For AISI $1020$ Cold Drawn steel, using distortion$-$energy and maximum$-$shear$-$stress theories determine the factors of safety for the following plane stress states:

a$){}_x-180$MPa and ${}_y=100$MPa

b$){}_x=180$MPa and ${}_{xy}=100$MPa

c$){}_x=160$MPa and ${}_{xy}=100$MPa

d$){}_{xy}-150$MPa

Repeat Problem $1$ by first plotting the failure loci in the A and $B$ plane to scale; then for each stress state, plot the load line and by graphical measurement estimate the factors of safety.

Hint: Use Matlab