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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.

An aluminum bar with a 1.50-in. gage length, 0.130-in. width, and 0.100-in. thickness is loaded in tension. At the proportional limit, a load of 700 lb elongates the gage length by 0.00723 in. and reduces the width by 0.00019 in. Determine the modulus of elasticity.

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 530 MPa. Determine the factor of safety used in the design based on the maximum principal strain criterion. Assume ν = 0.17.σxx = –120 MPaσyy = 70 MPaσxy = 60 MPa