Four yellow pine [E = 12.2 GPa] boards are glued together to form a column with outer dimensions of 140 mm by 140 mm and a length of 7.9 m. The thickness of each board is 20 mm. One end of the column is clamped and the other end is clamped. Determine the critical buckling load.

The curved bar has a triangular cross section with dimensions b = 1.2 in. and d = 0.9 in. The inner radius of the curved bar is ri = 4.5 in. Determine the value of Am for the cross section.

A 14-ft-long simply supported timber beam carries vertical load P = 16.7 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.

A hollow rectangular tube with outside cross-sectional dimensions of 90 mm and 100 mm and a uniform wall thickness of 10 mm is used as a pinned-end column. It is made of structural steel [E = 195 GPa, ν = 0.28, Y = 260 MPa] and has a length of 6 m. Determine the critical buckling load.

A short steel I-beam [E = 200 GPa] has a length of L = 4.00 m, depth of 320 mm, flange width of 127 mm, and moment of inertia of Ix = 92.5 × 106 mm4. The beam rests on a hard rubber elastic foundation whose spring constant is k0 = 0.270 N/mm3. If the beam is subjected to a concentrated load P = 250 kN at its center, determine the maximum bending moment. The value of β is 0.8251 /m.

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 73 GPa, ν = 0.30], has an inside diameter of 180 mm, and has an outside diameter of 760 mm. The cylinder is subjected to an external pressure of 130 MPa and an axial load of P = 2,100 kN. Determine the axial stress.

The curved tee shape is subjected to a bending moment of M = 3,290 N·m. Dimensions of the cross section are b1 = 16 mm, d1 = 67 mm, b2 = 49 mm, and d2 = 19 mm. The radial distance from O to A is ri = 85 mm. Determine the circumferential stress σθθ at point B.

The design of a white oak [E = 12.6 GPa, σPL = 22 MPa] column of square cross section has the following requirements. It must be 9.0 m long, it must have pinned ends, and it must support an axial load of 90 kN with a factor of safety of 2.0 against buckling. Determine the required width of the cross section.

The curved tee shape is subjected to a bending moment of M = 3,090 N·m. Dimensions of the cross section are b1 = 14 mm, d1 = 61 mm, b2 = 46 mm, and d2 = 23 mm. The radial distance from O to A is ri = 83 mm. Determine the value of Am’ used for the radial stress σrr at the intersection of the flange and web.

The curved tee shape is subjected to a bending moment of M = 3,000 N·m. Dimensions of the cross section are b1 = 12 mm, d1 = 65 mm, b2 = 47 mm, and d2 = 20 mm. The radial distance from O to A is ri = 88 mm. Determine the circumferential stress σθθ at point B.