Alternate span loading is the common loading pattern for determining maximum negative moments at supports due to live load.

A classmate has suggested a beam design that has dimensions of b = 12 in., h = 24 in., and d = 21.5 in. and is reinforced with 5 No. 7 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?

A continuous beam’s flexural reinforcement must extend at least _____ from the point where it is no longer needed to resist tension. Assume f’c = 4,000 psi, fyt = 40,000 psi, d = 24 in., w = 16.5 in., and t = 5 in. There are five No. 6 longitudinal tension bars and No. 5 stirrups at 12 in. o.c.

If φVc = 43 kip and Vu = 54 kip, are stirrups required?

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 4,000 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 5.216 in., determine the strain in the compression reinforcement, ε’s.

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 4,000 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 5.216 in., determine the strain in the compression reinforcement, ε’s.

Because a slab is thinner than the beams supporting it, the concrete in the slab shrinks more rapidly than the concrete in the beams.

At a point subjected to plane stress, the stresses are σx = 20 ksi, σy = 10 ksi, and τxy = –10 ksi. Determine the angle θp corresponding to the orientation of the principal planes at the point.

ACI 318 does not provide rules for designing hanger reinforcement.

A 123-mm-long beam supports a load of P = 40 N at midspan. The cross section is rectangular with width b = 29 mm and height h = 60 mm. Determine the magnitude of the horizontal shear stress at the centroid of the cross section.