You have designed a ductile hot-rolled steel bar that has yield strength in tension and compression of 400 MPa. Using the distortion energy theory. Maximum shear stress theory, and Maximum normal stress theory define the Factor of safety for the following three scenarios.

Scenario one: Plane stress where the principle stresses are σA=100 MPa and σB=50 MPa.
Scenario two: Plane stress where the principle stresses are σA=-50 MPa and σB=50 MPa.
Scenario three: The dimensional stress where σx=150 MPa and σy=0 MPa and Txx=100 MPa and the other stresses are zero.