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.

A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000230/°C, E = 71 GPa, ν = 0.32], has an inside diameter of 180 mm, and has an outside diameter of 840 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.

A cast iron disk has an inner radius of a = 130 mm and an outer radius of b = 295 mm, with material properties ρ = 7,600 kg/m3, E = 73 GPa, ν = 0.23. Determine the maximum circumferential stress in the disk for a speed of revolution of 5,200 rpm.

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.

The curved bar has a triangular cross section with dimensions b = 1.3 in. and d = 0.5 in. The inner radius of the curved bar is ri = 4.5 in. Determine the value of Am for the cross section.

A pinned-end column has a cross-sectional area of 1,800 mm2, radius of gyration of 11.968 mm, and length of 740 mm. It is made of 7070-T5 aluminum alloy [E = 73 GPa, ν = 0.34, σPL = 500 MPa]. The column has a solid circular cross section. Determine the critical buckling stress.

A 14-ft-long simply supported timber beam carries vertical load P = 16.8 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.

Beam ABC is subjected to moment M = 210 kN·m. Determine the slope at C. Assume L = 8.0 m and EI = 7.2 x 107 N·m2. Only consider the strain energy related to bending moments.

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 = 30 mm from the center of the beam. The value of β is 1.470 /m.