Simplified Shear Design of Structural Concrete Members: Appendixes (2005) / Chapter Skim
Currently Skimming:
Pages 269-338
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 269... ...
Appendix J: Examples of Shear Design The purpose of these design examples is to demonstrate the application of the shear design methods developed in Tasks 4 through 6, i.e., Proposal 1 (Modified STD Approach) and Proposal 2 (Modified CSA Approach)
|
From page 270... ...
J.1 Example 1: Precast, Pretensioned Non-Composite Box Beam J.1.1 Example Description This example demonstrates the shear design at a specific section of a 95-ft single-span AASHTO Type BIII-48 box beam bridge with no skew. The bridge is that of Example 9.2 of the PCI Bridge Design Manual.
|
From page 271... ...
J.1.3 Material Properties The material properties are given in Table J-1. Table J-1 Material Properties CONCRETE PROPERTIES Concrete strength at 28 days, f'c 5 ksi Concrete unit weight, wc 0.150 kcf Modulus of elasticity of concrete, Ec = '5.1)
|
From page 272... ...
Section modulus for the extreme bottom fiber, Sb 8,728 in3 Section modulus for the extreme top fiber, St 8,542 in3 Area of non-prestressed tension reinforcement, As 0 in2 Distance from extreme compression fiber to centroid of longitudinal tension reinforcement, ds 0 in Area of prestressed tension reinforcement, Ap =29(0.153) =4.437 in2 Distance from the top fiber to the centroid of prestressed tendons, dp 36.59 in Weight of beam 0.847 kip/ft SECTIONAL FORCES AT DESIGN SECTION Unfactored shear force caused by dead load, Vd 47.6 kips Factored shear force, Vu 146.5 kips Unfactored moment caused by dead load, Md 176.0 ft-kips Factored moment, Mu 424.6 ft-kips Figure J-3 Cross-Section of AASHTO Box Beam Type BIII-48 J-4
|
From page 273... ...
Figure J-4 Strand Pattern at Midspan Figure J-5 Strand Pattern at the Design Section Calculation of effective depth, : vd Note that only 22 strands (16@2 in.
|
From page 274... ...
The design shear stress is: 146.5 0 0.496 (0.9)
|
From page 275... ...
Stress due to service dead load: 176.0(12)
|
From page 276... ...
Therefore, use #3 single leg stirrups in each side of web at 18 in. spacing provided > required /vA s 20.22 /18 0.0122 .
|
From page 277... ...
where Ac = area of concrete on the flexural tension side as shown in Fig.
|
From page 278... ...
The shear strength provided by transverse reinforcement is: s dfA V vyvs ααθ sin)
|
From page 279... ...
J.1.7 Summary and Conclusions Shear design procedures in accordance with the Modified STD Approach and the Modified CSA Approach were used to determine the amount and spacing of the transverse reinforcement required at a section 42.74 in. from the support of a 95-ft single-span AASHTO Type BIII-48 box beam with straight strands and of which seven strands are debonded at the design section..
|
From page 280... ...
J.2 Example 2: Three-Span Continuous Precast, Pretensioned Girders J.2.1 Example Description This example is based on Example 9.6 of the PCI Bridge Design Manual. The bridge uses 72-inch bulb -tee beams with harped (draped)
|
From page 281... ...
Table J-4 Material Properties and Basic Information CONCRETE PROPERTIES Concrete strength of girder at 28 days, f'c 7.0 ksi Concrete strength of deck at 28 days, f'c 4.0 ksi Concrete unit weight, wc 0.150 kcf Modulus of elasticity of concrete for girder, Ec,beam = '5.1)
|
From page 282... ...
Distance from centroid to extreme top fiber, yt 35.40 in. Section modulus for the extreme bottom fiber, Sb 14,915 in3 Section modulus for the extreme top fiber, St 15,421 in3 Weight of beam 0.799 kip/ft Composite Section Overall depth of the composite section, hc 80 in.
|
From page 283... ...
Figure J-9 Cross-Section of AASHTO-PCI, BT-72 Bulb-Tee Beam Figure J-10 Composite Section J-15
|
From page 284... ...
Figure J-11 Strand Pattern at Midspan and at Ends Calculation of effective depth, : vd Note that the design section (7.10 ft from the interior support) is located in the negative moment zone.
|
From page 285... ...
Shear design procedures in accordance with the Modified STD Approach are used to determine the amount and spacing of the shear reinforcement required at a distance of 7.10 ft from the interior support.
|
From page 286... ...
1,097,252 (0.2 4.0 0 0.106) /12 1,061.3 25.33cr M ft kips= + − = ⋅ The flexure-shear cracking strength, , is: ciV 276.1(1,061.3)
|
From page 287... ...
When , [LRFD Eqs.
|
From page 289... ...
When , [LRFD Eqs.
|
From page 290... ...
J.3 Example 3: Reinforced Concrete Cap Beam J.3.1 Example Description This design example demonstrates the shear design of a section of a 15-ft span cap beam sitting on three circular columns of 3-ft diameter.. The cap beam supports a 3-lane superstructure consisting of six AASHTO Type IV beams.
|
From page 291... ...
Overall depth of beam, h 39 in. Width of web, bv 39 in.
|
From page 292... ...
The design shear stress is: 321.7 0.286 (0.9)
|
From page 293... ...
When , [LRFD Eqs.
|
From page 294... ...
329 7,000(1.2 10 ) 37.4−= + × = ° Assume that at least minimum required amount of shear reinforcement is provided.
|
From page 295... ...
When , [LRFD Eqs.
|
From page 296... ...
J.4 Example 4: Reinforced Concrete Column and Footing J.4.1 Example Description This design example demonstrates shear design for two sections of a reinforced concrete column and footing, which are part of a pier designed by Modjeski and Masters, Inc.. The shear design is accomplished in accordance with the Proposal 1 (Modified STD Approach)
|
From page 297... ...
J.4.3 Material Properties The material properties are given in Table J-10. Table J-10 Material Properties CONCRETE PROPERTIES Concrete strength at 28 days, f'c 3.0 ksi Concrete unit weight, wc 0.150 kcf Modulus of elasticity of concrete, Ec = '5.1)
|
From page 298... ...
SECTIONAL FORCES AT DESIGN SECTION Unfactored shear force due to dead load, Vd 0.0 kips* 0.0 kips*
|
From page 299... ...
The design shear stress is: 44.8 0.044 (0.9)
|
From page 300... ...
21.9 0.9(44.9) 40.4u cV kips V kipsφ= < = = Therefore, shear reinforcement is not required.
|
From page 301... ...
The contribution of the concrete to the nominal shear resistance is: vvcc dbfV '0316.0 β= 0.0316(5.28)
|
From page 302... ...
429 7,000(7.0 10 ) 33.9−= + × = ° Assume that at least the minimum amount of shear reinforcement required is provided.
|
From page 303... ...
Reinforcement Provided Not Required Not Required J-35
|
From page 304... ...
J.5 Example 5: Two-Span Continuous Post-Tensioned Box Bridge in Nevada J.5.1 Example Description This design example demonstrates shear design in the vicinity of the inflection point, (0.9L from the exterior support) , of two-span, cast-in-place, post-tensioned box girder bridge.
|
From page 305... ...
REINFORCING BARS Yield strength, fy 60 ksi Modulus of elasticity, Es [LRFD Art.
|
From page 306... ...
Figure J-19 Girder Cross-Section (BERGER/ABAM) Effective depth or distance from the top fiber to the centroid of the tension steel including the prestressed steel is calculated as: 42 .p ps p s y se p ps s y A f d A f d d A f A f += + in= n n n [LRFD Eqs.
|
From page 307... ...
b) Evaluation of Flexure-Shear Cracking Strength Compute flexure-shear cracking strength, : ciV ' max 0.02 crci c v v d i MV f b d V V M = + + '0.06 c v vf b d≥ , 2,387 1,114 1,273i u dV V V kips= − = − = max 18,694 15,612 3,082u dM M M ft kip= − = − = ⋅ s .
|
From page 308... ...
Therefore, transverse reinforcement must be provided. The shear force required is ( / )
|
From page 309... ...
/ 0.5 2( ) u v u u p ps po x c c s s p ps M d N V V A f E A E A E A ε + + − −= + + Where the area of concrete on the flexural tension side is the area above mid-height for the negative moment region; i.e., Ac = 8,126 in.2 .
|
From page 310... ...
Therefore, use #3 double-leg stirrups in each web at 10 in. spacing / provided > required vA s 20.11 2 7 /10 0.154 .
|
From page 311... ...
J.6 Example 6: Shear Design Example of a Multi-Post Bent Cap J.6.1 Example Description This design example is from Tennessee DOT and is for a multi-post bent cap beam that is 86 feet wide. The beam is supported on four columns distributed at 22 ft centers below the beam.
|
From page 312... ...
Figure J-22 Reinforcement Layout for sections through cap J.6.3 Material Properties The material properties are given in Table J-16. Table J-16 Material Properties CONCRETE PROPERTIES Concrete strength at 28 days, f'c 3.0 ksi Concrete unit weight, wc 0.150 kcf Modulus of elasticity of concrete, Ec = '5.1)
|
From page 313... ...
Section modulus for the extreme top fiber, St 33,592 in3 Area of non-prestressed tension reinforcement, As 30.48 in2 Distance from extreme compression fiber to centroid of longitudinal tension reinforcement, ds 58.8 in Area of prestressed tension reinforcement, Ap Distance from the bottom fiber to the centroid of prestressed tendons, dp Weight of beam Varies with sections SECTIONAL FORCES AT DESIGN SECTION* Unfactored shear force due to dead load, Vd Factored shear force, Vu 1222.4 kips Unfactored moment due to dead load, Md Factored moment, Mu 3477.1 ft-kips *
|
From page 314... ...
a) Evaluation of concrete contribution Vc '0.06c cV f= v vb d 0.06 3.0(48)
|
From page 315... ...
In order to ensure that the concrete in the web of the girder will not crush prior to yielding of the transverse reinforcement, the LRFD Specifications specify an upper limit on Vn as follows: '0.25n c v vV f b d≤ + pV 264 1242 1506c sV V kips+ = + = '0.25 0.25(3.0)
|
From page 316... ...
The shear strength provided by the transverse reinforcement is: s dfA V vyvs ααθ sin)
|
From page 317... ...
Figure J-23 Strut-and-Tie Model h =16.62"a h =48.18"b 44.4" w = 24" θ b P=1212.3kips θ = 47.6o b = 28.9" a P=1212.3kips T(tie) =1118.7kips P(strut)
|
From page 318... ...
/ tan( )
|
From page 319... ...
calculated Approach Approach ( + ) , kips cV pV 264 268.2 sV , kips 809.2 805 θ , deg.
|
From page 320... ...
J.7 Example 7: Type IV Beam J.7.1 Example Description This example demonstrates the shear design of a section of a 100-ft span AASHTO Type IV beam bridge. Bridge details were provided by Tim Bradberry of the Texas Department of Transportation.
|
From page 321... ...
The material properties are given in Table J-19. Table J-19 Material Properties CONCRETE PROPERTIES Concrete strength of girder at 28 days, f'c 6.5 ksi Concrete strength of deck at 28 days, f'c 4.0 ksi Concrete unit weight, wc 0.150 kcf Modulus of elasticity of concrete for girder, Ec,beam = '5.1)
|
From page 322... ...
Distance from centroid to extreme top fiber, yt 29.25 in. Section modulus for the extreme bottom fiber, Sb 10,521 in3 Section modulus for the extreme top fiber, St 8,902 in3 Weight of beam 0.821 kip/ft Composite Section Overall depth of the composite section, hc 62 in.
|
From page 323... ...
Figure J-27 Cross-Section of AASHTO Box Beam Type BIII-48 Figure J-28 Typical Strand Pattern at Midspan Table J-21 Strand Pattern at the Design Section (a total of 40 strands, 8 draped strands)
|
From page 325... ...
, 265.0 82.4 182.6i u dV V V kips= − = − = max 1,125.0 429.2 695.8u dM M M ft kip= − = − = ⋅ s . Moment causing flexural cracking at the design section due to externally applied loads: '(0.2 )
|
From page 326... ...
'cot 1 3 / 1.80pc cf fθ = + ≤ cot 1 3(0.735) / 6.5 1.86 1.80θ = + = > (Governs)
|
From page 328... ...
When vertical stirrups are used, 90α = ° . Then, the required area of transverse reinforcement within a spacing (s)
|
From page 329... ...
Table J-22 Summary of Results Required or calculated Proposal 1: Modified STD Approach Proposal 2: Modified CSA Approach ( + ) , kips cV pV 152.2 188.5 sV , kips 142.2 105.9 θ , deg.
|
From page 330... ...
J.8 Example 8: Precast Balanced Cantilever Construction Using the AASHTO-PCIASBI Segmental Box Girder Standards J.8.1 Example Description This example gives the shear design calculations for a 5-span Precast Balanced Cantilever Bridge constructed using AASHTO-PCI-ASBI segmental box girders. The design section is taken from the second bay near the support.
|
From page 331... ...
Fig. J-31 illustrates the Post-Tensioning anchorages and reinforcement layout.
|
From page 332... ...
Modulus of elasticity, Ep [LRFD Art.
|
From page 334... ...
Stress due to service dead load: 22793 12 0.569 480562 d d t Mf ksi S ×= = = Therefore, 480562(0.2 6.1 1.652 0.569) 63152crM ft kips= + − = ⋅ The flexure-shear cracking strength, , is: ciV 805(63152)
|
From page 335... ...
Therefore, use 2-25M bars in each web at a spacing of 24 in.
|
From page 336... ...
Since the value of xε is negative, a different equation must be used: / 0.5 0.003 2( ) u v u u p ps po x c c s s p ps M d N V V A f E A E A E A ε + + − −= ≤+ + where Ac = area of concrete on the flexural tension side(top half of beam)
|
From page 337... ...
Therefore, use 2-25M bars in each web at a spacing of 24 in.
|
From page 338... ...
sV , kips 821 789 θ , deg. 29.0 28.6 Reinforcement Provided 4- 25M bars @24 inches 4- 25M bars @24 inches J-70
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.