Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 16 in. and d = 24 in., three epoxy-coated No. 6 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 5,000-psi normal-weight concrete and a clear cover of 2 in.

Determine the size modification factor, ψs, for a rectangular beam with b = 18 in. and d = 23 in., four epoxy-coated No. 8 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 40 stirrups located every 6 in. along the span. Assume 8,000-psi normal-weight concrete and a clear cover of 1.5 in.

A pipeline with an outside diameter of 495 mm and a wall thickness of 5 mm is pressurized to 1.5 MPa. Due to thermal expansion, a compressive force of 29 kN is generated along the length of the pipes. Determine the normal stress along the length of the pipes. Ignore the bending stresses due to the weight of the pipes and the fluid that they contain.

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 366 mm and a thickness of 5.3 mm. If the shield is successfully pressure tested to 960 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.

A driver accidentally bumped a fire hydrant creating a bending moment of 695 N·m in the pipe below. The pipe has an inside diameter of 150 mm and a wall thickness of 5 mm and is pressurized to 330 kPa. Determine the largest normal stress along the length of the pipe.

The pressure hull of a space station module has an inside diameter of 4.6 m, a length of 5.2 m, and a wall thickness of 2.8 mm. It is made from an aluminum alloy with a yield strength of 243 MPa. If the hull is successfully pressure tested to 165 kPa on Earth, determine the factor of safety with respect to yielding.

Force P = 41 N is applied to a lever at the end of a 31-mm-diameter shaft. Force Q = 830 N is applied directly to the shaft. Determine the magnitude of the shear stress τxy at point H. Let a = 145 mm and b = 200 mm.

Force P = 45 N is applied to a lever at the end of a 33-mm-diameter shaft. Force Q = 180 N is applied directly to the shaft. Determine the magnitude of the shear stress τyz at point K. Let a = 145 mm and b = 200 mm.

The spherical face shield of an astronaut’s helmet is made from polycarbonate with a yield strength of 120 MPa. The shield has an outside diameter of 368 mm and a thickness of 4.0 mm. If the shield is successfully pressure tested to 920 kPa on Earth, determine the factor of safety with respect to yielding.