A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000230/°C, E = 71 GPa, ν = 0.32], has an inside diameter of 180 mm, and has an outside diameter of 840 mm. Determine the circumferential stress at the outer radius for a steady-state temperature change with the temperature at the inner radius 105°C greater than the temperature at the outer radius.

A cast iron disk has an inner radius of a = 130 mm and an outer radius of b = 295 mm, with material properties ρ = 7,600 kg/m3, E = 73 GPa, ν = 0.23. Determine the maximum circumferential stress in the disk for a speed of revolution of 5,200 rpm.

A steel I-beam [E = 200 GPa] has a depth of 136 mm, width of 75 mm, moment of inertia of Ix = 5.99 × 106 mm4, and length of 5 m. It rests on a hard rubber foundation. The value of the spring constant for the hard rubber is k0 = 0.300 N/mm3. If the beam is subjected to a concentrated load, P = 70 kN, at the center of the beam, determine the bending moment at the center of the beam. The value of β is 1.472 /m.

The curved bar has a triangular cross section with dimensions b = 1.3 in. and d = 0.5 in. The inner radius of the curved bar is ri = 4.5 in. Determine the value of Am for the cross section.

A pinned-end column has a cross-sectional area of 1,800 mm2, radius of gyration of 11.968 mm, and length of 740 mm. It is made of 7070-T5 aluminum alloy [E = 73 GPa, ν = 0.34, σPL = 500 MPa]. The column has a solid circular cross section. Determine the critical buckling stress.

A 14-ft-long simply supported timber beam carries vertical load P = 16.8 kip at midspan. The cross-sectional dimensions of the timber are shown. At section a-a, determine the magnitude of the bending stress in the beam at point K.

Beam ABC is subjected to moment M = 210 kN·m. Determine the slope at C. Assume L = 8.0 m and EI = 7.2 x 107 N·m2. Only consider the strain energy related to bending moments.

A steel I-beam rests on a hard rubber foundation. If the beam is subjected to a concentrated load at the center of the beam, determine the value of Dβz at a distance of z = 30 mm from the center of the beam. The value of β is 1.470 /m.

A 70-kN capacity hoist may be moved along a steel I-beam [E = 200 GPa]. The I-beam has a depth of 157 mm and moment of inertia Ix = 11.4 × 106 mm4. The beam is hung from a series of vertical steel rods [E = 200 GPa] of length 3.00 m, of diameter 17 mm, and spaced 300 mm center to center. For capacity load at the center of the beam, located under one of the rods, determine the value of β.

A steel I-beam [E = 200 GPa] has a depth of 137 mm, width of 71 mm, moment of inertia of Ix = 4.50 × 106 mm4, and length of 5 m. It rests on a hard rubber foundation. The value of the spring constant for the hard rubber is k0 = 0.240 N/mm3. If the beam is subjected to a concentrated load, P = 40 kN, at the center of the beam, determine the bending moment at the center of the beam. The value of β is 1.475 /m.