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A beam has dimensions of b = 20 in., h = 10 in., and d = 7.5 in. and is reinforced with 4 No. 9 bars. The concrete strength is 4,700 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 3.686 in., does the reinforcement yield?

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°.

It is rare to design beams where the b and h values are already known.

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°.

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b = 16 in., d = 28 in., and that there are four No. 8 longitudinal tension bars and No. 4 stirrups at 12 in. o.c. The stirrup hooks are 135°.

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.

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

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?

If φVc = 50 kip and Vu = 58 kip, are stirrups required?