Question No$\mathrm{.}13$: The normal stresses acting on two perpendicular planes at a point in a strained material are $70$ MN$/$ m$2$ tensile, $35$ MN$/$ m$2$ compressive. In addition, shear stress of $40$ N$/$mm$2$ act on these planes. Calculate the following: $($i$)$ The magnitude of the principle stresses $($ii$)$ The direction of the principal planes $($iii$)$ The magnitude of the maximum shear stress.