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: Understanding Maximum Shear Stress Theory.
The maximum shear stress failure theory, also known as Tresca's theory, posits that yielding happens when the maximum shear stress attains a critical threshold.The maximum shear stress is determined by:\[\tau_{\text{max}} = \frac{\sigma_1 - \sigma_3}{2}\]Here, \( \sigma_1 \) and \( \sigma_3 \) represent the largest and smallest principal stresses, respectively.Step 2: Relate the theory to yield stress.
Tresca's theory dictates that yielding occurs when:\[\tau_{\text{max}} = \frac{\sigma_{\text{yield}}}{\sqrt{2}}\]Therefore, the solution is:Maximum shear stress = \( \sqrt{2} \times \text{yield stress} \). Final Answer: \[ \boxed{\sqrt{2} \times \text{yield stress}}\]