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At a critical point in a machine part, the nonzero stress components are as follows. The yield strength of the material is Y = 275 MPa. Determine the factor of safety used in the design based on the octahedral shear-stress criterion.σxx = 70 MPaσyy = 100 MPaσxy = 60 MPa

At a point in a structural-steel member, the stresses are σxx = 60 MPa, σyy = 80 MPa, σzz = 10 MPa, σxy = 60 MPa, σxz = 30 MPa, and σyz = 90 MPa. Determine the third stress invariant I3.

At a point subjected to plane stress on the surface of a gusset plate, the stresses are σx = –40 MPa, σy = 60 MPa, and τxy = –50 MPa. Determine principal stress σ1 at the point.

Consider a point on the free surface of a structure made of AISI-C 1030 normalized steel [E = 200 GPa, ν = 0.29] that is tangent to the (x,y) plane. Determine the smallest principal strain ε3 for the following stresses.σxx = 230 MPaσyy = –110 MPaσxy = –200 MPa

A simply supported timber beam with length L = 6 m carries a uniformly distributed load w = 15 kN/m. Determine the magnitude of the maximum bending stress that occurs in the beam at any location within the 6-m span length.

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 = 275 MPa. Determine the factor of safety used in the design, assuming that the material is a Tresca material.σxx = 60 MPaσyy = 60 MPaσxy = 50 MPa

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 470 MPa. Determine the factor of safety used in the design based on the maximum principal strain criterion. Assume ν = 0.20.σxx = –60 MPaσyy = 80 MPaσxy = 80 MPa

A bronze alloy specimen having a diameter of 12.8 mm and a gage length of 50 mm was tested to fracture. Stress and strain data obtained during the test are shown. Note that the “Lower scale” is a zoomed-in portion of the Upper scale. Determine the ultimate strength.

At a point subjected to plane stress on the surface of a structural-steel member, the stresses are σx = 12 MPa, σy = 69 MPa, and τxy = –100 MPa. Determine the center σcenter of the corresponding in-plane Mohr’s circle.

A simply supported timber beam with length L = 6 m carries a uniformly distributed load w = 14 kN/m. Determine the magnitude of the maximum bending stress that occurs in the beam at any location within the 6-m span length.