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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 = 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

For a beam with the cross-section shown (w = 15.0 in. and h = 21.5 in.), find the distance from the bottom surface of the beam to the centroid.

Consider a point on the free surface of a structure made of AISI-C 1040 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 = 170 MPaσyy = –80 MPaσxy = –180 MPa

The nonzero strain components at a critical point in a machine component made of 2024-T4 aluminum [E = 74.5 GPa, ν = 0.33] are measured on a free surface as follows. Determine the corresponding stress σyy.εxx = 0.0020εyy = 0.0008εxy = 0.0011