When a beam is supported by a girder or other beam of essentially the same depth, hanger reinforcement should not be provided in the joint.

A 116-mm-long beam supports a load of P = 43 N at midspan. The cross section is rectangular with width b = 29 mm and height h = 45 mm. Determine the magnitude of the horizontal shear stress at the centroid of the cross section.

Is the strength reduction factor greater for shear or flexure?

Determine the lightweight modification factor, λ, for a rectangular beam with b = 16 in. and d = 22 in., five galvanized No. 7 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 4 Grade 40 stirrups located every 8 in. along the span. Assume 8,000-psi normal-weight concrete and a clear cover of 1.5 in.

Aggregate interlock is when aggregate particles on two faces of a crack are interlocked. This encourages sliding of the faces past each other.

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 = 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.

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.