Compute φVn for the cross section shown. Assume f’c = 5,500 psi, fyt = 60,000 psi, b1 = 26 in., b2 = 10 in., d = 22 in., h1 = 4 in., h2 = 14 in., h3 = 9 in., t = 6 in., and that there are six No. 6 longitudinal tension bars and No. 4 stirrups at 12 in. o.c.

Compute φVn for the cross section shown. Assume f’c = 5,000 psi, fyt = 40,000 psi, d = 28 in., w = 22.5 in., t = 4 in., and that there are four No. 7 longitudinal tension bars and No. 3 stirrups at 10 in. o.c.

Compute φVn for the cross section shown. Assume f’c = 4,000 psi, fyt = 60,000 psi, b = 10 in., d = 26 in., and that there are four No. 7 longitudinal tension bars and No. 4 stirrups at 8 in. o.c.

The strength-reduction factor, φ, for shear and torsion is _____.

What kind of cracks must exist before a beam can fail in shear?

Compute φVn for the cross section shown. Assume f’c = 8,000 psi, fyt = 60,000 psi, b = 15 in., d = 23 in., and that there are four No. 6 longitudinal tension bars and No. 5 stirrups at 11 in. o.c.

You are considering a beam design that has dimensions of b = 18 in., h = 26 in., and d = 23.5 in. The beam is singly reinforced with all of the reinforcement in a single row. The concrete strength is 10,000 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?

If a beam is supported by a girder of essentially the same depth, the compression fans that form in the supported beam tend to push the bottom off the supporting beam.

Compute φVn for the cross section shown. Assume f’c = 8,000 psi, fyt = 60,000 psi, b = 15 in., d = 23 in., and that there are four No. 6 longitudinal tension bars and No. 5 stirrups at 11 in. o.c.

At a point subjected to plane stress, the stresses are σx = 70 MPa, σy = –60 MPa, and τxy = 10 MPa. Determine the angle θp corresponding to the orientation of the principal planes at the point.