A rectangular element ABCD of an elastic material is subjected to a shear stress

of $17\mathrm{.}5$ MPa. The planes at right angles carry tensile stress of $70$ MPa and

compressive stress of $35$ MPa respectively.

Determine:

i$)$ The magnitude of the principal stresses.

ii$)$ The direction of the principal planes.

iii$)$ The magnitude of maximum shear stress.

iv$)$ The orientation of the plane of maximum shear stress.