Compute φVn for the cross section shown. Assume f’c = 8,000 psi, fyt = 40,000 psi, b1 = 30 in., b2 = 11 in., d = 22 in., h1 = 5 in., h2 = 13 in., h3 = 9 in., t = 7 in., and that there are six No. 8 longitudinal tension bars and No. 3 stirrups at 8 in. o.c.

In high-strength concrete, cracks tend to go around pieces of the aggregate rather than penetrating them.

Compute φVn for the cross section shown. Assume f’c = 6,000 psi, fyt = 40,000 psi, b = 16 in., d = 23 in., and that there are four No. 6 longitudinal tension bars and No. 4 stirrups at 10 in. o.c.

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b = 14 in., d = 28 in., and that there are four No. 9 longitudinal tension bars and No. 4 stirrups at 7 in. o.c. The stirrup hooks are 135°.

In a tapered beam, the tension force due to flexure acts perpendicular to the centroid of the tension reinforcement.

A 125-mm-long beam supports a load of P = 30 N at midspan. The cross section is rectangular with width b = 28 mm and height h = 45 mm. Determine the magnitude of the horizontal shear stress at the centroid of the cross section.

When the steel ratio is small, flexural cracks extend higher into the beam and open wider.

Bond stress values do not vary from point to point between cracks.

Compute φVn for the cross section shown. Assume f’c = 5,000 psi, fyt = 60,000 psi, b1 = 31 in., b2 = 13 in., d1 = 8 in., d2 = 15 in., and that there are three No. 6 longitudinal tension bars and No. 5 stirrups at 9 in. o.c.

If φVc = 75 kip and Vu = 55 kip, are stirrups required?