Problem $1(10$ points total$)$

Determine:

$($a$)$ the principal stresses and $(4$ points$)$

$($b$)$ the maximum in$-$plane shear stress and $(2$ points$)$

$($c$)$ average normal stress. $(2$ points$)$

$($d$)$ What is the angle between the principal stress orientation and the maximum in$-$plane shear stress orientation? $(2$ points$)$