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If w = 9.75 in., find the moment of inertia Iz about the z axis. The centroid of the section is located 2.9142 in. above the bottom surface of the beam.

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?

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.

A pinned-end column has a cross-sectional area of 2,200 mm2, radius of gyration of 13.231 mm, and length of 720 mm. It is made of 7070-T5 aluminum alloy [E = 73 GPa, ν = 0.32, σPL = 520 MPa]. The column has a solid circular cross section. Determine the critical buckling stress.

The curved tee shape is subjected to a bending moment of M = 3,000 N·m. Dimensions of the cross section are b1 = 13 mm, d1 = 66 mm, b2 = 47 mm, and d2 = 22 mm. The radial distance from O to A is ri = 78 mm. Determine the value of Am’ used for the radial stress σrr at the intersection of the flange and web.

Four yellow pine [E = 12.2 GPa] boards are glued together to form a column with outer dimensions of 170 mm by 170 mm and a length of 6.2 m. The thickness of each board is 20 mm. One end of the column is clamped and the other end is free. Determine the critical buckling load.

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 = 100 mm from the center of the beam. The value of β is 1.616 /m.

A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000230/°C, E = 72 GPa, ν = 0.33], has an inside diameter of 220 mm, and has an outside diameter of 770 mm. Determine the circumferential stress at the outer radius for a steady-state temperature change with the temperature at the inner radius 110°C greater than the temperature at the outer radius.

Which point experiences the largest magnitude of horizontal shear stress?

Four yellow pine [E = 12.1 GPa] boards are glued together to form a column with outer dimensions of 180 mm by 180 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 free. Determine the critical buckling load.