For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b = 13 in., d = 22 in., and that there are four No. 7 longitudinal tension bars and No. 4 stirrups at 7 in. o.c. The stirrup hooks are 135°.

At a point subjected to plane stress, the stresses are σx = –20 MPa, σy = –40 MPa, and τxy = –40 MPa. Determine the angle θp corresponding to the orientation of the principal planes at the point.

Which of the following descriptions best describes a substrate?

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.