Consider a rectangular steel [G = 79 GPa] shaft with a cross section of 90 mm by 225 mm and a length of 790 mm. Determine the maximum torque that can be applied to the shaft for an allowable shear stress of 23 MPa.

Beam ABC is subjected to moment M = 250 kN·m. Determine the slope at C. Assume L = 7.8 m and EI = 7.2 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 = 21 kN/m, L = 0.60 m, b = 40 mm, h = 70 mm, E = 180 GPa, and G = 77 GPa.

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 machine part made of ASTM A36 structural steel [E = 200 GPa, ν = 0.29] is subjected to a state of plane strain (εzz = εzx = εzy = 0). Determine σzz for the following stresses.σxx = 50 MPaσyy = –55 MPaσxy = 75 MPa

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 point in a structural-steel member, the stresses are σxx = 65 MPa, σyy = 0 MPa, σzz = 40 MPa, σxy = 0 MPa, σxz = 40 MPa, and σyz = 0 MPa. Determine the largest principal stress σ1.

A 0.916-in.-diameter automotive sway bar failed when the shear stress reached 86 ksi on the outer surface. Assuming the sway bar did not yield prior to failure, determine the torque that caused this failure.

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 = 0.0034εyy = 0.0005εxy = 0.0005

The nonzero strain components at a critical point in a machine component made of AISI-C 1018 cold drawn [E = 200 GPa, ν = 0.29] are measured on a free surface as follows. Determine the corresponding octahedral shear stress τoct.εxx = 0.0028εyy = 0.0006εxy = 0.0010