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At a point subjected to plane stress, the stresses are σx = –20 MPa, σy = –40 MPa, and τxy = –40 MPa. Determine the angle θp corresponding to the orientation of the principal planes at the point.

Use ACI 318-14 Table 25.4.2.2 to determine the development length for the straight tension bars (no hooks) in a rectangular beam with b = 16 in. and d = 22 in., five uncoated No. 7 Grade 60 bars placed in the bottom of the beam, and No. 3 Grade 40 stirrups located every 8 in. along the span. Assume 6,000-psi lightweight concrete and a clear cover of 1.5 in.

Determine the casting-position modification factor, ψt, for a rectangular beam with b = 16 in. and d = 23 in., three uncoated No. 7 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 60 stirrups located every 6 in. along the span. Assume 7,000-psi lightweight concrete and a clear cover of 2 in.

Determine the bar-spacing factor, cb, for a simply supported rectangular beam with b = 22 in. and No. 3 stirrups. This beam has five No. 7 bars as longitudinal reinforcement. The clear cover is 1.9 in.

Use ACI 318-14 Table 25.4.2.2 to determine the development length for the straight tension bars (no hooks) in a rectangular beam with b = 18 in. and d = 22 in., five uncoated No. 8 Grade 60 bars placed in the bottom of the beam, and No. 3 Grade 40 stirrups located every 12 in. along the span. Assume 5,000-psi lightweight concrete and a clear cover of 1.75 in.

A rectangular beam with cross section b = 16 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 3.40 kips/ft, including its own dead load. The beam is simply supported with a 20-ft span. It is reinforced with five No. 8 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 4,200 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 = 309.7 kip-ft, and the strength of the remaining two bars is φMn = 132.7 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

Determine the epoxy modification factor, ψe, for a rectangular beam with b = 18 in. and d = 24 in., three galvanized No. 8 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 60 stirrups located every 8 in. along the span. Assume 8,000-psi normal-weight concrete and a clear cover of 2 in.

A rectangular beam has a cross section of b = 14 in., h = 30 in., and d = 27.5 in. It is reinforced with four No. 5 Grade 60 bars. The concrete strength is 9,100 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. Determine the strength φMn for this beam.

Use ACI 318-14 Table 25.4.2.2 to determine the development length for the straight tension bars (no hooks) in a rectangular beam with b = 18 in. and d = 20 in., four galvanized No. 9 Grade 60 bars placed in the top of the beam, and No. 4 Grade 60 stirrups located every 12 in. along the span. Assume 7,000-psi normal-weight concrete and a clear cover of 2 in.

Determine the epoxy modification factor, ψe, for a rectangular beam with b = 16 in. and d = 23 in., three galvanized No. 8 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 60 stirrups located every 8 in. along the span. Assume 8,000-psi normal-weight concrete and a clear cover of 1.75 in.