A long steel bar is under a tensile stress due to a force F as shown. For what angle  the tensile and shearing stress are maximum?

Tensile stress = $\frac{\mathrm{Fcos}\left(90-\mathrm{\theta }\right)}{{\displaystyle \frac{\mathrm{A}}{\cos \left(90-\mathrm{\theta }\right)}}}=\frac{{\mathrm{Fsin}}^2\mathrm{\theta }}{\mathrm{A}}$
$\mathrm{\theta }$ = 90^o, Tensile stress is maximum 
shear stress =
$\frac{\mathrm{Fcos}\left(90-\mathrm{\theta }\right)}{{\displaystyle \frac{\mathrm{A}}{\cos \left(90-\mathrm{\theta }\right)}}}=\frac{\mathrm{Fcos\theta sin\theta }}{\mathrm{A}} \mathrm{x} \frac{2}{2}=\frac{\mathrm{Fsin}2\mathrm{\theta }}{2\mathrm{A}}$
$\mathrm{\theta }$ = 45^o, shear stress is maximum