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The design of a white oak [E = 12.5 GPa, σPL = 27 MPa] column of square cross section has the following requirements. It must be 7.5 m long, it must have pinned ends, and it must support an axial load of 80 kN with a factor of safety of 5.0 against buckling. Determine the required width of the cross section.

A beam with hollow, rectangular, symmetric cross section has a yield stress of Y = 290 MPa. Determine the fully plastic moment MP. Assume b = 180 mm, t = 15 mm, h1 = 30 mm, and h2 = 60 mm.

At a critical point in a machine part, the nonzero stress components are as follows. The yield strength of the material is Y = 320 MPa. Determine the factor of safety used in the design based on the maximum shear-stress criterion.σxx = 70 MPaσyy = 50 MPaσxy = 50 MPa

Consider a rectangular steel [G = 78 GPa] shaft with a cross section of 100 mm by 250 mm and a length of 570 mm. Determine the maximum torque that can be applied to the shaft for an allowable shear stress of 18 MPa.

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 = 45 mmc = 90 mmt = 6 mmI = 4,498,000 mm4

Beam ABC is subjected to moment M = 210 kN·m. Determine the slope at C. Assume L = 8.9 m and EI = 7.6 x 107 N·m2. Only consider the strain energy related to bending moments.

A thin-wall brass [G = 24.4 GPa] tube with an equilateral triangular cross section is subjected to a torque of 30 N·m. The mean length of one side of the triangle is 26 mm, and the wall thickness is 2.0 mm. Determine the maximum shear stress.

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