A rectangular beam has a cross section of b = 16 in., h = 22 in., and d = 19.5 in. It is reinforced with three No. 6 Grade 60 bars. The concrete strength is 3,700 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. Determine the strength φMn for this beam.

If φVc = 67 kip and Vu = 17 kip, are stirrups required?

When the steel ratio is small, flexural cracks extend higher into the beam and open wider.

A simply-supported beam has a 5 kip/ft uniformly-distributed load over the left half of its 9-ft span. What is the magnitude of the maximum shear force in the beam?

Simplify the expression. (5 points)

The textbook author recommends the use of 135° stirrups throughout, except in certain cases where 180° stirrups are needed to prevent overlap.

A rectangular beam with cross section b = 14 in., h = 20 in., and d = 17.5 in. supports a total factored uniform load of 3.20 kips/ft, including its own dead load. The beam is simply supported with a 19-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 3,300 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 = 214.5 kip-ft, and the strength of the remaining two bars is φMn = 115.8 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

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Compute φVn for the cross section shown. Assume f’c = 3,500 psi, fyt = 60,000 psi, d = 30 in., w = 20.5 in., t = 6 in., and that there are four No. 6 longitudinal tension bars and No. 5 stirrups at 9 in. o.c.

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