Compute φVn for the cross section shown. Assume f’c = 5,500 psi, fyt = 60,000 psi, b1 = 27 in., b2 = 11 in., d = 26 in., h1 = 5 in., h2 = 16 in., h3 = 10 in., t = 7 in., and that there are six No. 6 longitudinal tension bars and No. 4 stirrups at 7 in. o.c.

A rectangular beam with cross section b = 14 in., h = 26 in., and d = 23.5 in. supports a total factored uniform load of 2.80 kips/ft, including its own dead load. The beam is simply supported with a 20-ft span. It is reinforced with four No. 7 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 5,400 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 = 241.7 kip-ft, and the strength of the remaining two bars is φMn = 123.9 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b1 = 25 in., b2 = 12 in., d1 = 8 in., d2 = 15 in., and that there are three No. 6 longitudinal tension bars and No. 3 stirrups at 6 in. o.c. The stirrup hooks are 90°.

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 17 in. and d = 24 in., four epoxy-coated No. 6 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 40 stirrups located every 6 in. along the span. Assume 8,000-psi lightweight concrete and a clear cover of 1.75 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 1.70 kips/ft, including its own dead load. The beam is simply supported with a 24-ft span. It is reinforced with four No. 7 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 = 197.8 kip-ft, and the strength of the remaining two bars is φMn = 102.1 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

Determine the size modification factor, ψs, for a rectangular beam with b = 17 in. and d = 23 in., four uncoated No. 8 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 3 Grade 60 stirrups located every 6 in. along the span. Assume 4,000-psi normal-weight concrete and a clear cover of 2 in.

Determine the casting-position modification factor, ψt, for a rectangular beam with b = 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.

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 = 7,500 psi, fyt = 60,000 psi, b = 13 in., d = 18 in., and that there are four No. 6 longitudinal tension bars and No. 3 stirrups at 10 in. o.c. The stirrup hooks are 135°.

Use ACI 318-14 Table 25.4.2.2 to determine the development length for the straight tension bars (no hooks) in a rectangular beam with b = 17 in. and d = 24 in., four galvanized No. 8 Grade 60 bars placed in the top of the beam, and No. 3 Grade 40 stirrups located every 12 in. along the span. Assume 7,000-psi lightweight concrete and a clear cover of 1.75 in.

Determine the lightweight modification factor, λ, for a rectangular beam with b = 16 in. and d = 20 in., five uncoated No. 7 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 60 stirrups located every 6 in. along the span. Assume 6,000-psi lightweight concrete and a clear cover of 1.5 in.