For problems $1-4.(20$ points$)$ The drive shaft $($link $2,A{O}_2)$ of the oil pump shown below is loaded in torsion at $6500in-lbf$ and bending at $9800in-lbf.$ Units in the figure are inches. The point on the shaft with maximum stress is located away from the key that connects the shaft to the crank. Use class $20$ gray cast iron and assume the shaft diameter is $3$ inches.

$(5$ points$)$ What is the value of the principal stress ${}_1?$

$(5$ points$)$ What is the value of the principal stress ${}_2?$

$(5$ points$)$ What is the value of the principal stress ${}_3?$

$(5$ points$)$ What is the factor of safety for this shaft? Use Modified$-$Mohr with effective stress.