Problem $1(10+10=20$ points$).$ 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:

$($a$){}_x=-50$MPa,${}_y=-75$MPa,${}_{xy}=-50$MPa

$($b$){}_x=100$MPa,${}_y=20$MPa,${}_{xy}=-20$MPa