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The nonzero strain components at a critical point in a machine component made of ASTM A36 structural steel [E = 200 GPa, ν = 0.29] are measured on a free surface as follows. Determine the corresponding stress σyy.εxx = 0.0024εyy = 0.0005εxy = 0.0006

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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 = 320 MPa. Determine the factor of safety used in the design based on the maximum shear-stress criterion.σxx = 80 MPaσyy = 60 MPaσxy = 50 MPa

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 = 552 με, εb = –704 με, and εc = –306 με. Poisson’s ratio for the material is ν = 0.30. Determine the strain component εy at the point.

A steel rod with a 1.75-in. gage length and a 0.160-in. diameter is loaded in tension. At the proportional limit, a load of 640 lb elongates the gage length by 0.00196 in. and reduces the diameter by 0.000047 in. Determine the modulus of elasticity.

At a point subjected to plane stress on the surface of a structural-steel member, the stresses are σx = 26 MPa, σy = 85 MPa, and τxy = –25 MPa. Determine the center σcenter of the corresponding in-plane Mohr’s circle.

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.