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Determine the total strain energy U in the rectangular beam due to both bending moment and shear force. Assume w = 23 kN/m, L = 0.65 m, b = 25 mm, h = 65 mm, E = 190 GPa, and G = 78 GPa.

A 0.5-m-long steel [G = 74 GPa] channel is subjected to a torque of 700 N·m. Determine the unit angle of twist of the channel. Assume bf = 110 mm, tf = 9 mm, d = 210 mm, and tw = 5 mm.

Determine the distance e to the shear center O for the beam cross section. Assume the following dimensions and moment of inertia.a = 65 mmb = 40 mmc = 85 mmt = 4 mmI = 2,437,000 mm4

A thin-wall brass [G = 24.1 GPa] tube with an equilateral triangular cross section is subjected to a torque of 23 N·m. The mean length of one side of the triangle is 24 mm, and the wall thickness is 3.0 mm. Determine the maximum shear stress.

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 72 GPa, ν = 0.30], has an inside diameter of 200 mm, and has an outside diameter of 830 mm. The cylinder is subjected to an internal pressure of 140 MPa and an external pressure of 150 MPa. Determine the radial stress at r = 310 mm.

The design of a white oak [E = 12.5 GPa, σPL = 23 MPa] column of square cross section has the following requirements. It must be 8.5 m long, it must have pinned ends, and it must support an axial load of 80 kN with a factor of safety of 3.0 against buckling. Determine the required width of the cross section.

The design of a white oak [E = 12.1 GPa, σPL = 23 MPa] column of square cross section has the following requirements. It must be 8.5 m long, it must have pinned ends, and it must support an axial load of 90 kN with a factor of safety of 3.0 against buckling. Determine the required width of the cross section.

A 14-ft-long simply supported timber beam carries load P = 3.8 kip at midspan. Load P and the ground reactions all lie in a plane that forms an angle θ = 24° counterclockwise from the y axis. Determine the magnitude of the maximum bending stress in the beam.

Structure ABC is subjected to load P = 18 kN. Determine the vertical reaction force at B. Assume L1 = 2.9 m, L2 = 2.3 m, and EI = 6.5 x 107 N·m2. Only consider the strain energy related to bending moments.

A brittle material has an ultimate strength of 470 MPa. A member made of this material is subjected to its design loads. At the critical point in the member, the nonzero stress components are as follows. Determine the factor of safety used in the design based on the maximum principal stress criterion.σxx = 100 MPaσyy = 70 MPaσxy = 90 MPa