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Determine the casting-position modification factor, ψt, for a rectangular beam with b = 16 in. and d = 20 in., five galvanized No. 7 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 40 stirrups located every 10 in. along the span. Assume 5,000-psi normal-weight concrete and a clear cover of 1.5 in.

A rectangular beam with cross section b = 16 in., h = 20 in., and d = 17.5 in. supports a total factored uniform load of 1.00 kips/ft, including its own dead load. The beam is simply supported with a 21-ft span. It is reinforced with four No. 5 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 6,300 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 = 95.23 kip-ft, and the strength of the remaining two bars is φMn = 48.22 kip-ft. If the distance from the support to the theoretical cutoff point is 6.784 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).

Determine the casting-position modification factor, ψt, for a rectangular beam with b = 18 in. and d = 23 in., five epoxy-coated No. 6 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 5,000-psi lightweight concrete and a clear cover of 2 in.

Determine the size modification factor, ψs, for a rectangular beam with b = 17 in. and d = 21 in., five uncoated No. 7 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 40 stirrups located every 10 in. along the span. Assume 8,000-psi lightweight concrete and a clear cover of 1.75 in.

A rectangular beam with cross section b = 16 in., h = 28 in., and d = 25.5 in. supports a total factored uniform load of 3.10 kips/ft, including its own dead load. The beam is simply supported with a 23-ft span. It is reinforced with four No. 8 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 5,100 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 = 343.2 kip-ft, and the strength of the remaining two bars is φMn = 176.4 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

Map cracking can be controlled by limiting the heat rise due to the heat of hydration and the rate of cooling, or both; by placing the wall in short lengths; or by reinforcement considerably in excess of normal shrinkage reinforcement.

Determine the epoxy modification factor, ψe, for a rectangular beam with b = 17 in. and d = 22 in., five epoxy-coated No. 8 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 40 stirrups located every 10 in. along the span. Assume 4,000-psi normal-weight concrete and a clear cover of 2 in.

Determine the bar-spacing factor, cb, for a simply supported rectangular beam with b = 18 in. and No. 3 stirrups. This beam has four No. 7 bars as longitudinal reinforcement. The clear cover is 1.8 in.

A simply supported beam with dimensions of b = 14 in., h = 26 in., d = 23.5 in., and L = 21 ft supports a uniform service (unfactored) dead load of 1.579167 kips/ft including its own self weight plus a uniform service (unfactored) live load of 0.8 kips/ft. The beam is reinforced with five No. 8 Grade 60 bars. The concrete strength is 2,500 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Using the effective moment of inertia, determine the immediate mid-span deflection of the beam due to the combined service loads (dead plus live).The effective moment of inertia Ie = 12,311 in.4.

The ACI Code allows the engineer to assume the transverse reinforcement index to be equal to 0, even if transverse reinforcement is present.