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Assuming Vs exceeds 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b = 13 in. and d = 51 in. There are four No. 8 longitudinal tension bars and No. 5 stirrups at 12 in. o.c.

Determine the size modification factor, ψs, for a rectangular beam with b = 17 in. and d = 22 in., three galvanized No. 8 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 60 stirrups located every 10 in. along the span. Assume 5,000-psi normal-weight concrete and a clear cover of 2 in.

A rectangular beam with cross section b = 14 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 1.20 kips/ft, including its own dead load. The beam is simply supported with a 21-ft span. It is reinforced with five No. 5 Grade 60 bars, three 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 3,900 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 five bars is φMn = 129 kip-ft, and the strength of the remaining two bars is φMn = 53.29 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

Compute φVn for the cross section shown. Assume f’c = 3,500 psi, fyt = 40,000 psi, b1 = 27 in., b2 = 12 in., d = 28 in., h1 = 7 in., h2 = 16 in., h3 = 10 in., t = 6 in., and that there are six No. 9 longitudinal tension bars and No. 3 stirrups at 11 in. o.c.

A continuous beam’s flexural reinforcement must extend at least _____ from the point where it is no longer needed to resist tension. Assume f’c = 4,000 psi, fyt = 40,000 psi, b1 = 28 in., b2 = 10 in., d1 = 4 in., d2 = 19 in., and that there are three No. 7 longitudinal tension bars and No. 5 stirrups at 12 in. o.c. The stirrup hooks are 90°.

A rectangular beam with cross section b = 14 in., h = 26 in., and d = 23.5 in. supports a total factored uniform load of 1.60 kips/ft, including its own dead load. The beam is simply supported with a 24-ft span. It is reinforced with five No. 6 Grade 60 bars, three 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 7,800 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 five bars is φMn = 225.6 kip-ft, and the strength of the remaining two bars is φMn = 91.93 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

A rectangular beam with cross section b = 14 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 2.30 kips/ft, including its own dead load. The beam is simply supported with a 21-ft span. It is reinforced with five No. 7 Grade 60 bars, three 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 6,000 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 five bars is φMn = 246.2 kip-ft, and the strength of the remaining two bars is φMn = 102.6 kip-ft. If the distance from the support to the theoretical cutoff point is 5.914 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).

Assuming Vs does not exceed 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 22 in., b2 = 12 in., d = 57 in., h1 = 6 in., h2 = 46 in., h3 = 10 in., and t = 7 in. There are six No. 9 longitudinal tension bars and No. 5 stirrups at 11 in. o.c.

If φVc = 23 kip and Vu = 63 kip, are stirrups required?

A rectangular beam with cross section b = 14 in., h = 24 in., and d = 21.5 in. supports a total factored uniform load of 1.60 kips/ft, including its own dead load. The beam is simply supported with a 19-ft span. It is reinforced with five No. 5 Grade 60 bars, three 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 6,900 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 five bars is φMn = 146 kip-ft, and the strength of the remaining two bars is φMn = 59.35 kip-ft. If the distance from the support to the theoretical cutoff point is 5.492 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).