Question $1$:

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 in the figure.

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

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

$($c$)$ Compute the absolute shear stress at the point.