When faced with severe architectural restrictions on the dimensions of a beam, a designer may be forced to use a singly reinforced section.

Assuming Vs exceeds 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let d = 57 in., w = 49.5 in., and t = 5 in. There are five No. 9 longitudinal tension bars and No. 3 stirrups at 7 in. o.c.

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b = 12 in., d = 27 in., and that there are four No. 9 longitudinal tension bars and No. 4 stirrups at 10 in. o.c. The stirrup hooks are 135°.

A continuous beam’s flexural reinforcement must extend at least _____ from the point where it is no longer needed to resist tension. Assume f’c = 4,000 psi, fyt = 40,000 psi, b1 = 20 in., b2 = 13 in., d = 21 in., h1 = 4 in., h2 = 12 in., h3 = 10 in., and t = 8 in. There are four No. 6 longitudinal tension bars and No. 3 stirrups at 8 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 = 24 in., five galvanized No. 6 Grade 60 bars placed in the bottom of the beam, and No. 4 Grade 40 stirrups located every 6 in. along the span. Assume 8,000-psi lightweight concrete and a clear cover of 1.75 in.

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 4,000 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 4.199 in., determine the force in the compression reinforcement, Cs.

A continuous beam’s flexural reinforcement must extend at least _____ from the point where it is no longer needed to resist tension. Assume f’c = 4,000 psi, fyt = 40,000 psi, b1 = 27 in., b2 = 11 in., d1 = 6 in., d2 = 17 in., and that there are three No. 6 longitudinal tension bars and No. 3 stirrups at 7 in. o.c. The stirrup hooks are 90°.

The traditional theory for shear stress assumes homogeneous, elastic, and uncracked beams.

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.