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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.

If w = 5.75 in., find the moment of inertia Iz about the z axis. The centroid of the section is located 2.6520 in. above the bottom surface of the beam.

A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000220/°C, E = 70 GPa, ν = 0.30], has an inside diameter of 220 mm, and has an outside diameter of 790 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.

The design of a white oak [E = 12.4 GPa, σPL = 30 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 90 kN with a factor of safety of 2.0 against buckling. Determine the required width of the cross section.

Structure ABC is subjected to load P = 17 kN. Determine the vertical reaction force at B. Assume L1 = 2.2 m, L2 = 1.6 m, and EI = 7.6 x 107 N·m2. Only consider the strain energy related to bending moments.

A hollow rectangular tube with outside cross-sectional dimensions of 85 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 = 0.30, Y = 260 MPa] and has a length of 6 m. Determine the critical buckling load.

The curved bar has a trapezoidal cross section with dimensions b1 = 73 mm, b2 = 35 mm, and d = 113 mm. The radial distance from O to A is ri = 130 mm. Determine the distance R from the center of curvature O to the centroid of the cross section.

A closed cylinder is made of a ductile steel that has a yield stress Y = 680 MPa. The inside diameter of the cylinder is 70 mm, and the outside diameter is 120 mm. It is subjected to an internal pressure of p1 = 100 MPa. Determine the factor of safety SF based on the maximum shear-stress criterion of failure.

An automotive lug nut was torqued too much and broke the wheel stud that it was attached to. The stud had a diameter of 0.424 in. and an allowable shear stress of 75 ksi. Ignoring any stress concentrations, determine the failure torque.

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.