3. Find the factor of safety for the following cases according to (a) maximum principal stress theory (b) Max shear stress theory (c) Distortion energy theory.
Assume yield strength of the material as 680 MPa.
(i) $\sigma_x$ = 480 MPa, $\sigma_y$ = 480 MPa and $\tau_{xy}$ = 0 MPa
(ii) $\sigma_x$ = 400 MPa, $\sigma_y$ = 275 MPa and $\tau_{xy}$ = -100 MPa
(iii) $\sigma_x$ = 0 MPa, $\sigma_y$ = 275 MPa and $\tau_{xy}$ = 310 MPa
(iv) $\sigma_x$ = -275 MPa, $\sigma_y$ = -400 MPa and $\tau_{xy}$ = 100 MPa