If φVc = 58 kip and Vu = 21 kip, are stirrups required?

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 strain in the compression reinforcement, ε’s.

At a point subjected to plane stress, the stresses are σx = –40 MPa, σy = 30 MPa, and τxy = –90 MPa. Determine the angle θp corresponding to the orientation of the principal planes at the point.

A simply supported beam with dimensions of b = 12 in., h = 26 in., d = 23.5 in., and L = 16 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 0.9 kips/ft. The concrete is normal-weight concrete. Determine the moment due to the factored loads, Mu.      

A classmate has suggested a beam design that has dimensions of b = 14 in., h = 30 in., and d = 27.5 in. and is reinforced with 5 No. 14 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?

Compute φVn for the cross section shown. Assume f’c = 7,000 psi, fyt = 60,000 psi, b1 = 29 in., b2 = 12 in., d1 = 8 in., d2 = 16 in., and that there are three No. 7 longitudinal tension bars and No. 3 stirrups at 8 in. o.c.

If φVc = 58 kip and Vu = 21 kip, are stirrups required?

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 strain in the compression reinforcement, ε’s.

Isolated beams with unsymmetrical cross sections can deflect vertically and laterally at the same time.

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 3,100 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 5.205 in., determine the strain in the compression reinforcement, ε’s.