A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000235/°C, E = 71 GPa, ν = 0.33], has an inside diameter of 220 mm, and has an outside diameter of 780 mm. Determine the circumferential stress at the inner radius for a steady-state temperature change with the temperature at the inner radius 80°C greater than the temperature at the outer radius.

A cast iron disk has an inner radius of a = 170 mm and an outer radius of b = 300 mm, with material properties ρ = 7,000 kg/m3, E = 71 GPa, ν = 0.27. Determine the maximum circumferential stress in the disk for a speed of revolution of 5,500 rpm.

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 73 GPa, ν = 0.30], has an inside diameter of 200 mm, and has an outside diameter of 790 mm. The cylinder is subjected to an internal pressure of 170 MPa and an external pressure of 120 MPa. Determine the circumferential stress at r = 140 mm.

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 74 GPa, ν = 0.33], has an inside diameter of 200 mm, and has an outside diameter of 750 mm. The cylinder is subjected to an internal pressure of 170 MPa. Determine the circumferential stress at r = 300 mm.

An infinite beam on an elastic foundation is subjected to a triangular load w = 29 N/mm over the segment L’ = 5 m. Determine the bending moment at point B. Use E = 200 GPa, Ix = 80 × 106 mm4, and k = 10.0 N/mm2. The value of β is 0.6287 /m.

Consider a 1-m length of an unloaded cylinder at a location in the cylinder some distance from the ends. The long closed cylinder is made of a steel for which E = 205 GPa and ν = 0.28. It has an internal radius a = 95 mm and an external radius b = 275 mm.   Determine the radial displacement at the outer surface after p1 = 95 MPa is applied?

If w = 9.75 in., find the moment of inertia Iy about the y axis.

A cast iron disk has an inner radius of a = 175 mm and an outer radius of b = 325 mm, with material properties ρ = 7,600 kg/m3, E = 65 GPa, ν = 0.23. Determine the maximum circumferential stress in the disk for a speed of revolution of 5,200 rpm.

Which point experiences the largest magnitude of horizontal shear stress?

If w = 8.25 in., find the moment of inertia Iz about the z axis. The centroid of the section is located 2.8320 in. above the bottom surface of the beam.