Determine the maximum and minimum principal stresses and the planes on which they act.

Question

At a point in a loaded components the state of stress is given by

$\sigma _{X}$ = 270 MPa ,   $\sigma _{y}$  = 130 MPa  and

$\tau _{XY}$  = ±40MPa

Determine

(i)   The maximum and minimum principal stresses and the planes on which they act.

(ii)  The maximum shearing stress in magnitude and direction