This question was previously asked in

GATE PI 2017 Official Paper

**Concept:**

According to Von-Mises theory:

\({\left( {{σ _1} - {σ _2}} \right)^2} + {\left( {{σ _2} - {σ _3}} \right)^2} + {\left( {{σ _1} - {σ _3}} \right)^2} \le \frac{{2{σ _{yt}^2}}}{{FOS}^2}\)

For plane stress condition σ3 = 0

\(σ^2_1+σ^2_2-σ_1σ_2\leq \left ( \frac{σ_{yt}}{FOS} \right )^2\)

Where σ_{1} and σ_{2} are principle stresses and σ_{yt} = yield strength of the material, FOS = Factor of safety

**Calculation:**

**Given:**

σ1 = σ2 = 500 MPa, S_{yt} = 700 MPa

\(σ^2_1+σ^2_2-σ_1σ_2\leq \left ( \frac{S_{yt}}{FOS} \right )^2\)

\(500^2+500^2-500\times 500\leq \left ( \frac{700}{FOS} \right )^2\)

\(500^2\leq \left ( \frac{700}{FOS} \right )^2\)

\(FOS = \frac{700}{500}\)

**FOS = 1.4**