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A rectangular beam has a cross section of b = 14 in., h = 30 in., and d = 27.5 in. It is reinforced with four No. 7 Grade 60 bars. The concrete strength is 5,200 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.

When the force in a reinforcing bar changes from point to point along its length, there must be bond stresses between it and the concrete.

A large stress concentration, possibly leading to large inclined cracks, happens when a tension bar is cutoff at a location of high shear force.

The ACI Code uses the concept of development length instead of _______, because the actual bond stress varies along the length of a reinforcing bar.

Is the actual size of hooks critical in detailing a structure?

Determine the bar-spacing factor, cb, for a simply supported rectangular beam with b = 18 in. and No. 4 stirrups. This beam has three No. 8 bars as longitudinal reinforcement. The clear cover is 1.5 in.

A rectangular beam with cross section b = 14 in., h = 24 in., and d = 21.5 in. supports a total factored uniform load of 2.00 kips/ft, including its own dead load. The beam is simply supported with a 21-ft span. It is reinforced with four No. 6 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 6,900 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 = 165.2 kip-ft, and the strength of the remaining two bars is φMn = 83.87 kip-ft. If the distance from the support to the theoretical cutoff point is 5.364 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).

A rectangular beam with cross section b = 16 in., h = 24 in., and d = 21.5 in. supports a total factored uniform load of 2.50 kips/ft, including its own dead load. The beam is simply supported with a 21-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 3,000 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 = 213.1 kip-ft, and the strength of the remaining two bars is φMn = 111.3 kip-ft. If the distance from the support to the theoretical cutoff point is 5.895 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).

The primary purpose for the continuity and structural integrity reinforcement requirements is to tie the structural elements together and prevent localized damage from spreading.

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 = 17 in. and d = 23 in., three epoxy-coated No. 6 Grade 60 bars placed in the bottom of the beam, and No. 4 Grade 60 stirrups located every 12 in. along the span. Assume 7,000-psi lightweight concrete and a clear cover of 1.75 in.