Determine the epoxy modification factor, ψe, for a rectangular beam with b = 17 in. and d = 21 in., five uncoated No. 8 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 40 stirrups located every 6 in. along the span. Assume 5,000-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 = 39 in., b2 = 16 in., d1 = 4 in., d2 = 29 in., and that there are three No. 9 longitudinal tension bars and No. 4 stirrups at 11 in. o.c. The stirrup hooks are 90°.

At a point subjected to plane stress, the stresses are σx = 25 ksi, σy = 5 ksi, and τxy = –20 ksi. Determine the angle θp corresponding to the orientation of the principal planes at the point.

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 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 = 15 in., d = 23 in., h1 = 6 in., h2 = 13 in., h3 = 9 in., and t = 6 in. There are four No. 8 longitudinal tension bars and No. 3 stirrups at 9 in. o.c.

A rectangular beam with cross section b = 14 in., h = 28 in., and d = 25.5 in. supports a total factored uniform load of 1.20 kips/ft, including its own dead load. The beam is simply supported with a 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 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 = 173.3 kip-ft, and the strength of the remaining two bars is φMn = 70.42 kip-ft. If the distance from the support to the theoretical cutoff point is 6.839 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 casting-position modification factor, ψt, for a rectangular beam with b = 18 in. and d = 24 in., four galvanized No. 7 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 3 Grade 40 stirrups located every 6 in. along the span. Assume 5,000-psi lightweight concrete and a clear cover of 1.5 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 3.40 kips/ft, including its own dead load. The beam is simply supported with a 20-ft span. It is reinforced with five No. 8 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 4,200 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 = 309.7 kip-ft, and the strength of the remaining two bars is φMn = 132.7 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard 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 = 30 in., b2 = 12 in., d1 = 4 in., and d2 = 29 in. There are three No. 7 longitudinal tension bars and No. 4 stirrups at 9 in. o.c.

Determine the bar-spacing factor, cb, for a simply supported rectangular beam with b = 24 in. and No. 4 stirrups. This beam has three No. 8 bars as longitudinal reinforcement. The clear cover is 1.5 in.