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).

Compression-development lengths are longer than tension-development lengths, because some force is transferred to the concrete by the bearing at the end of the bar and there are no cracks in such an anchorage region.

If the bond between concrete and steel in a beam disappears, the steel will not pull out of the concrete.

Compute φVn for the cross section shown. Assume f’c = 4,000 psi, fyt = 60,000 psi, b = 15 in., d = 24 in., and that there are four No. 7 longitudinal tension bars and No. 5 stirrups at 6 in. o.c.

When tension is applied to a smooth reinforcing bar, its diameter is decreased. Due to the decrease in diameter, the adhesion and friction bonds that originally held it in place are quickly lost.

If the depth of the beam varies, the compressive and tensile forces due to flexure will be parallel.

Determine the epoxy modification factor, ψe, for a rectangular beam with b = 16 in. and d = 24 in., three uncoated No. 9 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 40 stirrups located every 8 in. along the span. Assume 5,000-psi lightweight concrete and a clear cover of 1.75 in.

In a lapped splice, the force in one bar is transferred directly to the adjacent bar.

Assuming Vs does not exceed 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b = 14 in. and d = 41 in. There are four No. 7 longitudinal tension bars and No. 4 stirrups at 11 in. o.c.

At a point subjected to plane stress, the stresses are σx = 10 ksi, σy = 25 ksi, and τxy = –20 ksi. Determine the angle θp corresponding to the orientation of the principal planes at the point.