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Required information

Problem $05\mathrm{.}001-$ Determination of factor of safety using maximum$-$shear$-$stress and distortion$-$energy theory

A ductile hot$-$rolled steel bar has a minimum yield strength in tension and compression of $350$ MPa $.$ Using the distortion$-$energy and maximum$-$shear$-$stress theories, determine the factors of safety for the following plane stress states.

Problem $05\mathrm{.}001.$c $-$ case of extreme value shear stress with one zero value plane stress

${}_x=96$MPa, and $I_{xy}=-71$MPa

The factor of safety from the maximum$-$shear$-$stress theory is $,$ and the factor of safety from the distortion$-$energy theory is