Help answer this with sketchWhat is the shear yield limit$,S_{xy}$ of a steel, determined from a pure shear$-$stress state, $,$ in

terms of the tensile yield strength, $S_y,$ based on the

a$)$ Maximum shear stress theory $($MSST$),$ and the

b$)$ Distortion energy theory $($DET$).$ Then

c$)$ Mark your results, such as the values and locations, on the safe$-$region diagrams shown

below for ${}_A$ and ${}_B,$ the non$-$zero principal stresses.

d$)$ If the factor of safety based on the MSST is $n_S=1\mathrm{.}1,$ what is the factor of safety, $n_D,$

based on the DET for the same stress state and the same material? What is the ratio of the

two $\frac{n_D}{n_S}?$

e$)$ Knowing that the endurance limit for pure bending stress $$ is $S_e=0\mathrm{.}5S_u,$ with $S_u$ the

ultimate tensile strength, prove that the endurance limit for pure torsional shear stress $$ is

$S_{se}=0\mathrm{.}29S_u$ by means of the DET.