Question

A component is subjected to biaxial state of stress. ${\sigma }_x=400MPa,{\sigma }_y=0,{\tau }_{xy}=200MPa$. If the yield strength in tension is 500 MPa and ultimate strength in tension is 500 MPa. The factor of safety as per distortion energy theory is

Answer 1

${\sigma }_x=400MPa,{\sigma }_y=0,{\tau }_{xy}=200MPa$

$S_{yt}=S_{ut}=500MPa$

According to distortion energy,

${\sigma }_x^2+3{\tau }_{xy}^2={\left(\frac{S_{yt}}{N}\right)}^2$

$N=\frac{S_{yt}}{\sqrt{{\sigma }_x^2+3{\tau }_{xy}^2}}=0.95$