Determine the casting-position modification factor, ψt, for a rectangular beam with b = 16 in. and d = 23 in., three uncoated No. 7 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 60 stirrups located every 6 in. along the span. Assume 7,000-psi lightweight concrete and a clear cover of 2 in.

Determine the casting-position modification factor, ψt, for a rectangular beam with b = 16 in. and d = 23 in., four uncoated No. 7 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 4 Grade 60 stirrups located every 12 in. along the span. Assume 6,000-psi normal-weight concrete and a clear cover of 1.5 in.

Compute φVn for the cross section shown. Assume f’c = 7,500 psi, fyt = 40,000 psi, b1 = 29 in., b2 = 12 in., d1 = 6 in., d2 = 17 in., and that there are three No. 7 longitudinal tension bars and No. 4 stirrups at 10 in. o.c.

A rectangular beam has a cross section of b = 18 in., h = 24 in., and d = 21.5 in. It is reinforced with five No. 5 Grade 60 bars. The concrete strength is 8,200 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. Determine the strength φMn for this beam.

If φVc = 51 kip and Vu = 40 kip, are stirrups required?

A 122-mm-long beam supports a load of P = 27 N at midspan. The cross section is rectangular with width b = 29 mm and height h = 40 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 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°.

Determine the bar-spacing factor, cb, for a simply supported rectangular beam with b = 16 in. and No. 3 stirrups. This beam has three No. 9 bars as longitudinal reinforcement. The clear cover is 1.8 in.

A rectangular beam with cross section b = 14 in., h = 26 in., and d = 23.5 in. supports a total factored uniform load of 1.60 kips/ft, including its own dead load. The beam is simply supported with a 24-ft span. It is reinforced with five No. 6 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 7,800 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 = 225.6 kip-ft, and the strength of the remaining two bars is φMn = 91.93 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

A rectangular beam with cross section b = 14 in., h = 24 in., and d = 21.5 in. supports a total factored uniform load of 2.20 kips/ft, including its own dead load. The beam is simply supported with a 23-ft span. It is reinforced with four No. 7 Grade 60 bars, two 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 6,000 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 four bars is φMn = 221.3 kip-ft, and the strength of the remaining two bars is φMn = 113.4 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).