751.21 Prestressed Concrete Slab and Box Beams - Revision history

Hoskir: /* 751.22.2.3 Flexure */

2025-07-11T19:11:40Z

751.22.2.3 Flexure

← Older revision		Revision as of 14:11, 11 July 2025
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	~~===751.22.2.3 Flexure===~~
	~~Flexure capacity of girders shall be determined as the following.~~

	~~'''Flexural resistance at strength limit state'''<br/>~~

	~~<math>\,M_r = \phi M_n \ge M_u</math>~~

	~~Where:~~
	~~{\|border="0" cellpadding="5"~~
	~~\|<math>\,M_r</math>\|\|=\|\|Flexural resistance~~
	\|-
	~~\|<math>\,M_n</math>\|\|=\|\|Nominal flexural resistance~~
	\|-
	~~\|<math>\,M_u</math>\|\|=\|\|Total factored moment from Strength I load combination~~
	\|-
	~~\|valign="top"\|<math>\, \phi</math>~~
	~~\|valign="top"\|=~~
	~~\|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.~~


	~~<div id="Design A1 reinforcement in the top flange"></div>~~

	~~'''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.

	~~See guidance on [https://www.modot.org/bridge-standard-drawings Bridge Standard Drawings (Prestressed I-Girders - PSI)] for required lap lengths, if required.~~


	~~Required steel area is equal to:~~

	~~<math>\,A1=\frac{T_t}{f_s}</math>~~

	~~Where:~~
	{\|
	~~\|<math>\, f_s</math>\|\|= <math>\, 0.5 f_y \le 30 KSI</math>, allowable tensile stress of mild steel, (ksi)~~
	\|-
	~~\|<math>T_t</math>\|\|= 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, ''M<sub>r''</sub>, is at least equal to the lesser of:<br/>~~

	~~::1) M<sub>cr</sub>       LRFD Eq. 5.6.3.3-1~~
	~~::2) 1.33M<sub>u</sub>~~

	~~Where:~~
	~~{\|border="0" cellpadding="5"~~
	\|-
	~~\|M<sub>cr</sub>\|\|=\|\|Cracking moment, (kip-in.)~~
	\|-
	~~\|M<sub>u</sub> \|\|=\|\|Total factored moment from Strength I load combination, (kip-in.)~~
	\|}


	~~'''Limiting tensile stress'''~~

	~~For prestressed girders made continuous and where the A1 reinforcement is proportioned as stated above:~~

	~~The limiting tensile stress after losses at the top of girders near interior supports is~~

	~~0.24√f’c …(Service III)~~

	~~The above stress limit shall be checked even though the PS girder is designed as a reinforced concrete member at regions of negative flexure.~~


	~~The limiting tensile stress after losses near the midspan of girders is~~

	~~0.19√f’c ≤ 0.6 ksi …(Service III)~~


	~~The limiting tensile stress before losses at the top of girders is~~

	~~0.24√f’ci~~

	==751.21.3 Details==		==751.21.3 Details==

Hoskir: /* 751.21.2 Design */ updated per RR4046

2025-07-11T19:09:07Z

751.21.2 Design: updated per RR4046

Show changes

Hoskir: /* 751.21.3.6.3 Reinforcement */ updated per RR4028

2025-04-14T12:58:39Z

751.21.3.6.3 Reinforcement: updated per RR4028

← Older revision		Revision as of 07:58, 14 April 2025
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	=====751.21.3.6.3 Reinforcement=====		=====751.21.3.6.3 Reinforcement=====

	[[image:751.21.3.6.3 1.jpg\|center\|750px]]		{\| cellpadding="10" style="text-align:center; margin:auto"
	[[image:751.21.3.6.3 2.jpg\|center\|~~800px~~]]		\|-
			\| colspan="2" \| [[image:751.21.3.6.3 1.jpg\|center\|750px]]
			\|-
			\| colspan="2" \| [[image:751.21.3.6.3_03-25.jpg\|center\|800px]]
			\|-
			\| colspan="2" \| '''SECTION A-A''' (Structure skewed over 25° with skewed-end beams)
			\|-
			\| [[image:751.21.3.6.3_04-25.jpg\|center\|400px]] \|\| rowspan="4" style="text-align:left;"\| '''Detailing Guidance:''' <br><span style="color:#00B050">'''Green items'''</span> are guidance only and shall not be shown on the plans. <br>Bar marks shown are for these details only; vary as needed. <br>Bars will need to clear any required shear blocks for expansion bents. <br>[[image:751.21.3.6.3_06-25.jpg\|center\|300px]] <br><span style="color:#00B050">'''(ɑ)'''</span> One strand tie bar for each layer of bent up strands. <br><span style="color:#00B050">'''(b)'''</span> 19 inches minimum for #4 bars and full available width for #6 bars. <br><span style="color:#00B050">'''(c)'''</span> 11-inch centers may be used if necessary.
			\|-
			\| '''PART SECTION A-A''' <br>(Bend strand tie bars if necessary, for clearance)
			\|-
			\| [[image:751.21.3.6.3_05-25.png\|center\|400px]]
			\|-
			\| '''SECTION B-B''' <br>(Fixed bent and squared or skewed-end beams)
			\|}


	=====751.21.3.6.4 End and Edge Details=====		=====751.21.3.6.4 End and Edge Details=====

Hoskir: /* 751.21.3.3.1 Spread Box Beams */ updated per RR4028

2025-04-14T12:56:26Z

751.21.3.3.1 Spread Box Beams: updated per RR4028

← Older revision		Revision as of 07:56, 14 April 2025
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	Dimensions shown are out to out. Use symmetry for dimensions not shown. Use "ɑ" bars for squared-end beams. Use '''<font color="green">"b"</font color="green">''' bars for skewed-end beams.		Dimensions shown are out to out. Use symmetry for dimensions not shown. Use "ɑ" bars for squared-end beams. Use '''<font color="green">"b"</font color="green">''' bars for skewed-end beams.

	[[image:751.21.3.3.~~1 bending1 2021~~.~~jpg~~\|center\|650px]]		[[image:751.21.3.3.1_01-25.png\|center\|650px]]
	{\| style="margin: 1em auto 1em auto"		{\| style="margin: 1em auto 1em auto"
	\|-		\|-

Hoskir: Undo revision not ready to publish yet

2025-03-11T14:04:54Z

Undo revision not ready to publish yet

← Older revision		Revision as of 09:04, 11 March 2025
Line 276:		Line 276:
	Dimensions shown are out to out. Use symmetry for dimensions not shown. Use "ɑ" bars for squared-end beams. Use '''<font color="green">"b"</font color="green">''' bars for skewed-end beams.		Dimensions shown are out to out. Use symmetry for dimensions not shown. Use "ɑ" bars for squared-end beams. Use '''<font color="green">"b"</font color="green">''' bars for skewed-end beams.

	[[image:751.21.3.3.~~1_01-25~~.~~png~~\|center\|650px]]		[[image:751.21.3.3.1 bending1 2021.jpg\|center\|650px]]
	{\| style="margin: 1em auto 1em auto"		{\| style="margin: 1em auto 1em auto"
	\|-		\|-

Hoskir: /* 751.21.3.3.1 Spread Box Beams */

2025-03-11T14:03:19Z

751.21.3.3.1 Spread Box Beams

← Older revision		Revision as of 09:03, 11 March 2025
Line 276:		Line 276:
	Dimensions shown are out to out. Use symmetry for dimensions not shown. Use "ɑ" bars for squared-end beams. Use '''<font color="green">"b"</font color="green">''' bars for skewed-end beams.		Dimensions shown are out to out. Use symmetry for dimensions not shown. Use "ɑ" bars for squared-end beams. Use '''<font color="green">"b"</font color="green">''' bars for skewed-end beams.

	[[image:751.21.3.3.~~1 bending1 2021~~.~~jpg~~\|center\|650px]]		[[image:751.21.3.3.1_01-25.png\|center\|650px]]
	{\| style="margin: 1em auto 1em auto"		{\| style="margin: 1em auto 1em auto"
	\|-		\|-

Hoskir: /* 751.21.3.6.1 Dimensions */ updated per RR3915

2024-07-31T18:58:03Z

751.21.3.6.1 Dimensions: updated per RR3915

← Older revision		Revision as of 13:58, 31 July 2024
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	Bearing length and thickness is by design. Bearings may vary on each side of bent.		Bearing length and thickness is by design. Bearings may vary on each side of bent.

	'''<font color="green">(e)</font color="green">''' 3¾" minimum ~~for #4 stirrups in substructure beam and 5¼" minimum for #5 or #6 stirrups in substructure beam~~, ~~except~~ diaphragm ~~width shall not~~ be ~~less than 2’-6”. Make diaphragm~~ flush with substructure beams ~~less~~ than three feet wide.		'''<font color="green">(e)</font color="green">''' 3¾" minimum. With the approval of the SPM, the diaphragm may be made flush with substructure beams not greater than three feet wide.

	'''<font color="green">(f)</font color="green">''' Remove thickness for tapered bearings or when bearings vary on each side of bent.		'''<font color="green">(f)</font color="green">''' Remove thickness for tapered bearings or when bearings vary on each side of bent.

Hoskir: /* 751.21.3.6.1 Dimensions */ updated per RR3762

2023-08-22T16:19:56Z

751.21.3.6.1 Dimensions: updated per RR3762

← Older revision		Revision as of 11:19, 22 August 2023
Line 389:		Line 389:
	Bearing length and thickness is by design. Bearings may vary on each side of bent.		Bearing length and thickness is by design. Bearings may vary on each side of bent.

	'''<font color="green">(e)</font color="green">''' 3¾" minimum. Make diaphragm flush with substructure beams less than three feet wide.		'''<font color="green">(e)</font color="green">''' 3¾" minimum for #4 stirrups in substructure beam and 5¼" minimum for #5 or #6 stirrups in substructure beam, except diaphragm width shall not be less than 2’-6”. Make diaphragm flush with substructure beams less than three feet wide.

	'''<font color="green">(f)</font color="green">''' Remove thickness for tapered bearings or when bearings vary on each side of bent.		'''<font color="green">(f)</font color="green">''' Remove thickness for tapered bearings or when bearings vary on each side of bent.

Hoskir: /* 751.21.1.4 Span and Structure Lengths */ updated per RR3737

2023-07-26T20:11:50Z

751.21.1.4 Span and Structure Lengths: updated per RR3737

← Older revision		Revision as of 15:11, 26 July 2023
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	The span and structure lengths for prestressed beams shall be in accordance with [[751.22_Prestressed_Concrete_I_Girders#751.22.1.4_Span_and_Structure_Lengths\|EPG 751.22.1.4 Span and Structure Lengths]], except that skewed ends of prestressed beams shall be in accordance with [[751.21_Prestressed_Concrete_Slab_and_Box_Beams#751.21.3.2.1_Skewed_Ends\|EPG 751.21.3.2.1 Skewed Ends]] instead of the coping requirements used for the I-Girders.		The span and structure lengths for prestressed beams shall be in accordance with [[751.22_Prestressed_Concrete_I_Girders#751.22.1.4_Span_and_Structure_Lengths\|EPG 751.22.1.4 Span and Structure Lengths]], except that skewed ends of prestressed beams shall be in accordance with [[751.21_Prestressed_Concrete_Slab_and_Box_Beams#751.21.3.2.1_Skewed_Ends\|EPG 751.21.3.2.1 Skewed Ends]] instead of the coping requirements used for the I-Girders.

	The following ~~charts provide potential~~ span ~~ranges (limits) for~~ prestressed spread box beams based ~~on bridges that were designed between 2010 and 2023~~. ~~Because~~ the ~~span limit charts were~~ developed using ~~previously designed bridges with~~ standard materials and shapes~~, increased~~ span lengths are possible with modification. See Increasing Girder Capacity section above for more information. ~~These charts~~ shall be used for preliminary design only.		The following chart provides a general baseline for the maximum span lengths of prestressed spread box beams based off single span designs in accordance with LRFD, 9th Edition. The designs used for this chart use the maximum practical girder spacing (approximately 11’-6”). The chart was developed using designs that used standard materials and shapes. 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. This chart shall be used for preliminary design only.

	'''Limitations of the ~~Charts~~:'''		'''Limitations of the Chart:'''

	~~All charts contain~~ only ~~standard materials~~. ~~Referenced bridges contained both single and continuous span bridges~~. ~~Shapes are not modified in any way~~.		This chart only contains 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.

	<center><b><big>Prestressed Spread Box Beam Span Ranges</big></b></center>		<center><b><big>Prestressed Spread Box Beam Single Span Ranges</big></b></center>
	[[image:751.22.1.~~4_PS_Box_6ksi_06~~-23.png\|700px\|center]]		[[image:751.22.1.4_PS_Box_8ksi_07-23.png\|700px\|center]]
	~~[[image:751.22.1.4_PS_Box_7ksi_06-23.png\|700px\|center]]~~
	~~[[image:751.22.1.4_PS_Box_8ksi_06-23.png\|700px\|center]]~~
	~~{\| style="margin: auto; vertical-align:top;"~~
	~~\|- style="vertical-align:top;"~~
	~~\| <b>Note: </b> \|\| 27in, 33in, 39in, and 42in Spread Box Beams were excluded from some graphs due to there being</br>insufficient data to produce an accurate range of span lengths.</center>~~
	\|-
	~~\| \|\| A green bar denotes that the particular type of spread box beam has three or fewer entries and should</br>not be relied on as heavily as others.</center>~~
	\|}

	===751.21.1.5 Constant and Varied Joint Filler Loads===		===751.21.1.5 Constant and Varied Joint Filler Loads===

Hoskir: /* 751.21.1.4 Span and Structure Lengths */ updated per RR3719

2023-06-30T13:52:52Z

751.21.1.4 Span and Structure Lengths: updated per RR3719

@@ Line 108: / Line 108: @@
 ===751.21.1.4 Span and Structure Lengths===
-The span and structure lengths for prestressed beams shall be in accordance with [[751.22 Prestressed Concrete I Girders#751.22.1.4 Span and Structure Lengths|EPG 751.22.1.4 Span and Structure Lengths]], except that skewed ends of prestressed beams shall be in accordance with [[#751.21.3.2.1 Skewed Ends|EPG 751.21.3.2.1 Skewed Ends]] instead of the coping requirements used for the I-Girders.
+The span and structure lengths for prestressed beams shall be in accordance with [[751.22_Prestressed_Concrete_I_Girders#751.22.1.4_Span_and_Structure_Lengths|EPG 751.22.1.4 Span and Structure Lengths]], except that skewed ends of prestressed beams shall be in accordance with [[751.21_Prestressed_Concrete_Slab_and_Box_Beams#751.21.3.2.1_Skewed_Ends|EPG 751.21.3.2.1 Skewed Ends]] instead of the coping requirements used for the I-Girders.
 ===751.21.1.5 Constant and Varied Joint Filler Loads===