Question

In a plane stress system, two principal stresses are 785 N/mm² and 115 N/mm². If the system just causes yielding, what is the uni-axial yield stress of the material according to the Von Mises criterion:

• A. 887 N/mm²
• B. 734 N/mm²
• C. 635 N/mm²
• D. 903 N/mm²

Hint:

For Von Mises yield criterion the equivalent stress accounts for the interaction of principal stresses and provides an effective yield stress

Answer 1

The Correct Option is B

According to the Von Mises yield criterion, the equivalent stress σ_v is given by:

\( \sigma_v = \sqrt{\sigma_1^2 - \sigma_1\sigma_2 + \sigma_2^2} \)

Substitute \( \sigma_1 = 785 \, \text{N/mm}^2 \) and \( \sigma_2 = 115 \, \text{N/mm}^2 \):

\( \sigma_v = \sqrt{785^2 - 785 \times 115 + 115^2} \)
\( \sigma_v = \sqrt{616225 - 90275 + 13225} = \sqrt{536175} \approx 734 \, \text{N/mm}^2 \)

Thus, the uni-axial yield stress is 734 N/mm².