Compute φVn for the cross section shown. Assume f’c = 3,500 psi, fyt = 40,000 psi, b1 = 26 in., b2 = 12 in., d1 = 6 in., d2 = 16 in., and that there are three No. 9 longitudinal tension bars and No. 5 stirrups at 8 in. o.c.

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 17 in. and d = 24 in., five uncoated No. 9 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 4 Grade 40 stirrups located every 10 in. along the span. Assume 6,000-psi lightweight concrete and a clear cover of 2 in.

Determine the epoxy modification factor, ψe, for a rectangular beam with b = 17 in. and d = 20 in., five galvanized No. 8 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 7,000-psi normal-weight concrete and a clear cover of 2 in.

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 = 16 in. and d = 21 in., four galvanized No. 8 Grade 60 bars placed in the bottom of the beam, and No. 3 Grade 60 stirrups located every 12 in. along the span. Assume 7,000-psi normal-weight concrete and a clear cover of 1.5 in.

A rectangular beam has a cross section of b = 18 in., h = 24 in., and d = 21.5 in. It is reinforced with four No. 6 Grade 60 bars. The concrete strength is 2,800 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. Determine the strength φMn for this beam.

At a point subjected to plane stress, the stresses are σx = 10 ksi, σy = 15 ksi, and τxy = 15 ksi. Determine the angle θp corresponding to the orientation of the principal planes at the point.

Compute φVn for the cross section shown. Assume f’c = 7,500 psi, fyt = 40,000 psi, d = 21 in., w = 13.5 in., t = 5 in., and that there are four No. 8 longitudinal tension bars and No. 4 stirrups at 6 in. o.c.

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.