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What force does a trampoline have to apply to a 45.0-kg gymnast to accelerate her straight up at 7.50 m/s^2 ? Note that the answer is independent of the velocity of the gymnast—she can be moving either up or down, or be stationary.

Determine As,min for the following beam given that f’c = 3,500 psi and fy = 60,000 psi.

A beam has dimensions of b = 16 in., h = 24 in., and d = 21.5 in. and is reinforced with 2 No. 7 bars. The concrete strength is 4,000 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the compressive stress block is a = 1.323529 in. and the strain in the reinforcement is εs = 0.038423, determine the strength φMn for this beam. Assume the transverse reinforcement is not spirals.

A simply supported beam with dimensions of b = 12 in., h = 30 in., d = 27.5 in., and L = 15 ft supports a uniform service (unfactored) dead load consisting of its own weight plus 1.6 kips/ft and a uniform service (unfactored) live load of 1.0 kips/ft. The concrete is normal-weight concrete. Determine the moment due to the factored loads, Mu.      

A beam has dimensions of b = 18 in., h = 28 in., and d = 25.5 in. and is reinforced with 2 No. 7 bars. The concrete strength is 4,000 psi, and the yield strength of the reinforcement is 60,000 psi. Determine the nominal moment capacity, Mn, of the beam.

A beam has dimensions of b = 16 in., h = 26 in., and d = 23.5 in. and is reinforced with 2 No. 7 bars. The concrete strength is 4,900 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth to the neutral surface is c = 1.342152 in., determine the strain in the reinforcement.

A beam has dimensions of b = 18 in., h = 26 in., and d = 23.5 in. and is reinforced with 3 No. 8 bars. The concrete strength is 5,500 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.

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.

A beam has dimensions of b = 18 in., h = 22 in., and d = 19.5 in. and is reinforced with 5 No. 8 bars. The concrete strength is 4,600 psi, and the yield strength of the reinforcement is 60,000 psi. Determine the nominal moment capacity, Mn, of the beam.

A beam has dimensions of b = 18 in., h = 24 in., and d = 21.5 in. and is reinforced with 4 No. 6 bars. The concrete strength is 8,500 psi, and the yield strength of the reinforcement is 60,000 psi. Determine the nominal moment capacity, Mn, of the beam.