GATE 2026 ME – Question 34
A steel plate having yield strength of 550 MPa, is subjected to biaxial state of stress as $\sigma_x = \sigma$ and $\sigma_y = -2\sigma$. Using distortion energy theory and considering the factor of safety as 2, the permissible value of $\sigma$ that can be applied to the plate is ________ MPa (*rounded off to 1 decimal place*).
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Correct answer: 103.38 to 104.42
Explanation
The allowable equivalent stress is $\frac{550}{2} = 275$ MPa. By the distortion energy theory the equivalent stress is $\sqrt{\sigma_x^2 - \sigma_x\sigma_y + \sigma_y^2} = \sqrt{\sigma^2 + 2\sigma^2 + 4\sigma^2} = \sqrt{7}\sigma$. So $\sigma = \frac{275}{\sqrt{7}} = 103.9$ MPa.