Question $2$:

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 in the figure.

$($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, using Mohr's circle.

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