Problem $1$:

Consider a point in a structural member that is subjected to plane stress. Normal and shear stresses acting on horizontal and vertical planes at the point are shown.

$($a$)$ Draw Mohr's circle for this state of stress.

$($b$)$ Determine the principal stresses and the maximum in$-$plane shear stress acting at the point.

$($c$)$ Show these stresses on an appropriate sketch.

Problem $2$:

For the same point in Problem $1,$ determine the absolute maximum shear stress at the point. $[$you can assume ${}_z={}_{yz}={}_{xz}=0]$

Hint: draw the Mohr's circles for the $xy,yz,$ and $xz$ planes.