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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, b1 = 28 in., b2 = 10 in., d1 = 4 in., d2 = 19 in., and that there are three No. 7 longitudinal tension bars and No. 5 stirrups at 12 in. o.c. The stirrup hooks are 90°.

A rectangular beam with cross section b = 14 in., h = 26 in., and d = 23.5 in. supports a total factored uniform load of 1.60 kips/ft, including its own dead load. The beam is simply supported with a 24-ft span. It is reinforced with five No. 6 Grade 60 bars, three 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 7,800 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 five bars is φMn = 225.6 kip-ft, and the strength of the remaining two bars is φMn = 91.93 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

A rectangular beam with cross section b = 14 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 2.30 kips/ft, including its own dead load. The beam is simply supported with a 21-ft span. It is reinforced with five No. 7 Grade 60 bars, three 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 6,000 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 five bars is φMn = 246.2 kip-ft, and the strength of the remaining two bars is φMn = 102.6 kip-ft. If the distance from the support to the theoretical cutoff point is 5.914 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).

Assuming Vs does not exceed 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 22 in., b2 = 12 in., d = 57 in., h1 = 6 in., h2 = 46 in., h3 = 10 in., and t = 7 in. There are six No. 9 longitudinal tension bars and No. 5 stirrups at 11 in. o.c.

If φVc = 23 kip and Vu = 63 kip, are stirrups required?

A rectangular beam with cross section b = 14 in., h = 24 in., and d = 21.5 in. supports a total factored uniform load of 1.60 kips/ft, including its own dead load. The beam is simply supported with a 19-ft span. It is reinforced with five No. 5 Grade 60 bars, three 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 five bars is φMn = 146 kip-ft, and the strength of the remaining two bars is φMn = 59.35 kip-ft. If the distance from the support to the theoretical cutoff point is 5.492 ft, determine the distance from the support to the actual cutoff point (i.e. use ACI 318-14 Section 9.7.3.3).

If φVc = 18 kip and Vu = 34 kip, are stirrups required?

At a point subjected to plane stress, the stresses are σx = –10 ksi, σy = 25 ksi, and τxy = 20 ksi. Determine the angle θp corresponding to the orientation of the principal planes at the point.

Assuming Vs does not exceed 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 26 in., b2 = 12 in., d = 59 in., h1 = 4 in., h2 = 51 in., h3 = 9 in., and t = 7 in. There are six No. 7 longitudinal tension bars and No. 3 stirrups at 11 in. o.c.

A 122-mm-long beam supports a load of P = 27 N at midspan. The cross section is rectangular with width b = 29 mm and height h = 40 mm. Determine the magnitude of the horizontal shear stress at the centroid of the cross section.