A beam has dimensions of b = 14 in., h = 22 in., and d = 19.5 in. and is reinforced with 2 No. 7 bars. The concrete strength is 6,400 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the compressive stress block is a = 0.945378 in. and the strain in the reinforcement is εs = 0.042172, determine the strength φMn for this beam. Assume the transverse reinforcement is not spirals.

Determine As,min for the following beam given that f’c = 8,750 psi and fy = 60,000 psi.

Determine As,min for the following beam given that f’c = 7,250 psi and fy = 60,000 psi.

A beam has dimensions of b = 14 in., h = 28 in., and d = 25.5 in. and is reinforced with 2 No. 7 bars. The concrete strength is 5,800 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the compressive stress block is a = 1.043176 in. and the strain in the reinforcement is εs = 0.052734, determine the strength φMn for this beam. Assume the transverse reinforcement is not spirals.

A beam has dimensions of b = 14 in., h = 30 in., and d = 27.5 in. and is reinforced with 5 No. 5 bars. The concrete strength is 4,300 psi, and the yield strength of the reinforcement is 60,000 psi. Assuming the reinforcement has yielded, determine the depth to the neutral axis, c.

According to the theory of flexure for reinforced concrete, the strain in the reinforcement is less than the strain in the concrete at the same level.

Determine β1 given that f’c = 8,200 psi.

One of the three basic assumptions in the theory of flexure for reinforce concrete is that the strain in the reinforcement is greater than the strain in the concrete at the same level.

A beam has dimensions of b = 20 in., h = 10 in., and d = 7.5 in. and is reinforced with 4 No. 6 bars. The concrete strength is 2,000 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 3.654 in., does the reinforcement yield?

A beam has dimensions of b = 14 in., h = 28 in., d’ = 2.5 in., and d = 25.5 in. It is reinforced with 2 No. 5 bars on the compression side and 5 No. 8 bars on the tension side. The concrete strength is 3,700 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 5.588 in., determine the strain in the compression reinforcement, ε’s.