$(19$ pts $)$ The beam from Problem $1$ was made of a ductile steel bar with a yield strength of $350$ MPa $.$ Assume the critical point is at some point with $x=100$ MPa and $xy=75$MPa. Based on maximum shear stress theory,

$($a$)(5$ pts$)$ Plot the failure envelope

$($b$)(5$ pts$)$ Mark the stress state in the figure

$($c$)(3$ pts$)$ Plot the load line

$($d$)(3$ pts$)$ Based on the location of the stress state on the failure envelope, do you think the beam will yield?

$($e$)(3)$ If not, what is the safety factor based on the graphical method?