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Determine the total strain energy U in the rectangular beam due to both bending moment and shear force. Assume w = 24 kN/m, L = 0.60 m, b = 40 mm, h = 70 mm, E = 190 GPa, and G = 79 GPa.

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 73 GPa, ν = 0.33], has an inside diameter of 190 mm, and has an outside diameter of 760 mm. The cylinder is subjected to an internal pressure of 190 MPa and an external pressure of 130 MPa. Determine the circumferential stress at the outer radius.

An elliptical shaft has major and minor dimensions of 44 mm and 32 mm, respectively. The allowable shear stress of the material is 150 MPa. Determine the maximum torque that can be applied using a factor of safety of 1.5.

Structure ABC is subjected to load P = 14 kN. Determine the vertical reaction force at B. Assume L1 = 2.8 m, L2 = 2 m, and EI = 7.6 x 107 N·m2. Only consider the strain energy related to bending moments.

A 14-ft-long simply supported timber beam carries load P = 2.0 kip at midspan. Load P and the ground reactions all lie in a plane that forms an angle θ = 22° counterclockwise from the y axis. Determine the magnitude of the maximum bending stress in the beam.

For a beam with the cross-section shown (w = 15.0 in. and h = 19.0 in.), find the distance from the bottom surface of the beam to the centroid.

The nonzero strain components at a critical point in a machine component made of 2024-T4 aluminum [E = 74.5 GPa, ν = 0.33] are measured on a free surface as follows. Determine the corresponding stress σyy.εxx = 0.0036εyy = 0.0008εxy = 0.0014

A 14-ft-long simply supported timber beam carries load P = 2.8 kip at midspan. Load P and the ground reactions all lie in a plane that forms an angle θ = 25° counterclockwise from the y axis. Determine the magnitude of the maximum bending stress in the beam.

A member is subjected to its design loads. The nonzero stress components at the points of maximum stress are as follows. The yield stress of the material is Y = 320 MPa. Determine the factor of safety used in the design, assuming that the material is a von Mises material.σxx = 70 MPaσyy = 50 MPaσxy = 80 MPa

For a beam with the cross-section shown, find the distance from the bottom surface of the beam to the centroid. Let w = 1.60 in. and h = 2.95 in.