Recommended LRFD Minimum Flexural Reinforcement Requirements (2010) / Chapter Skim
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Appendix B Design Examples
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B-1 B.1 MULTI-SPAN PRECAST CONCRETE GIRDER MADE CONTINUOUS WITH COMPOSITE DECK This is one of the most common types of structures used for freeway bridges and overpasses. This three-span precast/prestressed girder example features a single long span in the middle along with two short side spans, as shown in Figure B-1.
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B-2 Material properties ksif c 5.7' (girders) ksif ci 5.5' (girders)
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B-3 inh f 6 (compression flange) 433.26 ftI nc (non-composite section)
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B-4 ftkM PCDL 27 ftkM deck 408 ftkM DCADL 38 ftkM DWADL 60 ftkM HL 036,193 9375.165.09.0) (25.1 HLDWADLDCADLdeckPCDLSWStrengthIu MMMMMMM 036,175.1)
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B-5 ksi I yeP A P f nc nc bncf nc f cpe 166.11233.26 6.3610.34325 1233.5 325 42 3 4 279,20 38.55 1216.54 in y IS c b c c ftkMMMM deckPCDLSWndc 78940827354 3 4 917,14 6.36 1233.26 in y IS nc b nc nc ftkM fcr 638,3)
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B-6 ftk baf dfAM fcppsps ps n 010,312) 2 12913.15.485.0787.268736.1( 2 '85.0 22 The section is tension-controlled and 00.1 ftkM psn 010,3010,300.1 ftkMftkM StrengthIu ps n 623,333.1010,3 so additional strands are required.
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B-7 Figure B-2. Moment Profiles for the Precast Girder Example
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B-9 B.2 CAST-IN-PLACE CONCRETE BOX GIRDER A three-span cast-in-place concrete box girder bridge that is commonly built in California and Nevada is the subject of this design example. As with the first example, the side spans are far shorter than the end spans while the depth of the bridge is constant for along the entire length.
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B-10 ksif c 4' ksiEc 644,3 ksif y 60 ksiEs 000,29 ksif pu 270 ksiE ps 500,28 Prestress Forces The allowable tension stress is limited to 0 under permanent loads and 0.19 cf ' (ksi) under the sum of the permanent and live loads.
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B-11 inbw 72 403.538 ftI 278.90 ftA inyb 96.40 (distance from section CG to bottom fiber) iny t 04.37 (distance from section CG to top fiber)
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B-12 ftk baf dfAM fcppsps ps n 586,4012) 2 34205.7485.090.629.26762.30( 2 '85.0 22 005.001973.03 ps the section is tension-controlled and 95.0 ftkMftkM StrengthIIu ps n 830,43557,38586,4095.0 so mild steel is required.
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B-13 Also, the net tensile strain is greater than 0.0075, which satisfies Article 5.7.3.5 for redistribution. Therefore, per the proposed revised Article 5.7.3.3.2, minimum reinforcement is not required to be checked for negative bending.
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B-14 iny t 89.32 (distance from section CG to top fiber) Minimum reinforcement by the Modified LRFD Method: fcrn MM where SffM cperfcr )
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B-15 At decompression: 00014.0)
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B-16 Figure B-4. CIP Box Girder Moment Profiles
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B-17 B.3 SPAN-BY-SPAN SEGMENTAL BRIDGE WITH EXTERNAL TENDONS INTRODUCTION A two-span precast segmental bridge is the subject of this design example. The bridge is built using the span-by-span construction method.
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B-18 Figure B-6. Cross section (Span 2)
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B-19 ksif y 60 ksiEs 000,29 ksif pu 270 ksiE ps 500,28 PRESTRESS DESIGN For precast segmental bridges with no bonded reinforcement or bonded tendons crossing the joints, no tensile stresses are allowed at all segment-to-segment joints under service loads. Longitudinal analysis and design of this bridge included concrete stresses under service loads, flexural capacity, shear capacity, principal stresses in the box girder webs and minimum flexural reinforcement requirements.
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B-20 Figure B-8. Cracking Moment, Factored Moment and Flexural Capacity of a Precast Segmental Span-By-Span Bridge Example Analysis of this bridge was done using LARSA 4D.
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B-21 TGTUIHLSSecPDWDC StrengthI uu MMMMMMMM 50.050.075.100.150.125.1 93/ )
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B-22 Depth of compression zone: Assume ksifksif pyps 243228 in bf fA c fc psps 53.2 85.0 1 ' Depth of neutral axis is smaller than deck thickness. Thus, use of equations for rectangular sections is justified.
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B-23 ftkMftkxSff ucpecr 826,45142,4912 663,215)
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B-24 Figure B-9. Variation of Cracking Moment, Factored Moment and Moment Capacity with Number of Strands in External Tendons It is interesting to note that with the current AASHTO LRFD MFR requirements, the curve representing minimum design moment in Figure B-9 does not intersect with the curve representing the moment capacity, which indicates that no convergence may be obtained to satisfy the MFR by increasing the number of strands (unless 1.33Mu controls the MFR requirement)
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B-25 B.4 BALANCED CANTILEVER BRIDGE WITH INTERNAL TENDONS INTRODUCTION A four-span precast segmental bridge is the subject of this design example. The bridge is built using the cantilever construction method.
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B-26 Figure B-11. Cross section (Span 2)
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B-27 Figure B-13. Tendon Layout for the Precast Segmental Cantilever Bridge Design Example SPECIFICATIONS This example is designed based on the AASHTO LRFD Bridge Design Specifications 4th Edition, 2007.
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B-28 and minimum flexural reinforcement requirements. At the first segment-to-segment joint next to Pier 8-3 in Span 4 (most critical section for negative moment)
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B-29 use of the Modified LRFD method significantly reduces the required MFR design moment compared to the current AASHTO LRFD provisions. For sections away from the supports, the minimum design moment according to the Modified LRFD method controls over 1.33Mu, whereas 1.33Mu controls MFR for sections near the supports.
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B-30 ftkM LT 842,1 Long-term effects (concrete creep & shrinkage and relaxation of prestressing steel) ftkM SSecP 000,25/ Secondary effects from prestressing ftkM TU 2 Uniform temperature rise ftkM TG 628,1 Temperature gradient ftkM IHL 727,793 TGTU IHLSSecPLTDWDC StrengthI uu MM MMMMMMM 50.050.0 75.100.150.050.125.1 93/ )
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B-31 infth 1089 The sacrificial surface is included as external load only inh f 0.9 (minimum thickness of compression flange for negative moment section) inh f 5.9 (minimum thickness of compression flange for positive moment section)
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B-32 Effective length of external tendons: ft N l l i i e 33.100) 2( 2 Depth of compression zone: Assume ksifksif pyps 243182 in d f Akbf fAfAfA c p pu psfc yspspspups 22.25 85.0 1 11 ' 221 (k = 0.28 for low-relaxation strands)
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B-33 Section B: Section at Maximum Positive Moment in Span 4: Prestressing tendons at this section is composed of external (unbonded) tendons only.
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B-34 Minimum reinforcement by the proposed method (Modified LRFD) : Section B: Section at Maximum Positive Moment in Span 4: fcrn MM or un MM 33.1 ; where SffM cpecrfcr )
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B-35 B.5 CAP BEAM DESCRIPTION OF CAP The cap beam has a main span of 23 ft and 2 cantilever spans of 12.5 ft each. The cap is 6.5 ft wide and 6 ft deep.
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B-36 ksiEc 644,3 ksif y 60 ksiEs 000,29 MOMENT DIAGRAMS Figure B-17. Cap Beam Design Example Strength limit bending moments At the inside face of support (negative moment)
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B-37 Section properties: infth 726 inftb 785.6 4117 ftI 239 ftA iny t 36 (distance from section CG to top fiber) Required flexural reinforcement: )
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B-38 9375.165.09.0 HLDWDCStrengthIu MMMM )
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B-39 9375.150.125.1 HLDWDCStrengthIu MMMM )
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