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Strut-and-Tie Resources Web Site Worked Design Examples Using Strut-and-Tie Strut-and-Tie Method – Dapped-Beam End (ACI 318-02 Appendix A)
Example Design of A Dapped-Beam End Using Strut and Tie Method per ACI 318-02 Appendix A
A dapped-beam end shown in Figure 1 is to be designed to transmit a factored vertical reaction force of 60 kips and a factored horizontal reaction force of 12 kips to the support. The vertical reaction is assumed to act 2 in. from the left end of the beam. The beam is 16 in. wide and made from 6 ksi concrete (normal density) and 60 ksi steel reinforcement. 4" x 4" x 5/8" angle 2052 k-in 16" 12 k 30" N u = 12 k
14"
60 k V u = 60 k
2"
4" 6"
30" 36"
Figure 1
Define the D-Region and Calculate the Forces acting on the Boundary of the Region:
The extension of the D-region is assumed to be one member depth plus the extended part, i.e. 30 + 6 = 36 in. The forces at the right end are a moment of 60(36-2) + 12(15-14) = 2052 kin., an axial tension force of 12 kips, and a shear force of 60 kips. Figure 1 shows the forces acting on the D-region.
Determine Determine the Bearing Plate Dimensions:
Choose a 4 in. × 4 in. × 5/8 in. steel angle placed across the width of the beam at the support. The bearing plate area is Ac = 16(4) = 64 in., 2 and the bearing stress is V u Ac
=
60(1000 ) 64
= 938 psi. Since this is less than the bearing stress limit, i.e.
φ f cu = φ(0.85β n f c' )= 0.75[0.85(0.80)(6000 )] = 3060 psi, the bearing size is adequate.