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 member has a rectangular cross section with dimensions of b = 1.6 in. and d = 5.3 in. The inside radius of the curved bar is ri = 3.6 in. A load of P is applied at a distance of a = 8 in. from the center of curvature O. For an applied load of P = 5.6 kips, determine the magnitude of the bending moment M that occurs at the centroid of the cross section between points A and B.

The curved bar has a trapezoidal cross section with dimensions b1 = 70 mm, b2 = 40 mm, and d = 100 mm. The radial distance from O to A is ri = 145 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 116 mm, width of 78 mm, moment of inertia of Ix = 5.48 × 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 maximum flexural stress at the center of the beam. The bending moment at the center of the beam is 11.51 kN·m.

The curved tee shape is subjected to a bending moment of M = 3,050 N·m. Dimensions of the cross section are b1 = 16 mm, d1 = 66 mm, b2 = 50 mm, and d2 = 19 mm. The radial distance from O to A is ri = 93 mm. Determine the circumferential stress σθθ at point A.

A steel I-beam [E = 200 GPa] has a depth of 143 mm, width of 82 mm, moment of inertia of Ix = 5.11 × 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 = 70 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 11.81 kN·m.

The curved member has a rectangular cross section with dimensions of b = 1.2 in. and d = 5.4 in. The inside radius of the curved bar is ri = 3.5 in. A load of P is applied at a distance of a = 10 in. from the center of curvature O. For an applied load of P = 6.5 kips, determine the magnitude of the bending moment M that occurs at the centroid of the cross section between points A and B.

The curved flanged shape is subjected to a bending moment of M = 3,600 N·m. Dimensions of the cross section are b1 = 71 mm, d1 = 16 mm, b2 = 16 mm, d2 = 61 mm, b3 = 32 mm, and d3 = 16 mm. The radial distance from O to A is ri = 185 mm. Determine the value of Am for the cross section.

A steel I-beam [E = 200 GPa] has a depth of 139 mm, width of 78 mm, moment of inertia of Ix = 4.02 × 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 = 0.320 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 1.669 /m.

The curved flanged shape is subjected to a bending moment of M = 4,100 N·m. Dimensions of the cross section are b1 = 66 mm, d1 = 19 mm, b2 = 19 mm, d2 = 58 mm, b3 = 33 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.