The design of a white oak [E = 12.6 GPa, σPL = 27 MPa] column of square cross section has the following requirements. It must be 6.5 m long, it must have pinned ends, and it must support an axial load of 80 kN with a factor of safety of 4.0 against buckling. Determine the required width of the cross section.

A pinned-end column has a cross-sectional area of 2,000 mm2, radius of gyration of 12.616 mm, and length of 720 mm. It is made of 7070-T5 aluminum alloy [E = 70 GPa, ν = 0.34, σPL = 470 MPa]. The column has a solid circular cross section. Determine the critical buckling stress.

Four yellow pine [E = 12.5 GPa] boards are glued together to form a column with outer dimensions of 130 mm by 130 mm and a length of 6.7 m. The thickness of each board is 20 mm. One end of the column is clamped and the other end is guided. Determine the critical buckling load.

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 71 GPa, ν = 0.32], has an inside diameter of 180 mm, and has an outside diameter of 820 mm. The cylinder is subjected to an external pressure of 150 MPa and an axial load of P = 1,500 kN. Determine the axial stress.

A cast iron disk has an inner radius of a = 160 mm and an outer radius of b = 295 mm, with material properties ρ = 7,100 kg/m3, E = 73 GPa, ν = 0.27. Determine the maximum circumferential stress in the disk for a speed of revolution of 5,400 rpm.

A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000220/°C, E = 74 GPa, ν = 0.34], has an inside diameter of 220 mm, and has an outside diameter of 780 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.

Determine the distance e to the shear center O for the beam cross section. Assume the following dimensions and moment of inertia.b = 45 mmh = 65 mmt = 4 mmI = 1,113,000 mm4

A pinned-end column has a cross-sectional area of 2,200 mm2, radius of gyration of 13.231 mm, and length of 760 mm. It is made of 7070-T5 aluminum alloy [E = 71 GPa, ν = 0.34, σPL = 450 MPa]. The column has a solid circular cross section. Determine the critical buckling stress.

If w = 7.25 in., find the moment of inertia Iy about the y axis.

A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000220/°C, E = 70 GPa, ν = 0.32], has an inside diameter of 210 mm, and has an outside diameter of 830 mm. Determine the circumferential stress at r = 385 mm for a steady-state temperature change with the temperature at the inner radius 85°C greater than the temperature at the outer radius.