Question

According to maximum shear stress failure theory, yielding in material occurs when:

• A. Maximum shear stress = \( \sqrt{2} \times \text{yield stress} \)
• B. Maximum shear stress = \( 2 \times \text{yield stress} \)
• C. Maximum shear stress = \( 2 \times \text{yield stress} \)
• D. Maximum shear stress = \( \sqrt{\frac{2}{3}} \times \text{yield stress} \)

Hint:

In the maximum shear stress failure theory, yielding occurs when the maximum shear stress reaches \( \sqrt{2} \) times the yield stress.

Answer 1

The Correct Option is A

Step 1: Understand the maximum shear stress failure theory.
According to the maximum shear stress failure theory (also known as Tresca's theory), yielding occurs when the maximum shear stress reaches a critical value. The maximum shear stress is calculated as: \[ \tau_{\text{max}} = \frac{\sigma_1 - \sigma_3}{2} \] Where \( \sigma_1 \) and \( \sigma_3 \) are the maximum and minimum principal stresses, respectively. Step 2: Apply the theory to yield stress.
According to Tresca's theory, yielding will occur when: \[ \tau_{\text{max}} = \frac{\sigma_{\text{yield}}}{\sqrt{2}} \] Therefore, the correct answer is: Maximum shear stress = \( \sqrt{2} \times \text{yield stress} \). Final Answer: \[ \boxed{\sqrt{2} \times \text{yield stress}} \]