Determine the lightweight modification factor, λ, for a rectangular beam with b = 16 in. and d = 22 in., four uncoated No. 8 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 40 stirrups located every 12 in. along the span. Assume 4,000-psi normal-weight concrete and a clear cover of 2 in.

A rectangular beam with cross section b = 16 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 1.80 kips/ft, including its own dead load. The beam is simply supported with a 22-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 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 = 185 kip-ft, and the strength of the remaining two bars is φMn = 75.94 kip-ft. If the distance from the support to the theoretical cutoff point is 4.948 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 18 in. and d = 22 in., four epoxy-coated No. 7 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 4 Grade 40 stirrups located every 12 in. along the span. Assume 7,000-psi normal-weight concrete and a clear cover of 2 in.

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b1 = 22 in., b2 = 11 in., d1 = 8 in., d2 = 15 in., and that there are three No. 9 longitudinal tension bars and No. 5 stirrups at 9 in. o.c. The stirrup hooks are 90°.

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).

Assuming Vs exceeds 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 20 in., b2 = 11 in., d = 45 in., h1 = 6 in., h2 = 35 in., h3 = 9 in., and t = 7 in. There are sixNo. 8 longitudinal tension bars and No. 3 stirrups at 11 in. o.c.

Compute φVn for the cross section shown. Assume f’c = 7,500 psi, fyt = 40,000 psi, b1 = 29 in., b2 = 12 in., d1 = 6 in., d2 = 17 in., and that there are three No. 7 longitudinal tension bars and No. 4 stirrups at 10 in. o.c.

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 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.

Determine the casting-position modification factor, ψt, for a rectangular beam with b = 16 in. and d = 23 in., five epoxy-coated No. 8 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 60 stirrups located every 8 in. along the span. Assume 7,000-psi normal-weight concrete and a clear cover of 2 in.