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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

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 = 90 MPaσyy = 80 MPaσxy = 70 MPa

At a point in a structural-steel member, the principal stresses are σ1 = 142 MPa, σ2 = 44.1 MPa, and σ3 = –26.1 MPa. Determine the absolute maximum shear stress.

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 shear stress τxy.εxx = 0.0040εyy = 0.0006εxy = 0.0008

At a point in a structural-steel member, the stresses are σxx = 20 MPa, σyy = 50 MPa, σzz = 80 MPa, σxy = 10 MPa, σxz = 70 MPa, and σyz = 60 MPa. Determine the third stress invariant I3.

A steel rod with a 1.25-in. gage length and a 0.165-in. diameter is loaded in tension. At the proportional limit, a load of 1,200 lb elongates the gage length by 0.00212 in. and reduces the diameter by 0.000076 in. Determine the modulus of elasticity.

An aluminum bar with a 1.75-in. gage length, 0.240-in. width, and 0.095-in. thickness is loaded in tension. At the proportional limit, a load of 1,000 lb elongates the gage length by 0.00926 in. and reduces the width by 0.00037 in. Determine the modulus of elasticity.

The nonzero strain components at a critical point in a machine component made of AISI-C 1040 normalized steel [E = 200 GPa, ν = 0.29] are measured on a free surface as follows. Determine the corresponding shear stress τxy.εxx = 0.0021εyy = 0.0006εxy = 0.0007