A crank setup is subjected to the vertical load $P$ as shown in the figure. The diameter of the EDB shaft is $0\mathrm{.}8$ in$.$

Consider force $P,$ in kN $,$ to be equal to the last two numerical digits of your student PID plus $10.$ For example, if your PID is $A18752350,$ then $P=50+10=60kN$

Point $H$ is located on top of the shaft section, as shown.

$($a$)$ Determine the state of stress $($all possible stresses$)$ at point $H$

$($b$)$ the principal stresses, principal orientation, and maximum shear stress at point $H$

$($c$)$ if we rotate $y,y$ through an angle of $15$ counterclockwise about the $z-$axis, determine the transformed stresses $($relative to the $x^{\text{'}},y^{\text{'}})$ at point $H.$

$($you may use $2$D stress transformation when applicable.$)$

$(15$ points$)$