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At a point in a structural-steel member, the stresses are σxx = 80 MPa, σyy = 70 MPa, σzz = 60 MPa, σxy = 90 MPa, σxz = 10 MPa, and σyz = 20 MPa. Determine the third stress invariant I3.

The stresses shown in the figure act at a point in a stressed body. If τo = 134 MPa in the directions shown and θ = 34°, determine shear stress τAA at this point.

At a point in a structural-steel member, the principal stresses are σ1 = 138 MPa, σ2 = 2.9 MPa, and σ3 = –50.9 MPa. Determine the absolute maximum shear stress.

At a point in a structural-steel member, the stresses are σxx = 10 MPa, σyy = 40 MPa, σzz = 30 MPa, σxy = 70 MPa, σxz = 10 MPa, and σyz = 30 MPa. Determine the third stress invariant I3.

The nonzero strain components at a critical point in a machine component made of 6061-T6 aluminum [E = 69 GPa, ν = 0.33] are measured on a free surface as follows. Determine the corresponding stress σyy.εxx = 0.0035εyy = 0.0010εxy = 0.0012

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 450 MPa. Determine the factor of safety used in the design based on the maximum principal stress criterion.σxx = –90 MPaσyy = 70 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 = 370 MPa. Determine the factor of safety used in the design, assuming that the material is a Tresca material.σxx = 90 MPaσyy = 60 MPaσxy = 100 MPa

The stresses shown in the figure act at a point in a stressed body. If τo = 83 MPa in the directions shown and θ = 38°, determine shear stress τAA at this point.

A simply supported timber beam with length L = 3 m carries a uniformly distributed load w = 10 kN/m. Determine the magnitude of the maximum bending stress that occurs in the beam at any location within the 3-m span length.

At a point in a structural-steel member, the stresses are σxx = 40 MPa, σyy = 0 MPa, σzz = 20 MPa, σxy = 0 MPa, σxz = 40 MPa, and σyz = 0 MPa. Determine the largest principal stress σ1.