In an I-beam subjected to simple bending about a horizontal axis, the maximum bending stress occurs _______.  

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 72 GPa, ν = 0.32], has an inside diameter of 180 mm, and has an outside diameter of 850 mm. The cylinder is subjected to an external pressure of 160 MPa. Determine the circumferential stress at the inner radius.

A steel I-beam [E = 200 GPa] has a depth of 123 mm, width of 71 mm, moment of inertia of Ix = 4.38 × 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 = 0.310 N/mm3. If the beam is subjected to a concentrated load, P = 80 kN, at the center of the beam, determine the maximum flexural stress at the center of the beam. The bending moment at the center of the beam is 12.63 kN·m.

A cast iron disk has an inner radius of a = 160 mm and an outer radius of b = 285 mm, with material properties ρ = 7,100 kg/m3, E = 65 GPa, ν = 0.26. Determine the maximum circumferential stress in the disk for a speed of revolution of 5,800 rpm.

A hollow rectangular tube with outside cross-sectional dimensions of 90 mm and 110 mm and a uniform wall thickness of 10 mm is used as a pinned-end column. It is made of structural steel [E = 205 GPa, ν = 0.28, Y = 240 MPa] and has a length of 6 m. Determine the critical buckling load.

The design of a white oak [E = 12.1 GPa, σPL = 29 MPa] column of square cross section has the following requirements. It must be 6.0 m long, it must have pinned ends, and it must support an axial load of 70 kN with a factor of safety of 2.0 against buckling. Determine the required width of the cross section.

A solid bar with cross-sectional dimensions of 95 mm by 95 mm is used as a pinned-end column. It is made of structural steel [E = 200 GPa, ν = 0.31, Y = 230 MPa] and has a length of 5.0 m. Determine the slenderness ratio.

A steel I-beam [E = 200 GPa] has a depth of 122 mm, width of 78 mm, moment of inertia of Ix = 4.25 × 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 = 0.320 N/mm3. If the beam is subjected to a concentrated load, P = 50 kN, at the center of the beam, determine the bending moment at the center of the beam. The value of β is 1.646 /m.

A hollow rectangular tube with outside cross-sectional dimensions of 95 mm and 110 mm and a uniform wall thickness of 10 mm is used as a pinned-end column. It is made of structural steel [E = 210 GPa, ν = 0.27, Y = 230 MPa] and has a length of 5 m. Determine the critical buckling load.

A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000230/°C, E = 73 GPa, ν = 0.31], has an inside diameter of 220 mm, and has an outside diameter of 750 mm. Determine the circumferential stress at the inner radius for a steady-state temperature change with the temperature at the inner radius 105°C greater than the temperature at the outer radius.