A beam has dimensions of b = 14 in., h = 28 in., and d = 25.5 in. and is reinforced with 3 No. 6 bars. The concrete strength is 8,200 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the compressive stress block is a = 0.811642 in. and the strain in the reinforcement is εs = 0.058265, determine the strength φMn for this beam. Assume the transverse reinforcement is not spirals.

A simply supported beam with dimensions of b = 10 in., h = 22 in., d = 19.5 in., and L = 19 ft supports a uniform service (unfactored) dead load consisting of its own weight plus 1.2 kips/ft and a uniform service (unfactored) live load of 1.5 kips/ft. The concrete is normal-weight concrete. Determine the moment due to the factored loads, Mu.      

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A beam has dimensions of b = 18 in., h = 30 in., and d = 27.5 in. and is reinforced with 5 No. 6 bars. The concrete strength is 4,000 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth to the neutral surface is c = 2.537486 in., determine the strain in the reinforcement.

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Determine As,min for the following beam given that f’c = 3,750 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 3 No. 6 bars. The concrete strength is 3,700 psi, and the yield strength of the reinforcement is 60,000 psi. Assuming the reinforcement has yielded, determine the tensile force T in the reinforcement.

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