Find the limit of the function by using direct substitution. (6 points)  

A beam has dimensions of b = 14 in., h = 24 in., and d = 21.5 in. and is reinforced with 5 No. 7 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.

A beam has dimensions of b = 14 in., h = 24 in., and d = 21.5 in. and is reinforced with 2 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.

A beam has dimensions of b = 14 in., h = 22 in., and d = 19.5 in. and is reinforced with 3 No. 6 bars. The concrete strength is 9,700 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the compressive stress block is a = 0.68613 in. and the strain in the reinforcement is εs = 0.05242, determine the strength φMn for this beam. Assume the transverse reinforcement is not spirals.

Find an equation in standard form for the hyperbola with vertices at (0, ±8) and asymptotes at y = ± x. (5 points)

Live load reduction is not permitted on one-way slabs.

(04.02 MC)  Suppose 70% of jurors come to a just decision. In a jury of ten people, what is the probability more than half come to a just decision? (4 points)

A beam has dimensions of b = 14 in., h = 30 in., d’ = 2.5 in., and d = 27.5 in. It is reinforced with 2 No. 5 bars on the compression side and 4 No. 8 bars on the tension side. The concrete strength is 2,800 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 5.68 in., determine the force in the compression reinforcement, Cs.

A beam is singly reinforced with the reinforcement in two rows. The bottom row contains 10 No. 8 bars at a depth of 20 in. The top row contains 7 No. 5 bars at a depth of 16 in. Determine the effective (centroidal) depth, d, of the steel.

A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 13 feet and the height from the ground to the front doors is 5 feet, how long is the ramp? (Round to the nearest tenth.) (5 points)