Bars of longitudinal reinforcement often do not have to extend the full length of a beam.

Compute φVn for the cross section shown. Assume f’c = 7,500 psi, fyt = 40,000 psi, b = 12 in., d = 25 in., and that there are four No. 8 longitudinal tension bars and No. 3 stirrups at 9 in. o.c.

A beam is singly reinforced with the reinforcement in two rows. The bottom row contains 9 No. 5 bars at a depth of 14 in. The top row contains 6 No. 8 bars at a depth of 8 in. Determine the effective (centroidal) depth, d, of the steel.

A beam has dimensions of b = 18 in., h = 24 in., and d = 21.5 in. and is reinforced with 3 No. 5 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 classmate has suggested a beam design that has dimensions of b = 16 in., h = 22 in., and d = 19.5 in. and is reinforced with 5 No. 9 bars. Assuming a cover of 1.5 in. and a stirrup diameter of 0.5 in., does the reinforcement fit within a single row as suggested?

You are considering a beam design that has dimensions of b = 16 in., h = 28 in., and d = 25.5 in. The beam is singly reinforced with all of the reinforcement in a single row. The concrete strength is 8,800 psi, and the yield strength of the reinforcement is 60,000 psi. What cross-sectional area of reinforcement is needed to achieve a strain in the reinforcement of 0.0075?

A beam has dimensions of b = 20 in., h = 12 in., and d = 9.5 in. and is reinforced with 4 No. 10 bars. The concrete strength is 4,400 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 4.909 in., does the reinforcement yield?

A beam has dimensions of b = 14 in., h = 26 in., d’ = 2.5 in., and d = 23.5 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 3,700 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 4.481 in., determine the strain in the compression reinforcement, ε’s.

A beam has dimensions of b = 18 in., h = 24 in., and d = 21.5 in. and is reinforced with 3 No. 5 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 = 14 in., h = 26 in., and d = 23.5 in. and is reinforced with 3 No. 5 bars. The concrete strength is 4,000 psi, and the yield strength of the reinforcement is 60,000 psi. Determine the strength Mn for this beam.