Problem $5-19$

$5-19$ A britule material has the properties $S_{ar}=210$MPa and $S_{mc}=630$MPa. Using the britte Coulomb$-$Mohr and modified$-$Mohr theories, determine the factor of safety for the following states of plane stress.

$($a$){}_x=175$MPa,${}_y=105$MPa

$($b$){}_x=105$MPa,${}_y=-105$MPa

$($c$){}_x=140$MPa,${}_{xy}=-70$MPa

$($d$){}_x=-105$MPa,${}_y=-70$MPA,${}_{xy}=-105$MPa

$($e$){}_x=-84$MPa,${}_{xy}=-105$MPa