A rectangular beam has a cross section of b = 16 in., h = 24 in., and d = 21.5 in. It is reinforced with five No. 6 Grade 60 bars. The concrete strength is 5,500 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.

The spherical face shield of an astronaut’s helmet is made from polycarbonate with a yield strength of 110 MPa. The shield has an outside diameter of 352 mm and a thickness of 4.7 mm. If the shield is successfully pressure tested to 940 kPa on Earth, determine the factor of safety with respect to yielding.

Force P = 45 N is applied to a lever at the end of a 32-mm-diameter shaft. Force Q = 850 N is applied directly to the shaft. Determine the magnitude of the shear stress τxy at point H. Let a = 155 mm and b = 210 mm.

The spherical face shield of an astronaut’s helmet is made from polycarbonate with a yield strength of 117 MPa. The shield has an outside diameter of 359 mm and a thickness of 4.2 mm. If the shield is successfully pressure tested to 980 kPa on Earth, determine the factor of safety with respect to yielding.

A 695 N person stands in the middle of a 2.51 m simply-supported beam. The beam has a base of 95 mm and a height of 160 mm. Determine the maximum horizontal shear stress in the beam.

The spherical face shield of an astronaut’s helmet is made from polycarbonate with a yield strength of 113 MPa. The shield has an outside diameter of 357 mm and a thickness of 5.4 mm. If the shield is successfully pressure tested to 855 kPa on Earth, determine the factor of safety with respect to yielding.

A rectangular beam with cross section b = 16 in., h = 24 in., and d = 21.5 in. supports a total factored uniform load of 2.60 kips/ft, including its own dead load. The beam is simply supported with a 19-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 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 = 201.4 kip-ft, and the strength of the remaining two bars is φMn = 83.31 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 635 N person stands at the end of a 1.22 m cantilever beam. The beam has a base of 90 mm and a height of 155 mm. Determine the maximum bending stress in the beam.

Determine the epoxy modification factor, ψe, for a rectangular beam with b = 18 in. and d = 21 in., five epoxy-coated No. 6 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 40 stirrups located every 8 in. along the span. Assume 4,000-psi normal-weight concrete and a clear cover of 1.5 in.

A driver accidentally bumped a fire hydrant creating a bending moment of 610 N·m in the pipe below. The pipe has an inside diameter of 180 mm and a wall thickness of 6 mm and is pressurized to 330 kPa. Determine the largest normal stress along the length of the pipe.