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Compute φVn for the cross section shown. Assume f’c = 7,500 psi, fyt = 40,000 psi, d = 21 in., w = 13.5 in., t = 5 in., and that there are four No. 8 longitudinal tension bars and No. 4 stirrups at 6 in. o.c.

A rectangular beam with cross section b = 14 in., h = 20 in., and d = 17.5 in. supports a total factored uniform load of 2.40 kips/ft, including its own dead load. The beam is simply supported with a 24-ft span. It is reinforced with five No. 8 Grade 60 bars, three of which are cutoff between midspan and the support and two of which extend 10 in. past the centers of the supports. The concrete strength is 5,700 psi (normal weight). The beam has Grade 60 No. 3 stirrups satisfying ACI 318-14 Sections 9.7.6.2.2 and 9.6.3.3. The strength of the five bars is φMn = 280 kip-ft, and the strength of the remaining two bars is φMn = 119.5 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b1 = 36 in., b2 = 12 in., d1 = 8 in., d2 = 19 in., and that there are three No. 6 longitudinal tension bars and No. 3 stirrups at 10 in. o.c. The stirrup hooks are 90°.

A 115-mm-long beam supports a load of P = 33 N at midspan. The cross section is rectangular with width b = 28 mm and height h = 45 mm. Determine the magnitude of the horizontal shear stress at the centroid of the cross section.

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b = 13 in., d = 22 in., and that there are four No. 7 longitudinal tension bars and No. 4 stirrups at 7 in. o.c. The stirrup hooks are 135°.

Assuming Vs exceeds 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 20 in., b2 = 10 in., d1 = 6 in., and d2 = 17 in. There are three No. 8 longitudinal tension bars and No. 4 stirrups at 6 in. o.c.

Assuming Vs exceeds 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 36 in., b2 = 13 in., d1 = 6 in., and d2 = 21 in. There are three No. 9 longitudinal tension bars and No. 5 stirrups at 11 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 = 18 in. and d = 24 in., five uncoated No. 9 Grade 60 bars placed in the bottom of the beam, and No. 4 Grade 60 stirrups located every 12 in. along the span. Assume 6,000-psi lightweight concrete and a clear cover of 1.75 in.

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For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b = 16 in., d = 25 in., and that there are four No. 9 longitudinal tension bars and No. 3 stirrups at 12 in. o.c. The stirrup hooks are 135°.