GATE2016-1-38

Question

The principal stresses at a point inside a solid object are $\sigma _1$ = $100$ $MPa$, $\sigma _2$ = $100$ $MPa$ and $\sigma _3$ = $0$ $MPa$. The yield strength of the material is $200$ $MPa$. The factor of safety calculated using Tresca (maximum shear stress) theory is $n_T$ and the factor of safety calculated using von Mises (maximum distortional energy) theory is $n_V$. Which one of the following relations is TRUE?

• A. $n_T=(\sqrt{3}/2)n_V$
• B. $n_T=(\sqrt{3})n_V$
• C. $n_T=n_V$
• D. $n_V=(\sqrt{3})n_T$