A material has a minimum yield strength in tension and compression of S$\_($y$)=700$MPa.

Determine whether or not it fails under the following loading condition with a factor of

safety of n$=1\mathrm{.}1.$

Use:

a$-$ Maximum shear stress theory $($MSS$)$

b$-$ Maximum distortion energy theory $($DE$)$

$\backslash$sigma $\_(1)=200$MPa,$\backslash$sigma $\_(2)=-200$MPa and $\backslash$sigma $\_(3)=-500$MPa