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 absolute maximum shear stress τabs max.εxx = 0.0023εyy = 0.0007εxy = 0.0010

Beam ABC is subjected to moment M = 175 kN·m. Determine the slope at C. Assume L = 7.9 m and EI = 7.3 x 107 N·m2. Only consider the strain energy related to bending moments.

A 0.6-m-long steel [G = 79 GPa] channel is subjected to a torque of 600 N·m. Determine the unit angle of twist of the channel. Assume bf = 100 mm, tf = 11 mm, d = 230 mm, and tw = 8 mm.

The design loads of a member made of a brittle material produce the following nonzero stress components at a critical section in the member. The ultimate strength of the material is 430 MPa. Determine the factor of safety used in the design based on the maximum principal strain criterion. Assume ν = 0.25.σxx = –110 MPaσyy = 50 MPaσxy = 80 MPa

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 = 250 MPa. Determine the factor of safety used in the design, assuming that the material is a von Mises material.σxx = 60 MPaσyy = 100 MPaσxy = 50 MPa

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 = 390 MPa. Determine the factor of safety used in the design, assuming that the material is a von Mises material.σxx = 90 MPaσyy = 90 MPaσxy = 50 MPa

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 = 65 mm, E = 210 GPa, and G = 80 GPa.

The design loads of a member made of a brittle material produce the following nonzero stress components at a critical section in the member. The ultimate strength of the material is 420 MPa. Determine the factor of safety used in the design based on the maximum principal stress criterion.σxx = –50 MPaσyy = 110 MPaσxy = 70 MPa

A simply supported timber beam with length L = 6 m carries a uniformly distributed load w = 13 kN/m. Determine the magnitude of the maximum bending stress that occurs in the beam at any location within the 6-m span length.

The strain rosette shown in the figure was used to obtain the following normal strain data at a point on the free surface of a machine part: εa = 538 με, εb = –706 με, and εc = –390 με. Poisson’s ratio for the material is ν = 0.30. Determine the strain component εy at the point.