Determine the casting-position modification factor, ψt, for a rectangular beam with b = 18 in. and d = 23 in., five uncoated No. 7 Grade 60 tension-reinforcement bars placed in the top 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 2 in.

Force P = 42 N is applied to a lever at the end of a 32-mm-diameter shaft. Force Q = 125 N is applied directly to the shaft. Determine the normal stress σy at point H. Let a = 140 mm and b = 240 mm.

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.