Beers $7\mathrm{.}81($Failure Theory, DE$)$

The state of plane stress shown occurs in a machine component made of a steel with ${}_Y=325$MPa. Using the maximum$-$distortion$-$energy criterion, determine whether yield will occur when $($a$){}_0=200$MPa, $($b$){}_0=240$MPa, $($c$){}_0=280$MPa. If yield does not occur, determine the corresponding factor of safety.