Question $2$

The solid rod shown in Figure $2$ is made from AISI $1050$ cold drawn steel. The rod is cantilevered at one end and subjected to point loads $\backslash (\backslash$mathrm$\{$Fz$\}=5\backslash$mathrm$\{$kN$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$Fy$\}=-8\backslash$mathrm$\{$kN$\}\backslash )$ as illustrated. Determine:

$($a$)$ The normal and shear stresses at point a$.$ Illustrate these stresses on an element.

$($b$)$ The principal stresses and the maximum shear stress at point a$.$

$($c$)$ The factor of safety guarding against static failure at point a using maximum shear stress theory. Figure $2$