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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?

The symbol λ in the 1994 version of the modified compression field theory, , is _______.

A simply-supported beam has a 3 kip/ft uniformly-distributed load over the entire 8-ft span. What is the magnitude of the maximum shear force in the beam?

Adhesion and friction between the concrete and reinforcement are quickly lost when the bar is loaded in tension, because the diameter of the bar _______ due to Poisson’s ratio.