For the $(x,y)2$D stress element shown in the figure:

$($a$)$ Calculate the Principal Stresses ${}_1$ and ${}_2,$ and the Principal Stress Angle, ${}_{p1}.$

$($b$)$ Calculate the maximum shear stress ${}_{s1},$ the normal stresses in the maximum shear planes ${}_{S1}$ and ${}_{S2},$ and the max shear angle ${}_{S1}.$

$($c$)$ Sketch the orientation of the Principal Stresses $("$Principal Stress Square"$)$ and the Maximum Shear Stresses $("$Max Shear Square"$)$ relative to the $(x,y)$ square.

$($d$)$ Draw the Mohr's Circle for this case, and on the circle identify the points relative to:

Directions $($faces$)x$ and $y$

Principal directions $1$ and $2$

Max shear directions $S1$ and $S2$