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An infinite beam on an elastic foundation is subjected to a triangular load w = 12 N/mm over the segment L’ = 4 m. Determine the bending moment at point B. Use E = 200 GPa, Ix = 75 × 106 mm4, and k = 9.0 N/mm2. The value of β is 0.6223 /m.

A steel I-beam [E = 200 GPa] has a depth of 130 mm, width of 76 mm, moment of inertia of Ix = 5.78 × 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. Determine the value of β.

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 Bβz at a distance of z = 40 mm from the center of the beam. The value of β is 1.580 /m.

The curved tee shape is subjected to a bending moment of M = 3,250 N·m. Dimensions of the cross section are b1 = 13 mm, d1 = 68 mm, b2 = 44 mm, and d2 = 21 mm. The radial distance from O to A is ri = 84 mm. Determine the circumferential stress σθθ at point A.

A steel I-beam [E = 200 GPa] has a depth of 115 mm, width of 78 mm, moment of inertia of Ix = 5.76 × 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 = 60 kN, at the center of the beam, determine the bending moment at the center of the beam. The value of β is 1.475 /m.

The curved tee shape is subjected to a bending moment of M = 3,500 N·m. Dimensions of the cross section are b1 = 12 mm, d1 = 62 mm, b2 = 46 mm, and d2 = 19 mm. The radial distance from O to A is ri = 82 mm. Determine the value of Am’ used for the radial stress σrr at the intersection of the flange and web.

A solid bar with cross-sectional dimensions of 95 mm by 95 mm is used as a pinned-end column. It is made of structural steel [E = 190 GPa, ν = 0.31, Y = 270 MPa] and has a length of 5.0 m. Determine the slenderness ratio.

The curved bar has a triangular cross section with dimensions b = 1.3 in. and d = 0.9 in. The inner radius of the curved bar is ri = 4.8 in. Determine the value of Am for the cross section.

A 60-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 = 11.5 × 106 mm4. The beam is hung from a series of vertical steel rods [E = 200 GPa] of length 2.40 m, of diameter 18 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 member has a rectangular cross section with dimensions of b = 1.4 in. and d = 5.3 in. The inside radius of the curved bar is ri = 3.7 in. A load of P is applied at a distance of a = 9 in. from the center of curvature O. For an applied load of P = 5.2 kips, determine the magnitude of the bending moment M that occurs at the centroid of the cross section between points A and B.