A hollow rectangular tube with outside cross-sectional dimensions of 90 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 = 195 GPa, ν = 0.27, Y = 260 MPa] and has a length of 5 m. Determine the critical buckling load.

Consider a rectangular steel [G = 73 GPa] shaft with a cross section of 90 mm by 225 mm and a length of 650 mm. Determine the maximum torque that can be applied to the shaft for an allowable shear stress of 22 MPa.

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 = 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.

Determine the total strain energy U in the rectangular beam due to both bending moment and shear force. Assume w = 24 kN/m, L = 0.70 m, b = 20 mm, h = 70 mm, E = 210 GPa, and G = 78 GPa.

Beam ABC is subjected to moment M = 240 kN·m. Determine the slope at C. Assume L = 8.8 m and EI = 7.1 x 107 N·m2. Only consider the strain energy related to bending moments.

Structure ABC is subjected to load P = 10 kN. Determine the vertical reaction force at B. Assume L1 = 2.2 m, L2 = 1.8 m, and EI = 7.5 x 107 N·m2. Only consider the strain energy related to bending moments.

The nonzero strain components at a critical point in a machine component made of 7075-T6 aluminum [E = 72 GPa, ν = 0.33] are measured on a free surface as follows. Determine the corresponding stress σyy.εxx = 0.0022εyy = 0.0006εxy = 0.0013

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.

If w = 5.75 in., find the moment of inertia Iz about the z axis. The centroid of the section is located 2.6520 in. above the bottom surface of the beam.