For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b = 16 in., d = 25 in., and that there are four No. 8 longitudinal tension bars and No. 4 stirrups at 10 in. o.c. The stirrup hooks are 135°.

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The shear failure of a slender beam without stirrups is _______.

When the steel ratio, ρw, is small, flexural cracks extend _______ into the beam and open _______ than would be the case with large values of ρw.

Assuming Vs exceeds 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 28 in., b2 = 12 in., d1 = 8 in., and d2 = 49 in. There are three No. 8 longitudinal tension bars and No. 3 stirrups at 11 in. o.c.

Assuming Vs does not exceed 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 31 in., b2 = 15 in., d1 = 4 in., and d2 = 53 in. There are three No. 7 longitudinal tension bars and No. 5 stirrups at 10 in. o.c.

If the depth of the beam varies, the compressive and tensile forces due to flexure will have vertical components.

Development length is the shortest length of bar in which the bar stress can increase from zero to the yield stress.

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

A rectangular beam with cross section b = 16 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 3.80 kips/ft, including its own dead load. The beam is simply supported with a 19-ft span. It is reinforced with four No. 8 Grade 60 bars, two of which are cutoff between midspan and the support and two of which extend 10 in. past the centers of the supports. The concrete strength is 6,900 psi (normal weight). The beam has Grade 60 No. 3 stirrups satisfying ACI 318-14 Sections 9.7.6.2.2 and 9.6.3.3. The strength of the four bars is φMn = 262.9 kip-ft, and the strength of the remaining two bars is φMn = 135.1 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).