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A rectangular beam with cross section b = 16 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 4.30 kips/ft, including its own dead load. The beam is simply supported with a 19-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 7,200 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. The strength of the five bars is φMn = 325.1 kip-ft, and the strength of the remaining two bars is φMn = 135.2 kip-ft. If the distance from the support to the theoretical cutoff point is 4.269 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).

Concrete does not crack due to imposed deformations, such as differential settlement, shrinkage, and temperature differentials.

Determine the epoxy modification factor, ψe, for a rectangular beam with b = 18 in. and d = 22 in., three epoxy-coated No. 9 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 8,000-psi normal-weight concrete and a clear cover of 1.75 in.

Compression-development lengths are considerably longer than tension-development lengths, because some force is transferred to the concrete by the bearing at the end of the bar.

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 top of the beam, and No. 3 Grade 60 stirrups located every 12 in. along the span. Assume 4,000-psi normal-weight concrete and a clear cover of 1.5 in.

Determine the bar-spacing factor, cb, for a simply supported rectangular beam with b = 24 in. and No. 3 stirrups. This beam has three No. 9 bars as longitudinal reinforcement. The clear cover is 1.9 in.

A rectangular beam has a cross section of b = 14 in., h = 24 in., and d = 21.5 in. It is reinforced with three No. 6 Grade 60 bars. The concrete strength is 9,400 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the cracked moment of inertia, Icr. The neutral axis location of the cracked beam (measured from the top of the beam) is 4.1442 in.

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 18 in. and d = 24 in., five galvanized No. 7 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 40 stirrups located every 8 in. along the span. Assume 4,000-psi lightweight concrete and a clear cover of 1.5 in.

The development length of a bar is _______.

Determine the casting-position modification factor, ψt, for a rectangular beam with b = 16 in. and d = 24 in., three epoxy-coated No. 7 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 4 Grade 60 stirrups located every 10 in. along the span. Assume 6,000-psi lightweight concrete and a clear cover of 1.75 in.