Determine the casting-position modification factor, ψt, for a rectangular beam with b = 16 in. and d = 23 in., five uncoated No. 9 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 3 Grade 60 stirrups located every 8 in. along the span. Assume 5,000-psi lightweight concrete and a clear cover of 2 in.

Determine the bar-spacing factor, cb, for a simply supported rectangular beam with b = 18 in. and No. 4 stirrups. This beam has four No. 7 bars as longitudinal reinforcement. The clear cover is 2 in.

Determine the casting-position modification factor, ψt, for a rectangular beam with b = 17 in. and d = 24 in., five galvanized No. 6 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 60 stirrups located every 12 in. along the span. Assume 8,000-psi normal-weight concrete and a clear cover of 1.5 in.

Compute φVn for the cross section shown. Assume f’c = 6,500 psi, fyt = 40,000 psi, b = 10 in., d = 24 in., and that there are four No. 7 longitudinal tension bars and No. 3 stirrups at 9 in. o.c.

A rectangular beam with cross section b = 16 in., h = 24 in., and d = 21.5 in. supports a total factored uniform load of 1.10 kips/ft, including its own dead load. The beam is simply supported with a 24-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 7,500 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 = 146.8 kip-ft, and the strength of the remaining two bars is φMn = 59.48 kip-ft. If the distance from the support to the theoretical cutoff point is 6.012 ft, determine the distance from the support to the actual cutoff point (i.e. use 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).

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.

If φVc = 79 kip and Vu = 66 kip, are stirrups required?

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 18 in. and d = 22 in., five uncoated No. 9 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 4 Grade 60 stirrups located every 12 in. along the span. Assume 4,000-psi lightweight concrete and a clear cover of 1.75 in.

Determine the size modification factor, ψs, for a rectangular beam with b = 18 in. and d = 22 in., four galvanized No. 6 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 3 Grade 60 stirrups located every 8 in. along the span. Assume 4,000-psi lightweight concrete and a clear cover of 1.75 in.