auto" style="text-align:center"
'''GROUP I'''
+
|+
|width="250"|Numbers shown on girders<br/>relate to strand locations.
+
| style="background:#BEBEBE" width="900"|'''No Skew'''
|}
+
|-
 
+
|[[image:751.22.3.3.2 no skew.jpg|center|750px]]
 
+
|-
ATTENTION: Location of harped strands shown in top flange are at end of girder and harped strands in bottom flange are at centerline.
+
| style="background:#BEBEBE" width="900"|'''>0° to 7° LA Skew''' (Mirror for right advanced.)
 
+
|-
If the web thickness is required to be increased, then the top and bottom flanges are to be increased by the same amount. (1" increments, 2"&nbsp;max.)
+
|[[image:751.22.3.3.2 0 to 7.jpg|center|850px]]
 
+
|-
====751.22.3.2.5 Beam Type 7 Dimensions/Strand Arrangements====
+
| style="background:#BEBEBE" width="900"|'''>7° to 14° LA Skew ''' (Mirror for right advanced.)
 
+
|-
 
+
|[[image:751.22.3.3.2 7 to 14.jpg|center|850px]]
{|border="0" cellpadding="5" align="center"
 
|[[Image:751.22_Beam_Type_7_dimensions.gif]]
 
|&nbsp;
 
{|border="0" cellpadding="5" align="right" width="150"
 
|align="center"|<math>\, A</math>||=||787.4 Sq. In.
 
 
|-
 
|-
|align="center"|<math>\, Y_b</math>||=||37.58 In.
+
| style="background:#BEBEBE" width="900"|'''>14° to 60° LA Skew ''' (Mirror for right advanced.)
 
|-
 
|-
|align="center"|<math>\, I</math>||=||571,047 In.<sup>4</sup>
+
|[[image:751.22.3.3.2 14 to 60.jpg|center|875px]]
|}
 
 
|}
 
|}
 +
</center>
 +
Choose one of the above four details for the top flange blockout detail and follow the provided detailing guidance.
  
 +
Blockout shall be dimensioned along the girder to 1 1/2 inches inside the face of the diaphragm and adjusted for any girder tilt.
  
{|border="0" cellpadding="5" align="center"
+
The left advanced details shown may be used for right advanced bridges. The mirror note may be removed if left advanced.
|align="center"|[[Image:751.22_Beam_Type_7_Group_I.gif]]<br/>&nbsp;<br/>
 
'''GROUP I'''
 
|width="250"|Numbers shown on girders<br/>relate to strand locations.
 
|}
 
  
 +
Revise bent references as required and specify the bent number if blockout varies by bent.
  
ATTENTION: Location of harped strands shown in top flange are at end of girder and harped strands in bottom flange are at centerline.
+
The skew angle value need not be shown for tangent bridges. Consult SPM or Liaison on replacing "skew angle" with actual value for curved bridges.
  
===751.22.3.3 NU Standard Girders===
+
Revised titles for non-integral end bents (exterior girder at end bent will be same detail as at intermediate bent).
  
<center>'''NU Girder Dimensions/Strand Arrangements'''</center>
 
[[image:751.22.3.3.jpg|center|350px|thumb|* Strands shall be placed on outer edge to help place confinement steel]]
 
  
::Note:  Strand arrangements shall start at the bottom row and then move up for the most efficient design.
+
<center>'''Flange Blockout Data'''
 
+
{| border="1" class="wikitable" style="margin: 1em auto 1em auto" style="text-align:center"
===751.22.3.4 Beam Section Properties Tables - Conventional Concrete Strength===
+
|+
 
+
! style="background:#BEBEBE" width="150"|Skew!! style="background:#BEBEBE" width="65"|X Eq.<br/>Spa. !! style="background:#BEBEBE" width="65"|X<br/>#4-G6 !! style="background:#BEBEBE" width="325"|Bar Lengths
<div id="e1, e2, e3, I_initial & I_final"></div>
+
|-
The properties of prestressed I-girders in the following tables are valid for <math>\, f'_{ci}</math> = 4.5 ksi and <math>\, f'_c</math> = 6 ksi.  The modular ratio , ''<math>\, n</math>'', is 8 for the initial moment of inertia, <math>\, I_{initial}</math>, and 7 for the final moment of inertia, <math>\, I_{final}</math>.
+
|>14° to 21°||3|| 2||rowspan="11"|G3 bar = <math>\frac {46.25''}{cos(skew)}</math><br/><br/>G5 bar = <math>\frac {32.125''}{cos(skew)}</math><br/><br/>'''For skews >7° to 14°:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''<br/>G6 bar = <math>\frac {G3\ bar + 46.25''}{2}</math><br/><br/>'''For skews >14° to 60°:'''<br/>report length of G6 bars as “Varies”
 
+
|-
Note: Moments of inertia, <math>\, I_{initial}</math> and <math>\, I_{final}</math> are computed based on transformed non-composite section and are used in camber calculations.
+
|>21° to 27°||4||3
 
 
Definitions used in tables are:
 
{|border="0" cellpadding="5"
 
|valign="top"|Section Area||valign="top"|=||Gross area of girder, (in.<sup>2</sup>)
 
 
|-
 
|-
|valign="top"|Section <math>\, Y_b</math> ||valign="top"|=||Distance from bottom of girder to center of gravity of non-transformed non-composite section, (in.)
+
|>27° to 32°||5||4
 
|-
 
|-
|valign="top"| <math>\, I_{nontransformed}</math> ||valign="top"|=||Moment of inertia of non-transformed non-composite section, (in.<sup>4</sup>)
+
|>32° to 37°||6||5
 
|-
 
|-
|valign="top"|Depth||valign="top"|=||Height of girder, (in.)
+
|>37° to 42°||7||6
 
|-
 
|-
|valign="top"|Strand size||valign="top"|=||Strand diameter, (in.)
+
|>42° to 46°||8||7
 
|-
 
|-
|valign="top"|e1*||valign="top"|=||Eccentricity between centroid of straight strands (CSS) and center of gravity of non-transformed non-composite section (CGB) as shown in figure below, (in.)
+
|>46° to 49°||9||8
 
|-
 
|-
|valign="top"|e2*||valign="top"|=||Eccentricity between centroid of harped strands (CHS) and center of gravity of non-transformed non-composite section (CGB) at midspan as shown in figure below, (in.)
+
|>49° to 52°||10||9
 
|-
 
|-
|valign="top"|e3*||valign="top"|=||Eccentricity between centroid of harped strands (CHS) and center of gravity of non-transformed non-composite section (CGB) at the end of girder as shown in figure below, (in.)
+
|>52° to 55°||11||10
|}
+
|-
 +
|>55° to 57°||12||11
 +
|-
 +
|>57° to 60°||13||12
 +
|}
 +
</center>
  
 +
===751.22.3.4 Girder Reinforcement===
  
<math>\, *</math> A more accurate value can be used based on transformed non-composite section. The final camber calculation will not be significantly different using values between transformed and non-transformed sections.
+
====751.22.3.4.1 Reinforcing Steel Details ====
  
+
'''I Girders and Bulb-Tee Girders'''
<center>[[Image:751.22_Girder_Plan_showing_strands.gif]]</center>
 
  
 +
See [http://www.modot.org/business/standard_drawings2/psi_girders_new_title_block.htm Bridge Standard Drawings] for details not shown below.
  
'''Steps for detailing strand patterns from Prestressed Beam Tables'''
+
{|border="1" cellpadding="3" cellspacing="0" style="text-align:center" align="center"
#For strand locations at mid-span of girder: Look up the "Total Number of Strands" value for the corresponding strand pattern number.  The strands will then be located at that number and all numbers below that number.  Ex.  For 14 total strands, the strands will be placed at all locations numbered ≤14.
 
#For harped strand locations at end of girder:  Look up the "Number of Harped Strands" value for the corresponding strand pattern number.  The strands will then be located at that number and all numbers below that number.  Ex.  For 6 harped strands, the strands will be placed at all locations numbered ≤6.
 
  
+
|&nbsp;
<center>[[Image:751.22_Girder_Section_showing_strands.gif]]</center>
+
|colspan="13"|TABLE OF DIMENSIONS BY GIRDER TYPE
 
+
|-
:::::::::::'''GROUP I'''
+
|&nbsp;
 
+
|colspan="3"|TYPE 2
 
+
|colspan="3"|TYPE 3
 
+
|colspan="3"|TYPE 4
 
+
|colspan="3"|TYPE 6
'''Section Properties'''<br/>
+
|TYPE 7
'''Beam Type 2 -- 6" Web'''
+
|-
 
+
|WEB||6"||7"||8"||6"||7"||8"||6"||7"||8"||6½"||7½"||8½"||6"
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|310.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
 
|-
 
|-
|&nbsp;||T||=||total number of strands
+
|"A"||6"|| 6"|| 6"|| 6"|| 6"|| 6"|| 6"|| 6"|| 6"|| 9¼"|| 9¼"|| 9¼"|| 10½"
 
|-
 
|-
|&nbsp;||H||=||number of harped strands
+
|"B"||4"||4"||4"||4"||4"||4"||4"||4"||4"||4"||4"||4"||4"
 
|-
 
|-
|&nbsp;||S||=||number of straight strands
+
|"C"||5¾"|| 5¾"|| 5¾"|| 5¾"|| 5¾"|| 5¾"|| 5¾"|| 5¾"|| 5¾"|| 6¾"|| 6¾"|| 6¾"|| 4¼"
|}
 
 
|-
 
|-
|align="right"|Section <math>\, Y_b</math> =
+
|"D"||"|| 3¼"|| 3¼"|| 4¾"|| 4¾"|| 4¾"|| 5¾"|| 5¾"|| 5¾"|| 4"|| 4"|| 4"|| 4"
|align="center"|14.08||in
 
 
|-
 
|-
|align="right"| <math>\, I_{nontransformed}</math> =
+
|"E"||13"||14"||15"||13"||14"||15"||13"||14"||15"||18"||19"||20"||20"
|align="center"|33,974||in<sup>4</sup>
 
 
|-
 
|-
|align="right"|Depth=
+
|"F"||2"||2"||2"||2"||2"||2"||2"||2"||2"||3"||3"||3"||7¾"
|align="center"|32||in
 
 
|-
 
|-
|align="right"|Strand Size=
+
|"G"||11"||12"||13"||11"||12"||13"||11"||12"||13"||22"||23"||24"||2'-10"
|align="center"|½||in
 
 
|-
 
|-
|align="right"| <math>\, f'_{ci}</math> =
+
|"H"||2'-6"||2'-6"||2'-6"||3'-1"||3'-1"||3'-1"||3'-7"||3'-7"||3'-7"||4'-4"||4'-4"||4'-4"||5'-10½"
|align="center"|4.5||ksi
 
 
|-
 
|-
|align="right"|<math>\, f'_c</math> =
+
|"I"
|align="center"|6||ksi
+
|3'-0½"||3'-0½"||3'-0½"||3'-7½"||3'-7½"||3'-7½"||4'-1½"||4'-1½"||4'-1½"||4'-10½"||4'-10½"||4'-10½"||6'-5"
 
|}
 
|}
  
  
{|border="1" cellpadding="5" cellspacing="0" text-align="center"
+
<center>Note: Dimensions shown above are out to out.</center>
 +
 
  
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
{|border="1" cellpadding="1" cellspacing="0" style="text-align:center" align="center"
|align="center" colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]
+
 
|align="center" colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
+
|&nbsp;
 +
|colspan="13"|TOTAL BAR LENGTH BY GIRDER TYPE
 
|-
 
|-
 
|&nbsp;
 
|&nbsp;
|align="center"|#
+
|colspan="3"|TYPE 2
|align="center"|T
+
|colspan="3"|TYPE 3
|align="center"|H
+
|colspan="3"|TYPE 4
|align="center"|S
+
|colspan="3"|TYPE 6
|align="center"|[[#e1, e2, e3, I_initial & I_final|e1]]
+
|TYPE 7
|align="center"|[[#e1, e2, e3, I_initial & I_final|e2]]
 
|align="center"|[[#e1, e2, e3, I_initial & I_final|e3]]
 
|align="center"|A1 Bars<br/>2-#5
 
|align="center"|A1 Bars<br/>2-#6
 
|align="center"|A1 Bars<br/>2-#5
 
|align="center"|A1 Bars,<br/>2-#6
 
 
|-
 
|-
!Group
+
|width="32pt"|WEB||width="45pt"|6"||width="45pt"|7"||width="45pt"|8"||width="45pt"|6"||width="45pt"|7"||width="45pt"|8"||width="50pt"|6"||width="50pt"|7"||width="50pt"|8"||width="50pt"|6½"||width="50pt"|7½"||width="50pt"|8½"||width="100pt"|6"
|align="center"|1
 
|align="center"|8
 
|align="center"|4
 
|align="center"|4
 
|align="center"|11.08
 
|align="center"|11.08
 
|align="center"|13.92
 
|align="center"|36,147
 
|align="center"|36,627
 
|align="center"|35,837
 
|align="center"|36,248
 
 
|-
 
|-
!I
+
|#4-B1||4'-1"||4'-1"||4'-1"||4'-8"||4'-8"||4'-8"||5'-2"||5'-2"||5'-2"||5'-11"||5'-11"||5'-11"||7'-8"
|align="center"|2
 
|align="center"|10
 
|align="center"|4
 
|align="center"|6
 
|align="center"|11.41
 
|align="center"|11.08
 
|align="center"|13.92
 
|align="center"|36,453
 
|align="center"|36,938
 
|align="center"|36,100
 
|align="center"|36,515
 
 
|-
 
|-
|&nbsp;
+
|#5-B1||4'-1"||4'-1"||4'-1"||4'-8"||4'-8"||4'-8"||5'-2"||5'-2"||5'-2"||5'-11"||5'-11"||5'-11"||7'-7"  
|align="center"|3
 
|align="center"|12
 
|align="center"|6
 
|align="center"|6
 
|align="center"|11.41
 
|align="center"|10.08
 
|align="center"|12.92
 
|align="center"|36,587
 
|align="center"|37,075
 
|align="center"|36,215
 
|align="center"|36,632
 
 
|-
 
|-
|&nbsp;
+
|#6-B1||3'-11"||3'-11"||3'-11"||4'-6"||4'-6"||4'-6"||5'-0"||5'-0"||5'-0"||5'-9"||5'-9"||5'-9"||7'-6"  
|align="center"|4
 
|align="center"|14
 
|align="center"|6
 
|align="center"|8
 
|align="center"|11.08
 
|align="center"|10.08
 
|align="center"|12.92
 
|align="center"|36,794
 
|align="center"|37,286
 
|align="center"|36,394
 
|align="center"|36,814
 
 
|-
 
|-
|&nbsp;
+
|#6-B2||3'-5"||3'-5"||3'-5"||4'-0"||4'-0"||4'-0"||4'-6"||4'-6"||4'-6"||5'-3"||5'-3"||5'-3"||6'-11"  
|align="center"|5
 
|align="center"|16
 
|align="center"|8
 
|align="center"|8
 
|align="center"|11.08
 
|align="center"|9.08
 
|align="center"|11.92
 
|align="center"|36,866
 
|align="center"|37,360
 
|align="center"|36,456
 
|align="center"|36,878
 
 
|-
 
|-
|&nbsp;
+
|#4-C1||13"||14"||15"||13"||14"||15"||13"||14"||15"||2'-2"||2'-3"||2'-4"||3'-5"  
|align="center"|6
 
|align="center"|18
 
|align="center"|8
 
|align="center"|10
 
|align="center"|10.48
 
|align="center"|9.08
 
|align="center"|11.92
 
|align="center"|36,994
 
|align="center"|37,491
 
|align="center"|36,568
 
|align="center"|36,992
 
 
|-
 
|-
!Group
+
|#4-D1||2'-3"||2'-4"||2'-5"||2'-5"||2'-6"||2'-7"||2'-6"||2'-7"||2'-8"||3'-0"||3'-1"||3'-2"||3'-1"  
|align="center"|7
+
|}
|align="center"|8
+
 
|align="center"|2
+
 
|align="center"|6
+
Note:  When required create new B1 and C1 bars and adjust heights in one-inch increments to ensure at least 2 1/2 inches of embedment into slab. This limit provides for a half inch variance in the field.
|align="center"|11.41
+
 
|align="center"|10.08
+
 
|align="center"|14.92
+
{|border="0" cellpadding="1" cellspacing="0" style="text-align:center" align="center"
|align="center"|36,147
+
 
|align="center"|36,627
+
|[[Image:751.22.3.6 C1.jpg|200px]]
|align="center"|35,837
+
|rowspan="2"|[[Image:751.22.3.6 B1 and B2.jpg|325px]]
|align="center"|36,248
+
|[[Image:751.22.3.6 C1 Type 7.jpg|225px]]
 
|-
 
|-
!II
+
|valign="top"|C1 BAR</br>
|align="center"|8
+
Shape 10S</br>
|align="center"|10
+
(Girders Type 2-6)
|align="center"|2
+
|valign="top"|C1 BAR
|align="center"|8
+
Shape19S</br>
|align="center"|11.58
+
(Girder Type 7)<!--column 2 occupied by cell [[Image:751.22_B1_&_B2_Bar.gif]]-->
|align="center"|10.08
 
|align="center"|14.92
 
|align="center"|36,453
 
|align="center"|36,938
 
|align="center"|36,100
 
|align="center"|36,515
 
 
|-
 
|-
 
|&nbsp;
 
|&nbsp;
|align="center"|9
+
|B1 and B2 Bar
|align="center"|12
+
Shape 11S
|align="center"|4
+
|rowspan="3"|[[Image:751.22_Section_Thru_Girder_Type_7.gif]]
|align="center"|8
 
|align="center"|11.08
 
|align="center"|11.08
 
|align="center"|13.92
 
|align="center"|36,663
 
|align="center"|37,151
 
|align="center"|36,280
 
|align="center"|36,698
 
 
|-
 
|-
|&nbsp;
+
|rowspan="2"|[[Image:751.22_Section_Thru_Girder_2-6.gif]]
|align="center"|10
+
|valign="bottom"|[[Image:751.22.3.6 D1.jpg|175px]]
|align="center"|14
 
|align="center"|4
 
|align="center"|10
 
|align="center"|11.28
 
|align="center"|9.08
 
|align="center"|13.92
 
|align="center"|36,794
 
|align="center"|37,286
 
|align="center"|36,394
 
|align="center"|36,814
 
 
|-
 
|-
|&nbsp;
+
|D1 BAR <!--column 1 occupied by cell [[Image:751.22_Section_Thru_Girder_2-6.gif]]-->
|align="center"|11
+
Shape 9S
|align="center"|16
 
|align="center"|6
 
|align="center"|10
 
|align="center"|11.28
 
|align="center"|8.08
 
|align="center"|12.92
 
|align="center"|36,866
 
|align="center"|37,360
 
|align="center"|36,456
 
|align="center"|36,878
 
 
|-
 
|-
 +
|SECTION THRU GIRDER
 +
(Type 2, 3, 4 and 6 Girders)
 
|&nbsp;
 
|&nbsp;
|align="center"|12
+
|SECTION THRU GIRDER
|align="center"|18
+
(Type 7 Girder)
|align="center"|6
 
|align="center"|12
 
|align="center"|10.75
 
|align="center"|8.08
 
|align="center"|12.92
 
|align="center"|36,994
 
|align="center"|37,491
 
|align="center"|36,568
 
|align="center"|36,992
 
|-
 
|&nbsp;
 
|align="center"|13
 
|align="center"|20
 
|align="center"|6
 
|align="center"|14
 
|align="center"|10.65
 
|align="center"|6.08
 
|align="center"|12.92
 
|align="center"|37,024
 
|align="center"|37,522
 
|align="center"|36,594
 
|align="center"|37,019
 
 
|}
 
|}
  
 +
'''Welded Wire Reinforcing Steel Details for NU Girders'''
 +
 +
See [http://www.modot.org/business/standard_drawings2/psi_girders_new_title_block.htm Bridge Standard Drawings] for details.
  
'''Section Properties'''<br/>
+
When required create new WWR and adjust heights in one-inch increments to ensure at least 2 1/2 inches of embedment into slab. This limit provides for a half inch variance in the field.
'''Beam Type 2 -- 7" Web'''
 
  
 +
Length of WWR sections should be based on shear and confinement requirements before adjusting height to avoid multiple short sections.
  
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
The height of the WWR6 at the ends of NU girders shall not be adjusted. The top horizontal legs of WWR6 will need to be removed for a flange depth increase greater than 4¾”.
  
|align="right"|Section Area =
+
'''Alternate Bar Reinforcing Steel Details for NU Girders'''
|align="center"|342.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|14.26||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|36,812||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|32||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|½||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|4.5||ksi
 
|-
 
|align="right"| <math>\, f'_{c}</math> =
 
|align="center"|6||ksi
 
|}
 
  
 +
Alternate bar reinforcing steel details shall be provided for all NU girders for all spans.
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
+
See [http://www.modot.org/business/standard_drawings2/psi_girders_new_title_block.htm Bridge Standard Drawings] for details.
  
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
When required create new B1 bars and adjust heights in one-inch increments to ensure at least 2 1/2 inches of embedment into slab. This limit provides for a half inch variance in the field.
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]
+
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
+
====751.22.3.4.2 Shear Reinforcement====
|-
+
 
|&nbsp;||#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
+
The following criteria are preferred by girder manufacturers and reinforcement suppliers. If the design requires a deviation from the preferred criteria then feasibility should be verified with a manufacturer.
|-
+
 
!Group
+
'''I Girders, Bulb-Tee Girders, and NU Girders with Alternate Bar Reinforcing Steel'''
|1||8||4||4||11.26||11.26||13.74||38,994||39,464||38,683||39,085
+
 
|-
+
:* B1 bars shall be either #4 or #5 epoxy-coated bars with #4 bars preferred to allow permissible alternate bar shape. Using #6 B1 bars does not provide one-inch clearance when center strands are spaced one inch off centerline of girder between hold down devices because of bend radius of the #6 bars.  
!I
+
:* The same shear reinforcement bar size shall be used in a girder. Using the same shear reinforcement bar size for all of the spans is preferred but not required for girders of different spans lengths.
|2||10||4||6||11.59||11.26||13.74||39,310||39,784||38,954||39,360
+
:* 6” is the preferred minimum spacing.
|-
+
:* 5” spacing may be used for first set if required.
|&nbsp;||3||12||6||6||11.59||10.26||12.74||39,450||39,927||39,075||39,482
+
:* 21” is the maximum spacing for #4 bars.
|-
+
:* 24” is the maximum spacing for #5 bars.
|&nbsp;||4||14||6||8||11.26||10.26||12.74||39,666||40,146||39,261||39,671
+
:* 3” increment spacing shall be used (i.e. 6”, 9”, 12”, 15”, 18”, 21” and 24”) except when less than 6” spacing is required for the first set. In this case, 6” or 9” shall be used for the next set of B1 bars.
|-
+
:* Four or less spacing changes are preferred for spans up to 100 feet.
|&nbsp;||5||16||8||8||11.26||9.26||11.74||39,742||40,225||39,327||39,739
+
:* Six spacing changes may be used for spans greater than 100 feet.
|-
+
:* Using the same spacing scenario (i.e. sets of B1 bars at 6”, 12” and 18” spacing) for all of spans is preferred but not required for girders of different span lengths.
|&nbsp;||6||18||8||10||10.66||9.26||11.74||39,877||40,363||39,444||39,858
 
|-
 
!Group
 
|7||8||2||6||11.59||10.26||14.74||38,994||39,464||38,683||39,085
 
|-
 
!II
 
|8||10||2||8||11.76||10.26||14.74||39,310||39,784||38,954||39,360
 
|-
 
|&nbsp;||9||12||4||8||11.26||11.26||13.74||39,528||40,005||39,142||39,550
 
|-
 
|&nbsp;||10||14||4||10||11.46||9.26||13.74||39,666||40,146||39,261||39,671
 
|-
 
|&nbsp;||11||16||6||10||11.46||8.26||12.74||39,742||40,225||39,327||39,739
 
|-
 
|&nbsp;||12||18||6||12||10.93||8.26||12.74||39,877||40,363||39,444||39,858
 
|-
 
|&nbsp;||13||20||6||14||10.83||6.26||12.74||39,910||39,473||39,473||39,888
 
|}
 
  
 +
'''NU Girders with Welded Wire Reinforcing Steel'''
  
'''Section Properties '''<br/>
+
:* WWR shall be uncoated and shall use either D18, D20, D22 or D31 vertical wire sizes. W8 horizontal wires sizes shall be used with D18 and D20 vertical wires. W9 horizontal wire sizes shall be used with D22 vertical wires. W12 horizontal wire sizes shall be used with D31 vertical wires.
'''Beam Type 2 -- 8" Web'''
+
:* The same shear reinforcement wire size shall be used in a girder. Using the same shear reinforcement wire size for all of the spans is preferred but not required for girders of different spans lengths.
 +
:* 4” is the preferred minimum spacing.
 +
:* 20” is the maximum spacing for the D18, D20 and D22 wire sizes.
 +
:* 24” is the maximum spacing for the D31 wire size.
 +
:* 4” increment spacing shall be used (i.e. 4”, 8”, 12”, 16”, 20” and 24”).
 +
:* Three or less spacing changes (WWR pieces) are preferred for spans less than 100 feet.
 +
:* An additional spacing change (WWR piece) may be used in spans greater than 100 feet.
 +
:* Using the same spacing scenario (i.e. S1=4”, S2=12” and S3=20”) for all of the spans is preferred but not required for girders of different span lengths.
  
 +
====751.22.3.4.3 Anchorage Zone Reinforcement====
  
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
The following details satisfy the criteria for anchorage zone reinforcement in [[#Pretensioned anchorage zones|EPG 751.22.2.5 Pretensioned Anchorage Zones]] for up to the maximum number of bonded strands specified in EPG 751.22.2.5.
  
|align="right"|Section Area =
+
'''I Girders and Bulb-Tee Girders'''
|align="center"|374.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|14.41||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|39,632||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|32||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|½||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|4.5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|6||ksi
 
|}
 
  
 +
[[Image:751.22.3.4.3 I girders.jpg|675px|center]]
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
  
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
'''NU Girders'''
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]
+
[[image:751.22.3.4.3 NU Girders.jpg|center|700px|thumb|
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
+
{| style="margin: 1em auto 1em auto"
 
|-
 
|-
|&nbsp;||#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
+
|colspan="2" height="5"| ||rowspan="2" width="15"| ||rowspan="2"|[[image:751.22.3.6 wwr6 2021.jpg|center|180px]]||rowspan="2"|[[image:751.22.3.6 wwr6 table 2021.jpg|center|170px]]
 
|-
 
|-
!Group
+
!width="25" valign="top"|'''<font color = "grass">(ɑ)</font color = "grass">''' ||width="250" valign="top" align="left"|The overall height of the WWR6 shall not be increased for girder steps. Reduce this dimension by the accumulated girder step height.  
|1||8||4||4||11.41||11.41||13.59||41,823||42,283||41,510||41,905
+
|}
|-
+
]]
!I
 
|2||10||4||6||11.74||11.41||13.59||42,147||42,611||41,789||42,186
 
|-
 
|&nbsp;||3||12||6||6||11.74||10.41||12.59||42,292||42,760||41,914||42,313
 
|-
 
|&nbsp;||4||14||6||8||11.41||10.41||12.59||42,515||42,985||42,106||42,508
 
|-
 
|&nbsp;||5||16||8||8||11.41||9.41||11.59||42,596||43,068||42,176||42,579
 
|-
 
|&nbsp;||6||18||8||10||10.81||9.41||11.59||42,737||43,212||42,298||42,703
 
|-
 
!Group
 
|7||8||2||6||11.74||10.41||14.59||41,823||42,283||41,510||41,905
 
|-
 
!II
 
|8||10||2||8||11.91||10.41||14.59||42,147||42,611||41,789||42,186
 
|-
 
|&nbsp;||9||12||4||8||11.41||11.41||13.59||42,371||42,839||41,982||42,382
 
|-
 
|&nbsp;||10||14||4||10||11.61||9.41||13.59||42,515||42,985||42,106||42,508
 
|-
 
|&nbsp;||11||16||6||10||11.61||8.41||12.59||42,596||43,068||42,176||42,579
 
|-
 
|&nbsp;||12||18||6||12||11.08||8.41||12.59||42,737||43,212||42,298||42,703
 
|-
 
|&nbsp;||13||20||6||14||10.98||6.41||12.59||42,772||43,249||42,329||42,736
 
|}
 
  
  
'''Section Properties'''<br/>
+
'''Bearing Plate Anchor Studs'''
'''Beam Type 3 -- 6" Web'''
 
  
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
The standard ½" bearing plate will be anchored with four ½" x 4" studs for MoDOT shapes and eight ½” x 5” studs for NU shapes.
  
|align="right"|Section Area =
+
If required, increase the number of ½" studs and space between wires of WWR6.
|align="center"|381.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|17.08||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|61,841||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|39||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|½||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|4.5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|6||ksi
 
|}
 
  
 +
The minimum ¼" fillet weld between the ½" bearing plate and 1½" sole plate is adequate for all cases.
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
+
'''LFD Seismic Design'''
  
!Cont.
+
Studs shall be designed to meet the criteria of 2002 AASHTO 17<sup>th</sup> Edition Division I-A in Seismic Performance Category C or D.
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]
+
Stud capacity is determined as follows for:
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
+
 
|-
+
:Stud Cap. = (n)(A<sub>s</sub>)(0.4F<sub>y</sub>)(1.5)
!valign="top"|Span
+
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
+
::Where:
 +
:::N = number of studs
 +
:::A<sub>s</sub> = area of stud
 +
:::F<sub>y</sub> = yield strength of stud (50 ksi)
 +
:::0.4F<sub>y</sub> = Allowable Shear in Pins AASHTO Table 10.32.1A
 +
:::1.5 = seismic overload factor
 +
 
 +
If required, increase the number of 1/2” studs to six and space between wires of WWR6.  If this is still not adequate, 5/8” studs may be used.  The following table may be used as a guide for upper limits of dead load reactions:
 +
 
 +
{|border="1" cellpadding="3" cellspacing="0" style="text-align:center" align="center"
 
|-
 
|-
!Group
+
!rowspan="2"|No. of Studs||rowspan="2"| Stud Dia.||colspan="2"|Max Allowable D.L Reaction (kips)
|1||8||4||4||13.08||14.08||17.92||65,179||65,930||64,702||65,346
 
 
|-
 
|-
!I
+
!A = 0.30!! A = 0.36
|2||10||4||6||13.75||14.08||17.92||65,659||66,415||65,114||65,762
 
 
|-
 
|-
|&nbsp;||3||12||4||8||13.58||14.08||17.92||66,014||66,776||65,421||66,072
+
|4|| 1/2”|| 78 ||65
 
|-
 
|-
|&nbsp;||4||14||6||8||13.58||13.08||16.92||66,265||67,032||65,637||66,292
+
|6|| 1/2”|| 117 ||98
 
|-
 
|-
|&nbsp;||5||16||6||10||13.48||13.08||16.92||66,614||67,386||65,938||66,597
+
|4|| 5/8”|| 122|| 102
 
|-
 
|-
|&nbsp;||6||18||8||10||13.48||12.08||15.92||66,776||67,552||66,079||66,740
+
|6|| 5/8”|| 184|| 153
 
|-
 
|-
|&nbsp;||7||20||8||12||13.08||12.08||15.92||67,020||67,799||66,290||66,954
+
|8|| 1/2”|| 156|| 130
 
|-
 
|-
|&nbsp;||8||22||8||14||12.51||12.08||15.92||67,178||67,961||66,427||67,095
+
|10|| 1/2”|| 195|| 163
 
|-
 
|-
|&nbsp;||9||24||10||14||12.51||11.08||14.92||67,270||68,056||66,508||67,177
+
|8|| 5/8”|| 244|| 204
 
|-
 
|-
!Group
+
|10|| 5/8”|| 306|| 255
|10||8||2||6||13.75||13.08||18.92||65,179||65,930||64,702||65,346
+
|}
 +
 
 +
===751.22.3.5 Strands at Girder Ends===
 +
 
 +
A portion of the prestressing strands at girder ends, sufficient to resist positive moments over the bents, shall be projected into integral end bents and closed or open concrete intermediate diaphragms (continuous superstructure). This strand projection is shown on the standard drawings for [https://www.modot.org/prestressed-i-girders-psi prestressed girders] similar to the following detail.
 +
 
 +
The detail on the standard drawing shall be modified appropriately when the ends of girders are located inside concrete end diaphragms or with a change in girder height at closed concrete intermediate diaphragms. See Structural Project Manager for preference on modifying this detail when either the end bent or intermediate bent is not applicable for the span.
 +
[[image:751.22.3.5.jpg|center|850px]]
 +
{| style="margin: 1em auto 1em auto"
 
|-
 
|-
!II
+
|align="left|'''<font color = "grass">(a)</font color = "grass">''' Use 3'-0" projection for NU girders.<br/>'''<font color = "grass">(b)</font color = "grass">''' #5 bars typical at each layer of bent-up strands at intermediate bents.
|11||10||2||8||14.08||13.08||18.92||65,659||66,415||65,114||65,762
+
|}
|-
 
|&nbsp;||12||12||2||10||13.88||13.08||18.92||66,014||66,776||65,421||66,072
 
|-
 
|&nbsp;||13||14||4||10||13.48||14.08||17.92||66,366||67,134||65,724||66,379
 
|-
 
|&nbsp;||14||16||4||12||13.75||12.08||17.92||66,614||67,386||65,938||66,597
 
|-
 
|&nbsp;||15||18||6||12||13.75||11.08||16.92||66,776||67,552||66,079||66,740
 
|-
 
|&nbsp;||16||20||6||14||13.37||11.08||16.92||67,020||67,799||66,290||66,954
 
|-
 
|&nbsp;||17||22||6||16||12.83||11.08||16.92||67,178||67,961||66,427||67,095
 
|-
 
|&nbsp;||18||24||8||16||12.83||10.08||15.92||67,270||68,056||66,508||67,177
 
|}
 
  
 +
Actual strand arrangement, quantity of bent-up strands and debonding (if any) shall be determined by design.
  
'''Section Properties'''<br/>
+
Tables below show the minimum number of bent-up strands at the bottom of girder ends adequate to resist a positive moment over the bents.
'''Beam Type 3 -- 7" Web'''
+
{|border="1" cellpadding="5" style="text-align: center;" align="center"
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|420.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
 
|-
 
|-
|&nbsp;||T||=||total number of strands
+
|rowspan="2"|WEB<br/>THICKNESS<br/>(INCHES)||colspan="5"|NUMBER OF BOTTOM STRANDS FOR POSITIVE MOMENT CONNECTION<sup>'''1'''</sup>
 
|-
 
|-
|&nbsp;||H||=||number of harped strands
+
|BEAM TYPE 2|| BEAM TYPE 3|| BEAM TYPE 4|| BEAM TYPE 6|| BEAM TYPE 7<br/>(BULB-TEE)
 
|-
 
|-
|&nbsp;||S||=||number of straight strands
+
|6|| 6|| 6|| 8|| ---|| 12
|}
 
 
|-
 
|-
|align="right"|Section <math>\, Y_b</math> =
+
|6-1/2|| ---|| ---|| ---|| 10|| ---
|align="center"|17.31||in
 
 
|-
 
|-
|align="right"| <math>\, I_{nontransformed}</math> =
+
|7<sup>'''2'''</sup> || 6|| 8|| 8|| ---|| ---
|align="center"|66,991||in<sup>4</sup>
 
 
|-
 
|-
|align="right"|Depth=
+
|7-1/2<sup>'''3'''</sup> || ---|| ---|| ---|| 12|| ---
|align="center"|39||in
 
 
|-
 
|-
|align="right"|Strand Size=
+
|8<sup>'''2'''</sup> || 6|| 8|| 10|| ---|| ---
|align="center"|½||in
 
 
|-
 
|-
|align="right"| <math>\, f'_{ci}</math> =
+
|8-1/2<sup>'''3'''</sup> || ---|| ---|| ---|| 12|| ---
|align="center"|4.5||ksi
 
 
|-
 
|-
|align="right"| <math>\, f'_c</math> =
+
|colspan="6" align="left"|<sup>'''1'''</sup> If available. Otherwise, bend all bottom strands.<br/><sup>'''2'''</sup> Modified Beam Type 2, 3 or 4.<br/><sup>'''3'''</sup>  Modified Beam Type 6.
|align="center"|6||ksi
 
 
|}
 
|}
  
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
+
{|border="1" cellpadding="5" style="text-align: center;" align="center"
 
 
!Cont.
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
 
|-
 
!valign="top"|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||13.31||14.31||17.69||70,343||71,077||69,865||70,493
 
 
|-
 
|-
!I
+
|colspan="2"|NUMBER OF BOTTOM STRANDS FOR POSITIVE MOMENT CONNECTION<sup>'''1'''</sup>
|2||10||4||6||13.98||14.31||17.69||70,838||71,577||70,289||70,922
 
 
|-
 
|-
|&nbsp;||3||12||4||8||13.81||14.31||17.69||71,207||71,951||70,607||71,243
+
|NU 35, 43 and 53|| 10
 
|-
 
|-
|&nbsp;||4||14||6||8||13.81||13.31||16.69||71,469||72,218||70,833||71,473
+
|NU 63, 70 and 78|| 12
 
|-
 
|-
|&nbsp;||5||16||6||10||13.71||13.31||16.69||71,832||72,585||71,146||71,789
+
|colspan="2" align="left"|<sup>'''1'''</sup>  If available. Otherwise, bend all bottom strands.
|-
 
|&nbsp;||6||18||8||10||13.71||12.31||15.69||72,004||72,760||71,295||71,940
 
|-
 
|&nbsp;||7||20||8||12||13.31||12.31||15.69||72,259||73,019||71,516||72,164
 
|-
 
|&nbsp;||8||22||8||14||12.74||12.31||15.69||72,427||73,190||71,662||72,312
 
|-
 
|&nbsp;||9||24||10||14||12.74||11.31||14.69||72,526||73,292||71,749||72,401
 
|-
 
!Group
 
|10||8||2||6||13.98||13.31||18.69||70,343||71,077||69,865||70,493
 
|-
 
!II
 
|11||10||2||8||14.31||13.31||18.69||70,838||71,577||70,289||70,922
 
|-
 
|&nbsp;||12||12||2||10||14.11||13.31||18.69||71,207||71,951||70,607||71,243
 
|-
 
|&nbsp;||13||14||4||10||13.71||14.31||17.69||71,572||72,322||70,922||71,562
 
|-
 
|&nbsp;||14||16||4||12||13.98||12.31||17.69||71,832||72,585||71,146||71,789
 
|-
 
|&nbsp;||15||18||6||12||13.98||11.31||16.69||72,004||72,760||71,295||71,940
 
|-
 
|&nbsp;||16||20||6||14||13.60||11.31||16.69||72,259||73,019||71,516||72,164
 
|-
 
|&nbsp;||17||22||6||16||13.06||11.31||16.69||72,427||73,190||71,662||72,312
 
|-
 
|&nbsp;||18||24||8||16||13.06||10.31||15.69||72,526||73,292||71,749||72,401
 
 
|}
 
|}
  
 +
===751.22.3.6 Camber, Haunching, and Stepping and Sloping of Top Flange===
  
'''Section Properties'''<br/>
+
'''Camber'''
'''Beam Type 3 -- 8" Web'''
 
  
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
Compute theoretical camber of girder at 90 days and show on the plan as a “Theoretical camber of girder after erection (Estimated at 90 days)". Compute theoretical camber of girder at 7 days and show on the plan as a “Theoretical camber of girder after strand release (Estimated at 7 days)".  Camber shall be reported to the nearest 1/8 inch.
  
|align="right"|Section Area =
+
Theoretical camber of prestressed girders after erection are estimated at 90 days for typical projects. While some projects may require prestressed girders to be erected in less than 90 days in order to meet fast construction timelines or emergency repair requirements, using less than 90 days (i.e, 45 or 60) would potentially result in lower camber estimates and higher beam seat elevations. The cost risk is believed to be greater for underestimating the camber since it may require an increase in final grade. Due to the risk in underestimating camber and the multitude of variables that affect the actual camber (variability in predicting concrete modulus of elasticity, coarse aggregate effect on initial concrete modulus of elasticity, actual concrete strength, differential temperature at strand release, etc…) the 90 day estimate should be adequate for most projects.
|align="center"|459.9||in<sup>2</sup>
+
 
|rowspan="4"|&nbsp;
+
<div id="Sample detail"></div>
{|border="0" cellpadding="0"
+
 
|NOTE:||#||=||strand pattern number
+
Sample detail:
|-
+
 
|&nbsp;||T||=||total number of strands
+
[[image: 751.22.3.8 camber 2013.jpg|center|850px]]
 +
 
 +
Show conversion factors for girder camber with camber diagram as per [[751.50 Standard Detailing Notes#(H2c6.1)|EPG 751.50 H2c6.1]].
 +
 
 +
Note: The example shows Dimension A as greater than Dimension C. When Dimension A is less than Dimension C, modify detail to show this correctly keeping definitions of Dimensions A and C the same.  MS Cells are given for each case.
 +
 
 +
'''Haunching'''
 +
 
 +
Haunching for a prestressed bridge is the distance between the top of the girder or spread beam and the bottom of the slab.
 +
 
 +
Haunching shall be computed at quarter (1/4) points for bridges with spans less than 75 feet, and at tenth (1/10) points for span 75 feet and longer. Haunching shall be reported to the nearest 1/8 inch. A typical theoretical slab haunching diagram as shown below shall be provided on all prestressed I-girder and spread prestressed beam bridges.
 +
 
 +
For full depth cast-in-place decks using conventional or SIP forms, a minimum haunch of one inch at the centerline of girder and 1/2 inch at the edge of the flange shall be provided to allow for construction tolerances and normal concrete variations. The minimum haunch may need to be increased for Type 7 and 8 girders, NU girders and spread beams. See the Structural Project Manager or Structural Liaison Engineer for full depth cast-in-place decks. 
 +
 
 +
For the same reasons the following minimum haunch shall be provided for precast prestressed panel deck slabs:
 +
 
 +
:1 1/8” for Type 2, 3 and 4 girders
 +
:1 1/4” for Type 6 girders
 +
:1 1/2” for Type 7 and 8 girders (bulb-tee), NU girders, and spread beams.
 +
 
 +
A minimum of one inch shall be made available below the precast prestressed panels to allow for adequate flow of concrete below the panel. This is accomplished by specifying the placement of one-inch minimum joint filler thickness under all panels. 
 +
 
 +
The following maximum haunch at the centerline of the girder is allowed when prestressed panels are used:
 +
 
 +
:2 1/2" for Type 2, 3 and 4 girders
 +
:4 1/2” for Type 6, 7 and 8 girders, NU girders, and spread beams.
 +
 
 +
These limits are ½” greater than the maximum allowable joint filler. This buffer allows for using the maximum joint filler on both sides of the girder flange while requiring minimal additional slab depth on the high side for a two-percent cross-sloped deck. The minimum 8½” slab isn’t possible at these limits even when varying the joint filler. The maximum joint filler thickness to be used for supporting panels shall be 2 inches for Type 2, 3 and 4 girders or 4 inches for Type 6, 7 and 8 girders, NU girders, and spread beams; the remaining haunch thickness will be addressed by varying the slab thickness.
 +
 
 +
Prestressed panels shall not be used when the maximum haunch exceeds the above limits. The top flange may be stepped within the limits specified below to make panels a viable option.
 +
 
 +
There is no maximum haunch for full depth cast-in-place decks using conventional or SIP forms but additional hairpin bars may be required in accordance with [[751.10_General_Superstructure#751.10.1.14_Girder_and_Beam_Haunch_Reinforcement|EPG 751.10.1.14 Girder and Beam Haunch Reinforcement]].
 +
 +
Sample detail:
 +
 
 +
[[Image:751.22.3.8 haunch.jpg|center|925px]]
 +
 
 +
'''Stepping of Top Flange'''
 +
 +
Flange steps shall be provided on prestressed girders and spread beams with precast prestressed panels as shown below to keep the haunch at centerline of girder from exceeding 2 1/2 inches for Type 2, 3 and 4 girders or exceeding 4 1/2 inches for Type 6, 7 and 8 girders, NU girders, and spread beams. The minimum step height shall be 1/2 inch with 1/2-inch increments. Designer shall check to ensure the panels can clear the flange steps by a minimum of one inch assuming the maximum change in joint filler thickness between adjacent eight-foot prestressed panels along the length of the beam is 1/2 inch.
 +
 
 +
<center>
 +
<table>
 +
<tr>
 +
<td>
 +
{|border="0" cellpadding="5" style="text-align: center;"
 
|-
 
|-
|&nbsp;||H||=||number of harped strands
+
| style="width: 400px;" | [[Image:751.22.3.6-part_elevation_girder-Feb-23.jpg|350px]]
 +
| style="width: 150px;" | [[Image:751.22.3.6-section_AA-Feb-23.jpg|100px]]
 
|-
 
|-
|&nbsp;||S||=||number of straight strands
+
| PART ELEVATION OF GIRDER
 +
| SECTION A-A
 
|}
 
|}
 +
</td>
 +
<td>
 +
{| border="1" style=text-align:center
 
|-
 
|-
|align="right"|Section <math>\, Y_b</math> =
+
| colspan="3" | Maximum Total Increase to Top Flange Depth X”
|align="center"|17.49||in
 
 
|-
 
|-
|align="right"| <math>\, I_{nontransformed}</math> =
+
| Beam Type
|align="center"|72,106||in<sup>4</sup>
+
| Preferred
 +
| Absolute
 
|-
 
|-
|align="right"|Depth=
+
| 2, 3 & 4
|align="center"|39||in
+
| 3"
 +
| 6"
 
|-
 
|-
|align="right"|Strand Size=
+
| 6
|align="center"|½||in
+
| 3"
 +
| 6"
 
|-
 
|-
|align="right"| <math>\, f'_{ci}</math> =
+
| 7 & 8
|align="center"|4.5||ksi
+
| 3"
 +
| 6"
 +
|-
 +
| NUs
 +
| 4"
 +
| 6"
 +
|-
 +
| Box
 +
| 3"
 +
| 6"
 
|-
 
|-
|align="right"| <math>\, f'_c</math> =
 
|align="center"|6||ksi
 
 
|}
 
|}
 +
{|
 +
|Consult SPM or SLE before exceeding the preferred</br>limits. Signifcant additional fabrication costs are</br>likely above the preferred limits.
 +
|-
 +
|The top horizontal legs of WWR6 will need to be</br>removed for a flange depth increase greater than 4¾”.
 +
|}
 +
</td>
 +
</tr>
 +
</table>
 +
</center>
 +
<center>'''Girder Top Flange Step Example and Maximum Total Increase to Top Flange'''</center>
  
 +
'''Sloping Top Flange'''
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
+
Tops of girders and spread beams, for bridges with a superelevation of more than 2 percent, shall be sloped across the top flange to match the superelevation as shown below. The minimum thickness of the top flange and the overall height at the minimum point shall match the top flange thickness and height of the girder or spread beam used in design.
  
!Cont.
+
Type 7 and 8 girders, NU girders, and spread beams with top flanges exceeding a 4 percent cross-slope may experience sweep after form removal because of the unsymmetrical section and a resulting imbalanced prestressed load. It is recommended that the flange thickness be increased to only half of that required (but less than or equal to 4 percent cross-slope) and the height difference mitigated using thicker joint filler on the high side. If thicker joint filler cannot be fully used to compensate for the height difference, the extra load of a thicker slab must be accounted for in the design of the girders.  
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]
+
<center>
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
+
{|
 
|-
 
|-
!valign="top"|Span
+
|<center>[[Image:751.22.3.6-superelevation slope-Feb-23.jpg|200px]]</center>
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
+
| The change in flange thickness due to</br>superelevation shall be added to the</br>change due to beam steps when</br>considering the Maximum Total Increase</br>to Top Flange Depth X” specified above.
 
|-
 
|-
!Group
+
| colspan="2" style=text-align:center | '''Top Flange Slope with Superelevation'''
|1||8||4||4||13.49||14.49||17.51||75,470||76,191||74,990||75,607
 
|-
 
!I
 
|2||10||4||6||14.16||14.49||17.51||75,977||76,703||75,425||76,046
 
|-
 
|&nbsp;||3||12||4||8||13.99||14.49||17.51||76,357||77,087||75,752||76,376
 
|-
 
|&nbsp;||4||14||6||8||13.99||13.49||16.51||76,628||77,363||75,986||76,613
 
|-
 
|&nbsp;||5||16||6||10||13.89||13.49||16.51||77,002||77,740||76,308||76,939
 
|-
 
|&nbsp;||6||18||8||10||13.89||12.49||15.51||77,182||77,923||76,464||77,096
 
|-
 
|&nbsp;||7||20||8||12||13.49||12.49||15.51||77,446||78,191||76,692||77,328
 
|-
 
|&nbsp;||8||22||8||14||12.92||12.49||15.51||77,622||78,370||76,845||77,483
 
|-
 
|&nbsp;||9||24||10||14||12.92||11.49||14.51||77,728||78,479||76,938||77,577
 
|-
 
!Group
 
|10||8||2||6||14.16||13.49||18.51||75,470||76,191||74,990||75,607
 
|-
 
!II
 
|11||10||2||8||14.49||13.49||18.51||75,977||76,703||75,425||76,046
 
|-
 
|&nbsp;||12||12||2||10||14.29||13.49||18.51||76,357||77,087||75,752||76,376
 
|-
 
|&nbsp;||13||14||4||10||13.89||14.49||17.51||76,733||77,468||76,076||76,704
 
|-
 
|&nbsp;||14||16||4||12||14.16||12.49||17.51||77,002||77,740||76,308||76,939
 
|-
 
|&nbsp;||15||18||6||12||14.16||11.49||16.51||77,182||77,923||76,464||77,096
 
|-
 
|&nbsp;||16||20||6||14||13.78||11.49||16.51||77,446||78,191||76,692||77,328
 
|-
 
|&nbsp;||17||22||6||16||13.24||11.49||16.51||77,622||78,370||76,845||77,483
 
|-
 
|&nbsp;||18||24||8||16||13.24||10.49||15.51||77,728||78,479||76,938||77,577
 
 
|}
 
|}
 +
</center>
 +
 +
===751.22.3.7 Closed Concrete Intermediate Diaphragms===
 +
 +
Concrete intermediate diaphragms are cast between the ends of simple-span precast girders at interior supports and make the girders continuous for loads applied after continuity is established.
  
 +
Closed concrete diaphragms are easier to construct than open concrete and provide better protection to bearings and the top of the beam cap but shall only be used with bearings that typically don’t need future rehabilitation (plain and laminated neoprene pads).
  
'''Section Properties'''<br/>
+
Closed concrete diaphragms are typically used at fixed bents where the superstructure is pinned to the beam cap with dowel bars centered in 3- by 6-inch keys formed in the top of the beam cap. Closed diaphragms at fixed bents allow for a change in girder heights within a continuous girder series (not to exceed next available girder height and only when specified on design layout or by the Structural Project Manager).
'''Beam Type 4 -- 6" Web'''
 
  
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
With approval of the Structural Project Manager or Structural Liaison Engineer, closed concrete diaphragms may be used at bents free to expand longitudinally over the beam cap, completely separated by joint filler. This option may be useful in reducing forces transmitted to a stiff bent but may only be used with laminated neoprene bearing pads in accordance with expansion limits of these bearings. A change in girder height is not permissible in closed concrete diaphragm at expansion bents.
 +
 
 +
Details for skewed bents are shown below. The dimensions, reinforcement and guidance shown are also applicable to squared bents.
 +
 
 +
====751.22.3.7.1 Dimensions====
 +
The following dimensions shall be detailed on the plan sheets for closed concrete intermediate diaphragms.
 +
 +
[[image:751.22.3.7.1.1.jpg|center|650px]]
 +
:::[[image:751.22.3.7.1.2.jpg|left|440px]]
  
|align="right"|Section Area =
 
|align="center"|428.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|19.54||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|92,450||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|45||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|½||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|4.5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|6||ksi
 
|}
 
  
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
  
!Cont.
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
 
|-
 
!valign="top"|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||15.54||16.54||21.46||97,077||98,118||96,416||97,308
 
|-
 
!I
 
|2||10||4||6||16.21||16.54||21.46||97,727||98,775||96,974||97,872
 
|-
 
|&nbsp;||3||12||4||8||16.04||16.54||21.46||98,231||99,286||97,408||98,310
 
|-
 
|&nbsp;||4||14||6||8||16.04||15.54||20.46||98,608||99,669||97,733||98,640
 
|-
 
|&nbsp;||5||16||6||10||15.94||15.54||20.46||99,103||100,170||98,160||99,071
 
|-
 
|&nbsp;||6||18||8||10||15.94||14.54||19.46||99,368||100,441||98,390||99,305
 
|-
 
|&nbsp;||7||20||8||12||15.54||14.54||19.46||99,735||100,813||98,707||99,626
 
|-
 
|&nbsp;||8||22||8||14||14.97||14.54||19.46||99,995||101,078||98,933||99,856
 
|-
 
|&nbsp;||9||24||8||16||15.29||12.54||19.46||100,168||101,254||99,083||100,009
 
|-
 
|&nbsp;||10||26||10||16||15.29||11.54||18.46||100,271||101,360||99,174||100,102
 
|-
 
|&nbsp;||11||28||10||18||15.32||9.54||18.46||100,323||101,414||99,220||100,149
 
|-
 
!Group
 
|12||8||2||6||16.21||15.54||22.46||97,077||98,118||96,416||97,308
 
|-
 
!II
 
|13||10||2||8||16.54||15.54||22.46||97,727||98,775||96,974||97,872
 
|-
 
|&nbsp;||14||12||4||8||16.04||16.54||21.46||98,231||99,286||97,408||98,310
 
|-
 
|&nbsp;||15||14||4||10||15.94||16.54||21.46||98,730||99,792||97,838||98,745
 
|-
 
|&nbsp;||16||16||4||12||16.21||14.54||21.46||99,103||100,170||98,160||99,071
 
|-
 
|&nbsp;||17||16||6||10||15.94||15.54||20.46||99,103||100,170||98,160||99,071
 
|-
 
|&nbsp;||18||18||6||12||16.21||13.54||20.46||99,368||100,441||98,390||99,305
 
|-
 
|&nbsp;||19||20||6||14||15.83||13.54||20.46||99,735||100,813||98,707||99,626
 
|-
 
|&nbsp;||20||22||6||16||15.29||13.54||20.46||99,995||101,078||98,933||99,856
 
|-
 
|&nbsp;||21||24||6||18||15.32||11.54||20.46||100,168||101,254||99,083||100,009
 
|-
 
|&nbsp;||22||26||6||20||15.14||9.54||20.46||100,271||101,360||99,174||100,102
 
|-
 
|&nbsp;||23||26||8||18||15.32||10.54||19.46||100,271||101,360||99,174||100,102
 
|-
 
|&nbsp;||24||28||6||22||14.81||7.54||20.46||100,323||101,414||99,220||100,149
 
|-
 
|&nbsp;||25||28||8||20||15.14||8.54||19.46||100,323||101,414||99,220||100,149
 
|-
 
|&nbsp;||26||30||8||22||14.81||6.54||19.46||100,341||101,433||99,236||100,166
 
|-
 
|&nbsp;||27||32||8||24||14.37||4.54||19.46||100,342||101,435||99,238||100,168
 
|}
 
  
 +
'''Detailing Guidance: '''
  
'''Section Properties'''<br/>
+
<font color = "grass">Green items</font color = "grass"> are guidance and shall not be shown on plans.
'''Beam Type 4 -- 7" Web'''
 
  
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
See [[#751.22.3.7.3 End and Edge Details|EPG 751.22.3.7.3]] for edge and end details.
  
|align="right"|Section Area =
+
<font color = "grass">(a)</font color = "grass"> For curved alignments this dimension will need to be increased on one side and “(Min.)” needs to be added to the dimension in the section near diaphragm or the dimension replaced with “Varies”.
|align="center"|473.9||in<sup>2</sup>
+
 
|rowspan="4"|&nbsp;
+
<font color = "grass">(b)</font color = "grass"> Dimension based on a tangent alignment and 7 inches between the ends of girders. Will vary for curved alignments.
{|border="0" cellpadding="0"
+
 
|NOTE:||#||=||strand pattern number
+
<font color = "grass">(c)</font color = "grass"> 2'-6" unless skew requires wider diaphragm to accommodate coil tie rods
|-
+
{| style="margin: 1em auto 1em auto"
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
 
|-
 
|-
|&nbsp;||S||=||number of straight strands
+
|width=1000px|<font color = "white">---___________________________________________________________________________________________________</font color = "white">
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|19.82||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|100,400||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|45||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|½||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|4.5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|6||ksi
 
 
|}
 
|}
 +
====751.22.3.7.2 Reinforcement====
 +
The reinforcement shall be detailed on the plan sheets for closed concrete intermediate diaphragms as shown below except:
 +
:* Bar marks revised as required.
 +
:* Abbreviations used as required.
 +
:* Add "(Typ.)" to dimensions and leader notes as appropriate.
 +
 +
All U bar reinforcement shall use stirrup bends.
 +
 +
All reinforcement in diaphragms shall be epoxy coated, except coating of dowel bars shall match the coating of intermediate bent reinforcement.
 +
 +
Coil ties and rods shall also be shown in the section near the diaphragm and the horizontal section near the top of diaphragm in accordance with [[#751.22.3.10 Coil Inserts and Tie Rods|EPG 751.22.3.10 Coil Inserts and Tie Rods]].
 +
 +
Unless specified the details shown are for the same girder heights within a continuous girder series.
 +
 +
'''I Girders Type 2, 3, 4 and 6'''
 +
[[image:751.22.3.7.2_I_Girders1.jpg|700px|center]]
 +
[[image:751.22.3.7.2_I_Girders2.jpg|700px|center]]
 +
 +
'''Bulb-Tee Girders Type 7 and 8'''
 +
[[image:751.22.3.7.2_BulbTee1.jpg|650px|center]]
 +
[[image:751.22.3.7.2_BulbTee2.jpg|700px|center]]
 +
 +
'''NU Girders'''
 +
 +
NU 53 girders are shown in the following details. The details for other NU girder types are similar.
 +
[[image:751.22.3.7.2_NU1.jpg|650px|center]]
 +
[[image:751.22.3.7.2_NU2.jpg|700px|center]]
 +
 +
'''Change in Girder Height'''
  
 +
The following details are based on I Girders Type 2, 3, 4 and 6. The details are appropriate for bulb-tee and NU girders by substituting the appropriate reinforcing details from above. The reinforcement is that of the taller girder with additional #6 bars located under the shorter girder. The section near the diaphragm shall be from the perspective of the shorter girders. The differences from uniform girder height details are highlighted.
 +
[[image:751.22.3.7.2_Change1.jpg|700px|center]]
 +
[[image:751.22.3.7.2_Change2.jpg|700px|center]]
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
+
====751.22.3.7.3 End and Edge Details====
 +
The end and edge details (standard cells in MicroStation) shall be provided on the plan sheets for closed concrete intermediate diaphragms. See [[#751.22.3.7.1 Dimensions|EPG 751.22.3.7.1 Dimensions]] for location of the corresponding detail circles
 +
 +
[[image:751.22.3.7.3.jpg|650px|center]]
  
!Cont.
+
====751.22.3.7.4 Bent Details====
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
The following details are required for closed concrete intermediate diaphragms and shall be provided on the plan sheets for intermediate bents as shown below.
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]
+
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
+
'''Dowel Bars and Keys'''
|-
 
!valign="top"|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||15.82||16.82||21.18||105,048||106,065||104,384||105,256
 
|-
 
!I
 
|2||10||4||6||16.49||16.82||21.18||105,719||106,743||104,960||105,837
 
|-
 
|&nbsp;||3||12||4||8||16.32||16.82||21.18||106,242||107,272||105,410||106,291
 
|-
 
|&nbsp;||4||14||6||8||16.32||15.82||20.18||106,636||107,671||105,750||106,635
 
|-
 
|&nbsp;||5||16||6||10||16.22||15.82||20.18||107,151||108,192||106,193||107,083
 
|-
 
|&nbsp;||6||18||8||10||16.22||14.82||19.18||107,431||108,476||106,436||107,328
 
|-
 
|&nbsp;||7||20||8||12||15.82||14.82||19.18||107,815||108,866||106,768||107,664
 
|-
 
|&nbsp;||8||22||8||14||15.25||14.82||19.18||108,090||109,145||107,007||107,906
 
|-
 
|&nbsp;||9||24||8||16||15.57||12.82||19.18||108,275||109,334||107,168||108,070
 
|-
 
|&nbsp;||10||26||10||16||15.57||11.82||18.18||108,388||109,449||107,266||108,171
 
|-
 
|&nbsp;||11||28||10||18||15.60||9.82||18.18||108,446||109,510||107,318||108,224
 
|-
 
!Group
 
|12||8||2||6||16.49||15.82||22.18||105,048||106,065||104,384||105,256
 
|-
 
!II
 
|13||10||2||8||16.82||15.82||22.18||105,719||106,743||104,960||105,837
 
|-
 
|&nbsp;||14||12||4||8||16.32||16.82||21.18||106,242||107,272||105,410||106,291
 
|-
 
|&nbsp;||15||14||4||10||16.22||16.82||21.18||106,760||107,796||105,857||106,742
 
|-
 
|&nbsp;||16||16||4||12||16.49||14.82||21.18||107,151||108,192||106,193||107,083
 
|-
 
|&nbsp;||17||16||6||10||16.22||15.82||20.18||107,151||108,192||106,193||107,083
 
|-
 
|&nbsp;||18||18||6||12||16.49||13.82||20.18||107,431||108,476||106,436||107,328
 
|-
 
|&nbsp;||19||20||6||14||16.11||13.82||20.18||107,815||108,866||106,768||107,664
 
|-
 
|&nbsp;||20||22||6||16||15.57||13.82||20.18||108,090||109,145||107,007||107,906
 
|-
 
|&nbsp;||21||24||6||18||15.60||11.82||20.18||108,275||109,334||107,168||108,070
 
|-
 
|&nbsp;||22||26||6||20||15.42||9.82||20.18||108,388||109,449||107,266||108,171
 
|-
 
|&nbsp;||23||26||8||18||15.60||10.82||19.18||108,388||109,449||107,266||108,171
 
|-
 
|&nbsp;||24||28||6||22||15.09||7.82||20.18||108,446||109,510||107,318||108,224
 
|-
 
|&nbsp;||25||28||8||20||15.42||8.82||19.18||108,446||109,510||107,318||108,224
 
|-
 
|&nbsp;||26||30||8||22||15.09||6.82||19.18||108,469||109,533||107,338||108,245
 
|-
 
|&nbsp;||27||32||8||24||14.65||4.82||19.18||108,472||109,537||107,341||108,248
 
|}
 
  
 +
The dowel bars and keys are required at fixed bents and shall be shown in the plan of beam showing reinforcement and in a section thru key detail (standard cell in MicroStation). For the sake of clarity only the keys (not the dowel bars) are shown in the plan of beam (plan showing joint filler). For the sake of clarity neither the dowel bars nor keys are shown in the elevation of the bent.
 +
[[image:751.22.3.7.4.1.jpg|650px|center]]
  
'''Section Properties'''<br/>
+
Dowel bars shall be determined by design in accordance with [[#751.22.2.7 Dowel Bars|EPG 751.22.2.7 Dowel Bars]]. The minimum reinforcement is #6 bars at 12-inch centers.
'''Beam Type 4 -- 8" Web'''
 
  
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
'''Joint Filler and Bearings'''
  
|align="right"|Section Area =
+
The joint filler required for closed concrete intermediate diaphragms shall be shown in the plan of beam along with the bearings and girder chairs.
|align="center"|518.9||in<sup>2</sup>
+
:'''- At Fixed Bents'''
|rowspan="4"|&nbsp;
+
[[image:751.22.3.7.4.2.jpg|650px|center]]
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|20.06||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|108,288||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|45||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|½||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|4.5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|6||ksi
 
|}
 
  
 +
:Detailing guidance follows expansion bent details.
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
+
See [[751.11 Bearings#751.11.3.6 Girder/Beam Chairs|EPG 751.11.3.6 Girder/Beam Chairs]] for additional girder chair details.
 +
:'''- At Expansion Bents'''
 +
[[image:751.22.3.7.4-3.png|center]]
 +
<center>'''<big>PLAN OF BEAM</big>'''</center>
 +
:'''Detailing Guidance:'''
  
!Cont.
+
:<span style="color:green; font-weight:bold;">Green items</span> are guidance and shall not be shown on plans.
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]
+
:<span style="color:green; font-weight:bold;">(a)</span> For curved alignments, this dimension will need to be increased on one side.
|colspan="2"|[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
 
|-
 
!valign="top"|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||16.06||17.06||20.94||112,955||113,952||112,289||113,143
 
|-
 
!I
 
|2||10||4||6||16.73||17.06||20.94||113,645||114,648||112,881||113,739
 
|-
 
|&nbsp;||3||12||4||8||16.56||17.06||20.94||114,185||115,193||113,345||114,208
 
|-
 
|&nbsp;||4||14||6||8||16.56||16.06||19.94||114,594||115,607||113,698||114,563
 
|-
 
|&nbsp;||5||16||6||10||16.46||16.06||19.94||115,126||116,144||114,156||115,026
 
|-
 
|&nbsp;||6||18||8||10||16.46||15.06||18.94||115,419||116,442||114,409||115,282
 
|-
 
|&nbsp;||7||20||8||12||16.06||15.06||18.94||115,818||116,846||114,755||115,631
 
|-
 
|&nbsp;||8||22||8||14||15.49||15.06||18.94||116,107||117,138||115,004||115,884
 
|-
 
|&nbsp;||9||24||8||16||15.81||13.06||18.94||116,303||117,337||115,175||116,057
 
|-
 
|&nbsp;||10||26||10||16||15.81||12.06||17.94||116,424||117,461||115,281||116,165
 
|-
 
|&nbsp;||11||28||10||18||15.84||10.06||17.94||116,489||117,528||115,338||116,223
 
|-
 
!Group
 
|12||8||2||6||16.73||16.06||21.94||112,955||113,952||112,289||113,143
 
|-
 
!II
 
|13||10||2||8||17.06||16.06||21.94||113,645||114,648||112,881||113,739
 
|-
 
|&nbsp;||14||12||4||8||16.56||17.06||20.94||114,185||115,193||113,345||114,208
 
|-
 
|&nbsp;||15||14||4||10||16.46||17.06||20.94||114,720||115,734||113,806||114,673
 
|-
 
|&nbsp;||16||16||4||12||16.73||15.06||20.94||115,126||116,144||114,156||115,026
 
|-
 
|&nbsp;||17||16||6||10||16.46||16.06||19.94||115,126||116,144||114,156||115,026
 
|-
 
|&nbsp;||18||18||6||12||16.73||14.06||19.94||115,419||116,442||114,409||115,282
 
|-
 
|&nbsp;||19||20||6||14||16.35||14.06||19.94||115,818||116,846||114,755||115,631
 
|-
 
|&nbsp;||20||22||6||16||15.81||14.06||19.94||116,107||117,138||115,004||115,884
 
|-
 
|&nbsp;||21||24||6||18||15.84||12.06||19.94||116,303||117,337||115,175||116,057
 
|-
 
|&nbsp;||22||26||6||20||15.66||10.06||19.94||116,424||117,461||115,281||116,165
 
|-
 
|&nbsp;||23||26||8||18||15.84||11.06||18.94||116,424||117,461||115,281||116,165
 
|-
 
|&nbsp;||24||28||6||22||15.33||8.06||19.94||116,489||117,528||115,338||116,223
 
|-
 
|&nbsp;||25||28||8||20||15.66||9.06||18.94||116,489||117,528||115,338||116,223
 
|-
 
|&nbsp;||26||30||8||22||15.33||7.06||18.94||116,515||117,555||115,361||116,247
 
|-
 
|&nbsp;||27||32||8||24||14.89||5.06||18.94||116,520||117,560||115,366||116,252
 
|}
 
  
 +
:<span style="color:green; font-weight:bold;">(b)</span> Dimension based on a tangent alignment and 7 inches between the ends of girders. Will vary for curved alignments.
  
'''Section Properties'''<br/>
+
:<span style="color:green; font-weight:bold;">(c)</span> W" is width of bearing and is equal to width of bottom flange minus 1½ inches. Bearing length and thickness is by design.  
'''Beam Type 6 -- 6.5" Web'''
 
  
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
:<span style="color:green; font-weight:bold;">(d)</span> 3¾" minimum for #4 stirrups in beam and 5¼" minimum for #5 or #6 stirrups in beam, except diaphragm width shall not be less than 2’-6”.  Make diaphragm flush with beams less than three feet wide.
  
|align="right"|Section Area =
+
:<span style="color:green; font-weight:bold;">(e)</span> Remove thickness for tapered bearings.
|align="center"|643.6||in<sup>2</sup>
+
 
|rowspan="4"|&nbsp;
+
===751.22.3.8 Open Concrete Intermediate Diaphragms===
{|border="0" cellpadding="0"
+
Concrete intermediate diaphragms are cast between the ends of simple-span precast girders at interior supports and make the girders continuous for loads applied after continuity is established.
|NOTE:||#||=||strand pattern number
+
 
|-
+
Open concrete diaphragms allow clearance for jacks required for future bearing rehabilitation and therefore should be used at girder ends with bearing assemblies (laminated neoprene, Type N PTFE, Pot and Disc bearings).
|&nbsp;||T||=||total number of strands
+
 
|-
+
Details for skewed bents are shown below. The dimensions, reinforcement and guidance shown are also applicable to squared bents.
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|25.92||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|235,735||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|54||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|½||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|4.5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|6||ksi
 
|}
 
  
 +
====751.22.3.8.1 Dimensions====
 +
The following dimensions shall be detailed on the plan sheets for open concrete intermediate diaphragms.
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
+
[[image:751.22.3.8.1.1.jpg|650px|center]]
 +
[[image:751.22.3.8.1.2.jpg|650px|center]]
 +
 +
====751.22.3.8.2 Reinforcement====
 +
The reinforcement shall be detailed on the plan sheets for open concrete intermediate diaphragms as shown below except:
 +
:* Bar marks revised as required.
 +
:* Abbreviations used as required.
 +
:* Add "(Typ.)" to dimensions and leader notes as appropriate.
  
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]||[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
+
All U bar reinforcement shall use stirrup bends.
|-
 
|&nbsp;||#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#6||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||14||4||10||23.52||22.92||23.08||248,115||246,353
 
|-
 
!I
 
|2||16||4||12||23.25||22.92||23.08||249,115||247,213
 
|-
 
|&nbsp;||3||18||6||12||23.25||21.92||22.08||249,933||247,918
 
|-
 
|&nbsp;||4||20||6||14||23.06||21.92||22.08||250,920||248,769
 
|-
 
|&nbsp;||5||22||6||16||22.92||21.92||22.08||251,901||249,616
 
|-
 
|&nbsp;||6||24||8||16||22.92||20.92||21.08||252,545||250,173
 
|-
 
|&nbsp;||7||26||8||18||22.59||20.92||21.08||253,342||250,862
 
|-
 
|&nbsp;||8||28||8||20||22.32||20.92||21.08||254,133||251,547
 
|-
 
|&nbsp;||9||30||10||20||22.32||19.92||20.08||254,626||251,975
 
|-
 
|&nbsp;||10||32||10||22||22.10||19.92||20.08||255,408||252,653
 
|-
 
|&nbsp;||11||34||10||24||21.75||19.92||20.08||256,032||253,195
 
|-
 
|&nbsp;||12||36||10||26||21.46||19.92||20.08||256,651||253,734
 
|-
 
|&nbsp;||13||38||12||26||21.46||18.92||19.08||257,011||254,048
 
|}
 
  
 +
All reinforcement in diaphragms shall be epoxy coated.
  
'''Section Properties'''<br/>
+
Coil ties and rods shall also be shown in the section near the diaphragm and the horizontal section near the top of diaphragm in accordance with [[#751.22.3.10 Coil Inserts and Tie Rods|EPG 751.22.3.10 Coil Inserts and Tie Rods]].
'''Beam Type 6 -- 7.5" Web'''
 
  
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
'''I Girders Type 2, 3, 4 and 6'''
  
|align="right"|Section Area =
+
[[image:751.22.3.8.2_I_Girders1.jpg|750px|center]]
|align="center"|697.6||in<sup>2</sup>
+
[[image:751.22.3.8.2_I_Girders2.jpg|700px|center]]
|rowspan="4"|&nbsp;
+
 
{|border="0" cellpadding="0"
+
'''Bulb-Tee Girders Type 7 and 8'''
|NOTE:||#||=||strand pattern number
+
 
|-
+
[[image:751.22.3.8.2_BulbTee1.jpg|750px|center]]
|&nbsp;||T||=||total number of strands
+
[[image:751.22.3.8.2_BulbTee2.jpg|700px|center]]
|-
+
 
|&nbsp;||H||=||number of harped strands
+
'''NU Girders'''
|-
+
 
|&nbsp;||S||=||number of straight strands
+
NU 53 girders are shown in the following details. The details for other NU girder types are similar.
|}
+
[[image:751.22.3.8.2_NU1.jpg|750px|center]]
|-
+
[[image:751.22.3.8.2_NU2.jpg|700px|center]]
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|26.00||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|248,915||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|54||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|½||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|4.5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|6||ksi
 
|}
 
  
 +
===751.22.3.9 Concrete End Diaphragms===
 +
End diaphragms (either at end bents or at intermediate bents) are necessary where joints are required in a bridge superstructure. End diaphragms transfer loads at the end of slab to the girders and serve to tie girders together to better enable the bridge cross section to function as a unit. When end bent foundation can accommodate the expansion of the superstructure, the diaphragm can be constructed integral with the bent in accordance with [[751.35 Concrete Pile Cap Integral End Bents|EPG 751.35 Concrete Pile Cap Integral End Bents]].
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
+
Bearing assembles are typically required at end diaphragms and therefore, for the sake of future bearing rehabilitation, it is standard practice to detail as open-end diaphragms in accordance with the next two articles. The one exception is that a closed-end diaphragm may be detailed in accordance with [[#751.22.3.9.3 Closed Diaphragm|EPG 751.22.3.9.3]] at finger plate expansion device connected to a steel girder series.
  
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]||[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
+
Details for skewed bents are shown below. The dimensions, reinforcement and guidance shown are also applicable to squared bents.
|-
 
|&nbsp;||#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#6||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||14||4||10||23.60||23.00||23.00||262,852||260,864
 
|-
 
!I
 
|2||16||4||12||23.33||23.00||23.00||263,868||261,737
 
|-
 
|&nbsp;||3||18||6||12||23.33||22.00||22.00||264,701||262,454
 
|-
 
|&nbsp;||4||20||6||14||23.14||22.00||22.00||265,707||263,319
 
|-
 
|&nbsp;||5||22||6||16||23.00||22.00||22.00||266,706||264,180
 
|-
 
|&nbsp;||6||24||8||16||23.00||21.00||21.00||267,365||264,749
 
|-
 
|&nbsp;||7||26||8||18||22.67||21.00||21.00||268,178||265,452
 
|-
 
|&nbsp;||8||28||8||20||22.40||21.00||21.00||268,987||266,150
 
|-
 
|&nbsp;||9||30||10||20||22.40||20.00||20.00||269,493||266,589
 
|-
 
|&nbsp;||10||32||10||22||22.18||20.00||20.00||270,294||267,282
 
|-
 
|&nbsp;||11||34||10||24||21.83||20.00||20.00||270,933||267,836
 
|-
 
|&nbsp;||12||36||10||26||21.54||20.00||20.00||271,569||268,387
 
|-
 
|&nbsp;||13||38||12||26||21.54||19.00||19.00||271,941||268,712
 
|}
 
  
 +
Previous details showed the coping of the girders for the purpose of decreasing the length of the expansion device support piece. Alternatively, increasing the thickness of the support piece is a practical option. The standard support piece has been used with the details below for skew angles as large as 30 degrees. The method to account for an excessively long expansive device support piece shall be discussed with Structural Project Manager or Structural Liaison Engineer.
  
'''Section Properties'''<br/>
+
====751.22.3.9.1 Dimensions====
'''Beam Type 6 -- 8.5" Web'''
+
The following dimensions shall be detailed on the plan sheets for concrete end diaphragms.
 
   
 
   
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
[[image:751.22.3.9.1.1_2022.jpg|center|700px]]
 +
[[image:751.22.3.9.1.2_2022.jpg|center|700px]]
 +
[[image:751.22.3.9.1.3.jpg|center|650px]]
  
|align="right"|Section Area =
+
====751.22.3.9.2 Reinforcement====
|align="center"|751.6||in<sup>2</sup>
+
The reinforcement shall be detailed on the plan sheets for concrete end diaphragms as shown below except:
|rowspan="4"|&nbsp;
+
:* Bar marks revised as required.
{|border="0" cellpadding="0"
+
:* Abbreviations used as required.
|NOTE:||#||=||strand pattern number
+
:* Add "(Typ.)" to dimensions and leader notes as appropriate.
|-
+
 
|&nbsp;||T||=||total number of strands
+
All U bar reinforcement shall use stirrup bends.
|-
+
 
|&nbsp;||H||=||number of harped strands
+
All reinforcement in diaphragms shall be epoxy coated.
 +
 
 +
Coil ties and rods shall also be shown in the section near the diaphragm and the horizontal section near the top of diaphragm in accordance with [[#751.22.3.10 Coil Inserts and Tie Rods|EPG 751.22.3.10 Coil Inserts and Tie Rods]].
 +
 
 +
'''I Girders Type 2, 3, 4 and 6'''
 +
 +
[[image:751.22.3.9.2_IGirders1.jpg|center|750px]]
 +
[[image:751.22.3.9.2_IGirders2.jpg|center|700px]]
 +
 
 +
'''Bulb-Tee Girders Type 7 and 8'''
 +
 +
[[image:751.22.3.9.2_BulbTee1.jpg|center|750px]]
 +
[[image:751.22.3.9.2_BulbTee2.jpg|center|700px]]
 +
 
 +
'''NU Girders'''
 +
 
 +
NU 53 girders are shown in the following details. The details for other NU girder types are similar.
 +
 +
[[image:751.22.3.9.2_NU1.jpg|center|750px]]
 +
[[image:751.22.3.9.2_NU2.jpg|center|700px]]
 +
 
 +
====751.22.3.9.3 Closed Diaphragm====
 +
Use only when expansion device connects prestressed girder series and steel girder series, and laminated neoprene pads are used under the prestressed girders in accordance with expansion limits of these bearings and only with the approval of the Structural Project Manager or Structural Liaison Engineer.
 +
 
 +
The simplified detail below is for I girders. The actual details required on the plans can be developed for all girder types by substituting the dimensions and reinforcement of the corresponding section near the diaphragm detail of [[#751.22.3.7 Closed Concrete Intermediate Diaphragms|EPG 751.22.3.7]] and the dimensions from the corresponding Section A-A of [[#751.22.3.9.1 Dimensions|EPG 751.22.3.9.1 Dimensions]].
 +
 +
[[image:751.22.3.9.3_2022.jpg|center|650px]]
 +
 +
 
 +
===751.22.3.10 Coil Inserts and Tie Rods===
 +
Threaded rods (coil tie rods) installed in coil inserts (coil ties) that are cast into the ends of prestressed girders are provided to aid in transferring forces from the diaphragms into the girder ends. Additionally, coil tie rods are believed to provide some aid in resisting positive moment forces.
 +
 
 +
Coil ties and rods shall be detailed on the plan sheets for prestressed girders.
 +
 
 +
<center>
 +
{| border="1" class="wikitable" style="margin: 1em auto 1em auto" style="text-align:center"
 +
|+
 +
| style="background:#BEBEBE" width="300" |'''[http://www.modot.org/business/consultant_resources/bridgestandards.htm Bridge Standard Drawings]'''
 
|-
 
|-
|&nbsp;||S||=||number of straight strands
+
|align="center"|[https://www.modot.org/prestressed-i-girders-psi Prestressed I-Girders]
 
|}
 
|}
 +
</center>
 +
 +
Coil ties and coil tie rods shall be detailed on the plan sheets for concrete diaphragms as shown below. Girders and beams with coil ties and rods are available as standard cells under the concrete diaphragm tasks in MicroStation.
 +
 +
'''Closed Diaphragms'''
 +
 +
[[image:751.22.3.10_Closed1.jpg|center|700px]]
 +
[[image:751.22.3.10_Closed2.jpg|center|700px]]
 +
 +
:Detailing guidance follows open diaphragm details.
 +
 +
'''Open Diaphragms'''
 +
[[image:751.22.3.10_Open1.jpg|center|700px]]
 +
[[image:751.22.3.10_Open2.jpg|center|700px]]
 +
{| style="margin: 1em auto 1em auto"
 
|-
 
|-
|align="right"|Section <math>\, Y_b</math> =
+
| align="left|'''Detailing Guidance: '''
|align="center"|26.07||in
 
 
|-
 
|-
|align="right"| <math>\, I_{nontransformed}</math> =
+
| align="left|<font color = "grass">Green items</font color = "grass"> are guidance and shall not be shown on plans.
|align="center"|262,087||in<sup>4</sup>
 
 
|-
 
|-
|align="right"|Depth=
+
| align="left|Section A-A shows an intermediate diaphragm and I girders, but dimensions and coil tie orientation are applicable<br/>for end diaphragms and other prestressed girder types as well.
|align="center"|54||in
 
 
|-
 
|-
|align="right"|Strand Size=
+
|align="left width="750"|<font color = "grass">(a)</font color = "grass"> “Two” not required for end diaphragms.
|align="center"|½||in
 
 
|-
 
|-
|align="right"| <math>\, f'_{ci}</math> =
+
|align="left|<font color = "grass">(b)</font color = "grass"> “Two” not required for bulb-tee and NU girders.
|align="center"|4.5||ksi
+
|}
 +
 
 +
===751.22.3.11 Steel Intermediate Diaphragms===
 +
Use steel intermediate diaphragm for prestressed spans over 50 feet except for NU 35 and NU 43 girders.
 +
<center>
 +
{| border="1" class="wikitable" style="margin: 1em auto 1em auto" style="text-align:center"
 +
|+
 +
| style="background:#BEBEBE" width="300" |'''[http://www.modot.org/business/consultant_resources/bridgestandards.htm Bridge Standard Drawings]'''
 
|-
 
|-
|align="right"| <math>\, f'_c</math> =
+
|align="center"|[http://www.modot.org/business/standard_drawings2/diaphragms_new_title_block.htm Steel Intermediate Diaphragms]
|align="center"|6||ksi
 
 
|}
 
|}
 +
</center>
 +
 +
Use straight diaphragm normal to girders for skews thru 20°.
  
 +
Use stepped diaphragm for skews over 20°.
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
+
Spans of 90 feet or less require one intermediate diaphragm per span.
  
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]||[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
+
Spans over 90 feet require two intermediate diaphragms per span.
|-
+
 
|&nbsp;||#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>2-#6||A1 Bars<br/>2-#6
+
Spans over 140 feet require three intermediate diaphragms per span.
|-
+
 
!Group
+
Space diaphragms equally as allowed by clearance to harped strands.
|1||14||4||10||23.67||23.07||22.93||276,043||274,052
+
 
|-
+
Maximum spacing is 50 feet (from support and between diaphragms).
!I
+
 
|2||16||4||12||23.40||23.07||22.93||277,068||274,932
+
<u>NU 35 and NU 43 Girders</u>
|-
+
 
|&nbsp;||3||18||6||12||23.40||22.07||21.93||277,908||275,656
+
Permanent intermediate diaphragms are not required for NU 35 and NU 43 girders. Temporary intermediate diaphragms/bracing are required for construction of the bridge deck. See [[751.50 Standard Detailing Notes#(H2c2.2)|EPG 751.50 Note H2c2.2]].
|-
 
|&nbsp;||4||20||6||14||23.21||22.07||21.93||278,922||276,528
 
|-
 
|&nbsp;||5||22||6||16||23.07||22.07||21.93||279,930||277,396
 
|-
 
|&nbsp;||6||24||8||16||23.07||21.07||20.93||280,596||277,971
 
|-
 
|&nbsp;||7||26||8||18||22.74||21.07||20.93||281,418||278,680
 
|-
 
|&nbsp;||8||28||8||20||22.47||21.07||20.93||282,236||279,386
 
|-
 
|&nbsp;||9||30||10||20||22.47||20.07||19.93||282,750||279,831
 
|-
 
|&nbsp;||10||32||10||22||22.25||20.07||19.93||283,559||280,531
 
|-
 
|&nbsp;||11||34||10||24||21.90||20.07||19.93||284,207||281,093
 
|-
 
|&nbsp;||12||36||10||26||21.61||20.07||19.93||284,851||281,651
 
|-
 
|&nbsp;||13||38||12||26||21.61||19.07||18.93||285,230||281,981
 
|}
 
  
'''Section Properties'''<br/>
+
===751.22.3.12 Vent Holes===
'''Beam Type 7 -- 6" Web'''<br/>
 
'''Bulb-Tee Girder'''
 
  
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
+
::::Note:  Use vent holes on all stream crossing structures.
  
|align="right"|Section Area =
 
|align="center"|787.4||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|37.58||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|571,047||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|72.5||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|½||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|4.5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|6||ksi
 
|}
 
  
 +
<center>[[Image:751.22_Vent_Holes_Elevation_&_Section.gif]]</center>
  
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
+
{|border="0" cellpadding="5" align="center" style="text-align:center"
  
!Cont.
+
|width="300"|'''PART ELEVATION OF GIRDER'''
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||[[#e1, e2, e3, I_initial & I_final|I<sub>initial</sub>]]||[[#e1, e2, e3, I_initial & I_final|I<sub>final</sub>]]
+
|width="300"|'''PART SECTION NEAR VENT HOLE'''
|-
 
!valign="top|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final|e1]]||[[#e1, e2, e3, I_initial & I_final|e2]]||[[#e1, e2, e3, I_initial & I_final|e3]]||A1 Bars<br/>4-#6||A1 Bars<br/>4-#6
 
|-
 
!Group
 
|1||14||4||10||35.58||34.58||29.92||603,636||598,983
 
|-
 
!I
 
|2||16||4||12||35.25||34.58||29.92||606,025||601,033
 
|-
 
|&nbsp;||3||18||6||12||35.25||33.58||28.92||608,125||602,838
 
|-
 
|&nbsp;||4||20||6||14||35.01||33.58||28.92||610,490||604,871
 
|-
 
|&nbsp;||5||22||6||16||34.83||33.58||28.92||612,843||606,895
 
|-
 
|&nbsp;||6||24||8||16||34.83||32.58||27.92||614,652||608,453
 
|-
 
|&nbsp;||7||26||8||18||34.69||32.58||27.92||616,981||610,459
 
|-
 
|&nbsp;||8||28||8||20||34.58||32.58||27.92||619,299||612,457
 
|-
 
|&nbsp;||9||30||10||20||34.58||31.58||26.92||620,839||613,788
 
|-
 
|&nbsp;||10||32||10||22||34.31||31.58||26.92||622,864||615,536
 
|-
 
|&nbsp;||11||34||10||24||34.08||31.58||26.92||624,878||617,276
 
|-
 
|&nbsp;||12||36||10||26||33.89||31.58||26.92||626,881||619,009
 
|-
 
|&nbsp;||13||38||10||28||33.58||31.58||26.92||628,622||620,517
 
|-
 
|&nbsp;||14||40||12||28||33.58||30.58||25.92||629,902||621,627
 
|}
 
 
 
===751.22.3.5 Beam Section Properties Tables - Higher Concrete Strength===
 
 
 
<div id="e1, e2, e3, I_initial & I_final 1"></div>
 
The properties of prestressed I-girders in the following tables are valid for <math>\, f'_{ci}</math> = 5 ksi and <math>\, f'_c</math> = 7 ksi.  The modular ratio , ''<math>\, n</math>'', is 7 for the initial moment of inertia, <math>\, I_{initial}</math>, and 6 for the final moment of inertia, <math>\, I_{final}</math>.
 
  
Note: Moments of inertia, <math>\, I_{initial}</math> and <math>\, I_{final}</math> are computed based on transformed non-composite section and are used in camber calculations.  A1 Bar locations are assumed at 3" from the top of girder.
 
 
Definitions used in tables are:
 
{|border="0" cellpadding="5"
 
|Section Area||=||Gross area of girder, (in.<sup>2</sup>)
 
|-
 
|Section <math>\, Y_b</math> ||=||Distance from bottom of girder to center of gravity of non-transformed non-composite section, (in.)
 
|-
 
| <math>\, I_{nontransformed}</math> ||=||Moment of inertia of non-transformed non-composite section, (in.<sup>4</sup>)
 
|-
 
|Depth||=||Height of girder, (in.)
 
|-
 
|Strand size||=||Strand diameter, (in.)
 
|-
 
|e1*||=||Eccentricity between centroid of straight strands (CSS) and center of gravity of non-transformed non-composite section (CGB) as shown in figure below, (in.)
 
|-
 
|e2*||=||Eccentricity between centroid of harped strands (CHS) and center of gravity of non-transformed non-composite section (CGB) at midspan as shown in figure below, (in.)
 
|-
 
|e3*||=||Eccentricity between centroid of harped strands (CHS) and center of gravity of non-transformed non-composite section (CGB) at the end of girder as shown in figure below, (in.)
 
 
|}
 
|}
  
  
<math>\, *</math> A more accurate value can be used based on transformed non-composite section.  The final camber calculation will not be significantly different using values between transformed and non-transformed sections.
+
::::Note:  Place vent holes at or near upgrade of 1/3 point of girders and clear<br/>reinforcing steel or strands by 1-1/2" minimum and steel intermediate<br/>diaphragms bolt connection by 6" minimum.
 
 
 
<center>[[Image:751.22_Girder_Plan_showing_strands.gif]]</center>
 
 
 
 
 
'''Steps for detailing strand patterns from Prestressed Beam Tables'''
 
#For strand locations at mid-span of girder:  Look up the "Total Number of Strands" value for the corresponding strand pattern number.  The strands will then be located at that number and all numbers below that number.  Ex.  For 14 total strands, the strands will be placed at all locations numbered ≤14.
 
#For harped strand locations at end of girder:  Look up the "Number of Harped Strands" value for the corresponding strand pattern number.  The strands will then be located at that number and all numbers below that number.  Ex.  For 6 harped strands, the strands will be placed at all locations numbered ≤6.
 
 
 
 
<center>[[Image:751.22_Girder_Section_showing_strands.gif]]</center>
 
 
 
:::::::::::'''GROUP I'''
 
 
 
 
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 2 -- 6" Web'''
 
 
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|310.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|14.08||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|33,974||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|32||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" text-align="center"
 
 
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|align="center" colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]
 
|align="center" colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
|&nbsp;
 
|align="center"|#
 
|align="center"|T
 
|align="center"|H
 
|align="center"|S
 
|align="center"|[[#e1, e2, e3, I_initial & I_final 1|e1]]
 
|align="center"|[[#e1, e2, e3, I_initial & I_final 1|e2]]
 
|align="center"|[[#e1, e2, e3, I_initial & I_final 1|e3]]
 
|align="center"|A1 Bars<br/>2-#5
 
|align="center"|A1 Bars<br/>2-#6
 
|align="center"|A1 Bars<br/>2-#5
 
|align="center"|A1 Bars,<br/>2-#6
 
|-
 
!Group
 
|align="center"|1
 
|align="center"|8
 
|align="center"|4
 
|align="center"|4
 
|align="center"|11.08
 
|align="center"|11.08
 
|align="center"|13.92
 
|align="center"|36,407
 
|align="center"|36,838
 
|align="center"|36,062
 
|align="center"|36,429
 
|-
 
!I
 
|align="center"|2
 
|align="center"|10
 
|align="center"|4
 
|align="center"|6
 
|align="center"|11.41
 
|align="center"|11.08
 
|align="center"|13.92
 
|align="center"|36,828
 
|align="center"|37,265
 
|align="center"|36,424
 
|align="center"|36,797
 
|-
 
|&nbsp;
 
|align="center"|3
 
|align="center"|12
 
|align="center"|6
 
|align="center"|6
 
|align="center"|11.41
 
|align="center"|10.08
 
|align="center"|12.92
 
|align="center"|36,983
 
|align="center"|37,424
 
|align="center"|36,559
 
|align="center"|36,935
 
|-
 
|&nbsp;
 
|align="center"|4
 
|align="center"|14
 
|align="center"|6
 
|align="center"|8
 
|align="center"|11.08
 
|align="center"|10.08
 
|align="center"|12.92
 
|align="center"|37,265
 
|align="center"|37,711
 
|align="center"|36,804
 
|align="center"|37,183
 
|-
 
|&nbsp;
 
|align="center"|5
 
|align="center"|16
 
|align="center"|8
 
|align="center"|8
 
|align="center"|11.08
 
|align="center"|9.08
 
|align="center"|11.92
 
|align="center"|37,304
 
|align="center"|37,753
 
|align="center"|36,839
 
|align="center"|37,221
 
|-
 
|&nbsp;
 
|align="center"|6
 
|align="center"|18
 
|align="center"|8
 
|align="center"|10
 
|align="center"|10.48
 
|align="center"|9.08
 
|align="center"|11.92
 
|align="center"|37,465
 
|align="center"|37,917
 
|align="center"|36,980
 
|align="center"|37,364
 
|-
 
!Group
 
|align="center"|7
 
|align="center"|8
 
|align="center"|2
 
|align="center"|6
 
|align="center"|11.41
 
|align="center"|10.08
 
|align="center"|14.92
 
|align="center"|36,407
 
|align="center"|36,837
 
|align="center"|36,061
 
|align="center"|36,429
 
|-
 
!II
 
|align="center"|8
 
|align="center"|10
 
|align="center"|2
 
|align="center"|8
 
|align="center"|11.58
 
|align="center"|10.08
 
|align="center"|14.92
 
|align="center"|36,829
 
|align="center"|37,265
 
|align="center"|36,425
 
|align="center"|36,797
 
|-
 
|&nbsp;
 
|align="center"|9
 
|align="center"|12
 
|align="center"|4
 
|align="center"|8
 
|align="center"|11.08
 
|align="center"|11.08
 
|align="center"|13.92
 
|align="center"|37,112
 
|align="center"|37,553
 
|align="center"|36,670
 
|align="center"|37,046
 
|-
 
|&nbsp;
 
|align="center"|10
 
|align="center"|14
 
|align="center"|4
 
|align="center"|10
 
|align="center"|11.28
 
|align="center"|9.08
 
|align="center"|13.92
 
|align="center"|37,265
 
|align="center"|37,711
 
|align="center"|36,804
 
|align="center"|37,183
 
|-
 
|&nbsp;
 
|align="center"|11
 
|align="center"|16
 
|align="center"|6
 
|align="center"|10
 
|align="center"|11.28
 
|align="center"|8.08
 
|align="center"|12.92
 
|align="center"|37,304
 
|align="center"|37,753
 
|align="center"|36,839
 
|align="center"|37,221
 
|-
 
|&nbsp;
 
|align="center"|12
 
|align="center"|18
 
|align="center"|6
 
|align="center"|12
 
|align="center"|10.75
 
|align="center"|8.08
 
|align="center"|12.92
 
|align="center"|37,466
 
|align="center"|37,918
 
|align="center"|36,981
 
|align="center"|37,365
 
|-
 
|&nbsp;
 
|align="center"|13
 
|align="center"|20
 
|align="center"|6
 
|align="center"|14
 
|align="center"|10.65
 
|align="center"|6.08
 
|align="center"|12.92
 
|align="center"|37,409
 
|align="center"|37,864
 
|align="center"|36,934
 
|align="center"|37,320
 
|}
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 2 -- 7" Web'''
 
 
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|342.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|14.26||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|36,812||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|32||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
|&nbsp;||#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||11.26||11.26||13.74||39,272||39,691||38,922||39,281
 
|-
 
!I
 
|2||10||4||6||11.59||11.26||13.74||39,706||40,132||39,297||39,660
 
|-
 
|&nbsp;||3||12||6||6||11.59||10.26||12.74||39,871||40,300||39,440||39,806
 
|-
 
|&nbsp;||4||14||6||8||11.26||10.26||12.74||40,165||40,599||39,695||40,064
 
|-
 
|&nbsp;||5||16||8||8||11.26||9.26||11.74||40,211||40,648||39,736||40,108
 
|-
 
|&nbsp;||6||18||8||10||10.66||9.26||11.74||40,382||40,822||39,885||40,259
 
|-
 
!Group
 
|7||8||2||6||11.59||10.26||14.74||39,271||39,691||38,921||39,280
 
|-
 
!II
 
|8||10||2||8||11.76||10.26||14.74||39,707||40,133||39,297||39,660
 
|-
 
|&nbsp;||9||12||4||8||11.26||11.26||13.74||40,002||40,432||39,553||39,919
 
|-
 
|&nbsp;||10||14||4||10||11.46||9.26||13.74||40,165||40,599||39,695||40,064
 
|-
 
|&nbsp;||11||16||6||10||11.46||8.26||12.74||40,211||40,648||39,736||40,108
 
|-
 
|&nbsp;||12||18||6||12||10.93||8.26||12.74||40,383||40,823||39,886||40,260
 
|-
 
|&nbsp;||13||20||6||14||10.83||6.26||12.74||40,331||40,773||39,843||40,219
 
|}
 
 
 
 
 
'''Section Properties '''<br/>
 
'''Beam Type 2 -- 8" Web'''
 
 
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|374.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|14.41||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|39,632||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|32||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
|&nbsp;||#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||11.41||11.41||13.59||42,114||42,525||41,761||42,113
 
|-
 
!I
 
|2||10||4||6||11.74||11.41||13.59||42,561||42,977||42,146||42,502
 
|-
 
|&nbsp;||3||12||6||6||11.74||10.41||12.59||42,734||43,154||42,296||42,654
 
|-
 
|&nbsp;||4||14||6||8||11.41||10.41||12.59||43,039||43,463||42,560||42,921
 
|-
 
|&nbsp;||5||16||8||8||11.41||9.41||11.59||43,091||43,518||42,607||42,970
 
|-
 
|&nbsp;||6||18||8||10||10.81||9.41||11.59||43,270||43,700||42,764||43,129
 
|-
 
!Group
 
|7||8||2||6||11.74||10.41||14.59||42,114||42,525||41,761||42,112
 
|-
 
!II
 
|8||10||2||8||11.91||10.41||14.59||42,562||42,978||42,147||42,502
 
|-
 
|&nbsp;||9||12||4||8||11.41||11.41||13.59||42,867||43,288||42,411||42,769
 
|-
 
|&nbsp;||10||14||4||10||11.61||9.41||13.59||43,039||43,463||42,560||42,921
 
|-
 
|&nbsp;||11||16||6||10||11.61||8.41||12.59||43,091||43,518||42,607||42,970
 
|-
 
|&nbsp;||12||18||6||12||11.08||8.41||12.59||43,271||43,701||42,765||43,130
 
|-
 
|&nbsp;||13||20||6||14||10.98||6.41||12.59||43,224||43,655||42,725||43,092
 
|}
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 3 -- 6" Web'''
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|381.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|17.08||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|61,841||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|39||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
!Cont.
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
!valign="top"|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||13.08||14.08||17.92||65,603||66,291||65,068||65,656
 
|-
 
!I
 
|2||10||4||6||13.75||14.08||17.92||66,265||66,962||65,638||66,233
 
|-
 
|&nbsp;||3||12||4||8||13.58||14.08||17.92||66,753||67,457||66,060||66,660
 
|-
 
|&nbsp;||4||14||6||8||13.58||13.08||16.92||67,077||67,787||66,341||66,945
 
|-
 
|&nbsp;||5||16||6||10||13.48||13.08||16.92||67,555||68,271||66,755||67,364
 
|-
 
|&nbsp;||6||18||8||10||13.48||12.08||15.92||67,723||68,444||66,903||67,516
 
|-
 
|&nbsp;||7||20||8||12||13.08||12.08||15.92||68,042||68,769||67,182||67,799
 
|-
 
|&nbsp;||8||22||8||14||12.51||12.08||15.92||68,218||68,949||67,336||67,957
 
|-
 
|&nbsp;||9||24||10||14||12.51||11.08||14.92||68,260||68,994||67,376||67,998
 
|-
 
!Group
 
|10||8||2||6||13.75||13.08||18.92||65,604||66,292||65,068||65,657
 
|-
 
!II
 
|11||10||2||8||14.08||13.08||18.92||66,264||66,961||65,637||66,232
 
|-
 
|&nbsp;||12||12||2||10||13.88||13.08||18.92||66,753||67,457||66,060||66,660
 
|-
 
|&nbsp;||13||14||4||10||13.48||14.08||17.92||67,236||67,946||66,477||67,082
 
|-
 
|&nbsp;||14||16||4||12||13.75||12.08||17.92||67,556||68,272||66,756||67,366
 
|-
 
|&nbsp;||15||18||6||12||13.75||11.08||16.92||67,725||68,445||66,904||67,517
 
|-
 
|&nbsp;||16||20||6||14||13.37||11.08||16.92||68,045||68,771||67,184||67,800
 
|-
 
|&nbsp;||17||22||6||16||12.83||11.08||16.92||68,217||68,948||67,336||67,956
 
|-
 
|&nbsp;||18||24||8||16||12.83||10.08||15.92||68,259||68,993||67,375||67,998
 
|}
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 3 -- 7" Web'''
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|420.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|17.31||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|66,991||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|39||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
!Cont.
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
!valign="top"|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||13.31||14.31||17.69||70,792||71,464||70,251||70,826
 
|-
 
!I
 
|2||10||4||6||13.98||14.31||17.69||71,477||72,156||70,841||71,420
 
|-
 
|&nbsp;||3||12||4||8||13.81||14.31||17.69||71,985||72,670||71,279||71,864
 
|-
 
|&nbsp;||4||14||6||8||13.81||13.31||16.69||72,326||73,016||71,575||72,163
 
|-
 
|&nbsp;||5||16||6||10||13.71||13.31||16.69||72,823||73,520||72,006||72,599
 
|-
 
|&nbsp;||6||18||8||10||13.71||12.31||15.69||73,006||73,707||72,166||72,762
 
|-
 
|&nbsp;||7||20||8||12||13.31||12.31||15.69||73,342||74,049||72,459||73,060
 
|-
 
|&nbsp;||8||22||8||14||12.74||12.31||15.69||73,532||74,242||72,626||73,229
 
|-
 
|&nbsp;||9||24||10||14||12.74||11.31||14.69||73,584||74,298||72,675||73,280
 
|-
 
!Group
 
|10||8||2||6||13.98||13.31||18.69||70,793||71,465||70,252||70,826
 
|-
 
!II
 
|11||10||2||8||14.31||13.31||18.69||71,476||72,155||70,840||71,420
 
|-
 
|&nbsp;||12||12||2||10||14.11||13.31||18.69||71,985||72,670||71,279||71,864
 
|-
 
|&nbsp;||13||14||4||10||13.71||14.31||17.69||72,487||73,178||71,714||72,303
 
|-
 
|&nbsp;||14||16||4||12||13.98||12.31||17.69||72,825||73,522||72,007||72,600
 
|-
 
|&nbsp;||15||18||6||12||13.98||11.31||16.69||73,007||73,708||72,167||72,764
 
|-
 
|&nbsp;||16||20||6||14||13.60||11.31||16.69||73,344||74,051||72,461||73,061
 
|-
 
|&nbsp;||17||22||6||16||13.06||11.31||16.69||73,531||74,242||72,625||73,229
 
|-
 
|&nbsp;||18||24||8||16||13.06||10.31||15.69||73,584||74,298||72,674||73,280
 
|}
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 3 -- 8" Web'''
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|459.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|17.49||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|72,106||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|39||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.60||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
!Cont.
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
!valign="top"|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||13.49||14.49||17.51||75,940||76,598||75,394||75,957
 
|-
 
!I
 
|2||10||4||6||14.16||14.49||17.51||76,642||77,307||75,999||76,567
 
|-
 
|&nbsp;||3||12||4||8||13.99||14.49||17.51||77,166||77,837||76,451||77,023
 
|-
 
|&nbsp;||4||14||6||8||13.99||13.49||16.51||77,520||78,196||76,758||77,334
 
|-
 
|&nbsp;||5||16||6||10||13.89||13.49||16.51||78,034||78,716||77,203||77,783
 
|-
 
|&nbsp;||6||18||8||10||13.89||12.49||15.51||78,229||78,914||77,373||77,956
 
|-
 
|&nbsp;||7||20||8||12||13.49||12.49||15.51||78,580||79,270||77,678||78,265
 
|-
 
|&nbsp;||8||22||8||14||12.92||12.49||15.51||78,781||79,475||77,855||78,445
 
|-
 
|&nbsp;||9||24||10||14||12.92||11.49||14.51||78,843||79,540||77,911||78,504
 
|-
 
!Group
 
|10||8||2||6||14.16||13.49||18.51||75,941||76,599||75,395||75,958
 
|-
 
!II
 
|11||10||2||8||14.49||13.49||18.51||76,641||77,306||75,998||76,566
 
|-
 
|&nbsp;||12||12||2||10||14.29||13.49||18.51||77,166||77,837||76,451||77,023
 
|-
 
|&nbsp;||13||14||4||10||13.89||14.49||17.51||77,684||78,361||76,899||77,476
 
|-
 
|&nbsp;||14||16||4||12||14.16||12.49||17.51||78,036||78,718||77,204||77,785
 
|-
 
|&nbsp;||15||18||6||12||14.16||11.49||16.51||78,230||78,916||77,374||77,957
 
|-
 
|&nbsp;||16||20||6||14||13.78||11.49||16.51||78,582||79,273||77,680||78,267
 
|-
 
|&nbsp;||17||22||6||16||13.24||11.49||16.51||78,780||79,475||77,854||78,444
 
|-
 
|&nbsp;||18||24||8||16||13.24||10.49||15.51||78,842||79,540||77,911||78,503
 
|}
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 4 -- 6" Web'''
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|428.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|19.54||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|92,450||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|45||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
!Cont.
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
!valign="top"|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||15.54||16.54||21.46||97,723||98,691||96,972||97,800
 
|-
 
!I
 
|2||10||4||6||16.21||16.54||21.46||98,623||99,602||97,748||98,583
 
|-
 
|&nbsp;||3||12||4||8||16.04||16.54||21.46||99,318||100,305||98,347||99,189
 
|-
 
|&nbsp;||4||14||6||8||16.04||15.54||20.46||99,818||100,812||98,780||99,627
 
|-
 
|&nbsp;||5||16||6||10||15.94||15.54||20.46||100,497||101,501||99,369||100,223
 
|-
 
|&nbsp;||6||18||8||10||15.94||14.54||19.46||100,808||101,818||99,640||100,499
 
|-
 
|&nbsp;||7||20||8||12||15.54||14.54||19.46||101,297||102,314||100,066||100,930
 
|-
 
|&nbsp;||8||22||8||14||14.97||14.54||19.46||101,611||102,634||100,341||101,210
 
|-
 
|&nbsp;||9||24||8||16||15.29||12.54||19.46||101,761||102,789||100,475||101,347
 
|-
 
|&nbsp;||10||26||10||16||15.29||11.54||18.46||101,762||102,794||100,480||101,356
 
|-
 
|&nbsp;||11||28||10||18||15.32||9.54||18.46||101,633||102,667||100,372||101,250
 
|-
 
!Group
 
|12||8||2||6||16.21||15.54||22.46||97,724||98,692||96,973||97,801
 
|-
 
!II
 
|13||10||2||8||16.54||15.54||22.46||98,622||99,601||97,747||98,582
 
|-
 
|&nbsp;||14||12||4||8||16.04||16.54||21.46||99,318||100,305||98,347||99,189
 
|-
 
|&nbsp;||15||14||4||10||15.94||16.54||21.46||100,005||101,001||98,941||99,790
 
|-
 
|&nbsp;||16||16||4||12||16.21||14.54||21.46||100,499||101,503||99,370||100,224
 
|-
 
|&nbsp;||17||16||6||10||15.94||15.54||20.46||100,497||101,501||99,369||100,223
 
|-
 
|&nbsp;||18||18||6||12||16.21||13.54||20.46||100,810||101,819||99,641||100,500
 
|-
 
|&nbsp;||19||20||6||14||15.83||13.54||20.46||101,300||102,317||100,068||100,932
 
|-
 
|&nbsp;||20||22||6||16||15.29||13.54||20.46||101,610||102,633||100,340||101,209
 
|-
 
|&nbsp;||21||24||6||18||15.32||11.54||20.46||101,762||102,790||100,476||101,349
 
|-
 
|&nbsp;||22||26||6||20||15.14||9.54||20.46||101,762||102,794||100,480||101,356
 
|-
 
|&nbsp;||23||26||8||18||15.32||10.54||19.46||101,764||102,796||100,482||101,357
 
|-
 
|&nbsp;||24||28||6||22||14.81||7.54||20.46||101,629||102,663||100,369||101,246
 
|-
 
|&nbsp;||25||28||8||20||15.14||8.54||19.46||101,631||102,666||100,371||101,248
 
|-
 
|&nbsp;||26||30||8||22||14.81||6.54||19.46||101,381||102,417||100,158||101,037
 
|-
 
|&nbsp;||27||32||8||24||14.37||4.54||19.46||101,033||102,069||99,860||100,739
 
|}
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 4 -- 7" Web'''
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|473.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|19.82||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|100,400||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|45||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
!Cont.
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
!valign="top"|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||15.82||16.82||21.18||105,729||106,673||104,971||105,778
 
|-
 
!I
 
|2||10||4||6||16.49||16.82||21.18||106,661||107,614||105,773||106,587
 
|-
 
|&nbsp;||3||12||4||8||16.32||16.82||21.18||107,384||108,345||106,396||107,216
 
|-
 
|&nbsp;||4||14||6||8||16.32||15.82||20.18||107,908||108,876||106,850||107,675
 
|-
 
|&nbsp;||5||16||6||10||16.22||15.82||20.18||108,617||109,593||107,464||108,295
 
|-
 
|&nbsp;||6||18||8||10||16.22||14.82||19.18||108,950||109,931||107,753||108,589
 
|-
 
|&nbsp;||7||20||8||12||15.82||14.82||19.18||109,464||110,453||108,201||109,041
 
|-
 
|&nbsp;||8||22||8||14||15.25||14.82||19.18||109,801||110,795||108,495||109,340
 
|-
 
|&nbsp;||9||24||8||16||15.57||12.82||19.18||109,968||110,967||108,644||109,492
 
|-
 
|&nbsp;||10||26||10||16||15.57||11.82||18.18||109,984||110,986||108,661||109,512
 
|-
 
|&nbsp;||11||28||10||18||15.60||9.82||18.18||109,864||110,869||108,562||109,415
 
|-
 
!Group
 
|12||8||2||6||16.49||15.82||22.18||105,730||106,674||104,971||105,779
 
|-
 
!II
 
|13||10||2||8||16.82||15.82||22.18||106,660||107,613||105,772||106,586
 
|-
 
|&nbsp;||14||12||4||8||16.32||16.82||21.18||107,384||108,345||106,396||107,216
 
|-
 
|&nbsp;||15||14||4||10||16.22||16.82||21.18||108,100||109,069||107,015||107,841
 
|-
 
|&nbsp;||16||16||4||12||16.49||14.82||21.18||108,619||109,595||107,465||108,296
 
|-
 
|&nbsp;||17||16||6||10||16.22||15.82||20.18||108,617||109,593||107,464||108,295
 
|-
 
|&nbsp;||18||18||6||12||16.49||13.82||20.18||108,951||109,933||107,755||108,590
 
|-
 
|&nbsp;||19||20||6||14||16.11||13.82||20.18||109,467||110,456||108,203||109,044
 
|-
 
|&nbsp;||20||22||6||16||15.57||13.82||20.18||109,800||110,794||108,484||109,339
 
|-
 
|&nbsp;||21||24||6||18||15.60||11.82||20.18||109,970||110,969||108,645||109,494
 
|-
 
|&nbsp;||22||26||6||20||15.42||9.82||20.18||109,984||110,986||108,661||109,512
 
|-
 
|&nbsp;||23||26||8||18||15.60||10.82||19.18||109,985||110,988||108,663||109,514
 
|-
 
|&nbsp;||24||28||6||22||15.09||7.82||20.18||109,860||110,865||108,559||109,411
 
|-
 
|&nbsp;||25||28||8||20||15.42||8.82||19.18||109,862||110,867||108,561||109,413
 
|-
 
|&nbsp;||26||30||8||22||15.09||6.82||19.18||109,618||110,624||108,353||109,207
 
|-
 
|&nbsp;||27||32||8||24||14.65||4.82||19.18||109,271||110,278||108,056||108,910
 
|}
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 4 -- 8" Web'''
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|518.9||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|20.06||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|108,288||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|45||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
!Cont.
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]
 
|colspan="2"|[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
!valign="top"|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6||A1 Bars<br/>2-#5||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||8||4||4||16.06||17.06||20.94||113,668||114,591||112,902||113,692
 
|-
 
!I
 
|2||10||4||6||16.73||17.06||20.94||114,627||115,559||113,727||114,523
 
|-
 
|&nbsp;||3||12||4||8||16.56||17.06||20.94||115,375||116,314||114,372||115,174
 
|-
 
|&nbsp;||4||14||6||8||16.56||16.06||19.94||115,921||116,866||114,844||115,651
 
|-
 
|&nbsp;||5||16||6||10||16.46||16.06||19.94||116,655||117,608||115,480||116,291
 
|-
 
|&nbsp;||6||18||8||10||16.46||15.06||18.94||117,007||117,965||115,786||116,601
 
|-
 
|&nbsp;||7||20||8||12||16.06||15.06||18.94||117,544||118,509||116,252||117,073
 
|-
 
|&nbsp;||8||22||8||14||15.49||15.06||18.94||117,900||118,870||116,563||117,387
 
|-
 
|&nbsp;||9||24||8||16||15.81||13.06||18.94||118,084||119,058||119,725||117,553
 
|-
 
|&nbsp;||10||26||10||16||15.81||12.06||17.94||118,112||119,089||116,754||117,584
 
|-
 
|&nbsp;||11||28||10||18||15.84||10.06||17.94||118,001||118,981||116,662||117,494
 
|-
 
!Group
 
|12||8||2||6||16.73||16.06||21.94||113,669||114,592||112,903||113,693
 
|-
 
!II
 
|13||10||2||8||17.06||16.06||21.94||114,626||115,558||113,726||114,522
 
|-
 
|&nbsp;||14||12||4||8||16.56||17.06||20.94||115,375||116,314||114,372||115,174
 
|-
 
|&nbsp;||15||14||4||10||16.46||17.06||20.94||116,116||117,062||115,012||115,819
 
|-
 
|&nbsp;||16||16||4||12||16.73||15.06||20.94||116,657||117,610||115,481||116,293
 
|-
 
|&nbsp;||17||16||6||10||16.46||16.06||19.94||116,655||117,608||115,480||116,291
 
|-
 
|&nbsp;||18||18||6||12||16.73||14.06||19.94||117,009||117,967||115,787||116,603
 
|-
 
|&nbsp;||19||20||6||14||16.35||14.06||19.94||117,547||118,512||116,255||117,075
 
|-
 
|&nbsp;||20||22||6||16||15.81||14.06||19.94||117,899||118,869||116,562||117,387
 
|-
 
|&nbsp;||21||24||6||18||15.84||12.06||19.94||118,085||119,059||116,727||117,554
 
|-
 
|&nbsp;||22||26||6||20||15.66||10.06||19.94||118,112||119,089||116,754||117,584
 
|-
 
|&nbsp;||23||26||8||18||15.84||11.06||18.94||118,113||119,091||116,755||117,585
 
|-
 
|&nbsp;||24||28||6||22||15.33||8.06||19.94||117,997||118,977||116,659||117,490
 
|-
 
|&nbsp;||25||28||8||20||15.66||9.06||18.94||117,999||118,979||116,661||117,493
 
|-
 
|&nbsp;||26||30||8||22||15.33||7.06||18.94||117,760||118,742||116,458||117,291
 
|-
 
|&nbsp;||27||32||8||24||14.89||5.06||18.94||117,415||118,397||116,163||116,996
 
|}
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 6 -- 6.5" Web'''
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|643.6||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|25.92||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|235,735||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|54||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]||[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
|&nbsp;||#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#6||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||14||4||10||23.52||22.92||23.08||251,047||248,880
 
|-
 
!I
 
|2||16||4||12||23.25||22.92||23.08||252,425||250,070
 
|-
 
|&nbsp;||3||18||6||12||23.25||21.92||22.08||253,525||251,022
 
|-
 
|&nbsp;||4||20||6||14||23.06||21.92||22.08||254,886||252,199
 
|-
 
|&nbsp;||5||22||6||16||22.92||21.92||22.08||256,238||253,370
 
|-
 
|&nbsp;||6||24||8||16||22.92||20.92||21.08||257,053||254,081
 
|-
 
|&nbsp;||7||26||8||18||22.59||20.92||21.08||258,130||255,017
 
|-
 
|&nbsp;||8||28||8||20||22.32||20.92||21.08||259,191||255,940
 
|-
 
|&nbsp;||9||30||10||20||22.32||19.92||20.08||259,751||256,433
 
|-
 
|&nbsp;||10||32||10||22||22.10||19.92||20.08||260,803||257,350
 
|-
 
|&nbsp;||11||34||10||24||21.75||19.92||20.08||261,604||258,052
 
|-
 
|&nbsp;||12||36||10||26||21.46||19.92||20.08||262,412||258,760
 
|-
 
|&nbsp;||13||38||12||26||21.46||18.92||19.08||262,739||259,053
 
|}
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 6 -- 7.5" Web'''
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|697.6||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|26.00||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|248,915||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|54||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]||[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
|&nbsp;||#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#6||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||14||4||10||23.60||23.00||23.00||264,293||262,115
 
|-
 
!I
 
|2||16||4||12||23.33||23.00||23.00||265,686||263,318
 
|-
 
|&nbsp;||3||18||6||12||23.33||22.00||22.00||266,801||264,281
 
|-
 
|&nbsp;||4||20||6||14||23.14||22.00||22.00||268,178||265,473
 
|-
 
|&nbsp;||5||22||6||16||23.00||22.00||22.00||269,548||266,658
 
|-
 
|&nbsp;||6||24||8||16||23.00||21.00||21.00||270,378||267,381
 
|-
 
|&nbsp;||7||26||8||18||22.67||21.00||21.00||271,472||268,330
 
|-
 
|&nbsp;||8||28||8||20||22.40||21.00||21.00||272,551||269,269
 
|-
 
|&nbsp;||9||30||10||20||22.40||20.00||20.00||273,125||269,772
 
|-
 
|&nbsp;||10||32||10||22||22.18||20.00||20.00||274,195||270,705
 
|-
 
|&nbsp;||11||34||10||24||21.83||20.00||20.00||275,014||271,420
 
|-
 
|&nbsp;||12||36||10||26||21.54||20.00||20.00||275,839||272,143
 
|-
 
|&nbsp;||13||38||12||26||21.54||19.00||19.00||276,180||272,447
 
|}
 
 
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 6 -- 8.5" Web'''
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|751.6||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|26.07||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|262,087||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|54||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]||[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
|&nbsp;||#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>2-#6||A1 Bars<br/>2-#6
 
|-
 
!Group
 
|1||14||4||10||23.67||23.07||22.93||277,522||275,336
 
|-
 
!I
 
|2||16||4||12||23.40||23.07||22.93||278,930||276,549
 
|-
 
|&nbsp;||3||18||6||12||23.40||22.07||21.93||280,057||277,523
 
|-
 
|&nbsp;||4||20||6||14||23.21||22.07||21.93||281,449||278,727
 
|-
 
|&nbsp;||5||22||6||16||23.07||22.07||21.93||282,834||279,925
 
|-
 
|&nbsp;||6||24||8||16||23.07||21.07||20.93||283,678||280,658
 
|-
 
|&nbsp;||7||26||8||18||22.74||21.07||20.93||284,786||281,620
 
|-
 
|&nbsp;||8||28||8||20||22.47||21.07||20.93||285,881||282,571
 
|-
 
|&nbsp;||9||30||10||20||22.47||20.07||19.93||286,468||283,085
 
|-
 
|&nbsp;||10||32||10||22||22.25||20.07||19.93||287,554||284,030
 
|-
 
|&nbsp;||11||34||10||24||21.90||20.07||19.93||288,388||284,758
 
|-
 
|&nbsp;||12||36||10||26||21.61||20.07||19.93||289,228||285,493
 
|-
 
|&nbsp;||13||38||12||26||21.61||19.07||18.93||289,581||285,807
 
|}
 
 
 
'''Section Properties'''<br/>
 
'''Beam Type 7 -- 6" Web'''<br/>
 
'''Bulb-Tee Girder'''
 
 
 
{|border="1" cellpadding="3" cellspacing="0" text-align="right"
 
 
 
|align="right"|Section Area =
 
|align="center"|787.4||in<sup>2</sup>
 
|rowspan="4"|&nbsp;
 
{|border="0" cellpadding="0"
 
|NOTE:||#||=||strand pattern number
 
|-
 
|&nbsp;||T||=||total number of strands
 
|-
 
|&nbsp;||H||=||number of harped strands
 
|-
 
|&nbsp;||S||=||number of straight strands
 
|}
 
|-
 
|align="right"|Section <math>\, Y_b</math> =
 
|align="center"|37.58||in
 
|-
 
|align="right"| <math>\, I_{nontransformed}</math> =
 
|align="center"|571,047||in<sup>4</sup>
 
|-
 
|align="right"|Depth=
 
|align="center"|72.5||in
 
|-
 
|align="right"|Strand Size=
 
|align="center"|0.6||in
 
|-
 
|align="right"| <math>\, f'_{ci}</math> =
 
|align="center"|5||ksi
 
|-
 
|align="right"| <math>\, f'_c</math> =
 
|align="center"|7||ksi
 
|}
 
 
 
 
 
{|border="1" cellpadding="5" cellspacing="0" style="text-align:center"
 
 
 
!Cont.
 
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||[[#e1, e2, e3, I_initial & I_final 1|I<sub>initial</sub>]]||[[#e1, e2, e3, I_initial & I_final 1|I<sub>final</sub>]]
 
|-
 
!valign="top|Span
 
|#||T||H||S||[[#e1, e2, e3, I_initial & I_final 1|e1]]||[[#e1, e2, e3, I_initial & I_final 1|e2]]||[[#e1, e2, e3, I_initial & I_final 1|e3]]||A1 Bars<br/>4-#6||A1 Bars<br/>4-#6
 
|-
 
!Group
 
|1||14||4||10||35.58||34.58||29.92||609,994||604,448
 
|-
 
!I
 
|2||16||4||12||35.25||34.58||29.92||613,316||607,307
 
|-
 
|&nbsp;||3||18||6||12||35.25||33.58||28.92||616,196||609,790
 
|-
 
|&nbsp;||4||20||6||14||35.01||33.58||28.92||619,469||612,612
 
|-
 
|&nbsp;||5||22||6||16||34.83||33.58||28.92||622,719||615,417
 
|-
 
|&nbsp;||6||24||8||16||34.83||32.58||27.92||625,140||617,512
 
|-
 
|&nbsp;||7||26||8||18||34.69||32.58||27.92||628,347||620,286
 
|-
 
|&nbsp;||8||28||8||20||34.58||32.58||27.92||631,536||623,046
 
|-
 
|&nbsp;||9||30||10||20||34.58||31.58||26.92||633,518||624,769
 
|-
 
|&nbsp;||10||32||10||22||34.31||31.58||26.92||636,280||627,166
 
|-
 
|&nbsp;||11||34||10||24||34.08||31.58||26.92||639,012||629,539
 
|-
 
|&nbsp;||12||36||10||26||33.89||31.58||26.92||641,737||631,909
 
|-
 
|&nbsp;||13||38||10||28||33.58||31.58||26.92||644,052||633,926
 
|-
 
|&nbsp;||14||40||12||28||33.58||30.58||25.92||645,607||635,289
 
|}
 
 
 
===751.22.3.6 Girder Reinforcement===
 
 
 
<center>'''Bar Reinforcing Steel Details for MoDOT Standard Girders'''</center>
 
{|border="1" cellpadding="3" cellspacing="0" style="text-align:center" align="center"
 
 
 
|&nbsp;
 
|colspan="13"|TABLE OF DIMENSIONS
 
|-
 
|&nbsp;
 
|colspan="3"|BEAM TYPE 2
 
|colspan="3"|BEAM TYPE 3
 
|colspan="3"|BEAM TYPE 4
 
|colspan="3"|BEAM TYPE 6
 
|BEAM TYPE 7
 
|-
 
|WEB||6"||7"||8"||6"||7"||8"||6"||7"||8"||6½"||7½"||8½"||6"
 
|-
 
|"a"||5½"||5½"||5½"||5½"||5½"||5½"||5½"||5½"||5½"||8¾"||8¾"||8¾"||10"
 
|-
 
|"b"||4"||4"||4"||4"||4"||4"||4"||4"||4"||4"||4"||4"||4"
 
|-
 
|"c"||6"||6"||6"||6"||6"||6"||6"||6"||6"||7"||7"||7"||4½"
 
|-
 
|"d"||3¼"||3¼"||3¼"||5⅛"||5⅛"||5⅛"||6¼"||6¼"||6¼"||4⅛"||4⅛"||4⅛"||4⅛"
 
|-
 
|"e"||13"||14"||15"||13"||14"||15"||13"||14"||15"||18"||19"||20"||20"
 
|-
 
|"f"||2"||2"||2"||2"||2"||2"||2"||2"||2"||3"||3"||3"||7¾"
 
|-
 
|"g"||11"||12"||13"||11"||12"||13"||11"||12"||13"||22"||23"||24"||2'-11½"
 
|-
 
|"h"||2'-6"||2'-6"||2'-6"||3'-1"||3'-1"||3'-1"||3'-7"||3'-7"||3'-7"||4'-4"||4'-4"||4'-4"||5'-10½"
 
|-
 
|"i"
 
|3'-0½"||3'-0½"||3'-0½"||3'-7½"||3'-7½"||3'-7½"||4'-1½"||4'-1½"||4'-1½"||4'-10½"||4'-10½"||4'-10½"||6'-5"
 
|}
 
 
 
 
 
<center>Note: Dimensions shown above are out to out.</center>
 
 
 
 
 
{|border="1" cellpadding="1" cellspacing="0" style="text-align:center" align="center"
 
 
 
|&nbsp;
 
|colspan="13"|TOTAL BAR LENGTH
 
|-
 
|&nbsp;
 
|colspan="3"|BEAM TYPE 2
 
|colspan="3"|BEAM TYPE 3
 
|colspan="3"|BEAM TYPE 4
 
|colspan="3"|BEAM TYPE 6
 
|BEAM TYPE 7
 
|-
 
|width="32pt"|WEB||width="45pt"|6"||width="45pt"|7"||width="45pt"|8"||width="45pt"|6"||width="45pt"|7"||width="45pt"|8"||width="50pt"|6"||width="50pt"|7"||width="50pt"|8"||width="50pt"|6½"||width="50pt"|7½"||width="50pt"|8½"||width="100pt"|6"
 
|-
 
|B1||4'-1"||4'-1"||4'-1"||4'-8"||4'-8"||4'-8"||5'-2"||5'-2"||5'-2"||5'-11"||5'-11"||5'-11"||7'-8"
 
|-
 
|B2||3'-6"||3'-6"||3'-6"||4'-1"||4'-1"||4'-1"||4'-7"||4'-7"||4'-7"||5'-4"||5'-4"||5'-4"||7'-0"
 
|-
 
|C1||13"||14"||15"||13"||14"||15"||13"||14"||15"||2'-2"||2'-3"||2'-4"||3'-6"
 
|-
 
|D1||2'-4"||2'-5"||2'-6"||2'-5"||2'-6"||2'-7"||2'-7"||2'-8"||2'-9"||3'-0"||3'-1"||3'-2"||3'-1"
 
|}
 
 
 
 
 
Note:  For girders that have stepped flanges, create new B1 and C1 Bars and adjust Bar Lengths for step heights.
 
 
 
 
 
{|border="0" cellpadding="1" cellspacing="0" style="text-align:center" align="center"
 
 
 
|[[Image:751.22 C1 Bar.gif]]
 
|rowspan="2"|[[Image:751.22_B1_&_B2_Bar.gif]]
 
|[[Image:751.22_C1_Bar_Type_7.gif]]
 
|-
 
|valign="top"|C1 BAR
 
(Beam Types 2-6)
 
|valign="top"|C1 BAR
 
(Beam Type 7)<!--column 2 occupied by cell [[Image:751.22_B1_&_B2_Bar.gif]]-->
 
|-
 
|&nbsp;
 
|B1 & B2 BAR
 
|rowspan="3"|[[Image:751.22_Section_Thru_Girder_Type_7.gif]]
 
|-
 
|rowspan="2"|[[Image:751.22_Section_Thru_Girder_2-6.gif]]
 
|valign="bottom"|[[Image:751.22_D1_Bar.gif]]
 
|-
 
|D1 BAR <!--column 1 occupied by cell [[Image:751.22_Section_Thru_Girder_2-6.gif]]-->
 
|-
 
|SECTION THRU GIRDER
 
(Typ. for MoDOT Standard Girder Types 2-6)
 
|&nbsp;
 
|SECTION THRU GIRDER
 
(MoDOT Standard Girder Type 7)
 
|}
 
 
 
'''Welded Wire Reinforcing Steel Details for NU Standard Girders'''
 
 
 
(See Bridge Standard Drawings for details.)
 
 
 
'''Alternate Bar Reinforcing Steel Details for NU Standard Girders'''
 
 
 
Alternate bar reinforcing steel details shall be provided for all NU girders for all spans.
 
 
 
Details shall be similar to details provided for MoDOT Standard Girders:
 
: End section reinforcement shall be designed using #6 B2 Bars @ 3 ½” cts.
 
: C1 bars shall be straight bars without legs.
 
: All B1 bars shall be epoxy coated.
 
: B1 bars shall be #4 or #5 bar maximum. (#4 bars are preferred to allow permissible alternate bar shape.)
 
 
 
'''Section Reinforcement Details'''
 
 
 
(Typ. for MoDOT Standard Girder Types 2 thru 6 and NU Standard Girders.)
 
 
 
 
 
{|border="0" cellpadding="5" cellspacing="0" align="center"
 
 
 
|colspan="2"|[[Image:751.22_Mild_Steel_Reinforcement.gif]]
 
|-
 
|rowspan="2" align="center" width="250pt"|'''MILD STEEL<br/>REINFORCEMENT'''
 
|Guidance:  For MoDOT Standard Girder Types 7 or 8, using #6 B1 bars does not provide 1” clearance when center strands are spaced 1” off centerline of girder between hold down devices because of bend radius of #6 bar.  Use of #5 bar is preferred.  For NU Standard Girders and alternate bar reinforcing steel details, use of #5 bar is preferred similarly.
 
|-
 
|Note: B1, B2 and D1 bars shall be placed in pairs.  A note on the girder sheet gives the fabricator the option of furnishing the 2-D1 bars as one bar.
 
|}
 
 
 
 
 
{|border="0" cellpadding="5" cellspacing="0" style="text-align:center" align="center"
 
 
 
 
 
|[[Image:751.22_B1_Bar_Alternate.gif]]
 
|-
 
|'''B1 BAR PERMISSIBLE<br/>ALTERNATE SHAPE'''
 
|-
 
|Note: Place the above detail on Prestress I-Girder sheets only where #4-B1 reinforcing bars are used.
 
|}
 
 
 
 
 
'''Anchorage Zone Reinforcement'''
 
 
 
The following details meet the criteria for anchorage zone reinforcement for pretensioned girders in [[#751.22.2.4 Shear|EPG 751.22.2.4]] for all MoDOT and NU standard girder shapes.
 
 
 
 
 
'''MoDOT Standard Girder End Section Reinforcement'''
 
 
 
[[Image:751.22.3.6 MoDOT Std Girder End Sect Reinf.jpg|675px|center]]
 
 
 
 
 
'''NU Standard Girder End Section Reinforcement'''
 
 
 
Typical end section reinforcement shall be all welded wire reinforcement (WWR) or all deformed bars.  If additional reinforcement is required with WWR, the following options shall be considered.
 
 
 
[[Image:751.22.3.6 NU Std Girder End Sect Reinf Dec 2010.jpg|700px|center|thumb|
 
{| style="margin: 1em auto 1em auto"
 
|-
 
!align="center" rowspan="2" width=280|Option 1 (Preferred)!!width=120| !!align="center" width=280|Option 2
 
|-
 
| ||width=280 align="center"|(Use for heavier reinforcement)
 
|}
 
]]
 
 
 
Minimum spacing of reinforcing bars shall be in accordance with LRFD 5.10.3.1.2. 
 
 
 
Consideration shall be given to spacing reinforcing bars 1” clear from welded studs on bearing plates (not shown).
 
 
 
 
 
'''Bearing Plate Anchor Studs'''
 
 
 
 
 
The standard ½" bearing plate will be anchored with four ½" x 4" studs for MoDOT shapes and eight ½” x 5” studs for NU shapes.
 
 
 
If required, increase the number of ½" studs and space between open B2 bars.
 
 
 
 
 
The minimum ¼" fillet weld between the ½" bearing plate and 1½" sole plate is adequate for all cases.
 
 
 
'''LFD Seismic Design'''
 
 
 
Studs shall be designed to meet the criteria of 2002 AASHTO 17<sup>th</sup> Edition Division I-A in Seismic Performance Category C or D.
 
 
 
Stud capacity is determined as follows for:
 
 
 
:Stud Cap. = (n)(A<sub>s</sub>)(0.4F<sub>y</sub>)(1.5)
 
 
 
::Where:
 
:::N = number of studs
 
:::A<sub>s</sub> = area of stud
 
:::F<sub>y</sub> = yield strength of stud (50 ksi)
 
:::0.4F<sub>y</sub> = Allowable Shear in Pins AASHTO Table 10.32.1A
 
:::1.5 = seismic overload factor
 
 
 
If required, increase the number of 1/2” studs to six and space between open B2 bars or WWF.  If this is still not adequate, 5/8” studs may be used.  The following table may be used as a guide for upper limits of dead load reactions:
 
 
 
{|border="1" cellpadding="3" cellspacing="0" style="text-align:center" align="center"
 
|-
 
!rowspan="2"|No. of Studs||rowspan="2"| Stud 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
 
|-
 
|8|| 1/2”|| 156|| 130
 
|-
 
|10|| 1/2”|| 195|| 163
 
|-
 
|8|| 5/8”|| 244|| 204
 
|-
 
|10|| 5/8”|| 306|| 255
 
|}
 
 
 
===751.22.3.7 Bent-up Strands===
 
 
 
'''Bent-up strands for positive moment connection'''
 
 
 
Tables below show the number of bent-up strands for closed and open diaphragms (with a continuous superstructure), respectively.  Provide a minimum number of bent-up strands as shown in tables at the bottom of girder ends.  These bent-up strands shall be adequate to resist a positive moment over the bents.
 
 
 
 
 
<center>[[Image:751.22_Bent_Up_Strands.jpg|750px]]</center>
 
 
 
<math>*</math> &nbsp; &nbsp; Varies<br/>
 
<math>**</math>&nbsp; #5 bars typical at each layer of bent-up strands.<br/>
 
<math>***</math>&nbsp; Use 3’-0” projection for NU Girders.<br/>
 
(1) &nbsp; #5-strand tie bars normal to girder.
 
 
 
 
 
{|border="1" cellpadding="5" style="text-align: center;" align="center"
 
 
 
|rowspan="2"|WEB<br/>THICKNESS<br/>(INCHES)
 
|colspan="5"|NUMBER OF BOTTOM STRANDS FOR POSITIVE MOMENT<BR/>CONNECTION (C)
 
|-
 
|BEAM TYPE 2 <!--column 1 occupied by cell WEB<br/>THICKNESS<br/>(INCHES)-->
 
|BEAM TYPE 3||BEAM TYPE 4||BEAM TYPE 6||BEAM TYPE 7<BR/>(BULB-TEE)
 
|-
 
|6||6||6||8||---||12
 
|-
 
|6-1/2||---||---||---||10||---
 
|-
 
|7(A)||6||8||8||---||---
 
|-
 
|7-1/2(B)||---||---||---||12||---
 
|-
 
|8(A)||6||8||10||---||---
 
|-
 
|8-1/2(B)||---||---||---||12||---
 
|}
 
::::::(A) Modified Beam Type 2, 3 or 4.
 
 
 
::::::(B) Modified Beam Type 6.
 
 
 
::::::(C) If available.  Otherwise, bend all bottom strands.
 
 
 
 
 
{|border="1" cellpadding="5" style="text-align: center;" align="center"
 
 
 
|colspan="5"|NUMBER OF BOTTOM STRANDS FOR POSITIVE MOMENT CONNECTION (C)
 
|-
 
|NU 35 || 10
 
|-
 
|NU 43 || 10
 
|-
 
|NU 53 || 10
 
|-
 
|NU 63 || 12
 
|-
 
|NU 70 || 12
 
|}
 
 
 
===751.22.3.8 Camber, Haunching and Girder Steps===
 
 
 
'''Camber'''
 
 
 
Compute theoretical camber of girder at 90 days and show on the plan as a “Theoretical camber of girder after erection” (Estimated at 90 days)". Compute theoretical camber of girder at 7 days and show on the plan as a “Theoretical camber of girder after strand release” (Estimated at 7 days)."
 
 
 
For example,
 
 
 
[[image: 751.22.3.8.jpg|center|800px]]
 
 
 
Show conversion factors for girder camber with camber diagram as per [[751.50 Standard Detailing Notes#(H2c6.1)|EPG 751.50 H2c6.1]].
 
 
 
'''Haunching'''
 
 
 
Haunching for a P/S I-Girder bridge is the distance between the top of the girder and the bottom of the slab.
 
 
 
Haunching shall be computed at quarter (1/4) points for bridges with spans less than 75 feet, and at tenth (1/10) points for span 75 feet and longer.  A typical theoretical slab haunching diagram as shown below shall be provided on all P/S I-Girder bridges.
 
 
 
For cast-in-place decks, a minimum haunch of 1" at the centerline of girder and 1/2" at the edge of the girder flange shall be provided to allow for construction tolerances and normal concrete variations.  For NU and MoDOT Bulb-Tee Standard Girders, the minimum haunch may need to be increased.  See the Structural Project Manager or Structural Liaison Engineer for cast-in-place decks. 
 
 
 
For precast prestressed panel decks, a minimum haunch of 1 1/8” shall be provided for MoDOT Standard Girders (Types 2, 3, 4, and 6) for the same reasons.  Provide 1 ½” min. haunch for NU and MoDOT Bulb-Tee Standard Girders.  A minimum of 1" shall be made available below the  precast prestressed panels to allow for adequate flow of concrete below the panel. This is accomplished by specifying and using 1” min. joint filler under the precast prestressed panels. 
 
 
 
A maximum haunch at the centerline of the girder of 2.5" for MoDOT Type 2, 3, 4 and 6 girders or 4.5” for all NU and MoDOT Bulb-Tee (Types 7 and 8) girders is allowed when prestressed panels are used, and 3.5" when only the cast-in-place option is used. (The maximum joint filler thickness to be used for supporting panels shall be 2" for MoDOT (Types 2, 3, 4 and 6) girders or 4” for all NU and MoDOT Bulb-Tee (Types 7 and 8) girders; the remaining haunch thickness will be addressed by varying the slab thickness.)
 
 
 
 
 
 
 
[[Image:751.22_Theoretical_Slab_Haunching_Diagram.gif|center|800px|thumb|<center>'''Theoretical Slab Haunching Diagram'''</center>]]
 
 
 
[[image:751.22.3.8 NU Girder Hairpin.jpg|center|450px|thumb|<center>'''NU and Bulb-Tee Girders, only'''</center>
 
<center>1) #4 Hairpin bars @ 12” cts. are required where haunch exceeds 4”.</center>]]
 
 
 
'''Girder Steps'''
 
 
 
Where haunches greater than 2.5" or 4.5", depending on girder type used, occur with prestressed panels, steps shall be provided on the girder as shown below, to keep the haunch less than 2" or 4" for MoDOT (Type 2, 3, 4 and 6) girders or all NU and Bulb-Tee (Types 7 and 8) girders, respectively.  The minimum step height shall be 1/2" with 1/2" increments with no limit of the number of steps.  If the steps accumulate to 1" or more, adjust the height of the B1 bars or WWR in 1" increments. Length of WWR sections for NU girders should be based on shear and confinement requirements before adjusting height to avoid multiple short length sections.
 
 
 
 
 
 
 
<center>[[Image:751.22_Girder_Steps.gif]]</center>
 
{|border="0" cellpadding="5" style="text-align: center;"
 
 
 
|width="575pt"|PART ELEVATION OF GIRDER
 
|width="125pt"|SECTION A-A
 
|}
 
 
 
 
 
<center>'''Girder Top Flange Step Example'''</center>
 
 
 
 
 
'''Top of Girder'''
 
 
 
Tops of girders, for bridges with superelevations of more than 2%, shall be sloped across the top flange to match the superelevation as shown below.  The minimum thickness of the top flange shall be the standard flange thickness and the overall height at the minimum point shall be the standard girder height.
 
 
 
NU and MoDOT Bulb-Tee Standard Girder top flanges exceeding a 4% cross-slope may experience sweep after form removal because of the unsymmetrical section and a resulting imbalanced prestressed load.  It is recommended that the flange thickness be increased to only half of that required (but less than or equal to 4% cross-slope) and the height difference mitigated using thicker joint filler on the high side.  If thicker joint filler cannot be fully used to compensate for the height difference, the extra load of a thicker slab must be accounted for in the design of the girders.
 
 
 
<center>[[Image:751.22_Superelevation_Slope.gif]]</center>
 
 
 
 
 
<center>'''Top Flange Slope with Superelevation'''</center>
 
 
 
===751.22.3.9 Open Intermediate Bent Diaphragms===
 
 
 
'''(Expansion Intermediate Bent with Continuous Slab)<br/>'''
 
 
 
'''Dimensions:'''
 
 
 
<center>[[Image:751.22_Open_Int_Bent_Diaphragms_Dim_Part_Elevations.jpg|800px]]</center>
 
 
 
{|border="0" cellpadding="5" style="text-align:center"
 
 
 
|width="300"|'''PART ELEVATION<br/>FOR BULB-TEE GIRDERS'''
 
|width="350"|'''PART ELEVATION'''
 
|}
 
 
 
<center>[[Image:751.22_Open_Int_Bent_Diaphragms_Dim_Part_Plan.jpg]]</center>
 
 
 
 
 
<center>'''PART PLAN'''</center>
 
 
 
 
 
{|border="0" cellpadding="5" style="text-align:center"
 
 
 
|[[Image:751.22_Open_Int_Bent_Diaphragms_Dim_Part_Section.jpg]]<br/>&nbsp;<br/>'''PART SECTION A-A'''
 
|align="left" width="200"|(*) A sloped diaphragm allows clearance for the future placement of jacks needed to replace bearings.
 
 
 
(**) For Bulb-Tee Girder, spacings less than 8'-8" dimensions "A", "B" & "C" may have to be modified.
 
 
 
(***) Make sure the diaphragm is wide enough to provide enough cover for the Coil Tie Rods.
 
|
 
{|border="1" cellpadding="5" style="text-align:center"
 
 
 
|rowspan="2"|GIRDER<br/>TYPE
 
|colspan="3"|DIMENSIONS
 
|-
 
|"A" <!-- column occupied by cell GIRDER<br/>TYPE -->
 
|"B"
 
|"C"
 
|-
 
|TYPE "2"<br/>2'-8"
 
|12"||15"||13"
 
|-
 
|TYPE "3"<br/>3'-3"
 
|17"||15"||19"
 
|-
 
|TYPE "4"<br/>3'-9"
 
|19"||18"||21"
 
|-
 
|TYPE "6"<br/>4'-6"
 
|2'-3"||21"||2'-1"
 
|-
 
|BULB-TEE<br/>6'-0½ *
 
|3'-0"||2'-6½"||2'-9"
 
|}
 
|}
 
 
 
 
 
 
 
'''(Expansion Intermediate Bent with Continuous Slab)<br/>'''
 
 
 
'''Coil Tie Rod:'''
 
 
 
<center>[[Image:751.22_Open_Int_Bent_Diaphragms_Coil_Tie_Rod_Part_Elevation.gif]]</center>
 
 
 
<center>'''PART ELEVATION'''</center>
 
 
 
 
 
<center>(*) 6" (Min.) shall be used for all I-Girders and Bulb-Tee Girders.</center>
 
 
 
 
 
<center>[[Image:751.22_Open_Int_Bent_Diaphragms_Coil_Tie_Rod_Part_Section_AA_Details.gif]]</center>
 
 
 
{|border="0" cellpadding="5" style="text-align:center" align="center"
 
 
 
|width="250pt"|'''PART SECTION A-A'''||width="400"|'''DETAILS OF COIL TIE RODS<BR/>IN BULB-TEE GIRDERS'''
 
|}
 
 
 
 
 
 
 
'''(Expansion Intermediate Bent with Continuous Slab)<br/>'''
 
 
 
'''Reinforcement:'''
 
 
 
 
 
<center>[[Image:751.22_Open_Int_Bent_Diaphragms_Reinf_Part_Elevations.gif]]</center>
 
 
 
{|border="0" cellpadding="5" style="text-align:center"
 
 
 
|width="350"|'''PART ELEVATION<br/>FOR BULB-TEE GIRDERS'''
 
|width="300"|'''PART ELEVATION'''
 
|}
 
 
 
 
 
<center>[[Image:751.22_Open_Int_Bent_Diaphragms_Reinf_Part_Plan.gif]]</center>
 
 
 
 
 
<center>'''PART PLAN'''</center>
 
 
 
 
 
 
 
{|border="0" cellpadding="5" style="text-align:center"
 
 
 
|align="left" valign="top"|(1) For Bulb-Tee Girders, the first #6 Bar shall be placed 10" from the centerline of Web (Top Flange will prevent some Bars from extending into the Slab).
 
|rowspan="3"|[[Image:751.22_Open_Int_Bent_Diaphragms_Reinf_Part_Section.gif]]
 
|-
 
|&nbsp;
 
|-
 
|&nbsp;
 
|-
 
|align="left" valign="bottom"|(*) See Section "A" for the placement of reinforcement.<br/>
 
(**) Use the same clearance as longitudinal slab steel.<br/>
 
(***) #5 Bars for each layer of bent up strands.
 
|'''PART SECTION A-A'''
 
|}
 
 
 
===751.22.3.10 Closed Intermediate Bent Diaphragms===
 
 
 
'''(Fixed Intermediate Bents with Continuous Slab)<br/>Dimensions:'''
 
 
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Diaphragms_Dim_Part_Elevations.gif]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="250"|'''PART ELEVATION FOR<br/>BULB-TEE GIRDERS'''
 
|width="450"|'''PART ELEVATION'''
 
|}
 
 
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Diaphragms_Dim_Part_Plan.gif]]</center>
 
 
 
<center>'''PART PLAN'''</center>
 
 
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Diaphragms_Dim_Part_Plan_Showing_Jt_Filler.gif]]</center>
 
 
 
<center>'''PART PLAN'''<br/>(Showing Joint Filler)</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|style="text-align:center" valign="top"|[[Image:751.22_Closed_Int_Bent_Diaphragms_Detail_of_Key.gif]]
 
|(*) Make flush with Bent Caps less than 3'-0" wide.  For Bent Caps 3'-0" and over, make Diaphragms 2'-6" wide unless skew requires wider Diaphragm to accommodate Coil Ties.<br/>&nbsp;<br/>(**) For tapered bearings or for bearings with different thickness use the following note: "Fill area under girders with Joint Filler."
 
|}
 
 
 
 
 
 
 
'''(Expansion Intermediate Bents with Continuous Slab)<br/>Dimensions:'''
 
 
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Expansion_Diaphragms_Dim_Part_Elevations.gif]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="250"|'''PART ELEVATION FOR<br/>BULB-TEE GIRDERS'''
 
|width="450"|'''PART ELEVATION'''
 
|}
 
 
 
[[image:751.22.3.10 part elev for NU girders, expansion.jpg|center|450px|thumb|<center>'''PART ELEVATION FOR NU GIRDERS'''</center>]]
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Expansion_Diaphragms_Dim_Part_Plan.gif]]</center>
 
 
 
<center>'''PART PLAN'''</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="400"|[[Image:751.22_Closed_Int_Bent_Expansion_Diaphragms_Dim_Part_Longitudinal_Elevation.gif]]
 
|style="text-align:left"|(*) Make flush with Bent Caps less than 3'-0" wide.  For Bent Caps 3'-0" and over, make Diaphragm 2'-6" wide unless skew requires wider Diaphragm to accommodate Coil Ties.
 
 
 
(**) Use Shear Blocks when Bent Cap steps down in one direction or when there are less than two steps in each direction with maximum step height less than 1 1/2" each.
 
 
 
Shear Blocks shall be detailed parallel to the centerline of roadway and shall be designed to resist 0.20 times the tributary weight where tributary weight is defined as the total bent dead load reaction.  See this section for shear block design method.
 
|-
 
|'''PART LONGITUDINAL ELEVATION'''
 
|&nbsp;
 
|}
 
 
 
 
 
 
 
'''(Fixed and Expansion Intermediate Bents with Continuous Slab)<br/>Reinforcement (Square Structure):'''
 
 
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Fixed_and_Expansion_Diaphragms_Reinf_Square_Structures_Part_Elevations.gif]]</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="250"|'''PART ELEVATION FOR<br/>BULB-TEE GIRDERS'''
 
|width="450"|'''PART ELEVATION'''
 
|}
 
 
 
[[image:751.22.3.10 part elev for NU girders, fixed and expansion.jpg|center|775px|thumb|<center>'''PART ELEVATION FOR NU GIRDERS'''</center>]]
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|align="left"|(1) For Bulb-Tee Girders, the #6 Bar shall be a min. of 15" from centerline of Girder and will not extend past the bottom of the top flange.
 
 
 
(2)For Bulb-Tee Girders, use 3-#4 Bars in each Diaphragm face.
 
 
 
<br/>
 
<br/>
 
 
 
(*) #5 Bars for each layer of bent up strands.
 
 
 
(**) Use the same clearance as the longitudinal slab steel.
 
 
 
(***) By design, Min. #6 Dowel bars @ 12" cts. (Typ.) (Fixed bent only).
 
|width="550"|[[Image:751.22_Closed_Int_Bent_Fixed_and_Expansion_Diaphragms_Reinf_Square_Structures_Part_Plan.gif]]
 
|}
 
 
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|[[Image:751.22_Closed_Int_Bent_Fixed_and_Expansion_Diaphragms_Reinf_Square_Structures_Part_Elevation_AA.gif]]
 
|[[Image:751.22_Closed_Int_Bent_Fixed_and_Expansion_Diaphragms_Reinf_Square_Structures_Section_Thru_Diaphragm.gif]]
 
|-
 
|'''PART ELEVATION A-A'''
 
|'''SECTION THRU DIAPHRAGM'''
 
|}
 
 
 
 
 
'''(Fixed and Expansion Intermediate Bents with Continuous Slab)<br/>Reinforcement (Skewed Structure):'''
 
 
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Fixed_and_Expansion_Diaphragms_Reinf_Skewed_Structures_Part_Elevations.gif]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="250"|'''PART ELEVATION FOR<br/>BULB-TEE GIRDERS'''
 
|width="450"|'''PART ELEVATION'''
 
|}
 
 
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|align="left"|(1) For Bulb-Tee Girders, the #6 Bar shall be a min. of 15" from centerline of Girder and will not extend past the bottom of the top flange.
 
 
 
(2)For Bulb-Tee Girders, use 3-#4 Bars in each Diaphragm face.
 
 
 
<br/>
 
<br/>
 
 
 
(*) #5 Bars for each layer of bent up strands.
 
 
 
(**) Omit leg on outside of exterior girder.
 
 
 
(***) By design, Min. #6 Dowel bars @ 12" cts. (Typ.) (Fixed bent only).
 
|width="550"|[[Image:751.22_Closed_Int_Bent_Fixed_and_Expansion_Diaphragms_Reinf_Skewed_Structures_Part_Plan.gif]]
 
|}
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="350"|[[Image:751.22_Closed_Int_Bent_Fixed_and_Expansion_Diaphragms_Reinf_Skewed_Structures_Thru_25_Deg.gif]]
 
|width="350"|[[Image:751.22_Closed_Int_Bent_Fixed_and_Expansion_Diaphragms_Reinf_Skewed_Structures_Over_25_Deg.gif]]
 
|-
 
|'''SKEWS THRU 25 DEG.'''
 
|'''SKEWS OVER 25 DEG.'''
 
|}
 
 
 
 
 
'''(Change in Girder Height at Fixed Bents)<br/>General:'''
 
 
 
Change girder heights within a continuous girder series only when specified on Design Layout or by Structural Project Manager.
 
 
 
Girder heights can only be changed at fixed bents for continuous series.
 
 
 
See [http://epg.modot.org/index.php?title=751.11_Bearings#751.11.3.6_Girder.2FBeam_Chairs EPG 751.11.3.6 Girder/Beam Chairs] for additional girder chair details.
 
 
 
'''(Change in Girder Height at Fixed Bents) Reinforcement:'''
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Diaphragms_Reinf_Change_in_Height_at_Fixed_Bents.gif]]</center>
 
 
 
<center>'''PART ELEVATION'''</center>
 
<br/>
 
<br/>
 
<center>[[Image:751.22_Closed_Int_Bent_Diaphragms_Reinf_Change_in_Height_at_Fixed_Bents_Part_Plan.gif]]</center>
 
 
 
<center>'''PART PLAN'''</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|(*) By design, min. #6 dowel bars @ 12" cts. (Typ.)
 
 
 
(1) At each layer of bent strands.
 
 
 
(2) For bulb-tee girders, use 3-#4 bars in each diaphragm face.
 
 
 
(3) 3" min. when using beam step.
 
 
 
(4) By design, min. #6 @ 12" cts. dowel bars (Typ.)
 
|}
 
 
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Diaphragms_Reinf_Change_in_Height_at_Fixed_Bents_Part_Section_AA_Thru_Diaphragm.gif]]</center>
 
 
 
<center>'''PART SECTION A-A THRU DIAPHRAGM'''</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|Note:  Girder heights can change a maximum of one girder type.
 
 
 
(1) For bulb-tee girders, use 3-#4 bars in each diaphragm face.
 
|}
 
 
 
 
 
 
 
'''(Change in Girder Height at Fixed Bents)<br/>Edge Distance Details:'''
 
 
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Diaphragms_Edge_Distance_Change_in_Height_at_Fixed_Bents_Part_Plan_Skewed.gif]]</center>
 
 
 
<center>'''PART PLAN SKEWED STRUCTURES'''</center>
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|valign="top"|NOTE:||Field bending may be required for #4 and #6 H Bars<br/>in skewed structures near short exterior girder.
 
|}
 
 
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Diaphragms_Edge_Distance_Change_in_Height_at_Fixed_Bents_Part_Plan_Square.gif]]</center>
 
 
 
<center>'''PART PLAN SQUARED STRUCTURES'''</center>
 
 
 
(1) When beam width is controlled by girder chair clearance, make diaphragm flush with beam cap.
 
 
 
 
 
 
 
'''3/4" Chamfer and 1/2" Joint Filler'''
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Diaphragms_Chamfer_&_Joint_Filler_Section.gif]]</center>
 
 
 
<center>'''SECTION THRU<BR/>INTERMEDIATE DIAPHRAGMS'''</center>
 
 
 
 
 
<center>[[Image:751.22_Closed_Int_Bent_Diaphragms_Chamfer_&_Joint_Filler_Detail.gif]]</center>
 
 
 
<center>'''DETAIL "A"'''</center>
 
 
 
===751.22.3.11 Non-integral End Bent Diaphragms===
 
 
 
 
 
'''(End Diaphragm with no Expansion Devices)<br/>Dimensions:'''
 
 
 
<center>[[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Dim_Part_Elevations.jpg|800px]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="175"|'''PART ELEVATION FOR<br/>BULB-TEE GIRDERS'''
 
|width="450"|'''PART ELEVATION NEAR END BENT'''
 
|}
 
 
 
 
 
<center>[[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Dim_Part_Plan.jpg]]</center>
 
 
 
 
 
<center>'''PART PLAN NEAR END BENT'''</center>
 
 
 
 
 
{|border="0" cellpadding="5" style="text-align:center"
 
 
 
|[[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Dim_Part_Section.jpg]]<br/>&nbsp;<br/>'''PART SECTION A-A'''
 
|align="left" width="200"|(*) A sloped diaphragm allows clearance for the future placement of jacks needed to replace bearings.<br/> &nbsp; <br/>
 
(**) For Bulb-Tee Girder, spacings less than 8'-8" dimensions "A", "B" & "C" may have to be modified.<br/> &nbsp; <br/>(***) Make sure the diaphragm is wide enough to provide cover for the coil tie rods.
 
|
 
{|border="1" cellpadding="5" style="text-align:center"
 
 
 
|rowspan="2"|GIRDER<br/>TYPE
 
|colspan="3"|DIMENSIONS
 
|-
 
|"A" <!-- column occupied by cell GIRDER<br/>TYPE -->
 
|"B"
 
|"C"
 
|-
 
|TYPE "2"<br/>2'-8"
 
|12"||15"||13"
 
|-
 
|TYPE "3"<br/>3'-3"
 
|17"||15"||19"
 
|-
 
|TYPE "4"<br/>3'-9"
 
|19"||18"||21"
 
|-
 
|TYPE "6"<br/>4'-6"
 
|2'-3"||21"||2'-1"
 
|-
 
|BULB-TEE<br/>6'-0½ *
 
|3'-0"||2'-6½"||2'-9"
 
|}
 
|}
 
 
 
 
 
'''(End Diaphragm with no Expansion Devices)<br/>Coil Tie Rods:'''
 
 
 
 
 
<center>[[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Coil_Tie_Rods_Part_Elevation.gif]]</center>
 
 
 
 
 
<center>'''PART ELEVATION NEAR END BENT'''</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|NOTE:||For location of the Coil Tie Rods in a plan view, see [[#plan of ciol tie rods|Coil Ties]].
 
|-
 
|&nbsp;||(*) 6" (Min.) shall be used for all I-Girders and Bulb-Tee Girders.
 
|}
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|[[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Coil_Tie_Rods_Part_Section.gif]]
 
|valign="bottom" colspan="2"|[[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Coil_Tie_Rods_Details.gif]]
 
|-
 
|&nbsp;||'''EXTERIOR GIRDERS'''||'''INTERIOR GIRDERS'''
 
|-
 
|'''PART SECTION A-A'''||colspan="2"|'''DETAILS OF COIL TIE RODS<br/>IN BULB-TEE GIRDERS'''
 
|}
 
 
 
 
 
 
 
'''(End Diaphragm with no Expansion Devices)<br/>Reinforcement:'''
 
 
 
 
 
<center>[[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Reinforcement_Part_Elevation.gif]]</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="175"|'''PART ELEVATION<br/>NEAR END BENT FOR<br/>BULB-TEE GIRDERS'''
 
|width="450"|'''PART ELEVATION NEAR END BENT'''
 
|}
 
 
 
 
 
<center>[[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Reinforcement_Part_Plan.gif]]</center>
 
 
 
<center>'''PART PLAN NEAR END BENT'''</center>
 
 
 
 
 
{|border="0" cellpadding="5"
 
 
 
|&nbsp;||(1) For Bulb-Tee Girders, the first #6 Bar shall be placed 10" from the centerline of Web (Top Flange will prevent some Bars from extending into the Slab).
 
|-
 
|rowspan="3"|[[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Reinforcement_Part_Section.gif]]
 
|&nbsp;
 
|-
 
|NOTE: Bars across end of girders to be continuous.<!--column 1 occupied by cell [[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Reinforcement_Part_Section.gif]]-->
 
|-
 
|(*) Use the same clearance as longitudinal slab steel.<br/>(**) Show this dimension Bridge Plan Sheets.<!--column 1 occupied by cell [[Image:751.22_Non_Integral_End_Bent_Diaphragms_No_Exp_Device_Reinforcement_Part_Section.gif]]-->
 
|}
 
 
 
:::::'''PART SECTION A-A'''
 
 
 
 
 
'''(End Diaphragm with Expansion Devices)<br/>Dimensions:'''
 
 
 
 
 
<center>[[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Dim_Part_Elevations.jpg]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="175"|'''PART ELEVATION<br/>FOR BULB-TEE GIRDERS'''
 
|width="450"|'''PART ELEVATION NEAR END BENT'''
 
|}
 
 
 
<center>[[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Dim_Part_Plan.gif]]</center>
 
 
 
<center>'''PART PLAN NEAR END BENT'''</center>
 
 
 
{|border="0" cellpadding="3" style="text-align:center"
 
 
 
|rowspan="3"|[[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Dim_Part_Section.jpg]]<br/>&nbsp;<br/>'''PART SECTION A-A'''
 
|align="left" width="140"|(*) For Bulb-Tee Girder, spacings less than 8'-8" dimensions "A", "B" & "C" may have to be modified.
 
|rowspan="3"|
 
{|border="1" cellpadding="4" style="text-align:center"
 
 
 
|rowspan="2"|GIRDER<br/>TYPE
 
|colspan="3"|DIMENSIONS
 
|-
 
|"A" <!-- column occupied by cell GIRDER<br/>TYPE -->
 
|"B"
 
|"C"
 
|-
 
|TYPE "2"<br/>2'-8"
 
|12"||15"||13"
 
|-
 
|TYPE "3"<br/>3'-3"
 
|17"||15"||19"
 
|-
 
|TYPE "4"<br/>3'-9"
 
|19"||18"||21"
 
|-
 
|TYPE "6"<br/>4'-6"
 
|2'-3"||21"||2'-1"
 
|-
 
|BULB-TEE<br/>6'-0½ *
 
|3'-0"||2'-6½"||2'-9"
 
|}
 
|-
 
|align="left"|(**) A sloped diaphragm allows clearance for the future placement of jacks needed to replace bearings.
 
|-
 
|align="left"| (***) Make sure the diaphragm is wide enough to provide cover for the coil tie rods.
 
|}
 
 
 
 
 
'''(End Diaphragm with Expansion Devices)<br/>Coil Tie Rods:'''
 
 
 
 
 
<center>[[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Coil_Tie_Rods_Part_Elevation.gif]]</center>
 
 
 
<center>'''PART ELEVATION NEAR END BENT'''</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|NOTE:||For location of the Coil Tie Rods in a plan view, see [[#plan of ciol tie rods|Coil Ties]].
 
|-
 
|&nbsp;||(*) 6" (Min.) shall be used for all I-Girders and Bulb-Tee Girders.
 
|}
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|[[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Coil_Tie_Rods_Part_Section_AA.gif]]
 
|valign="bottom" colspan="2"|[[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Coil_Tie_Rods_Details.gif]]
 
|-
 
|&nbsp;||'''EXTERIOR GIRDERS'''||'''INTERIOR GIRDERS'''
 
|-
 
|'''PART SECTION A-A'''||colspan="2"|'''DETAILS OF COIL TIE RODS<br/>IN BULB-TEE GIRDERS'''
 
|}
 
 
 
 
 
'''(End Diaphragm with Expansion Devices)<br/>Reinforcement:'''
 
 
 
 
 
<center>[[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Reinforcement_Part_Elevation.gif]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="175"|'''PART ELEVATION<br/>NEAR END BENT FOR<br/>BULB-TEE GIRDERS'''
 
|width="450"|'''PART ELEVATION NEAR END BENT'''
 
|}
 
 
 
<center>[[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Reinforcement_Part_Plan.gif]]</center>
 
 
 
<center>'''PART PLAN NEAR END BENT'''</center>
 
 
 
 
 
{|border="0" cellpadding="5"
 
 
 
|&nbsp;||(1) For Bulb-Tee Girders, the first #6 Bar shall be placed 10" from the centerline of Web (Top Flange will prevent some Bars from extending into the Slab).
 
|-
 
|rowspan="3"|[[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Reinforcement_Part_Section.gif]]
 
|&nbsp;
 
|-
 
|NOTE:  Epoxy Coat all Reinforcing Steel in the End of Diaphragms.
 
 
 
NOTE: Bars across end of girders to be continuous.<!--column 1 occupied by cell [[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Reinforcement_Part_Section.gif]]-->
 
|-
 
|(*) Use the same clearance as longitudinal slab steel.<br/>(**) Show this dimension Bridge Plan Sheets.<!--column 1 occupied by cell [[Image:751.22_Non_Integral_End_Bent_Diaphragms_with_Exp_Device_Reinforcement_Part_Section.gif]]-->
 
|}
 
 
 
:::::'''PART SECTION A-A'''
 
 
 
===751.22.3.12 Non-integral Intermediate Bent Diaphragms===
 
 
 
'''(End Diaphragms with Expansion Device)<br/>Dimensions:'''
 
 
 
 
 
::::::::::::::::NOTE:  Slope at top of Beam Cap and Protective<br/>Coating to be used on Structures with Expansion<br/>Devices.
 
 
 
<center>[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Exp_Device_Dim_Part_Elevation.jpg]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="175"|'''PART ELEVATION FOR<br/>BULB-TEE GIRDERS'''
 
|width="450"|'''PART ELEVATION NEAR INT. BENT'''
 
|}
 
 
 
 
 
<center>[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Exp_Device_Dim_Part_Plan.jpg]]</center>
 
 
 
 
 
<center>'''PART PLAN NEAR INT. BENT'''</center>
 
 
 
 
 
{|border="0" cellpadding="3" style="text-align:center"
 
 
 
|rowspan="3"|[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Exp_Device_Dim_Section.jpg]]<br/>&nbsp;<br/>'''PART SECTION A-A'''
 
|align="left" width="140"|(*) A sloped diaphragm allows clearance for the future placement of jacks needed to replace bearings.
 
|rowspan="3"|
 
{|border="1" cellpadding="5" style="text-align:center"
 
 
 
|rowspan="2"|GIRDER<br/>TYPE
 
|colspan="3"|DIMENSIONS
 
|-
 
|"A" <!-- column occupied by cell GIRDER<br/>TYPE -->
 
|"B"
 
|"C"
 
|-
 
|TYPE "2"<br/>2'-8"
 
|12"||15"||13"
 
|-
 
|TYPE "3"<br/>3'-3"
 
|17"||15"||19"
 
|-
 
|TYPE "4"<br/>3'-9"
 
|19"||18"||21"
 
|-
 
|TYPE "6"<br/>4'-6"
 
|2'-3"||21"||2'-1"
 
|-
 
|BULB-TEE<br/>6'-0½ *
 
|3'-0"||2'-6½"||2'-9"
 
|}
 
|-
 
|align="left" width="140"|(**) For Bulb-Tee Girder, spacings less than 8'-8" dimensions "A", "B" & "C" may have to be modified.
 
|-
 
|align="left" width="140"|(***) Make sure the diaphragm is wide enough to provide enough cover for the Coil Tie Rods.
 
|}
 
 
 
 
 
'''(End Diaphragms with Expansion Device)<br/>Coil Tie Rods:'''
 
 
 
 
 
<center>[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Exp_Device_Coil_Tie_Rod_Part_Elevation.gif]]</center>
 
 
 
 
 
<center>'''PART ELEVATION NEAR INT. BENT'''</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|NOTE:||For location of the Coil Tie Rods in a plan view, see [[#plan of ciol tie rods|Coil Ties]].
 
|-
 
|&nbsp;||(*) 6" (Min.) shall be used for all I-Girders and Bulb-Tee Girders.
 
|}
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|[[Image:751.22 Non Integral Intermediate Bent Diaphragm with Exp Device Coil Tie Rod Part Section.gif]]
 
|valign="bottom" colspan="2"|[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Exp_Device_Coil_Tie_Rod_Details.gif]]
 
|-
 
|&nbsp;||'''EXTERIOR GIRDERS'''||'''INTERIOR GIRDERS'''
 
|-
 
|'''PART SECTION A-A'''||colspan="2"|'''DETAILS OF COIL TIE RODS<br/>IN BULB-TEE GIRDERS'''
 
|}
 
 
 
 
 
'''(End Diaphragms with Expansion Device)<br/>Reinforcement:'''
 
 
 
 
 
<center>[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Exp_Device_Reinf_Elevations.gif]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="175"|'''PART ELEVATION<br/>NEAR INT. BENT FOR<br/>BULB-TEE GIRDERS'''
 
|width="450"|'''PART ELEVATION NEAR INT. BENT'''
 
|}
 
 
 
:::Note:  Slope at top of beam cap and protective coating to be used on structures with expansion devices.
 
 
 
 
 
:::(1) For Bulb-Tee Girders, the first #6 Bar shall be placed 10" from the centerline of Web (Top Flange will<br/>prevent some Bars from extending into the Slab).
 
 
 
<center>[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Exp_Device_Reinf_Part_Plan.gif]]</center>
 
 
 
<center>'''PART PLAN NEAR INT. BENT'''</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Exp_Device_Reinf_Part_Section.gif]]
 
|[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Exp_Device_Reinf_Detail.gif]]
 
|-
 
|'''PART SECTION A-A'''
 
|'''DETAIL "A"'''
 
|}
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|(*) See Detail "A" for the placement of reinforcement.
 
 
 
(**) Use the same clearance as longitudinal slab steel.
 
 
 
NOTE: Epoxy coat all reinforcing steel in the end diaphragms.
 
|}
 
 
 
 
 
'''(End Diaphragm with Finger Plate Expansion Device)<br/>Diaphragm Reinforcements:'''
 
 
 
 
 
'''CLOSED DIAPHRAGM:'''
 
:(NOTE: Use only when expansion device connects prestress girder series and steel girder series.)
 
 
 
<center>[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Finger_Plate_Exp_Device_Reinf_Closed_Diaphragm.gif]]</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|width="300"|NOTE: See preceding sheets for bar spacing and detail not shown.
 
 
 
A protective coating shall be applied to concrete surface exposed to drainage from roadway.  Indicate surface to be coated on plans.  Epoxy coat all reinforcing steel in the end diaphragms.
 
|width="50"|&nbsp;
 
|valign="top"|(2) For Bulb-Tee Girders use 3-#4 Bars in each face.
 
|}
 
 
 
 
 
'''OPEN DIAPHRAGM'''
 
 
 
<center>[[Image:751.22_Non_Integral_Intermediate_Bent_Diaphragm_with_Finger_Plate_Exp_Device_Reinf_Open_Diaphragm.gif]]</center>
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|(*)||Use only on Type 6 Girder
 
|-
 
|valign="top"|(**)||12" for #4 Bars<br/>14" for #6 Bars<br/>(Shown on Plans)
 
|width="300"|&nbsp;
 
 
 
|}
 
 
 
(1) Use the same clearance as longitudinal slab steel.
 
 
 
===751.22.3.13 Intermediate Diaphragms===
 
 
 
'''(Use Steel Intermediate Diaphragm for Prestress Spans over 50 feet)'''
 
 
 
 
 
<center>[[Image:751.22_Intermediate_Diaphragms_Part_Elevation.gif]]</center>
 
 
 
 
 
<center>'''PART SECTION SHOWING INTERMEDIATE DIAPHRAGMS'''</center>
 
<center>(MoDOT Type 2,3,4,6 and NU 53)</center>
 
 
 
 
 
<center>[[Image:751.22_Intermediate_Diaphragms_Details_A_&_B.gif]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="275"|'''DETAIL "A"'''||width="275"|'''DETAIL "B"'''
 
 
 
|}
 
 
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|valign="top" align="right"|(*)||In lieu of 2 1/2" O.D. washers, contractor may substitute a 3/16" (Min. thickness) plate with four 15/16"ø holes and one hardened washer per bolt.
 
|-
 
|valign="top" align="right"|(**)||Bolts shall be tightened to provide a tension of one-half that specified in Sec 712 for high strength bolt installation.  A325 bolts may be substituted for and installed in accordance with the requirements for the specified A307 bolts.
 
|-
 
|valign="top" align="right"|NOTE:||Use Detail "A" at interior girder for diaphragms straight in line across structure.  (Use straight diaphragm normal to girders for skews thru 20°).
 
 
 
Use Detail "B" for exterior girder and interior girder for diaphragms stepped across structure.  (Use stepped diaphragm for skews over 20°).
 
 
 
|}
 
 
 
 
 
<center>[[Image:751.22_Intermediate_Diaphragms_Sections_CC_&_DD.gif]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="275"|'''SECTION C-C'''||width="275"|'''SECTION D-D'''
 
 
 
|}
 
 
 
<div id="PART SECTION SHOWING"></div>
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|[[Image:751.22_Intermediate_Diaphragms_Section_EE.gif]]
 
|rowspan="3"|[[Image:751.22_Intermediate_Diaphragms_Part_Section.jpg]]
 
|-
 
|'''SECTION E-E'''
 
|-
 
|&nbsp;
 
|-
 
|&nbsp;||'''PART SECTION SHOWING<br/>INTERMEDIATE DIAPHRAGMS'''<br/>(MoDOT Type 7,8, NU 63 and 70)
 
|}
 
 
 
 
 
Bulb-Tee spans of 90 ft. or less require one intermediate diaphragm per span.  Bulb-Tee spans of over 90 ft. require two intermediate diaphragms per span (spaced equally as allowed by clearance to harped strands). Maximum spacing is 50 ft.
 
 
Permanent intermediate diaphragms are not required for NU 35 and NU 43 standard girders.  Temporary intermediate diaphragms/bracing are required for construction of the bridge deck.  See [[751.50 Standard Detailing Notes#(H2c2.2)|EPG 751.50 Note H2c2.2]].
 
 
 
The detailer shall check that the 1 1/2 inch ø holes for the diaphragms shown on the design plans will provide a minimum clearance of at least 1 1/2 inches to any prestressing strands.
 
 
 
 
 
<center>[[Image:751.22_Intermediate_Diaphragms_Details_A_&_B_enlarged.gif]]</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="350"|'''DETAIL "A"'''||width="350"|'''DETAIL "B"'''
 
 
 
|}
 
 
 
 
 
{|border="0" cellpadding="5" align="center"
 
 
 
|valign="top" align="right"|(*)||In lieu of 2 1/2" O.D. washers, the contractor may substitute a 3/16" (Min. thickness) plate with four 15/16"ø holes and one hardened washer per bolt.
 
|-
 
|valign="top" align="right"|(**)||Bolts shall be tightened to provide a tension of one-half that specified in Sec 712 for high strength bolt installation.  A325 bolts may be substituted for and installed in accordance with the requirements for the specified A307 bolts.
 
|-
 
|valign="top" align="right"|NOTE:||Use Detail "A" at interior girder for diaphragms straight in line across structure.  (Use straight diaphragm normal to girders for skews thru 20°).
 
 
 
Use Detail "B" for exterior girder and interior girder for diaphragms stepped across structure.  (Use stepped diaphragm for skews over 20°).
 
 
 
|}
 
 
 
 
 
<center>[[Image:751.22_Intermediate_Diaphragms_Sections_CC_&_DD_enlarged.gif]]</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="150"|'''SECTION C-C'''||width="375"|'''SECTION D-D'''
 
 
 
|}
 
 
 
===751.22.3.14 Coil Ties===
 
 
 
 
 
<center>[[Image:751.22_Coil_Ties_Part_Elevations.gif]]</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="150"|'''PART ELEVATION FOR<br/>BULB-TEE GIRDERS
 
|width="450"|'''PART ELEVATION'''
 
 
 
|}
 
 
 
<div id="plan of ciol tie rods"></div>
 
<center>[[Image:751.22_Coil_Ties_Part_Plan_Square.gif]]</center>
 
 
 
 
 
<center>'''PART PLAN<br/>(SQUARE)'''<br/>* 4" Min. (Typ.) (Do not show Dim. on Plans)</center>
 
 
 
 
 
<center>[[Image:751.22_Coil_Ties_Part_Plan_Skew_to_20_deg.gif]]</center>
 
  
 +
===751.22.3.13 Concrete Shear Blocks===
  
<center>'''PART PLAN<br/>(SKEWED TO 20 DEG.)'''</center>
+
Concrete shear blocks shall be used when 4 anchor bolts per bearing are insufficient, or for preventing loss of support on beams and stub bent footings. Design shear blocks in accordance with LRFD 5.7.4.3. The following dimensions and sizes are for rough guidelines only and may be altered to fit specific situations:
  
  
<center>[[Image:751.22_Coil_Ties_Part_Plan_Skew_over_20_deg.gif]]</center>
+
'''Concrete block dimensions'''
  
 +
L<sub>vi</sub> = Length shall extend all the way across the beam (for ease of forming), oriented parallel to centerline of roadway.
  
<center>'''PART PLAN<br/>(SKEWED OVER 20 DEG.)'''</center>
+
b<sub>vi</sub> = Width is as required for concrete area. Allow about 1/2 in. (typical) clearance between the edge of the sole plate and the edge of the block to allow engaging of anchor bolts.  
  
 +
H = height of shear block and shall extend to about an inch (+/-) above the top of the sole plate.
  
<center>[[Image:751.22_Coil_Ties_Ext_Girder_at_End_Bent.gif]]</center>
 
  
 +
'''Steel reinforcement'''
  
<center>'''EXTERIOR GIRDER AT END BENT'''</center>
+
Bar size = #4 min. to # 6 max. hairpins placed parallel to the centerline of the beam, with #4 horizontal straight bars at the top of the hairpin to ensure proper alignment.
  
 +
Space hairpin shear bars as required to provide the required steel area, with 6" minimum to 12" maximum. The maximum edge distance in the direction of the spacing = half of reinforcement spacing.
  
{|border="0" cellpadding="5" align="center"
 
  
|valign="top" align="right"|(1)||3" For Beam Type 2<br/>5" For Beam Type 3, 4 & 6
+
'''Demand shear per block'''
|-
 
|&nbsp;
 
|-
 
|NOTE:||See previous page for location of Coil Tie Rods on Bulb-Tee girders.
 
  
|}
+
For complete seismic analysis, F<sub>T</sub> = transverse component of total horizontal seismic force demand at the bent, normal to the centerline of the roadway, kips. Both seismic load cases, Case 1 = L + 0.3T and Case 2 = 0.3L + T, must be satisfied.
  
===751.22.3.15 Dowel Bars (Rods)===
+
For seismic details only (strength limit states), transverse F<sub>T</sub> = 0.25(DL). Where DL = unfactored dead load reaction at the bent, kips
  
 +
R = 1.0 for seismic details only (strength limit states) and 0.8 for complete seismic analysis
  
<center>[[Image:751.22_Dowel_Bars_Elevation_&_Section_AA.gif]]</center>
+
N<sub>B</sub> = the number of blocks resisting the seismic force. The designer should consider using a value of N<sub>B</sub> that is less than the total number of blocks, because all blocks may not resist equal amounts of force. For example, two shear blocks as shown in details below, only left side shear block will resist horizontal force when seismic forces act from right to left.  
 +
<center>
 +
<math>V_{ui} \le \emptyset V_{ni}</math>
 +
</center>
 +
:where:
  
 +
:<math>V_{ui} = factored \ shear \ force \ per \ block,\ kips </math>
 +
::<math>= \frac{F_T}{N_B R}</math>
  
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
  
|width="300"|'''PART ELEVATION<br/>(FIXED BENT)'''
+
'''Block shear resistance:'''
|width="300"|'''SECTION A-A'''
 
  
|}
+
∅ = 0.90 resistance for seismic details only (strength limit states) and 1.0 for complete seismic analysis
  
 +
:<math>V_{ni} = CA_{cv} + \mu (A_{vf}f_y) = nominal \ shear \ resistance \ per \ block, \ kips</math>
 +
     
 +
:<math>A_{cv} = b_{vi} L_{vi}</math>
 +
 
 +
b<sub>vi</sub> = width of the shear block, in.
  
::::Dowel bars shall be used for all fixed intermediate bents under prestressed superstructures. Generally, shear resistance from shear key is not considered for typical bridges in seismic performance Category A.
+
L<sub>vi</sub> = length of the shear block, in.
 
 
 
 
::::Dowel bars shall be determined by design.  (Minimum #6 Bars @ 12" Cts.) For shear stress, f<sub>v</sub>, computation, see [[751.9 LFD Seismic#751.9.3.1.2 Dowel Rods|EPG 751.9.3.1.2 Dowel Rods]].
 
 
 
:::::f<sub>v</sub> ≤ <math>\,\phi</math><sub>v</sub> ● Fv<sub>n</sub>
 
 
 
:::::Where,
 
 
 
::::::<math>\,\phi</math><sub>v</sub>  = Resistance factor
 
 
 
::::::f<sub>v</sub> = Shear stress (ksi)
 
 
 
::::::Fv<sub>n</sub> = Nominal shear resistance of dowel bar (ksi)
 
 
 
===751.22.3.16 Vent Holes===
 
 
 
 
 
::::Note:  Use vent holes on all stream crossing structures.
 
 
 
 
 
<center>[[Image:751.22_Vent_Holes_Elevation_&_Section.gif]]</center>
 
 
 
{|border="0" cellpadding="5" align="center" style="text-align:center"
 
 
 
|width="300"|'''PART ELEVATION OF GIRDER'''
 
|width="300"|'''PART SECTION NEAR VENT HOLE'''
 
 
 
|}
 
 
 
 
 
::::Note:  Place vent holes at or near upgrade of 1/3 point of girders and clear<br/>reinforcing steel or strands by 1-1/2" minimum and steel intermediate<br/>diaphragms bolt connection by 6" minimum.
 
 
 
===751.22.3.17 Shear Blocks===
 
 
 
 
 
A minimum of two Shear Blocks 12" wide x (1) 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:751.22_Shear_Blocks_Elevation_View_Open_Diaphragm.gif]]</center>
 
 
 
<center>'''ELEVATION VIEW'''</center>
 
 
 
 
 
 
 
::::::(1) Height of shear block shall extend a minimum of 1" above the top pf the sole plate.
 
 
 
  
 +
A<sub>vf</sub> = area of shear reinforcement crossing the shear plane, sq. in.
  
<center>[[Image:751.22_Shear_Blocks_Elevation_View.gif]]</center>
+
f<sub>y</sub> = yield strength of shear reinforcement not to exceed 60 ksi
  
  
<center>'''ELEVATION VIEW'''</center>
+
The nominal shear resistance is limited by the following equations:
 +
::<math>V_{ni} \le K1 f'_c A_{cv}</math>  and  <math>V_{ni} \le K2 A_{cv}</math>
  
 +
:<math>f'_c</math>= compressive strength of concrete at 28-day cure, ksi
  
<center>[[Image:751.22_Shear_Blocks_Plan_View.gif]]</center>
+
For new construction (monolithic construction):
 +
:C = 0.4 ksi
 +
:μ = 1.4
 +
:K1 = 0.25
 +
:K2 = 1.5 ksi
  
 +
For retrofits:
 +
:C = 0.24 ksi
 +
:μ = 1.0
 +
:K1 = 0.25
 +
:K2 = 1.5 ksi
  
<center>'''PLAN VIEW'''</center>
 
  
 +
'''Minimum area of shear reinforcement per shear block:'''
  
{|border="0" cellpadding="5" align="center"
+
::<math>A_{vf} \ge \frac{0.05A_{cv}}{f_y} </math>
|-
 
|width="375"|Note:<br/>Shear blocks shall be used at bents with open diaphragms when anchor bolts can not be designed to resist earthquake loading.
 
  
|}
 
  
<center>[[Image:751.22_Shear_Blocks_Plan_View_Exp_Bts_Open_Diaphragms.gif]]</center>
+
'''Concrete shear block details:'''
  
 +
A minimum of two shear blocks 12" wide by width of substructure beam will be detailed at effective locations on open diaphragm bent caps and closed diaphragm bent caps when adequate structural restraint cannot be provided with anchor bolts. Shear blocks shall be detailed parallel to the centerline of roadway.
  
<center>'''PLAN VIEW OF BEAM CAP'''</center>
+
[[image:751.22.3.14_elevation.jpg|center|700px]]
 +
<center>
 +
(1) Height of shear block shall extend a minimum of 1 inch above the top of the sole plate (typ.).
  
<center>'''EXPANSION BENTS WITH OPEN DIAPHRAGMS'''</center>
 
  
 +
[[image:751.22.3.14_plan.jpg|center|950px]]
 +
'''PLAN OF BEAM'''<br/>Anchor bolts and sole plates not shown for clarity.
  
{|border="0" cellpadding="5" align="center"
+
'''*''' With open diaphragm, beam steps normal to beam; with closed diaphragm, beam steps parallel to centerline roadway.
|-
+
</center>
|width="375"|Note:<br/>For Expansion Bents with open diaphragms, the steps or Shear Block (if applicable) should be normal to the length of cap.
 
  
|}
+
===751.22.3.14 Miscellaneous===
 
 
 
 
<center>[[Image:751.22_Shear_Blocks_Plan_View_Exp_Bts_Closed_Diaphragms.gif]]</center>
 
 
 
 
 
<center>'''PLAN VIEW OF BEAM CAP'''</center>
 
 
 
<center>'''EXPANSION BENTS WITH CLOSED DIAPHRAGMS'''</center>
 
 
 
 
 
{|border="0" cellpadding="5" align="center"
 
|-
 
|width="475"|Note:<br/>For Closed Diaphragm Expansion Bents, the steps or haunches shall be detailed parallel to the centerline of roadway.
 
 
 
For Integral End Bents the steps may be skewed due to stirrups being placed parallel to centerline of roadway.
 
 
 
Shear Blocks for Expansion Bents with Closed Diaphragms shall be detailed parallel to the centerline of roadway.  Shear Blocks used in conjunction with sole plates and anchor bolts shall be detailed parallel to the edge of sole plate.
 
 
 
|}
 
 
 
===751.22.3.18 Miscellaneous===
 
  
  
 
'''Dimensional Tolerances'''
 
'''Dimensional Tolerances'''
  
'''I-Girders, Solid Slab Beams, Voided Slab Beams, Box Beams, Double-Tee Girders, Deck Panels and Miscellaneous Prestress Units, see [http://www.modot.mo.gov/business/standards_and_specs/Sec1029.pdf Sec 1029]'''  
+
'''I-Girders, Solid Slab Beams, Voided Slab Beams, Box Beams, Double-Tee Girders, Deck Panels and Miscellaneous Prestress Units, see [http://www.modot.org/business/standards_and_specs/SpecbookEPG.pdf#page=14 Sec 1029]'''  
  
  
Line 5,326: Line 2,088:
 
If A.B. holes are formed with galvanized sheet metal, the forms may be left in place.
 
If A.B. holes are formed with galvanized sheet metal, the forms may be left in place.
  
Hole (1-1/2"ø) to be grouted with expansive type mortar meeting the requirements of Sec 1066.
+
Hole (1-1/2"ø) to be grouted with approved non-shrink grout meeting the requirements of ASTM C1107.
 
|}
 
|}
 
  
  

Revision as of 08:51, 22 March 2024

Video
Concrete Girder

Contents

751.22.1 General

EPG 751.22 illustrates the general design procedure for prestressed concrete I girders (Type 2, 3, 4 and 6), bulb-tee girders (Type 7 and 8) and NU girders (NU 35, 43, 53, 63, 70 and 78) using AASHTO LRFD Bridge Design Specifications except as noted.

751.22.1.1 Material Properties

751.22.1.1.jpg

Increasing Girder Capacity

The following allowable modification of material properties listed in order of increasing costs may be considered if required by design.

1. Increase concrete strength up to 8.0 ksi (f′c = 6.5 ksi) (readily producible by fabricator)
2. Increase concrete strength greater than 8.0 ksi (readily producible by fabricator)
3. Modify geometric properties (in order of increasing costs)
a. Increase top flange height (and overall height accordingly)
b. Use modified Type 2, 3, 4 and 6 girders (most costly and inconvenient due to required forming bed modifications)

Class A-1 Concrete

Conventional concrete with the following compression strengths shall be used as required for I girders and bulb-tee girders.

f′c = 6.0 ksi (f′ci = 4.5 ksi) → f′c = 7.0 ksi (f′ci = 5.0 ksi) → f′c = 8.0 ksi (f′ci = 6.5 ksi)

The lowest concrete strength satisfying the demand shall be used.

The NU girders shall use conventional concrete with the following compression strength.

f′c = 8.0 ksi (f′ci = 6.5 ksi)

High strength concrete with compressive strengths up to f′c =10 ksi (f′ci = 7.0 ksi) may be used with the permission of the Structural Project Manager or Structural Liaison Engineer. High strength concrete may increase costs due to production modifications necessary to obtain the required strength.

Modulus of Elasticity

Ec = 33,000K1wc1.5f′c (f′c in ksi)
where:
K1 = correction factor for source of aggregate = 1.0 unless determined by physical testing
wc = 0.140 + 0.001f′c (f′c in ksi)

Prestressing Strands

Prestressing strands shall be Grade 270 uncoated, low relaxation, seven-wire strands in accordance with AASHTO M 203 with the following design properties.

Ultimate tensile strength, fpu = 270 ksi 1/2-inch strand: diameter, dps = 0.5 in. and area, Aps = 0.153 in.2
Yield strength, fpy = 0.9fpu = 243 ksi 0.6-inch strand: diameter, dps = 0.6 in. and area, Aps = 0.217 in.2
Maximum allowed force per strand,
    fpbt Aps = 30.98 kips (1/2-inch strands)
    fpbt Aps = 43.94 kips (0.6-inch strands)
Modulus of elasticity, Ep = 28,500 ksi
Maximum allowed stress prior to transfer,
    fpbt = 0.75fpu = 202.5 ksi

Total initial prestress force equals the number of strands multiplied by the required initial prestress force per strand.

Typically, the required initial prestress force per strand is the maximum allowed force per strand.

Report on the plans the required number of strands by design and the total initial prestress force using EPG 751.50 Standard Detailing Notes H2c1.3.

Reinforcing Steel

Deformed bars shall be Grade 60 in accordance with AASHTO M 31 with the following design properties.

Yield strength, fy = 60.0 ksi Modulus of elasticity, Es = 29,000 ksi

Welded wire reinforcement shall be in accordance with AASHTO M 336 with the following design properties.

Yield strength, fy = 70.0 ksi Modulus of elasticity, Es = 29,000 ksi

All bars extending into slab shall be epoxy coated. Welded wired reinforcement shall not be epoxy coated.

751.22.1.2 Geometric Properties

The following sections, except those specified as modified, shall be preferred because of their familiarity to local precast plants. These sections have been entered into the beam section libraries of in-house design software. The top flange height and overall height may be increased if required but any deviation from the standard sections shown shall be discussed with Structural Project Manager or Structural Liaison Engineer. The use of the modified girders shall be discussed with Structural Project Manager or Structural Liaison Engineer.

I Girders:
751.22.1.2 type 2 2022.jpg


751.22.1.2 type 3 2022.jpg


751.22.1.2 type 4 2022.jpg


751.22.1.2 type 6 2022.jpg


Bulb-Tee Girders:
751.22.1.2 type 7 2022.jpg


NU Girders:
751.22.1.2 NU 35 43 53 2022.jpg


751.22.1.2 NU 63 70 78 2022.jpg

751.22.1.3 Typical Span Ranges

The following charts provide a general baseline for the maximum span lengths of prestressed I-girders and NU girders based off single span designs in accordance with LRFD, 9th Edition. The designs used for these charts use the maximum practical girder spacing (9’-6” for Type 2, 3 and 4 girders, approximately 11 feet to 11’-6” for all other girders shown). The charts were developed using designs that used standard materials and shapes and no debonding. Increased span lengths are possible with modification to the materials, shapes, and/or girder spacings used. Increased span lengths are also likely for continuous span bridges. See Increasing Girder Capacity section above for more information. These charts shall be used for preliminary design only.

Limitations of the Charts:

These charts only contain data on designs with a concrete compressive strength equal to 8.0ksi, this is due to a lack of sufficient data for designs using a concrete compressive strength of 6.0ksi or 7.0ksi.

Prestressed I-Girder Single Span Ranges
751.22.1.3 PSI 8ksi 07-23.png
Note: Type 7 I-Girder was not included due to there being insufficient data to report a justified range of span lengths.


Prestressed NU Girder Single Span Ranges
751.22.1.3 PSNU 8ksi 07-23.png
Note: Nu 78 Girders were excluded from this chart due to there being insufficient data to report an accurate
range of span lengths.

751.22.1.4 Span and Structure Lengths

751.22.1.4.1 Limits

Span Lengths

Designs using MoDOT standard Type 6 girders shall be limited to 105 feet maximum length to ensure stability during fabrication, shipping and erection.

No limits are set for other types of prestressed girders however the Structural Project Manager or Structural Liaison Engineer shall be consulted prior to the design of any unusually long prestressed girder.

Continuous Structure Lengths

751.22.1.4.1.jpg


751.22.1.4.2 Girder Length and Geometric Layout

Tangent Bridges
Girder lengths of exterior spans (i.e., end spans) and interior spans shall be computed using the requirements shown below.
751.22.1.4.2 2021.jpg


The layout length for single span shall be measured from centerline of bearing to centerline of bearing. If the difference between layout length of the end span and interior span is within one foot, then layout length should be adjusted if possible so the girder lengths are equal for end span and interior span.
(1) Minimum dimension from edge of bearing pad to end of girder equals one inch.
(2) Design layout lengths are horizontal lengths. Girder lengths should be adjusted according to grade and shall be specified to the nearest 1/8 inch.
(3) For large skews, end bent beam caps may need to be larger to provide edge distance.
(4) Horizontal distance along certerline of girder.
(5) = 1ʺ (minimum) + ½ bearing pad length which equals:
5ʺ (minimum) for I-girders and squared-end adjacent beams,
3 ½ʺ (minimum) for NU girders and spread beams with squared ends,
3⅝ʺ (minimum) for skewed-end spread beams, 3½ʺSEC(15°).
Curved Bridges
Layout of any curved structure may be done using any coordinate geometry programs available. To layout the bridge, use the following steps:
  1. Start out by laying in the centerline (CL) of the survey curve.
  2. Locate the tie point of the bridge. This point will usually be on the CL of the survey curve but may be on a baseline which is offset a certain distance to the CL of the survey curve.
  3. A second tie point may be required if the skew is not measured to the CL of roadway at the bridge tie point. If this is the case, establish the tie point at the specified station and plot the skew line at the required angle.
  4. Next, on the centerline of structure or baseline curve, locate the station of the CL of bent for each intermediate bent and the fill face for the end bents. Once these points are located, plot lines through these stations parallel to skew line. Normally the layout file will specify that all bents are parallel to the skew line; however, there may be times when the bents are radial or have varying skews.
  5. When locating the stations in the preceding step, the distance between CL of intermediate bents are exactly the layout lengths specified on the file. However, the end spans need to follow the procedure for calculating length set forth in Tangent Bridges.
  6. When the CL of the intermediate bents and the fill face lines have been added, chords should be drawn connecting these points sequentially. For example, if you have a three-span bridge, chords should be drawn from the fill face of bent 1 to CL of bent 2, CL bent 2 to CL bent 3, and CL bent 3 to fill face bent 4.
  7. When all the chords are in, offset each girder in each span parallel to this chord. The perpendicular distance between girders will be the same for all spans, but the skew distance between girders along the bent will vary from bent to bent depending on the skew to the CL at that point. The designer needs to be aware of the fact that at an intermediate bent the distance between bearings on the approaching and leaving span sides will be different distances. These bearings will not line up across the bent and will actually diverge more the farther away they are from the CL of the survey.
  8. When establishing the CL of bearing points, the designer needs to allow for a minimum of seven (7) inches between ends of girders at the bents while keeping in mind that the girders will be offset and at different skews. If the offset is greater than half the girder bottom flange width, see Structural Project Manager. The distance from the end of girder to CL of bearing point should be half of the bearing length plus one inch minimum clearance. Once the distance for CL bent to CL of bearing is calculated, the designer should offset lines by that dimension on either side of the CL of bent. These lines will then be intersected with each of the girder lines to create the bearing points on each bent.
  9. Between the bearing points at the ends of the girders, quarter points or tenth points need to be established, depending on the girder span. These points will be used in calculating the haunch and bottom of slab elevations for the bridge deck.
  10. The bridge deck and barrier or railing can be laid in by offsetting the centerline of roadway to each side by the proper distance. Curves should be laid in to designate both the inside and outside edges of the barrier or railing. These will later be useful in laying in the wings and end bents.
  11. After the outside edge of slab curves are plotted, the curve offsets need to be found. The intersection points of the outside edge of slab and the centerline of each bent or fill face can be connected with chords. The distance between these chords and their partner curves need to be calculated at five-foot intervals beginning at the center point of each chord.
  12. Joints are placed in the barrier or railing at each bent. These joints are placed perpendicular to the centerline of the roadway through the intersection point of the centerline bent and the inside edge of barrier or railing.
  13. Wing layout length is given on the profile sheets in the layout file. An arc should be struck so as to intersect the inside edge of barrier or railing the specified length from a point at the intersection of the fill face and the inside edge of barrier or railing. This point will mark the end of the wing which is perpendicular to the centerline of the roadway.
The vertical curve information needs to be added so a program can calculate the elevations at the desired stations. After this is done, the designer can request any of the following information which will be needed:
  • Stations and elevations of all points
  • Offset distances to the chords
  • Lengths of girders
  • Distances between bearings
  • Angles between girders and each bent
  • Lengths of bents
  • Lengths of barrier or railing between joints
  • Minimum vertical clearance.

751.22.1.4.3 Coping of Girder Ends

Non-Integral end bents with skews greater than 40 degrees shall always have girder ends coped. Skews less than 40 degrees shall have girder ends coped on case by case basis. It is preferable to not cope across the web.

Check clearance from fill face of integral end bents to bottom flanges of NU girders. Maintain 3-inch minimum clearance. Coping may be permitted with approval of the Structural Project Manager or Structural Liaison Engineer.

751.22.1.4 coping detail.jpg
PART PLAN SHOWING COPING DETAIL
(I Girder shown; Bulb-Tee and NU Girder similar)

751.22.1.5 Constant and Varied Joint Filler Loads

Varied joint filler load

Girders shall be first designed assuming that the contractor will vary the joint filler supporting the panels on the girder flange. This assumption will maintain the minimum slab/panel combination thickness of 8 1/2 inches, and will eliminate the possibility of increased load due to varying slab thickness.


Constant joint filler load

With the girder designed and the camber and haunching dimensions calculated, the girder should be checked assuming the contractor will use a constant 1” joint filler. This will cause the slab thickness to vary due to camber of the girder, increasing load. This additional load shall be placed as a concentrated load at 1/8 point from each end of the girder.

An example of how this concentrated load could be calculated is shown as follows:

Load
Determine the concentrated load* to girders by distributing w transversely across the girders. If the minimum haunch is greater than 1” joint filler, the additional haunch shall be included in the slab thickness as a uniform load. If the use of these loads causes the girder design to change, it shall be the responsibility of the designer to determine if the camber and haunching should be recalculated.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle *} This load shall be positioned at the 1/8 point from centerline of bearing pad.

The girder and bearing designs should be checked for the constant joint filler option and constant joint filler load. However, camber, haunching and beam seat elevations shown on the plans should be based on the variable joint filler option.


751.22 Joint Filler Loads.gif
JOINT FILLER LOADS

751.22.2 Design

751.22.2.1 Load Combinations

In general, each component shall satisfy the following equation:


Where:

= Total factored force effect
= Force effect
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \,\eta_i} = Load modifier
Failed to parse (MathML with SVG or PNG fallback (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_i} = Load 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 \,\phi} = Resistance factor
= Nominal resistance
Failed to parse (MathML with SVG or PNG fallback (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_r} = Factored resistance


Limit States

The following limit states shall be considered for P/S Girder design:

SERVICE I - for compressive stress
SERVICE III - for tensile stress
STRENGTH I

See LRFD Table 3.4.1-1 for Loads and Load Factors applied at each given limit state.


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

STRENGTH limit states, see LRFD Article 6.5.4.2 & 5.5.4.2
For all other limit states, = 1.00


See EPG 751.2.3.1 Load Modifiers.

751.22.2.2 Prestressing Strands

Transfer Length of Prestressing Strands

The prestressing force may be assumed to vary linearly from zero at the point where bonding commences to a maximum at the transfer length. The transfer length may be taken as 60 times the strand diameter.


Development Length of Prestressing Strands

The development length for prestressing strands shall be taken 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 \,d_{ps}} = Nominal diameter of strand, (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 \,f_{ps}} = Average stress in prestressing strand at the time for which the nominal resistance of the girder is required, (ksi)


Stress limits for prestressing strands

Strand stress at service limit state shall not exceed the following:

At jacking:

ksi
(For typical girders and fabrication economy, Failed to parse (MathML with SVG or PNG fallback (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_{pj} = 0.75 f_{pu}} )

At service limit state after all losses:

Failed to parse (MathML with SVG or PNG fallback (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_{pe}\le0.80f_{py}} ksi

Where:

= Stress in prestressing strand at jacking, (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_{pe}} = Effective stress of strand after all losses, (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_{py}} = Yield strength of strand, (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_{pu}} = Ultimate tensile strength of strand, (ksi)


Prestress Losses

Refined estimates of time-dependent losses are used, based on AASHTO LRFD Article 5.9.3.4, as opposed to approximate lump sum estimate of losses in AASHTO LRFD Article 5.9.3.3.

The prestress losses shall be calculated to investigate concrete stresses at two different stages.

  1. Temporary stresses immediately after transfer:
  2. Final stresses


SERVICE I and SERVICE III Limit states shall be investigated at each stage.

Harped Strands

Harped strands, although they add to the shear strength of the girder, are primarily used to keep the girder stresses (both top and bottom) within allowable limits while developing the full capacity of the girder at midspan.

Harped strands should be held down at points of 0.4 of the distance from each end of the girder. Distances along girder to hold-down devices and between hold-down devices should be reported on the plans to the nearest inch. Per Sec 1029, precaster may position hold-down devices +/- 6 in. longitudinally from position shown on the plans.

751.22 harped strand layout.gif


Example Harped Strand Layout


The jacking force applied to prestress strands produces an excessive vertical uplift in short spans on tall girders resulting in failure of harped strand hold-downs. The allowable limits for hold-downs are as follows:

  1. 5 kip/strand
  2. 10 kip/bolt
  3. 42 kip/hold-down


751.22 hold-down device.gif


Hold-Down Device


If necessary lower harped strand end location to meet criteria or use straight strands only. Investigate the possibility of using all straight strands when strength check of a hold-down device exceeds allowable.

Straight Strands.

Short spans (<40 ft.) are to use straight strands only for all girders greater than 2'-8" tall. Use at least two straight strands at the top of the girder when straight strands are used. Where straight strands only will not work a single hold-down point may be used. Note: A single point hold-down has twice the uplift force.

Strand Arrangement Optimizing

Using all straight strands for girder lengths less than 70 feet shall be investigated for Type 6, 7 and 8 girders and all NU girders in order to reduce risk of strand or hold-down breakage, increase safety by reducing risk of injury during fabrication and reduce cost.

Consider using the same section for all spans. This permits the use of shorter girders in the casting bed with longer girders, even if straight strands are needed, in the top flanges of the girders. They can be placed at either end of the bed and still optimize the usage of the bed.

Consider using the same number of draped strands for all spans and debond where needed. Strand patterns should be similar between long and short spans. For example, the designer should not use a single column of draped strands on the short spans and two columns of draped strands on the long spans. This will prevent optimization of the bed.

When using straight strands in the top flange of NU Girders and harped strands, lower (drop) the harped strand end locations and vertically align straight strands directly over harped strands to facilitate top flange blockout fabrication by removing interference created between straight strands placed to the outside of the harped strands and the flange blockout forms. If for any reason this is not possible, then place straight strands to the outside of the harped strands.

Debonding Strands

Debonding at girder ends may be used to reduce concrete compressive forces and shall be used if required to reduce the prestress force at transfer to meet bursting/splitting requirements. Debonding strands shall be avoided at girder ends located underneath expansion joints.

In all debonding operations the prestressing forces must be in such a manner as to prevent any sudden or shock loading.

Debonding a strand consists of wrapping the unnecessary strand(s) with a polyethylene plastic sleeve that prevents interaction of the strand with the concrete during casting and release which prevents any prestress force transfer.

751.22.2.3 Flexure

Flexure capacity of girders shall be determined as the following.

Flexural resistance at strength limit state

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_r} = Flexural resistance
Failed to parse (MathML with SVG or PNG fallback (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_n} = Nominal flexural resistance
Failed to parse (MathML with SVG or PNG fallback (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} = Total factored moment from Strength I load combination
= Flexural resistance factor as calculated in LRFD 5.5.4.2


Negative moment reinforcement design

P/S I-girder shall be designed as a reinforced concrete section at regions of negative flexures (i.e., negative moments).

At least one-third of the total tensile reinforcement provided for negative moment at the support shall have an embedment length beyond the point of inflection not less than the specified development length of the bars used.

Slab longitudinal reinforcement that contributes to making the precast beam continuous over an intermediate bent shall be anchored in regions of the slab that can be shown to be crack-free at strength limit states. This reinforcement anchorage shall be staggered. Regular longitudinal slab reinforcement may be utilized as part of the total longitudinal reinforcement required.


Effective Slab Thickness

An effective slab thickness shall be used for design by deducting from the actual slab thickness a 1” integral, sacrificial wearing surface.


Design A1 reinforcement in the top flange

The A1 reinforcement shall resist the tensile force in a cracked section computed on the basis of an uncracked section.

For I girders and bulb-tee girders, A1 reinforcement shall consist of deformed bars (minimum #5 for Type 2, 3 and 4 and minimum #6 for Type 6, 7 and 8).

For NU girders, A1 reinforcement shall consist of the four 3/8-inch diameter reinforcement support strands with deformed bars added only as needed. The WWR in the top flange shall not be used for A1 reinforcement because there is insufficient clearance to splice the WWR.

Reinforcement shall be designed and spliced using f’ci in accordance with EPG 751.5.9.2.8 Development and Lap Splices.


Required steel area is equal 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 \,A1=\frac{T_t}{f_s}}


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_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 \, 0.5 f_y \le 30 KSI} , allowable tensile stress of mild steel, (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 T_t} = Resultant of total tensile force computed on the basis of an uncracked section, (kips)


Limits for reinforcement

The following criteria shall be considered only at composite stage.

Minimum amount of prestressed and non-prestressed tensile reinforcement shall be so that the factored flexural resistance, Mr, is at least equal to the lesser of:

1) Mcr       LRFD Eq. 5.6.3.3-1
2) 1.33Mu

Where:

Mcr = Cracking moment, (kip-in.)
Mu = Total factored moment from Strength I load combination, (kip-in.)

751.22.2.4 Shear

Shear capacity of girders shall be checked along girder length and girder-slab interface.


Shear resistance at strength limit state

Failed to parse (MathML with SVG or PNG fallback (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_r = \phi V_n \ge V_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 \, V_r} = Shear resistance
Failed to parse (MathML with SVG or PNG fallback (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_n} = Nominal shear resistance
= Total factored shear from Strength I load combination
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi} = Shear resistance factor


Nominal shear resistance

The nominal shear resistance, Failed to parse (MathML with SVG or PNG fallback (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_n} , shall be lesser 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 \, V_c + V_s + V_p} , or
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 0.25 f'_{c} b_v d_v + V_p}


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 \, V_c = 0.0316 \beta b_v d_v \sqrt{f'_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 \, V_s = \frac {A_v f_y d_v (cot \theta + cot \alpha) sin \alpha}{s}}


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 \, V_c} = Nominal concrete shear resistance, (kips)
Failed to parse (MathML with SVG or PNG fallback (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_s} = Nominal shear reinforcement resistance, (kips)
Failed to parse (MathML with SVG or PNG fallback (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_p} = Component of prestressing force in the direction of shear force, (kips)
Failed to parse (MathML with SVG or PNG fallback (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_v} = Thickness of web, (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_v} = Effective shear depth taken as the distance measured perpendicular to the neutral axis, between the resultants of tensile and compressive forces due to flexure, (in.)
= Spacing of shear reinforcement, (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 \, \beta} = Factor indicating ability of diagonally cracked concrete to transmit tension
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \theta} = Angle of inclination of diagonal compressive stress, (degree)
= 90.0, Angle of inclination of shear reinforcement to a longitudinal axis, (degree)
= Area of shear reinforcement, (in.2)
= Minimum yield strength of tension shear reinforcement, (ksi)


Design sections near supports

Where a reaction force in the direction of the applied shear introduces compression into the end region of girder, the location of the critical section for shear is measured from the internal face of support a distance, dv. Otherwise, the design section shall be taken at the internal face of the support.


Where:


= effective shear depth taken as the distance, measured perpendicular to the neutral axis, between the resultants of the tensile and compressive forces due to flexure; it need not be taken to be less than the greater of 0.9de and 0.72h.


Girder regions requiring shear reinforcement

Girder shear reinforcement, usually consisting of stirrups, shall be provided where:



Where:

= Factored shear force from Strength I load combination, (kips)
= Nominal concrete shear resistance, (kips)
Failed to parse (MathML with SVG or PNG fallback (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_p} = Component of prestressing force in the direction of shear force, (kips)
=
=
Shear resistance factor

0.9 for normal weight concrete


Shear Reinforcement Limits


Minimum reinforcement

Area of shear reinforcement shall not be less than:



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 \, A_v} = Area of shear reinforcement, (in.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 \, b_v} = Thickness of web, (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 \, s} = Spacing of shear reinforcement, (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 \, f'_c} = Final concrete compressive strength, (ksi)


Maximum spacing

Maximum spacing of shear reinforcement shall be determined as:
If Failed to parse (MathML with SVG or PNG fallback (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_u<0.125 f'_c} , then Failed to parse (MathML with SVG or PNG fallback (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_{max} = 0.8 d_v \le 24.0^{\prime\prime}}


If Failed to parse (MathML with SVG or PNG fallback (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_u \ge 0.125 f'_c} , then Failed to parse (MathML with SVG or PNG fallback (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_{max} = 0.4 d_{v} \le 12.0^ {\prime\prime}}


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_v} = Effective shear depth taken as the distance measured perpendicular to the neutral axis, between the resultants of tensile and compressive forces due to flexure, (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 \, v_u} = Shear stress on concrete, (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 s_{max}} = Maximum spacing of shear reinforcement, (in.)


Shear stress on concrete shall be determined 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 \, d_v = \Bigg( d_e - \frac{a}{2} \Bigg) \ge larger of \begin{cases}0.9 d_e\\0.72h\end{cases}}


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 \, v_u} = Shear stress on concrete, (ksi)
= Factored shear from Strength I load combination, (kips)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi} =
=
Shear resistance factor

0.9 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 \, b_v} = Thickness of web, (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 \, V_p} = Component of prestressing force in the direction of shear force, (kips)
Failed to parse (MathML with SVG or PNG fallback (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_v} = Effective shear depth taken as the distance measured perpendicular to the neutral axis, between the resultants of tensile and compressive forces due to flexure, (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 \, \frac{M_n}{A_s f_y + A_{ps} f_{ps}}}
Failed to parse (MathML with SVG or PNG fallback (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_e} = Distance from extreme compression fiber to the centroid of tensile force in the tensile reinforcement, (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 \, h} = Total height of girder including slab thickness, (in.)


Girder-Slab Interface

The horizontal shear between the girder and slab shall be determined as specified in LRFD 5.7.4.4. The nominal horizontal shear resistance of the interface plane shall be taken as specified in LRFD 5.7.4.3. Minimum interface shear reinforcement shall be provided as specified in LRFD 5.7.4.2. The parameters used in determining the nominal horizontal shear resistance shall be taken as specified for a “cast-in-place concrete slab on clean concrete girder surfaces, free of laitance with surface roughened to an amplitude of 0.25 inch.”

The interface shear shall be resisted by extending and anchoring the vertical shear reinforcement into the slab. If the resistance provided by extending the vertical shear reinforcement is inadequate then, in lieu of increasing shear reinforcement, additional U bars may be provided as shown for a Type 7 girder in EPG 751.22.3.4 Girder Reinforcement.

For NU girders and spread beams the top flange shall be debonded at the edges using a smooth finish and an applied bond breaker to help aid with future deck removal and minimize stress concerns with the thin flange of the NU girders. The debonded regions shall not be included when determining the nominal horizontal shear resistance. The minimum debonded width shown below may be increased in lieu of adding additional U bars in order to reduce the minimum interface shear reinforcement.

751.22.2.4 Minimum Debonded Width Oct 2021.jpg
751.22.2.4 footnote.jpg

The debonding regions shall be indicated on the plans by specifying the required smooth finish and applied bond breaker in the dimensions detail on the beam or girder sheet. Omit underlined portion of footnote (1) if prestressed panels are not used.

Similarly, for all other prestressed girders and beams, the joint filler width supporting precast panels shall be considered debonded and excluded when determining the interface resistance.

751.22.2.5 Pretensioned Anchorage Zones

                                                                                                                                                                                          (LRFD 5.9.4.4)


Bursting Resistance (AASHTO Splitting Resistance)

The bursting resistance of anchorage zones provided by vertical reinforcement (i.e., B2 bars and the D31 wires of WWR6) in the ends of prestressed girders at the service limit state shall be taken 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 \, P_r = f_s A_s \ge 0.04f_{pbt}}

The required vertical reinforcement shall be provided within the following end regions:

I Girders, NU 35, 43 & 53 Girders:
- Within h/3, in accordance with research by Davis, Buckner and Ozyildirimon (Dunkman et al. 2009).
Bulb-Tee Girders and NU 63, 70 & 78 Girders:
- Within h/4


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_s} = Stress in mild steel not exceeding 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 \, A_s} = Total area of vertical reinforcement located within the specified minimum distance from the end of the girder where h equals the overall depth of precast member as shown below.
Failed to parse (MathML with SVG or PNG fallback (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_{pbt}} = Prestressing force immediately prior to transfer


751.22.2.5 2022.jpg
Anchorage Zone (Bursting and Confinement) for I Girders
(Bursting zone or reinforcement may differ for other girder types)

The number of strands bonded in the anchorage zone is limited by the standard bursting reinforcement of EPG 751.22.3.4.3 Anchorage Zone Reinforcement and the 20 ksi resistance stress limit.

Maximum Number of Bonded Strands at Girder Ends, Ns
I Girders & Bulb-Tee Girdersa NU Girders
Type h/3 or
h/4 (in.)
#6-B2
Pairs
As
(in.2)
Ns Type h/3 or
h/4 (in.)
D31
Pairs
As
(in.2)
Ns
(0.5") (0.6") (0.5") (0.6")
Type 2 10.67 3.0 2.65 20 20 NU 35 11.81 5.5 3.41 54 38
Type 3 13.00 4.0 3.53 24 24 NU 43 14.44 7.0 4.34 62a 48
Type 4 15.00 4.0 3.53 32 32 NU 53 17.72 8.5 5.27 62a 52b
Type 6 18.00 4.0 3.53 38 38 NU 63 15.75 7.5 4.65 62a 52
Type 7 18.13 4.0 3.53 40 40 NU 70 17.72 8.5 5.27 62a 58
Type 8 15.88 4.0 3.53 40 40 NU 78 19.69 9.0 5.58 62a 62a
     Area of one #6-B2 bar = 0.4418 in.2      Area of one D31 wire = 0.31 in.2
a Maximum number capped by strand arrangements shown in this article and on the Bridge Standard Drawings.
b Maximum number capped not to exceed the maximum allowed for the NU 63 girder.
Ns ≤ As /As(req) (Rounded down to nearest even number for the purpose of symmetry.)
Where:
As(req) = Required bursting reinforcement for one prestressing strand.
= 0.04fpbtAps /fs
= (0.04)(202.5 ksi)(0.153 in.2)/(20 ksi) = 0.0620 in.2    (1/2-inch strand)
= (0.04)(202.5 ksi)(0.217 in.2)/(20 ksi) = 0.0879 in.2    (0.6-inch strand)


Confinement reinforcement

Confinement reinforcement (i.e., D1 bars or G1 bars spaced with WWR4) shown in the figure above shall be placed to confine the prestressing strands in the bottom flange for a minimum distance of 1.5d from the end of beam.

The reinforcement shall not be less than #3 deformed bar, with spacing not exceeding 6.0 inches and shaped to enclose the strands.

The use of D1 bars shall be extended for the full length of I girders, bulb-tee girders and alternate bar-reinforced NU girders.

The use of G1 bars at 6-inch spacing shall be extended for the first 10 feet and then at 12-inch spacing for the remaining length of welded wire-reinforced NU girders.

751.22.2.6 Deformations

Criteria for deflection

For investigating maximum absolute deflection, all design lanes shall be loaded, and all supporting components should be assumed to deflect equally.

For composite design, the design cross-section should include the entire width of the roadway and the structurally continuous portions of railings, sidewalks, and median barriers. Note that barrier and railing are usually discontinuous over the bents. For skewed bridges, a right cross-section may be used.

Service I load combination shall be used. Dynamic load allowance shall be applied.


See EPG 751.2.4.2 Live Load Deflection Limits.


Calculation of deflection and camber

Deflection and camber calculations shall consider all internal loads (i.e., prestressing, concrete creep, and shrinkage) and external loads such as dead loads and live loads.


Camber is an upward displacement caused by moment due to prestressing forces. Deflection is a downward displacement due to external loads. Therefore, both camber and deflection shall be considered in making an appropriate adjustment for final profile grade on the bridge.


Initial camber at transfer at midspan

Total initial camber at transfer due to self-weight of girder and prestressing forces shall be determined 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 \, \Delta_{IC} = \Delta_g + \Delta_{SS} + \Delta_{HS}}


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 \, \Delta_{IC}} = Initial camber at transfer
Failed to parse (MathML with SVG or PNG fallback (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_g} = Deflection due to self-weight of 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 \, \Delta_{SS}} = Camber due to prestressing straight 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 \, \Delta_{HS}} = Camber due to prestressing harped strands


Note: Positive and negative values indicate downward and upward displacements, respectively.


Camber at midspan after strand release (Estimated at 7 days)

Theoretical camber of girder after strand release due to self-weight of girder and prestressing forces shall be determined at 7 days 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 \, \Delta_7 = \Delta_{IC} + \Delta_{CR\ at\ 7\ days}}


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 \, \Delta_7} = Camber at 7 days after strand release with 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 \, \Delta_{CR\ at\ 7\ days}} = Time - dependent camber due to creep at 7 days

Note: Camber is calculated 7 days after strand release to allow sufficient time for inspection. See EPG 1029 Fabricating Prestressed Concrete Members for Bridges.

Camber at midspan after erection (Estimated at 90 days)

Theoretical camber of prestressed girders after erection are estimated at 90 days for typical projects. While some projects may require prestressed girders to be erected in less than 90 days in order to meet fast construction timelines or emergency repair requirements, using less than 90 days (i.e, 45 or 60) would potentially result in lower camber estimates and higher beam seat elevations. The cost risk is believed to be greater for underestimating the camber since it may require an increase in final grade. Due to the risk in underestimating camber and the multitude of variables that affect the actual camber (variability in predicting concrete modulus of elasticity, coarse aggregate effect on initial concrete modulus of elasticity, actual concrete strength, differential temperature at strand release, etc…) the 90 day estimate should be adequate for most projects.

Theoretical camber of girder after erection due to self-weight of girder and prestressing forces shall be determined at 90 days 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 \, \Delta_{90} = \Delta_{IC} + \Delta_{CR\ at\ 90\ days}}


Where:

= Camber at 90 days after strand release with 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 \, \Delta_{CR\ at\ 90\ days}} = Time - dependent camber due to creep at 90 days


Final camber at midspan after slab is poured

Total deformation after slab is poured can be determined as the sum of theoretical camber of girder after erection (90 days) and deflections due to slab and concentrated loads (haunch, diaphragms, etc.) before composite action between slab and 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 \, \Delta_{FC} = \Delta_{90} + \Delta_S + \sum \Delta_C}


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 \, \Delta_{FC}} = Final camber after slab is poured
Failed to parse (MathML with SVG or PNG fallback (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_s} = Deflection due to weight of slab
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \sum \Delta_c} = Deflection due to concentrated loads (haunch, diaphragms, etc.)


Final camber along span length

Deformations along the span length can be approximately determined as a product of final camber at midspan times correction factors.

Failed to parse (MathML with SVG or PNG fallback (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_{0.10}} = 0.3140 Failed to parse (MathML with SVG or PNG fallback (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_{FC}} at span fraction of 0.10
Failed to parse (MathML with SVG or PNG fallback (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_{0.20}} = 0.5930 Failed to parse (MathML with SVG or PNG fallback (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_{FC}} at span fraction of 0.20
Failed to parse (MathML with SVG or PNG fallback (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_{0.25}} = 0.7125 Failed to parse (MathML with SVG or PNG fallback (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_{FC}} at span fraction of 0.25
Failed to parse (MathML with SVG or PNG fallback (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_{0.30}} = 0.8130 Failed to parse (MathML with SVG or PNG fallback (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_{FC}} at span fraction of 0.30
Failed to parse (MathML with SVG or PNG fallback (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_{0.40}} = 0.9520 Failed to parse (MathML with SVG or PNG fallback (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_{FC}} at span fraction of 0.40
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 \, \Delta_{0.50}} = 1.0000 Failed to parse (MathML with SVG or PNG fallback (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_{FC}} at span fraction of 0.50

Calculation of camber (upward) using transformed properties

Camber at midspan due to strand forces is determined by the following:

For straight strands (groups determined by debonding lengths),


Failed to parse (MathML with SVG or PNG fallback (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_{SS} = \Delta_{ss-j} + \Delta_{ss-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 \, \Delta_{ss-j} = \sum \frac{F_{1-j} e_1}{8 E_{ci} I_{tri}} (L^2 - 4l_0^2)}


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 \, \Delta_{ss-l} = \Delta_{ss-j} \frac{Initial \ Loss}{f_{Pj}}}


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_{1-j}} = Total prestressing force of straight strand group just prior to transfer, (kips)
Failed to parse (MathML with SVG or PNG fallback (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} = Distance between centerlines of bearing pads, (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 \, l_0} = Debond length of straight strand group from end of girder, (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 \, E_{ci}} = Initial concrete modulus of elasticity based on Failed to parse (MathML with SVG or PNG fallback (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}} , (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 \, I_{tri}} = Moment of inertia of transformed non-composite section computed based on Failed to parse (MathML with SVG or PNG fallback (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_{ci}} , (in.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 \, e_1} = Eccentricity between centroid of straight strand group (CSS) and center of gravity of transformed non-composite section (CGB) as shown in Figure below, (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 \, f_{Pj}} = Prestressing force in the strand just prior to transfer, (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 \, Initial \ Loss} = Summation of the time dependent losses (7 or 90 day). Losses include relaxation, creep and shrinkage, but exclude elastic shortening.


Gross properties may be used to calculate losses and is consistent with AASHTO LRFD 5.9.3.4.

For two-point harped 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 \, \Delta_{HS} = \Delta_{HS-j} + \Delta_{HS-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 \, \Delta_{HS-j} = \frac {F_{2-j} e_2 L^2}{8 E_{ci} I_{tri}} - \frac {F_{2-j}(e_2 + e_3) a^2}{6 E_{ci} I_{tri}}}

Failed to parse (MathML with SVG or PNG fallback (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_{HS-l} = \frac {F_{2-l} e_2 L^2}{8 E_c I_{tr}} - \frac {F_{2-l}(e_2 + e_3) a^2}{6 E_c I_{tr}}}
Failed to parse (MathML with SVG or PNG fallback (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_{HS-l} = \Delta_{HS-j} \frac{Initial \ Loss}{f_{Pj}}}
Failed to parse (MathML with SVG or PNG fallback (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 = (L - b)/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 \, F_{2-j}} = Total prestressing force of harped strands just prior to transfer, (kips)
Failed to parse (MathML with SVG or PNG fallback (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} = Length between harped points, (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 \, e_2} = Eccentricity between centroid of harped strands (CHS) and center of gravity of transformed non-composite section (CGB) at midspan as shown in Figure below, (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 \, e_3} = Eccentricity between centroid of harped strands (CHS) and center of gravity of transformed non-composite section (CGB) at the end of girder as shown in Figure below, (in.)


751.22 details of girder showing distances and eccentricities used in camber calculations.gif


Details of girder showing distances and eccentricities used in camber calculations


Calculations of deflections (downward)

Deflections at midspan due to dead loads are determined as the following: For self-weight of 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 \, \Delta_g = \frac {5 W_g L^4}{384 E_{ci} I_{tri}}}


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 W_g} = Uniform load due to self-weight of girder, (kip/in.)


For self-weight of slab,


Failed to parse (MathML with SVG or PNG fallback (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_s = \frac {5 W_s L^4}{384 E_{c} I'_{tr}}}


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 \, W_s} = Uniform load due to self-weight of slab, (kip/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 \, E_c} = Final concrete modulus of elasticity based on f'c, (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 \, I'_{tr}} = Moment of inertia of transformed non-composite section based on Ec, (in.4)


Weight of additional slab haunch may be treated as uniform or concentrated load as appropriate. Diaphragm weight should be treated as concentrated load.

For one concentrated load at midspan,


Failed to parse (MathML with SVG or PNG fallback (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_c = \frac {PL^3}{48 E_c I'_{tr}}}


For two equal concentrated 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 \, \Delta_c = \frac {Px}{24 E_c I'_{tr}} (3L^2 - 4x^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 \, P} = Concentrated load due to diaphragm and/or additional slab haunch, (kips)
Failed to parse (MathML with SVG or PNG fallback (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 the centerline of bearing pad to the applied load, P, (in.)


Creep coefficient LRFD 5.4.2.3.2

Research has indicated that high strength concrete (HSC) undergoes less ultimate creep and shrinkage than conventional concrete.

Creep is a time-dependent phenomenon in which deformation increases under a constant stress. Creep coefficient is a ratio of creep strain over elastic strain, and it can be estimated 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 \, 1.9k_s k_{hc} k_f k_{td} t_{i}^{-0.118}}
Failed to parse (MathML with SVG or PNG fallback (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_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 \, k_{hc}} =
=
=


Where:

= Creep coefficient.
= 70, Average annual ambient relative humidity
= Maturity of concrete, (days)
    Use 7 days for camber design after strand release
    Use 90 days for camber design after erection
= Age of concrete when a load is initially applied, (days)
    Use 0.75 days for camber design.
= Volume-to-surface area ratio, (in.)
= Initial girder concrete compressive strength, (ksi)


751.22.2.7 Dowel Bars

751.22.3.15.jpg


PART ELEVATION
(FIXED BENT)
SECTION A-A


Dowel bars shall be used for all fixed intermediate bents under prestressed superstructures. Generally, for typical bridges that require seismic details only (strength limit states), shear resistance from shear key is not considered.


Dowel bars connect standard concrete diaphragms and beams on concrete girder bridges (standard fixed diaphragms are those with beam stirrups NOT extending up into the diaphragm). For a calculated seismic vertical reaction or an anticipated foundation settlement resulting in a net tensile reaction, use the development length of dowel bars into beam and into diaphragm based on dowel bar size. If the dowel bars are not exposed to net tension a 15-inch embedment shall be used regardless of bar size. Dowel bars size and spacing shall be determined by shear design of the bars. (Minimum #6 Bars @ 12" cts.). Dowel bars should be designed for a minimum horizontal force equal to 25% of the maximum dead load applied to the bearing. Live load is ignored in horizontal force computation.

The number of dowels must also fit into the space available on the key:
min. bar size = #6; max. bar size = #11
min. spacing = 6"; max. spacing = 12"
min. end distance = 3"; max. end distance = 6" (≤ half the spacing)

For seismic details only (strength limit states)

Horizontal factored shear force, in kips

For expansion bearings, transverse FT = 0.25(DL) & longitudinal FL = 0.

Where DL = unfactored dead load reaction at the bent, kips

For fixed bearings, Transverse FT = 0.25(DL) and Longitudinal FL = (0.25)(segment weight) at bent.

Segment weight includes the full width of superstructure and should be distributed appropriately among fixed bents.


For complete seismic analysis

Dowel bar designs must meet requirements for strength limit states from above as well as seismic force demand from seismic analysis.

At Intermediate bent,
where:
FH = horizontal seismic force per bent, kips
If columns are designed for plastic hinging, use the plastic hinging shear.
∑VL = summation of top of column longitudinal shears at the bent
∑VT = summation of top of column transverse shears at the bent
Pu = Horizontal factored shear force per dowel bar, kips
nd = number of dowel bars


Shear Resistance

Factored shear force shall be less than or equal to the nominal shear resistance.

Pu ≤ ∅s x Rn
where:
s = 0.75 resistance for seismic details only (strength limit states) and 1.0 for complete seismic analysis
Nominal shear resistance of the dowel bar, Rn = 0.625 AbFub, kips
Note: Since there is no reduced areas as seen in bolts and there is no reduction for bolted connection length, use 0.625 instead of 0.5.
Ab = = area of the dowel bar, square inches
Fub = minimum tensile strength of the dowel bar, ksi
Fub = 80 ksi for Grade 60
D = diameter of the dowel bar, inch


Tensile Resistance

Factored tensile force shall be less than or equal to the nominal tensile resistance.

T = the maximum seismic tensile (uplift) force (DL ± EQ) from the seismic analysis, kips. If (DL+EQ) and (DL-EQ) are both compressive, then there is no need to design the dowel for tensile force.
where:
t= 0.8 resistance factor for seismic details only (strength limit states) and 1.0 for complete seismic analysis
nd = the number of dowel bars
Nominal tensile resistance of the dowel bar, Tn = AbFub Kips
Note: Since there is no pretension or reduced areas as seen for bolts, the 0.76 factor is not warranted.
Ab = area of the dowel bar, square inches
Fub = minimum tensile strength of the dowel bar, ksi
Fub = 80 ksi for Grade 60


Combined Tension and Shear Resistance

The resistance of dowel bars for combined tension and shear force shall be determined in accordance with LRFD 6.13.2.11.

Note: Since there is no pretension or reduced areas as seen for bolts, the 0.76 factor is not warranted.


If , then Tn = AbFub
Otherwise


751.22.3 Details

751.22.3.1 Reinforcement Criteria

Minimum Concrete Cover

  • 2.0" (Min.) to centerline of strands
  • 1.0" for stirrups


Minimum Bend Diameter for Stirrups

  • #3 through #5 bars = 4.0 x Nominal Bar Diameter.
  • Deformed wire larger than D6 = 4.0 x Nominal Wire Diameter


Minimum Spacing of Reinforcement Bars and Wires For precast concrete, the clear distance between parallel bars in a layer shall not be lesser than:

  • Nominal Bar Diameter or Nominal Wire Diameter
  • 1.33 x Maximum Aggregate Size
  • 1.0"


Minimum Spacing of Prestressing Strands Spacing between each pretressing strand shall not be less than the larger of:

  • A clear distance of 1.33 x Maximum Aggregate Size
  • Center-to-center spacing of 2" for 0.6" strand diameter
  • Center-to-center spacing of 1.75" for 0.5" strand diameter

751.22.3.2 Strand Arrangements

Designers shall first attempt to use one of the strand arrangements specified in EPG 751.22.3.2.1 through EPG 751.22.3.2.5. The strand arrangement number shall be specified in the design. Bridge standard drawings for prestressed I-girders include strand details for each of these arrangements, by number, in the reference files for quick insertion by the technician.

For Group 1 arrangements, all strands in the center two columns are harped. For Group 2 arrangements, the bottom two center strands are straight (two less draped strands). Group 2 arrangements are not provided in diagrams below for Type 6, 7 and 8 girders, but may be derived similarly to how specified for the smaller girders.

Designers shall include an equivalent detail in the design computations when strand arrangements other than those shown are required.

The use of all straight strands (none harped) may be considered when strength check of a hold-down device exceeds allowable.

How Strand Arrangements are Detailed from Tables

1. For strand locations at mid-span (centerline of girder): Find the “#” designation that corresponds with the number of total strands (T) needed. The strands are to be placed at locations labeled up to and including that number. Example: For 14 total strands, the strands will be placed at all locations labeled 8 thru 14 and are designated as arrangement #14. (See Fig. 751.22.3.2.)
2. For harped strand locations at end of girder: Harped strands will be placed at locations labeled up to and including the number in the “H” column. Example: For 6 harped strands, the strands will be placed at all locations labeled 2 thru 6. (See Fig. 751.22.3.2.)
751.22.3.2.jpg

Fig. 751.22.3.2
Where:
# = Strand Arrangement Number
T = Total Number of Strands
H = Number of Harped Strands
S = Number of Straight Strands


751.22.3.2.1 Type 2 Girder

751.22.3.2.1 2022.jpg

See EPG 751.3.2.6 for guidance notes (1) and (2).


751.22.3.2.2 Type 3 Girder

751.22.3.2.2 2022.jpg

See EPG 751.3.2.6 for guidance notes (1) and (2).


751.22.3.2.3 Type 4 Girder

751.22.3.2.3 2022.jpg

See EPG 751.3.2.6 for guidance notes (1) and (2).


751.22.3.2.4 Type 6 Girder

751.22.3.2.4 2022.jpg

See EPG 751.3.2.6 for guidance notes (1) and (2).


751.22.3.2.5 Type 7 and 8 (Bulb-Tee) Girders

751.22.3.2.5 2022.jpg

See EPG 751.3.2.6 for guidance notes (1) and (2).

751.22.3.2.6 NU Girders

751.22.3.2.6 2022.jpg

Strand arrangements shall start at the bottom row and then move up for the most efficient design.

(1) Strands shall be placed on outer edge to help place confinement steel.
(2) If possible, strands shall not be placed at the specified location due to the conflict with B1 and B2 bars. Harped strands at this location are less problematic since this conflict only occurs between the hold-down devices where the B1 bars are spaced farther apart. If straight strands are required below the harped strands the designer shall first attempt to locate these straight strands in the second row. The use of the strands at the specified location shall be discussed with Structural Project Manager or Structural Liaison Engineer.

751.22.3.3 Top Flange Blockout for NU Girders

No Skew
751.22.3.3.2 no skew.jpg
>0° to 7° LA Skew (Mirror for right advanced.)
751.22.3.3.2 0 to 7.jpg
>7° to 14° LA Skew (Mirror for right advanced.)
751.22.3.3.2 7 to 14.jpg
>14° to 60° LA Skew (Mirror for right advanced.)
751.22.3.3.2 14 to 60.jpg

Choose one of the above four details for the top flange blockout detail and follow the provided detailing guidance.

Blockout shall be dimensioned along the girder to 1 1/2 inches inside the face of the diaphragm and adjusted for any girder tilt.

The left advanced details shown may be used for right advanced bridges. The mirror note may be removed if left advanced.

Revise bent references as required and specify the bent number if blockout varies by bent.

The skew angle value need not be shown for tangent bridges. Consult SPM or Liaison on replacing "skew angle" with actual value for curved bridges.

Revised titles for non-integral end bents (exterior girder at end bent will be same detail as at intermediate bent).


Flange Blockout Data
Skew X Eq.
Spa.
X
#4-G6
Bar Lengths
>14° to 21° 3 2 G3 bar =

G5 bar =

For skews >7° to 14°:      
G6 bar =

For skews >14° to 60°:
report length of G6 bars as “Varies”
>21° to 27° 4 3
>27° to 32° 5 4
>32° to 37° 6 5
>37° to 42° 7 6
>42° to 46° 8 7
>46° to 49° 9 8
>49° to 52° 10 9
>52° to 55° 11 10
>55° to 57° 12 11
>57° to 60° 13 12

751.22.3.4 Girder Reinforcement

751.22.3.4.1 Reinforcing Steel Details

I Girders and Bulb-Tee Girders

See Bridge Standard Drawings for details not shown below.

  TABLE OF DIMENSIONS BY GIRDER TYPE
  TYPE 2 TYPE 3 TYPE 4 TYPE 6 TYPE 7
WEB 6" 7" 8" 6" 7" 8" 6" 7" 8" 6½" 7½" 8½" 6"
"A" 6" 6" 6" 6" 6" 6" 6" 6" 6" 9¼" 9¼" 9¼" 10½"
"B" 4" 4" 4" 4" 4" 4" 4" 4" 4" 4" 4" 4" 4"
"C" 5¾" 5¾" 5¾" 5¾" 5¾" 5¾" 5¾" 5¾" 5¾" 6¾" 6¾" 6¾" 4¼"
"D" 3¼" 3¼" 3¼" 4¾" 4¾" 4¾" 5¾" 5¾" 5¾" 4" 4" 4" 4"
"E" 13" 14" 15" 13" 14" 15" 13" 14" 15" 18" 19" 20" 20"
"F" 2" 2" 2" 2" 2" 2" 2" 2" 2" 3" 3" 3" 7¾"
"G" 11" 12" 13" 11" 12" 13" 11" 12" 13" 22" 23" 24" 2'-10"
"H" 2'-6" 2'-6" 2'-6" 3'-1" 3'-1" 3'-1" 3'-7" 3'-7" 3'-7" 4'-4" 4'-4" 4'-4" 5'-10½"
"I" 3'-0½" 3'-0½" 3'-0½" 3'-7½" 3'-7½" 3'-7½" 4'-1½" 4'-1½" 4'-1½" 4'-10½" 4'-10½" 4'-10½" 6'-5"


Note: Dimensions shown above are out to out.


  TOTAL BAR LENGTH BY GIRDER TYPE
  TYPE 2 TYPE 3 TYPE 4 TYPE 6 TYPE 7
WEB 6" 7" 8" 6" 7" 8" 6" 7" 8" 6½" 7½" 8½" 6"
#4-B1 4'-1" 4'-1" 4'-1" 4'-8" 4'-8" 4'-8" 5'-2" 5'-2" 5'-2" 5'-11" 5'-11" 5'-11" 7'-8"
#5-B1 4'-1" 4'-1" 4'-1" 4'-8" 4'-8" 4'-8" 5'-2" 5'-2" 5'-2" 5'-11" 5'-11" 5'-11" 7'-7"
#6-B1 3'-11" 3'-11" 3'-11" 4'-6" 4'-6" 4'-6" 5'-0" 5'-0" 5'-0" 5'-9" 5'-9" 5'-9" 7'-6"
#6-B2 3'-5" 3'-5" 3'-5" 4'-0" 4'-0" 4'-0" 4'-6" 4'-6" 4'-6" 5'-3" 5'-3" 5'-3" 6'-11"
#4-C1 13" 14" 15" 13" 14" 15" 13" 14" 15" 2'-2" 2'-3" 2'-4" 3'-5"
#4-D1 2'-3" 2'-4" 2'-5" 2'-5" 2'-6" 2'-7" 2'-6" 2'-7" 2'-8" 3'-0" 3'-1" 3'-2" 3'-1"


Note: When required create new B1 and C1 bars and adjust heights in one-inch increments to ensure at least 2 1/2 inches of embedment into slab. This limit provides for a half inch variance in the field.


751.22.3.6 C1.jpg 751.22.3.6 B1 and B2.jpg 751.22.3.6 C1 Type 7.jpg
C1 BAR

Shape 10S
(Girders Type 2-6)

C1 BAR

Shape19S
(Girder Type 7)

  B1 and B2 Bar

Shape 11S

751.22 Section Thru Girder Type 7.gif
751.22 Section Thru Girder 2-6.gif 751.22.3.6 D1.jpg
D1 BAR

Shape 9S

SECTION THRU GIRDER

(Type 2, 3, 4 and 6 Girders)

  SECTION THRU GIRDER

(Type 7 Girder)

Welded Wire Reinforcing Steel Details for NU Girders

See Bridge Standard Drawings for details.

When required create new WWR and adjust heights in one-inch increments to ensure at least 2 1/2 inches of embedment into slab. This limit provides for a half inch variance in the field.

Length of WWR sections should be based on shear and confinement requirements before adjusting height to avoid multiple short sections.

The height of the WWR6 at the ends of NU girders shall not be adjusted. The top horizontal legs of WWR6 will need to be removed for a flange depth increase greater than 4¾”.

Alternate Bar Reinforcing Steel Details for NU Girders

Alternate bar reinforcing steel details shall be provided for all NU girders for all spans.

See Bridge Standard Drawings for details.

When required create new B1 bars and adjust heights in one-inch increments to ensure at least 2 1/2 inches of embedment into slab. This limit provides for a half inch variance in the field.

751.22.3.4.2 Shear Reinforcement

The following criteria are preferred by girder manufacturers and reinforcement suppliers. If the design requires a deviation from the preferred criteria then feasibility should be verified with a manufacturer.

I Girders, Bulb-Tee Girders, and NU Girders with Alternate Bar Reinforcing Steel

  • B1 bars shall be either #4 or #5 epoxy-coated bars with #4 bars preferred to allow permissible alternate bar shape. Using #6 B1 bars does not provide one-inch clearance when center strands are spaced one inch off centerline of girder between hold down devices because of bend radius of the #6 bars.
  • The same shear reinforcement bar size shall be used in a girder. Using the same shear reinforcement bar size for all of the spans is preferred but not required for girders of different spans lengths.
  • 6” is the preferred minimum spacing.
  • 5” spacing may be used for first set if required.
  • 21” is the maximum spacing for #4 bars.
  • 24” is the maximum spacing for #5 bars.
  • 3” increment spacing shall be used (i.e. 6”, 9”, 12”, 15”, 18”, 21” and 24”) except when less than 6” spacing is required for the first set. In this case, 6” or 9” shall be used for the next set of B1 bars.
  • Four or less spacing changes are preferred for spans up to 100 feet.
  • Six spacing changes may be used for spans greater than 100 feet.
  • Using the same spacing scenario (i.e. sets of B1 bars at 6”, 12” and 18” spacing) for all of spans is preferred but not required for girders of different span lengths.

NU Girders with Welded Wire Reinforcing Steel

  • WWR shall be uncoated and shall use either D18, D20, D22 or D31 vertical wire sizes. W8 horizontal wires sizes shall be used with D18 and D20 vertical wires. W9 horizontal wire sizes shall be used with D22 vertical wires. W12 horizontal wire sizes shall be used with D31 vertical wires.
  • The same shear reinforcement wire size shall be used in a girder. Using the same shear reinforcement wire size for all of the spans is preferred but not required for girders of different spans lengths.
  • 4” is the preferred minimum spacing.
  • 20” is the maximum spacing for the D18, D20 and D22 wire sizes.
  • 24” is the maximum spacing for the D31 wire size.
  • 4” increment spacing shall be used (i.e. 4”, 8”, 12”, 16”, 20” and 24”).
  • Three or less spacing changes (WWR pieces) are preferred for spans less than 100 feet.
  • An additional spacing change (WWR piece) may be used in spans greater than 100 feet.
  • Using the same spacing scenario (i.e. S1=4”, S2=12” and S3=20”) for all of the spans is preferred but not required for girders of different span lengths.

751.22.3.4.3 Anchorage Zone Reinforcement

The following details satisfy the criteria for anchorage zone reinforcement in EPG 751.22.2.5 Pretensioned Anchorage Zones for up to the maximum number of bonded strands specified in EPG 751.22.2.5.

I Girders and Bulb-Tee Girders

751.22.3.4.3 I girders.jpg


NU Girders

751.22.3.6 wwr6 2021.jpg
751.22.3.6 wwr6 table 2021.jpg
(ɑ) The overall height of the WWR6 shall not be increased for girder steps. Reduce this dimension by the accumulated girder step height.


Bearing Plate Anchor Studs

The standard ½" bearing plate will be anchored with four ½" x 4" studs for MoDOT shapes and eight ½” x 5” studs for NU shapes.

If required, increase the number of ½" studs and space between wires of WWR6.

The minimum ¼" fillet weld between the ½" bearing plate and 1½" sole plate is adequate for all cases.

LFD Seismic Design

Studs shall be designed to meet the criteria of 2002 AASHTO 17th Edition Division I-A in Seismic Performance Category C or D.

Stud capacity is determined as follows for:

Stud Cap. = (n)(As)(0.4Fy)(1.5)
Where:
N = number of studs
As = area of stud
Fy = yield strength of stud (50 ksi)
0.4Fy = Allowable Shear in Pins AASHTO Table 10.32.1A
1.5 = seismic overload factor

If required, increase the number of 1/2” studs to six and space between wires of WWR6. If this is still not adequate, 5/8” studs may be used. The following table may be used as a guide for upper limits of dead load reactions:

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
8 1/2” 156 130
10 1/2” 195 163
8 5/8” 244 204
10 5/8” 306 255

751.22.3.5 Strands at Girder Ends

A portion of the prestressing strands at girder ends, sufficient to resist positive moments over the bents, shall be projected into integral end bents and closed or open concrete intermediate diaphragms (continuous superstructure). This strand projection is shown on the standard drawings for prestressed girders similar to the following detail.

The detail on the standard drawing shall be modified appropriately when the ends of girders are located inside concrete end diaphragms or with a change in girder height at closed concrete intermediate diaphragms. See Structural Project Manager for preference on modifying this detail when either the end bent or intermediate bent is not applicable for the span.

751.22.3.5.jpg
(a) Use 3'-0" projection for NU girders.
(b) #5 bars typical at each layer of bent-up strands at intermediate bents.

Actual strand arrangement, quantity of bent-up strands and debonding (if any) shall be determined by design.

Tables below show the minimum number of bent-up strands at the bottom of girder ends adequate to resist a positive moment over the bents.

WEB
THICKNESS
(INCHES)
NUMBER OF BOTTOM STRANDS FOR POSITIVE MOMENT CONNECTION1
BEAM TYPE 2 BEAM TYPE 3 BEAM TYPE 4 BEAM TYPE 6 BEAM TYPE 7
(BULB-TEE)
6 6 6 8 --- 12
6-1/2 --- --- --- 10 ---
72 6 8 8 --- ---
7-1/23 --- --- --- 12 ---
82 6 8 10 --- ---
8-1/23 --- --- --- 12 ---
1 If available. Otherwise, bend all bottom strands.
2 Modified Beam Type 2, 3 or 4.
3 Modified Beam Type 6.


NUMBER OF BOTTOM STRANDS FOR POSITIVE MOMENT CONNECTION1
NU 35, 43 and 53 10
NU 63, 70 and 78 12
1 If available. Otherwise, bend all bottom strands.

751.22.3.6 Camber, Haunching, and Stepping and Sloping of Top Flange

Camber

Compute theoretical camber of girder at 90 days and show on the plan as a “Theoretical camber of girder after erection (Estimated at 90 days)". Compute theoretical camber of girder at 7 days and show on the plan as a “Theoretical camber of girder after strand release (Estimated at 7 days)". Camber shall be reported to the nearest 1/8 inch.

Theoretical camber of prestressed girders after erection are estimated at 90 days for typical projects. While some projects may require prestressed girders to be erected in less than 90 days in order to meet fast construction timelines or emergency repair requirements, using less than 90 days (i.e, 45 or 60) would potentially result in lower camber estimates and higher beam seat elevations. The cost risk is believed to be greater for underestimating the camber since it may require an increase in final grade. Due to the risk in underestimating camber and the multitude of variables that affect the actual camber (variability in predicting concrete modulus of elasticity, coarse aggregate effect on initial concrete modulus of elasticity, actual concrete strength, differential temperature at strand release, etc…) the 90 day estimate should be adequate for most projects.

Sample detail:

751.22.3.8 camber 2013.jpg

Show conversion factors for girder camber with camber diagram as per EPG 751.50 H2c6.1.

Note: The example shows Dimension A as greater than Dimension C. When Dimension A is less than Dimension C, modify detail to show this correctly keeping definitions of Dimensions A and C the same. MS Cells are given for each case.

Haunching

Haunching for a prestressed bridge is the distance between the top of the girder or spread beam and the bottom of the slab.

Haunching shall be computed at quarter (1/4) points for bridges with spans less than 75 feet, and at tenth (1/10) points for span 75 feet and longer. Haunching shall be reported to the nearest 1/8 inch. A typical theoretical slab haunching diagram as shown below shall be provided on all prestressed I-girder and spread prestressed beam bridges.

For full depth cast-in-place decks using conventional or SIP forms, a minimum haunch of one inch at the centerline of girder and 1/2 inch at the edge of the flange shall be provided to allow for construction tolerances and normal concrete variations. The minimum haunch may need to be increased for Type 7 and 8 girders, NU girders and spread beams. See the Structural Project Manager or Structural Liaison Engineer for full depth cast-in-place decks.

For the same reasons the following minimum haunch shall be provided for precast prestressed panel deck slabs:

1 1/8” for Type 2, 3 and 4 girders
1 1/4” for Type 6 girders
1 1/2” for Type 7 and 8 girders (bulb-tee), NU girders, and spread beams.

A minimum of one inch shall be made available below the precast prestressed panels to allow for adequate flow of concrete below the panel. This is accomplished by specifying the placement of one-inch minimum joint filler thickness under all panels.

The following maximum haunch at the centerline of the girder is allowed when prestressed panels are used:

2 1/2" for Type 2, 3 and 4 girders
4 1/2” for Type 6, 7 and 8 girders, NU girders, and spread beams.

These limits are ½” greater than the maximum allowable joint filler. This buffer allows for using the maximum joint filler on both sides of the girder flange while requiring minimal additional slab depth on the high side for a two-percent cross-sloped deck. The minimum 8½” slab isn’t possible at these limits even when varying the joint filler. The maximum joint filler thickness to be used for supporting panels shall be 2 inches for Type 2, 3 and 4 girders or 4 inches for Type 6, 7 and 8 girders, NU girders, and spread beams; the remaining haunch thickness will be addressed by varying the slab thickness.

Prestressed panels shall not be used when the maximum haunch exceeds the above limits. The top flange may be stepped within the limits specified below to make panels a viable option.

There is no maximum haunch for full depth cast-in-place decks using conventional or SIP forms but additional hairpin bars may be required in accordance with EPG 751.10.1.14 Girder and Beam Haunch Reinforcement.

Sample detail:

751.22.3.8 haunch.jpg

Stepping of Top Flange

Flange steps shall be provided on prestressed girders and spread beams with precast prestressed panels as shown below to keep the haunch at centerline of girder from exceeding 2 1/2 inches for Type 2, 3 and 4 girders or exceeding 4 1/2 inches for Type 6, 7 and 8 girders, NU girders, and spread beams. The minimum step height shall be 1/2 inch with 1/2-inch increments. Designer shall check to ensure the panels can clear the flange steps by a minimum of one inch assuming the maximum change in joint filler thickness between adjacent eight-foot prestressed panels along the length of the beam is 1/2 inch.

751.22.3.6-part elevation girder-Feb-23.jpg 751.22.3.6-section AA-Feb-23.jpg
PART ELEVATION OF GIRDER SECTION A-A
Maximum Total Increase to Top Flange Depth X”
Beam Type Preferred Absolute
2, 3 & 4 3" 6"
6 3" 6"
7 & 8 3" 6"
NUs 4" 6"
Box 3" 6"
Consult SPM or SLE before exceeding the preferred
limits. Signifcant additional fabrication costs are
likely above the preferred limits.
The top horizontal legs of WWR6 will need to be
removed for a flange depth increase greater than 4¾”.
Girder Top Flange Step Example and Maximum Total Increase to Top Flange

Sloping Top Flange

Tops of girders and spread beams, for bridges with a superelevation of more than 2 percent, shall be sloped across the top flange to match the superelevation as shown below. The minimum thickness of the top flange and the overall height at the minimum point shall match the top flange thickness and height of the girder or spread beam used in design.

Type 7 and 8 girders, NU girders, and spread beams with top flanges exceeding a 4 percent cross-slope may experience sweep after form removal because of the unsymmetrical section and a resulting imbalanced prestressed load. It is recommended that the flange thickness be increased to only half of that required (but less than or equal to 4 percent cross-slope) and the height difference mitigated using thicker joint filler on the high side. If thicker joint filler cannot be fully used to compensate for the height difference, the extra load of a thicker slab must be accounted for in the design of the girders.

751.22.3.6-superelevation slope-Feb-23.jpg
The change in flange thickness due to
superelevation shall be added to the
change due to beam steps when
considering the Maximum Total Increase
to Top Flange Depth X” specified above.
Top Flange Slope with Superelevation

751.22.3.7 Closed Concrete Intermediate Diaphragms

Concrete intermediate diaphragms are cast between the ends of simple-span precast girders at interior supports and make the girders continuous for loads applied after continuity is established.

Closed concrete diaphragms are easier to construct than open concrete and provide better protection to bearings and the top of the beam cap but shall only be used with bearings that typically don’t need future rehabilitation (plain and laminated neoprene pads).

Closed concrete diaphragms are typically used at fixed bents where the superstructure is pinned to the beam cap with dowel bars centered in 3- by 6-inch keys formed in the top of the beam cap. Closed diaphragms at fixed bents allow for a change in girder heights within a continuous girder series (not to exceed next available girder height and only when specified on design layout or by the Structural Project Manager).

With approval of the Structural Project Manager or Structural Liaison Engineer, closed concrete diaphragms may be used at bents free to expand longitudinally over the beam cap, completely separated by joint filler. This option may be useful in reducing forces transmitted to a stiff bent but may only be used with laminated neoprene bearing pads in accordance with expansion limits of these bearings. A change in girder height is not permissible in closed concrete diaphragm at expansion bents.

Details for skewed bents are shown below. The dimensions, reinforcement and guidance shown are also applicable to squared bents.

751.22.3.7.1 Dimensions

The following dimensions shall be detailed on the plan sheets for closed concrete intermediate diaphragms.

751.22.3.7.1.1.jpg
751.22.3.7.1.2.jpg



Detailing Guidance:

Green items are guidance and shall not be shown on plans.

See EPG 751.22.3.7.3 for edge and end details.

(a) For curved alignments this dimension will need to be increased on one side and “(Min.)” needs to be added to the dimension in the section near diaphragm or the dimension replaced with “Varies”.

(b) Dimension based on a tangent alignment and 7 inches between the ends of girders. Will vary for curved alignments.

(c) 2'-6" unless skew requires wider diaphragm to accommodate coil tie rods

---___________________________________________________________________________________________________

751.22.3.7.2 Reinforcement

The reinforcement shall be detailed on the plan sheets for closed concrete intermediate diaphragms as shown below except:

  • Bar marks revised as required.
  • Abbreviations used as required.
  • Add "(Typ.)" to dimensions and leader notes as appropriate.

All U bar reinforcement shall use stirrup bends.

All reinforcement in diaphragms shall be epoxy coated, except coating of dowel bars shall match the coating of intermediate bent reinforcement.

Coil ties and rods shall also be shown in the section near the diaphragm and the horizontal section near the top of diaphragm in accordance with EPG 751.22.3.10 Coil Inserts and Tie Rods.

Unless specified the details shown are for the same girder heights within a continuous girder series.

I Girders Type 2, 3, 4 and 6

751.22.3.7.2 I Girders1.jpg
751.22.3.7.2 I Girders2.jpg

Bulb-Tee Girders Type 7 and 8

751.22.3.7.2 BulbTee1.jpg
751.22.3.7.2 BulbTee2.jpg

NU Girders

NU 53 girders are shown in the following details. The details for other NU girder types are similar.

751.22.3.7.2 NU1.jpg
751.22.3.7.2 NU2.jpg

Change in Girder Height

The following details are based on I Girders Type 2, 3, 4 and 6. The details are appropriate for bulb-tee and NU girders by substituting the appropriate reinforcing details from above. The reinforcement is that of the taller girder with additional #6 bars located under the shorter girder. The section near the diaphragm shall be from the perspective of the shorter girders. The differences from uniform girder height details are highlighted.

751.22.3.7.2 Change1.jpg
751.22.3.7.2 Change2.jpg

751.22.3.7.3 End and Edge Details

The end and edge details (standard cells in MicroStation) shall be provided on the plan sheets for closed concrete intermediate diaphragms. See EPG 751.22.3.7.1 Dimensions for location of the corresponding detail circles

751.22.3.7.3.jpg

751.22.3.7.4 Bent Details

The following details are required for closed concrete intermediate diaphragms and shall be provided on the plan sheets for intermediate bents as shown below.

Dowel Bars and Keys

The dowel bars and keys are required at fixed bents and shall be shown in the plan of beam showing reinforcement and in a section thru key detail (standard cell in MicroStation). For the sake of clarity only the keys (not the dowel bars) are shown in the plan of beam (plan showing joint filler). For the sake of clarity neither the dowel bars nor keys are shown in the elevation of the bent.

751.22.3.7.4.1.jpg

Dowel bars shall be determined by design in accordance with EPG 751.22.2.7 Dowel Bars. The minimum reinforcement is #6 bars at 12-inch centers.

Joint Filler and Bearings

The joint filler required for closed concrete intermediate diaphragms shall be shown in the plan of beam along with the bearings and girder chairs.

- At Fixed Bents
751.22.3.7.4.2.jpg
Detailing guidance follows expansion bent details.

See EPG 751.11.3.6 Girder/Beam Chairs for additional girder chair details.

- At Expansion Bents
751.22.3.7.4-3.png
PLAN OF BEAM
Detailing Guidance:
Green items are guidance and shall not be shown on plans.
(a) For curved alignments, this dimension will need to be increased on one side.
(b) Dimension based on a tangent alignment and 7 inches between the ends of girders. Will vary for curved alignments.
(c) W" is width of bearing and is equal to width of bottom flange minus 1½ inches. Bearing length and thickness is by design.
(d) 3¾" minimum for #4 stirrups in beam and 5¼" minimum for #5 or #6 stirrups in beam, except diaphragm width shall not be less than 2’-6”. Make diaphragm flush with beams less than three feet wide.
(e) Remove thickness for tapered bearings.

751.22.3.8 Open Concrete Intermediate Diaphragms

Concrete intermediate diaphragms are cast between the ends of simple-span precast girders at interior supports and make the girders continuous for loads applied after continuity is established.

Open concrete diaphragms allow clearance for jacks required for future bearing rehabilitation and therefore should be used at girder ends with bearing assemblies (laminated neoprene, Type N PTFE, Pot and Disc bearings).

Details for skewed bents are shown below. The dimensions, reinforcement and guidance shown are also applicable to squared bents.

751.22.3.8.1 Dimensions

The following dimensions shall be detailed on the plan sheets for open concrete intermediate diaphragms.

751.22.3.8.1.1.jpg
751.22.3.8.1.2.jpg

751.22.3.8.2 Reinforcement

The reinforcement shall be detailed on the plan sheets for open concrete intermediate diaphragms as shown below except:

  • Bar marks revised as required.
  • Abbreviations used as required.
  • Add "(Typ.)" to dimensions and leader notes as appropriate.

All U bar reinforcement shall use stirrup bends.

All reinforcement in diaphragms shall be epoxy coated.

Coil ties and rods shall also be shown in the section near the diaphragm and the horizontal section near the top of diaphragm in accordance with EPG 751.22.3.10 Coil Inserts and Tie Rods.

I Girders Type 2, 3, 4 and 6

751.22.3.8.2 I Girders1.jpg
751.22.3.8.2 I Girders2.jpg

Bulb-Tee Girders Type 7 and 8

751.22.3.8.2 BulbTee1.jpg
751.22.3.8.2 BulbTee2.jpg

NU Girders

NU 53 girders are shown in the following details. The details for other NU girder types are similar.

751.22.3.8.2 NU1.jpg
751.22.3.8.2 NU2.jpg

751.22.3.9 Concrete End Diaphragms

End diaphragms (either at end bents or at intermediate bents) are necessary where joints are required in a bridge superstructure. End diaphragms transfer loads at the end of slab to the girders and serve to tie girders together to better enable the bridge cross section to function as a unit. When end bent foundation can accommodate the expansion of the superstructure, the diaphragm can be constructed integral with the bent in accordance with EPG 751.35 Concrete Pile Cap Integral End Bents.

Bearing assembles are typically required at end diaphragms and therefore, for the sake of future bearing rehabilitation, it is standard practice to detail as open-end diaphragms in accordance with the next two articles. The one exception is that a closed-end diaphragm may be detailed in accordance with EPG 751.22.3.9.3 at finger plate expansion device connected to a steel girder series.

Details for skewed bents are shown below. The dimensions, reinforcement and guidance shown are also applicable to squared bents.

Previous details showed the coping of the girders for the purpose of decreasing the length of the expansion device support piece. Alternatively, increasing the thickness of the support piece is a practical option. The standard support piece has been used with the details below for skew angles as large as 30 degrees. The method to account for an excessively long expansive device support piece shall be discussed with Structural Project Manager or Structural Liaison Engineer.

751.22.3.9.1 Dimensions

The following dimensions shall be detailed on the plan sheets for concrete end diaphragms.

751.22.3.9.1.1 2022.jpg
751.22.3.9.1.2 2022.jpg
751.22.3.9.1.3.jpg

751.22.3.9.2 Reinforcement

The reinforcement shall be detailed on the plan sheets for concrete end diaphragms as shown below except:

  • Bar marks revised as required.
  • Abbreviations used as required.
  • Add "(Typ.)" to dimensions and leader notes as appropriate.

All U bar reinforcement shall use stirrup bends.

All reinforcement in diaphragms shall be epoxy coated.

Coil ties and rods shall also be shown in the section near the diaphragm and the horizontal section near the top of diaphragm in accordance with EPG 751.22.3.10 Coil Inserts and Tie Rods.

I Girders Type 2, 3, 4 and 6

751.22.3.9.2 IGirders1.jpg
751.22.3.9.2 IGirders2.jpg

Bulb-Tee Girders Type 7 and 8

751.22.3.9.2 BulbTee1.jpg
751.22.3.9.2 BulbTee2.jpg

NU Girders

NU 53 girders are shown in the following details. The details for other NU girder types are similar.

751.22.3.9.2 NU1.jpg
751.22.3.9.2 NU2.jpg

751.22.3.9.3 Closed Diaphragm

Use only when expansion device connects prestressed girder series and steel girder series, and laminated neoprene pads are used under the prestressed girders in accordance with expansion limits of these bearings and only with the approval of the Structural Project Manager or Structural Liaison Engineer.

The simplified detail below is for I girders. The actual details required on the plans can be developed for all girder types by substituting the dimensions and reinforcement of the corresponding section near the diaphragm detail of EPG 751.22.3.7 and the dimensions from the corresponding Section A-A of EPG 751.22.3.9.1 Dimensions.

751.22.3.9.3 2022.jpg

751.22.3.10 Coil Inserts and Tie Rods

Threaded rods (coil tie rods) installed in coil inserts (coil ties) that are cast into the ends of prestressed girders are provided to aid in transferring forces from the diaphragms into the girder ends. Additionally, coil tie rods are believed to provide some aid in resisting positive moment forces.

Coil ties and rods shall be detailed on the plan sheets for prestressed girders.

Bridge Standard Drawings
Prestressed I-Girders

Coil ties and coil tie rods shall be detailed on the plan sheets for concrete diaphragms as shown below. Girders and beams with coil ties and rods are available as standard cells under the concrete diaphragm tasks in MicroStation.

Closed Diaphragms

751.22.3.10 Closed1.jpg
751.22.3.10 Closed2.jpg
Detailing guidance follows open diaphragm details.

Open Diaphragms

751.22.3.10 Open1.jpg
751.22.3.10 Open2.jpg
Detailing Guidance:
Green items are guidance and shall not be shown on plans.
Section A-A shows an intermediate diaphragm and I girders, but dimensions and coil tie orientation are applicable
for end diaphragms and other prestressed girder types as well.
(a) “Two” not required for end diaphragms.
(b) “Two” not required for bulb-tee and NU girders.

751.22.3.11 Steel Intermediate Diaphragms

Use steel intermediate diaphragm for prestressed spans over 50 feet except for NU 35 and NU 43 girders.

Bridge Standard Drawings
Steel Intermediate Diaphragms

Use straight diaphragm normal to girders for skews thru 20°.

Use stepped diaphragm for skews over 20°.

Spans of 90 feet or less require one intermediate diaphragm per span.

Spans over 90 feet require two intermediate diaphragms per span.

Spans over 140 feet require three intermediate diaphragms per span.

Space diaphragms equally as allowed by clearance to harped strands.

Maximum spacing is 50 feet (from support and between diaphragms).

NU 35 and NU 43 Girders

Permanent intermediate diaphragms are not required for NU 35 and NU 43 girders. Temporary intermediate diaphragms/bracing are required for construction of the bridge deck. See EPG 751.50 Note H2c2.2.

751.22.3.12 Vent Holes

Note: Use vent holes on all stream crossing structures.


751.22 Vent Holes Elevation & Section.gif
PART ELEVATION OF GIRDER PART SECTION NEAR VENT HOLE


Note: Place vent holes at or near upgrade of 1/3 point of girders and clear
reinforcing steel or strands by 1-1/2" minimum and steel intermediate
diaphragms bolt connection by 6" minimum.

751.22.3.13 Concrete Shear Blocks

Concrete shear blocks shall be used when 4 anchor bolts per bearing are insufficient, or for preventing loss of support on beams and stub bent footings. Design shear blocks in accordance with LRFD 5.7.4.3. The following dimensions and sizes are for rough guidelines only and may be altered to fit specific situations:


Concrete block dimensions

Lvi = Length shall extend all the way across the beam (for ease of forming), oriented parallel to centerline of roadway.

bvi = Width is as required for concrete area. Allow about 1/2 in. (typical) clearance between the edge of the sole plate and the edge of the block to allow engaging of anchor bolts.

H = height of shear block and shall extend to about an inch (+/-) above the top of the sole plate.


Steel reinforcement

Bar size = #4 min. to # 6 max. hairpins placed parallel to the centerline of the beam, with #4 horizontal straight bars at the top of the hairpin to ensure proper alignment.

Space hairpin shear bars as required to provide the required steel area, with 6" minimum to 12" maximum. The maximum edge distance in the direction of the spacing = half of reinforcement spacing.


Demand shear per block

For complete seismic analysis, FT = transverse component of total horizontal seismic force demand at the bent, normal to the centerline of the roadway, kips. Both seismic load cases, Case 1 = L + 0.3T and Case 2 = 0.3L + T, must be satisfied.

For seismic details only (strength limit states), transverse FT = 0.25(DL). Where DL = unfactored dead load reaction at the bent, kips

R = 1.0 for seismic details only (strength limit states) and 0.8 for complete seismic analysis

NB = the number of blocks resisting the seismic force. The designer should consider using a value of NB that is less than the total number of blocks, because all blocks may not resist equal amounts of force. For example, two shear blocks as shown in details below, only left side shear block will resist horizontal force when seismic forces act from right to left.

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 V_{ui} = factored \ shear \ force \ per \ block,\ kips }
Failed to parse (MathML with SVG or PNG fallback (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{F_T}{N_B R}}


Block shear resistance:

∅ = 0.90 resistance for seismic details only (strength limit states) and 1.0 for complete seismic analysis

Failed to parse (MathML with SVG or PNG fallback (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_{ni} = CA_{cv} + \mu (A_{vf}f_y) = nominal \ shear \ resistance \ per \ block, \ kips}

bvi = width of the shear block, in.

Lvi = length of the shear block, in.

Avf = area of shear reinforcement crossing the shear plane, sq. in.

fy = yield strength of shear reinforcement not to exceed 60 ksi


The nominal shear resistance is limited by the following equations:

Failed to parse (MathML with SVG or PNG fallback (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_{ni} \le K1 f'_c A_{cv}} and Failed to parse (MathML with SVG or PNG fallback (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_{ni} \le K2 A_{cv}}
= compressive strength of concrete at 28-day cure, ksi

For new construction (monolithic construction):

C = 0.4 ksi
μ = 1.4
K1 = 0.25
K2 = 1.5 ksi

For retrofits:

C = 0.24 ksi
μ = 1.0
K1 = 0.25
K2 = 1.5 ksi


Minimum area of shear reinforcement per shear block:

Failed to parse (MathML with SVG or PNG fallback (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_{vf} \ge \frac{0.05A_{cv}}{f_y} }


Concrete shear block details:

A minimum of two shear blocks 12" wide by width of substructure beam will be detailed at effective locations on open diaphragm bent caps and closed diaphragm bent caps when adequate structural restraint cannot be provided with anchor bolts. Shear blocks shall be detailed parallel to the centerline of roadway.

751.22.3.14 elevation.jpg

(1) Height of shear block shall extend a minimum of 1 inch above the top of the sole plate (typ.).


751.22.3.14 plan.jpg

PLAN OF BEAM
Anchor bolts and sole plates not shown for clarity.

* With open diaphragm, beam steps normal to beam; with closed diaphragm, beam steps parallel to centerline roadway.

751.22.3.14 Miscellaneous

Dimensional Tolerances

I-Girders, Solid Slab Beams, Voided Slab Beams, Box Beams, Double-Tee Girders, Deck Panels and Miscellaneous Prestress Units, see Sec 1029


Expansion Device Support Slots


Used with preformed compression joint seal, flat plate, strip seal or finger plate expansion devices.


751.22 Miscellaneous Exp Device Support Part Plan.gif


PART PLAN OF P/S CONC. I-GIRDER @ EXP. DEVICE END


751.22 Miscellaneous Exp Device Support Part Elevation.gif


PART ELEVATION OF P/S CONC. I-GIRDER @ EXP. DEVICE END


(*) Show these dimensions on the P/S concrete girder sheet.


Anchor Bolts
Simple Spans


751.22 Miscellaneous Anchor Bolts Part Elevation.gif


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"ø) to be grouted with approved non-shrink grout meeting the requirements of ASTM C1107.