Force P = 50 N is applied to a lever at the end of a 30-mm-diameter shaft. Force Q = 955 N is applied directly to the shaft. Determine the normal stress σy at point K. Let a = 120 mm and b = 210 mm.

Determine the lightweight modification factor, λ, for a rectangular beam with b = 17 in. and d = 22 in., four uncoated No. 8 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 3 Grade 60 stirrups located every 8 in. along the span. Assume 5,000-psi normal-weight concrete and a clear cover of 1.75 in.

A rectangular beam with cross section b = 16 in., h = 20 in., and d = 17.5 in. supports a total factored uniform load of 0.96 kips/ft, including its own dead load. The beam is simply supported with a 23-ft span. It is reinforced with four No. 5 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 5,100 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. The strength of the four bars is φMn = 94.66 kip-ft, and the strength of the remaining two bars is φMn = 48.08 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 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 2 in.

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 16 in. and d = 22 in., four epoxy-coated No. 6 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 60 stirrups located every 12 in. along the span. Assume 8,000-psi normal-weight concrete and a clear cover of 1.75 in.

The spherical face shield of an astronaut’s helmet is made from polycarbonate with a yield strength of 102 MPa. The shield has an outside diameter of 365 mm and a thickness of 5.1 mm. If the shield is successfully pressure tested to 800 kPa on Earth, determine the factor of safety with respect to yielding.

The pressure hull of a space station module has an inside diameter of 4.4 m, a length of 5.5 m, and a wall thickness of 3.1 mm. It is made from an aluminum alloy with a yield strength of 256 MPa. If the hull is successfully pressure tested to 180 kPa on Earth, determine the factor of safety with respect to yielding.

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 17 in. and d = 23 in., four uncoated No. 8 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 40 stirrups located every 8 in. along the span. Assume 6,000-psi normal-weight concrete and a clear cover of 1.5 in.

A rectangular beam with cross section b = 14 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 2.40 kips/ft, including its own dead load. The beam is simply supported with a 20-ft span. It is reinforced with four No. 7 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 3,300 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 = 190.8 kip-ft, and the strength of the remaining two bars is φMn = 100.3 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

Force P = 48 N is applied to a lever at the end of a 31-mm-diameter shaft. Force Q = 190 N is applied directly to the shaft. Determine the normal stress σy at point H. Let a = 170 mm and b = 210 mm.