When faced with severe architectural restrictions on the dimensions of a beam, a designer may be forced to use a doubly reinforced section.

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, b = 13 in., d = 17 in., and that there are four No. 7 longitudinal tension bars and No. 3 stirrups at 7 in. o.c. The stirrup hooks are 135°.

If φVc = 35 kip and Vu = 72 kip, are stirrups required?

Assuming Vs does not exceed 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let d = 49 in., w = 41.5 in., and t = 5 in. There are five No. 9 longitudinal tension bars and No. 4 stirrups at 8 in. o.c.

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b1 = 35 in., b2 = 16 in., d1 = 6 in., d2 = 23 in., and that there are three No. 7 longitudinal tension bars and No. 5 stirrups at 7 in. o.c. The stirrup hooks are 90°.

If φVc = 33 kip and Vu = 51 kip, are stirrups required?

Web reinforcement is normally provided to ensure that the beam reaches the full _______ capacity.

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 4 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 = 4,000 psi, fyt = 40,000 psi, d = 22 in., w = 16.5 in., t = 4 in., and that there are four No. 8 longitudinal tension bars and No. 3 stirrups at 6 in. o.c.

The adhesive force between a smooth reinforcement bar and concrete is too weak to be practical in construction; therefore, smooth bars are commonly used as longitudinal reinforcement in concrete.