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.

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 = 11.4 × 106 mm4. The beam is hung from a series of vertical steel rods [E = 200 GPa] of length 3.00 m, of diameter 17 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.

A steel I-beam [E = 200 GPa] has a depth of 137 mm, width of 71 mm, moment of inertia of Ix = 4.50 × 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 = 40 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.

An infinite beam on an elastic foundation is subjected to a triangular load w = 19 N/mm over the segment L’ = 4 m. Determine the deflection at point B. Use E = 200 GPa, Ix = 85 × 106 mm4, and k = 6.0 N/mm2. The value of β is 0.5450 /m.

The curved tee shape is subjected to a bending moment of M = 3,180 N·m. Dimensions of the cross section are b1 = 13 mm, d1 = 65 mm, b2 = 49 mm, and d2 = 19 mm. The radial distance from O to A is ri = 88 mm. Determine the circumferential stress σθθ at point B.

For a beam with the cross-section shown, find the distance from the bottom surface of the beam to the centroid. Let w = 1.55 in. and h = 3.00 in.

The curved tee shape is subjected to a bending moment of M = 3,460 N·m. Dimensions of the cross section are b1 = 12 mm, d1 = 67 mm, b2 = 50 mm, and d2 = 23 mm. The radial distance from O to A is ri = 96 mm. Determine the circumferential stress σθθ at point B.

A hollow rectangular tube with outside cross-sectional dimensions of 85 mm and 105 mm and a uniform wall thickness of 10 mm is used as a pinned-end column. It is made of structural steel [E = 205 GPa, ν = 0.28, Y = 260 MPa] and has a length of 5 m. Determine the critical buckling load.

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 = 100 mm from the center of the beam. The value of β is 1.616 /m.