A rectangular beam has a cross section of b = 16 in., h = 30 in., and d = 27.5 in. It is reinforced with two No. 7 Grade 60 bars. The concrete strength is 8,200 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. Determine the strength φMn for this beam.

A 119-mm-long beam supports a load of P = 38 N at midspan. The cross section is rectangular with width b = 25 mm and height h = 60 mm. Determine the magnitude of the horizontal shear stress at the centroid of the cross section.

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., three uncoated No. 8 Grade 60 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 1.75 in.

Assuming Vs does not exceed 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let d = 33 in., w = 25.5 in., and t = 5 in. There are five No. 7 longitudinal tension bars and No. 3 stirrups at 6 in. o.c.

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 = 20 in., three uncoated No. 8 Grade 60 bars placed in the top of the beam, and No. 3 Grade 60 stirrups located every 8 in. along the span. Assume 5,000-psi normal-weight concrete and a clear cover of 1.5 in.

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b = 14 in., d = 24 in., and that there are four No. 8 longitudinal tension bars and No. 3 stirrups at 11 in. o.c. The stirrup hooks are 135°.

A rectangular beam with cross section b = 16 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 2.10 kips/ft, including its own dead load. The beam is simply supported with a 22-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 5,700 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 = 200.6 kip-ft, and the strength of the remaining two bars is φMn = 102.8 kip-ft. If the distance from the support to the theoretical cutoff point is 6.194 ft, determine the distance from the support to the actual cutoff point (i.e. use 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 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?