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_______ cracks occur first due to flexural stresses and start at the bottom of the beam.

The traditional theory for shear stress assumes homogeneous, elastic, and cracked beams.

Compute φVn for the cross section shown. Assume f’c = 3,000 psi, fyt = 40,000 psi, b = 14 in., d = 25 in., and that there are four No. 8 longitudinal tension bars and No. 3 stirrups at 12 in. o.c.

Determine the bar-spacing factor, cb, for a simply supported rectangular beam with b = 22 in. and No. 3 stirrups. This beam has three No. 7 bars as longitudinal reinforcement. The clear cover is 1.6 in.

Compute φVn for the cross section shown. Assume f’c = 4,000 psi, fyt = 60,000 psi, b = 15 in., d = 24 in., and that there are four No. 7 longitudinal tension bars and No. 5 stirrups at 6 in. o.c.

A combination of horizontal and vertical reinforcement is used to prevent cracks from being too narrow.

Stirrups are able to resist shear unless they are crossed by an inclined crack.

Assuming Vs does not exceed 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b = 15 in. and d = 43 in. There are four No. 9 longitudinal tension bars and No. 4 stirrups at 7 in. o.c.

A rectangular beam with cross section b = 16 in., h = 20 in., and d = 17.5 in. supports a total factored uniform load of 2.20 kips/ft, including its own dead load. The beam is simply supported with a 22-ft span. It is reinforced with four No. 8 Grade 60 bars, two of which are cutoff between midspan and the support and two of which extend 10 in. past the centers of the supports. The concrete strength is 5,100 psi (normal weight). The beam has Grade 60 No. 3 stirrups satisfying ACI 318-14 Sections 9.7.6.2.2 and 9.6.3.3. The strength of the four bars is φMn = 229.4 kip-ft, and the strength of the remaining two bars is φMn = 119.6 kip-ft. If the distance from the support to the theoretical cutoff point is 7.497 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).

As the size of coarse aggregate decreases, the roughness of the crack increases. This allows higher shear stresses to be transferred across the crack.