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A short steel I-beam [E = 200 GPa] has a length of L = 2.50 m, depth of 300 mm, flange width of 131 mm, and moment of inertia of Ix = 97.8 × 106 mm4. The beam rests on a hard rubber elastic foundation whose spring constant is k0 = 0.320 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 0.8556 /m.

A steel I-beam [E = 200 GPa] has a depth of 120 mm, width of 75 mm, moment of inertia of Ix = 5.72 × 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 = 0.260 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 10.44 kN·m.

A 70-kN capacity hoist may be moved along a steel I-beam [E = 200 GPa]. The I-beam has a depth of 157 mm and moment of inertia Ix = 10.1 × 106 mm4. The beam is hung from a series of vertical steel rods [E = 200 GPa] of length 2.80 m, of diameter 20 mm, and spaced 350 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 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.

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 bending moment at point B. Use E = 200 GPa, Ix = 85 × 106 mm4, and k = 10.0 N/mm2. The value of β is 0.6193 /m.

A 80-kN capacity hoist may be moved along a steel I-beam [E = 200 GPa]. The I-beam has a depth of 155 mm and moment of inertia Ix = 11.8 × 106 mm4. The beam is hung from a series of vertical steel rods [E = 200 GPa] of length 3.00 m, of diameter 19 mm, and spaced 400 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 tee shape is subjected to a bending moment of M = 3,240 N·m. Dimensions of the cross section are b1 = 13 mm, d1 = 66 mm, b2 = 44 mm, and d2 = 21 mm. The radial distance from O to A is ri = 85 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 136 mm, width of 75 mm, moment of inertia of Ix = 5.99 × 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 = 0.300 N/mm3. If the beam is subjected to a concentrated load, P = 70 kN, at the center of the beam, determine the bending moment at the center of the beam. The value of β is 1.472 /m.

A cast iron disk has an inner radius of a = 170 mm and an outer radius of b = 300 mm, with material properties ρ = 7,000 kg/m3, E = 71 GPa, ν = 0.27. Determine the maximum circumferential stress in the disk for a speed of revolution of 5,500 rpm.

A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000235/°C, E = 70 GPa, ν = 0.34], has an inside diameter of 200 mm, and has an outside diameter of 840 mm. Determine the circumferential stress at the inner radius for a steady-state temperature change with the temperature at the inner radius 80°C greater than the temperature at the outer radius.