The strength-reduction factor, φ, for shear and torsion is _____.

At a point subjected to plane stress, the stresses are σx = –20 ksi, σy = –30 ksi, and τxy = –25 ksi. Determine the angle θp corresponding to the orientation of the principal planes at the point.

A simply-supported beam has a 3 kip/ft uniformly-distributed load over the left half of its 11-ft span. What is the magnitude of the maximum shear force in the beam?

A beam has dimensions of b = 14 in., h = 30 in., d’ = 2.5 in., and d = 27.5 in. It is reinforced with 2 No. 5 bars on the compression side and 5 No. 8 bars on the tension side. The concrete strength is 3,700 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 5.588 in., determine the strain in the compression reinforcement, ε’s.

A beam has dimensions of b = 14 in., h = 26 in., d’ = 2.5 in., and d = 23.5 in. It is reinforced with 2 No. 5 bars on the compression side and 4 No. 8 bars on the tension side. The concrete strength is 3,700 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 4.481 in., determine the strain in the compression reinforcement, ε’s.

The addition of compression reinforcement to an existing beam section increases the ductility of the section.

Compute φVn for the cross section shown. Assume f’c = 4,500 psi, fyt = 60,000 psi, b1 = 24 in., b2 = 13 in., d = 23 in., h1 = 6 in., h2 = 14 in., h3 = 8 in., t = 8 in., and that there are six No. 6 longitudinal tension bars and No. 5 stirrups at 11 in. o.c.

The shear failure of a slender beam without stirrups is slow and predictable.

Smaller diameter aggregate creates a rougher crack surface, allowing higher shear stresses to be transferred across cracks.

Assuming Vs exceeds 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 28 in., b2 = 12 in., d1 = 8 in., and d2 = 49 in. There are three No. 8 longitudinal tension bars and No. 3 stirrups at 11 in. o.c.