178

From Equations 8.33a and 8.33b, the maximum allowable bearing pressure on the concrete is the lesser of fb < o.7/c0vAMg fb < 2.25f'i

Assume that the initial concrete strength at stressing is f0 = 0.75£' = 0.75 x 5000 = 3750 psi. The concentric area, A, of concrete with the bearing plates = ( 1 4 + 4)(11 + 4) + (6 + 4)(4 + 4) = 350 in.2 Allowable bearing stress, fb = 0.7 x 0.90 x 3750^/322/178 = 3178 psi > 3020 psi, OK. The bearing stress does not control. It should be noted that the area Ag of the rigid steel plate or plates, and the corresponding concrete pyramid base area A within the end block assumed to receive the bearing stress, are purely determined by engineering judgment. The areas are based on the geometry of the web and bottom flange of the section, the rectangular dimension of the beam end, and the arrangement and spacing of the strand anchorages in contact with the supporting steel end bearing plates.

3. Draw the strut-and-tie model. Total length of distance a between forces Pu1 — Pu3 = 11.5—2.5 = 9.0 in. Hence depth a/2 ahead of the anchorages = 9.0/2 = 4.5 in. Construct the strut-and-tie model assuming it to be as shown in Figure 8.5. The geometrical dimensions for finding the horizontal force components from the ties 1-2 and 3-2 have cotangent values of 26.5/15.5 and 13.0/15.5, respectively. From statics, truss analysis in Figure 8.5 gives the member forces as follows:

24:5

tension tie 1-2 = 118,973 x — = 188,054 lb (836 kN)

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