Determine the size modification factor, ψs, for a rectangular beam with b = 18 in. and d = 23 in., three epoxy-coated No. 9 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 4,000-psi lightweight concrete and a clear cover of 1.75 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 = 6,000 psi, fyt = 40,000 psi, b = 12 in., d = 18 in., and that there are four No. 8 longitudinal tension bars and No. 5 stirrups at 7 in. o.c. The stirrup hooks are 135°.

If φVc = 67 kip and Vu = 17 kip, are stirrups required?

Compute φVn for the cross section shown. Assume f’c = 4,000 psi, fyt = 40,000 psi, b = 11 in., d = 20 in., and that there are four No. 6 longitudinal tension bars and No. 5 stirrups at 10 in. o.c.

The traditional theory for shear stress assumes non-homogeneous, elastic, and uncracked beams.

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 18 in. and d = 22 in., four galvanized No. 9 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 5,000-psi lightweight concrete and a clear cover of 1.5 in.

A rectangular beam with cross section b = 16 in., h = 20 in., and d = 17.5 in. supports a total factored uniform load of 3.60 kips/ft, including its own dead load. The beam is simply supported with a 18-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 6,300 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 = 286.5 kip-ft, and the strength of the remaining two bars is φMn = 120.5 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

A rectangular beam has a cross section of b = 18 in., h = 26 in., and d = 23.5 in. It is reinforced with four No. 5 Grade 60 bars. The concrete strength is 7,600 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.

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 18 in. and d = 24 in., three galvanized No. 9 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 lightweight concrete and a clear cover of 2 in.

ACI 318 provides rules for designing hanger reinforcement.