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.

Force P = 48 N is applied to a lever at the end of a 30-mm-diameter shaft. Force Q = 135 N is applied directly to the shaft. Determine the normal stress σy at point H. Let a = 120 mm and b = 240 mm.

Force P = 41 N is applied to a lever at the end of a 30-mm-diameter shaft. Force Q = 165 N is applied directly to the shaft. Determine the normal stress σy at point H. Let a = 170 mm and b = 225 mm.

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.

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 = 23 in., three uncoated No. 6 Grade 60 bars placed in the bottom of the beam, and No. 3 Grade 40 stirrups located every 12 in. along the span. Assume 4,000-psi normal-weight concrete and a clear cover of 1.5 in.

Force P = 50 N is applied to a lever at the end of a 33-mm-diameter shaft. Force Q = 115 N is applied directly to the shaft. Determine the magnitude of the shear stress τyz at point K. Let a = 165 mm and b = 205 mm.

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.