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A pinned-end column has a cross-sectional area of 2,200 mm2, radius of gyration of 13.231 mm, and length of 800 mm. It is made of 7070-T5 aluminum alloy [E = 71 GPa, ν = 0.32, σPL = 450 MPa]. The column has a solid circular cross section. Determine the critical buckling stress.

A 80-kN capacity hoist may be moved along a steel I-beam [E = 200 GPa]. The I-beam has a depth of 141 mm and moment of inertia Ix = 11.6 × 106 mm4. The beam is hung from a series of vertical steel rods [E = 200 GPa] of length 2.00 m, of diameter 18 mm, and spaced 300 mm center to center. For capacity load at the center of the beam, located under one of the rods, determine the value of β.

The curved bar has a trapezoidal cross section with dimensions b1 = 73 mm, b2 = 33 mm, and d = 103 mm. The radial distance from O to A is ri = 140 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 = 700 MPa. The inside diameter of the cylinder is 80 mm, and the outside diameter is 180 mm. It is subjected to an internal pressure of p1 = 85 MPa. Determine the factor of safety SF based on the maximum shear-stress criterion of failure.

For the shape below, assume the following dimensions:b = 90 mmd = 150 mmt = 6 mmThe vertical distance from point H to the centroid is 111.45 mm. The horizontal distance from point H to the centroid is 26.774 mm. Determine the product of inertia Iyz with respect to the y and z centroidal axes.

An infinite beam on an elastic foundation is subjected to a triangular load w = 24 N/mm over the segment L’ = 3 m. Determine the deflection at point B. Use E = 200 GPa, Ix = 80 × 106 mm4, and k = 6.0 N/mm2. The value of β is 0.5533 /m.

A short steel I-beam [E = 200 GPa] has a length of L = 3.00 m, depth of 290 mm, flange width of 145 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 = 0.330 N/mm3. If the beam is subjected to a concentrated load P = 280 kN at its center, determine the maximum bending moment. The value of β is 0.8967 /m.

The curved tee shape is subjected to a bending moment of M = 3,640 N·m. Dimensions of the cross section are b1 = 16 mm, d1 = 61 mm, b2 = 43 mm, and d2 = 21 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.

A steel I-beam [E = 200 GPa] has a depth of 120 mm, width of 73 mm, moment of inertia of Ix = 4.03 × 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 = 0.240 N/mm3. If the beam is subjected to a concentrated load, P = 60 kN, at the center of the beam, determine the deflection at the center of the beam. The value of β is 1.527 /m.

A steel I-beam [E = 200 GPa] has a depth of 129 mm, width of 75 mm, moment of inertia of Ix = 4.97 × 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 = 0.290 N/mm3. If the beam is subjected to a concentrated load, P = 60 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 9.808 kN·m.