Chapter 6. Example 3a: Inverted-T Straddle Bent Cap (Moment Frame)
6.4.10 Step 10: Perform Shear Serviceability Check
To determine the likelihood of diagonal crack formation, the service level shear can be compared to the estimated diagonal cracking strength of the concrete. The TxDOT Project 0- 5253 expression for estimation of the diagonal cracking strength is repeated here for convenience (refer to Section 2.7):
[ ( )] √
but not greater than √ nor less than √ where:
a = shear span (in.)
d = effective depth of the member (in.)
f’c = specified compressive strength of concrete (psi) bw = width of member’s web (in.)
The AASHTO LRFD (2010) Service I load case is applied to the frame shown in Figure 6.7, assuming the self-weight is distributed along the length of the bent cap. An elastic analysis reveals that the maximum shear force occurs near the right end of the cap; the service level shear force at the interior face of the right column is 675.9 kips. The risk of service crack formation within the region between Beam Line 3 and the right column (Column B) should be checked.
Considering the likelihood of diagonal cracking due to the stresses within Strut EL, the shear span a is taken as the horizontal distance between Beam Line 3 and Node L, or 59.9 inches. The effective depth, d, is taken as the distance from the bottom of the bent cap to the centroid of the top chord reinforcement, or 55.4 inches. The estimated diagonal cracking strength is:
[ (
)] (√ )( )( ) - Expect diagonal cracks
(6.3)
This value is within the √ and √ limits. The check alerts the designer that diagonal cracking should be expected within the region near Column B. Modifications to the bent cap geometry or the concrete strength can reduce the risk of service crack formation (refer to Section 2.7).
Another critical region of the bent cap is between the left column (Column A) and Beam Line 1. The maximum service shear force in this region occurs at the interior face of the left column and is equal to 388.6 kips. Due to the long shear span, a, between the applied beam load and the supporting column, the √ limit controls, and the value of Vcr is:
√ √ ( )( )
- Expect diagonal cracks
The shear serviceability checks reveals that the designer should consider the risk of diagonal crack formation within both critical shear spans when full service loads are applied.
This concern is further addressed for the inverted-T bent cap in Sections 7.6 and 7.7 of Example 3b.
Reinforcement Layout 6.5
The reinforcement details for the load case considered in this design example are presented in Figures 6.26 and 6.27. Any reinforcement details not previously described within the example are consistent with standard TxDOT practice.
177
Elev. 81.41’
Elev. 80.41’
5.00’
4Eq. Spa. at 5.5” = 1.83’
(Dbl. No. 6 Stirrups)
5.00’
No. 11 Bars No. 6 Bars No. 6
Bars No. 6 Stirrups (Bars A)
No. 6 Bar B
B
5.00’
A A
No. 6 Bars 0.25’
0.25’
0.25’
8 Eq. Spa.
at 7” = 4.50’
(No. 6 Bars)
18 Eq. Spa. at 7” = 10.67’
(No. 6 Stirrups) 0.50’
35 Eq. Spa. at 5.5” = 16.50’ (No. 6 Stirrups) 35 Eq. Sp. at 5.5” = 16.50’ (No. 6 Ledge Stirrups – Bars A)
10 Eq. Spa. at 6” = 5.00’ (Dbl. No. 6 Stirrups)
10 Eq. Spa. at 6”= 5.00’ (No. 6 Ledge Stirrups – Bars A) 8 Eq. Spa.
at 7” = 4.50’
(No. 6 Bars) 0.25’
7Eq. Spa. at 5” = 3.00’
(No. 6 Stirrups)
No. 11 Bars
Figure 6.26: Reinforcement details – elevation (design per proposed STM specifications – moment frame case)
Figure 6.27: Reinforcement details – cross-sections (design per proposed STM specifications – moment frame case)
2” Clear
2” Clear
15 - No. 11 Bars
No. 6 Stirrups 0.52’
3.34’
5.00’ 4EqSp(No. 6 Bars) (s ≈ 7.0”)
22 - No. 11 Bars
1.33’ 3.34’ 1.33’
2” Clear
5.00’ 3.17’1.83’
0.52’
4EqSp(No. 6 Bars) (s ≈ 7.0”)0.79’ 1.64’
No. 6 Stirrups 15 - No. 11 Bars
22 - No. 11 Bars No. 6
Bars
No. 6 Stirrups (A) No. 11 Bars
Section A-A
Section B-B
Summary 6.6
The design of an inverted-T straddle bent cap was completed in accordance with the strut-and-tie model specifications of Chapter 3 and all relevant provisions of AASHTO LRFD (2010) and TxDOT’s Bridge Design Manual - LRFD (2009). The substructure was designed to behave as a moment frame. The defining features and challenges of this design example are listed below:
Modeling frame corners as full moment connections
Determining D-region/B-region boundary forces from a moment frame analysis in order to calculate the member forces of the STM
Developing local, or sectional, STMs to design the ledge of an inverted-T bent cap (essentially developing a three-dimensional STM)
Detailing transverse ledge reinforcement using local STMs
Detailing hanger reinforcement along an inverted-T ledge to transfer applied superstructure loads to the top chord of the global STM
Designing curved-bar nodes at the outside of the frame corners (i.e., determining the required bend radius of the longitudinal bars)
Example 3b in Chapter 7 presents the design of the same inverted-T straddle bent cap assuming the cap is simply supported at the columns. The existing field structure, designed in accordance with the sectional design procedure of the AASHTO LRFD provisions, has experienced significant diagonal cracking. The observed serviceability behavior of the in-service bent cap will be discussed in Section 7.7.