At a point subjected to plane stress, the stresses are σx = –15 ksi, σy = 15 ksi, and τxy = 5 ksi. Determine the angle θp corresponding to the orientation of the principal planes at the point.

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b1 = 39 in., b2 = 15 in., d1 = 8 in., d2 = 19 in., and that there are three No. 6 longitudinal tension bars and No. 3 stirrups at 12 in. o.c. The stirrup hooks are 90°.

ACI 318 provides rules for designing hanger reinforcement.

Larger 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 b = 16 in. and d = 35 in. There are four No. 7 longitudinal tension bars and No. 5 stirrups at 12 in. o.c.

Determine the size modification factor, ψs, for a rectangular beam with b = 17 in. and d = 24 in., five epoxy-coated No. 9 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 3 Grade 60 stirrups located every 8 in. along the span. Assume 7,000-psi lightweight concrete and a clear cover of 1.75 in.

Axial tension tends to increase shear strength.

Actual bond stresses remain constant between cracks.

The strength-reduction factor, φ, for shear and torsion is 0.75.

When the steel ratio is large, flexural cracks extend higher into the beam and open wider.