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 steel I-beam [E = 200 GPa] has a depth of 132 mm, width of 79 mm, moment of inertia of Ix = 5.93 × 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 = 0.280 N/mm3. If the beam is subjected to a concentrated load, P = 40 kN, at the center of the beam, determine the deflection at the center of the beam. The value of β is 1.469 /m.

The curved flanged shape is subjected to a bending moment of M = 3,800 N·m. Dimensions of the cross section are b1 = 74 mm, d1 = 19 mm, b2 = 19 mm, d2 = 58 mm, b3 = 31 mm, and d3 = 19 mm. The radial distance from O to A is ri = 170 mm. Determine the value of Am for the cross section.

The curved bar has a trapezoidal cross section with dimensions b1 = 70 mm, b2 = 37 mm, and d = 114 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 short steel I-beam [E = 200 GPa] has a length of L = 3.00 m, depth of 315 mm, flange width of 132 mm, and moment of inertia of Ix = 95.9 × 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 = 280 kN at its center, determine the value of β.

A steel I-beam [E = 200 GPa] has a depth of 122 mm, width of 81 mm, moment of inertia of Ix = 5.29 × 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 = 0.220 N/mm3. If the beam is subjected to a concentrated load, P = 40 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 6.981 kN·m.

A short steel I-beam [E = 200 GPa] has a length of L = 3.00 m, depth of 280 mm, flange width of 122 mm, and moment of inertia of Ix = 91.7 × 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 = 250 kN at its center, determine the value of β.

The curved tee shape is subjected to a bending moment of M = 3,150 N·m. Dimensions of the cross section are b1 = 15 mm, d1 = 64 mm, b2 = 48 mm, and d2 = 23 mm. The radial distance from O to A is ri = 80 mm. Determine the circumferential stress σθθ at point A.

A short steel I-beam [E = 200 GPa] has a length of L = 3.00 m, depth of 315 mm, flange width of 135 mm, and moment of inertia of Ix = 97.1 × 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 value of β.

A rectangular steel plate [E = 200 GPa, ν = 0.28, and Y = 240 MPa] has a width of 0.7 m, a length of 1.3 m, and a thickness of 15 mm. All four edges are simply supported. The plate is subjected to a uniform pressure of 200 kPa. Considering the effect of Poisson’s ratio, determine the maximum bending moment per unit width in the plate.