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Mechanical Engineering QUESTION #2504
Question 1
The octahedral shear stress theory (von Mises criterion) for yielding states that yielding begins when:
  • \(\sigma_{vm} = \sqrt{\sigma_1^2 + \sigma_2^2 + \sigma_3^2} \geq S_y\)
  • \(\sigma_{vm} = \sigma_1 - \sigma_3 \geq S_y\)
  • \(\sigma_{vm} = \frac{1}{\sqrt{2}}\sqrt{(\sigma_1-\sigma_2)^2+(\sigma_2-\sigma_3)^2+(\sigma_3-\sigma_1)^2} \geq S_y\)✔️
  • \(\sigma_{vm} = \frac{\sigma_1+\sigma_2+\sigma_3}{3} \geq S_y\)
Correct Answer Explanation
The von Mises (distortion energy) criterion: \(\sigma_{vm}=\frac{1}{\sqrt{2}}\sqrt{(\sigma_1-\sigma_2)^2+(\sigma_2-\sigma_3)^2+(\sigma_3-\sigma_1)^2}\geq S_y\).