Question

If the yield point shear stress obtained from the torsion test of a cylindrical specimen is \( \tau_y \), then what is the maximum value of principal strain at yielding? (\( \mu \) is Poisson's ratio and \( E \) is Young's modulus)

• A. \( \frac{\tau_y}{E} \)
• B. \( \frac{(1 + \mu)\tau_y}{E} \)
• C. \( \frac{\tau_y}{2E} \)
• D. \( \frac{(1 - \mu)\tau_y}{E} \)

Hint:

In torsion tests, the principal strain at yielding can be calculated using the relationship between shear stress, Young's modulus, and Poisson's ratio.

Answer 1

The Correct Option is B

The principal strain \( \varepsilon_1 \) at yielding is related to the shear stress \( \tau_y \) by the following relation: \[ \varepsilon_1 = \frac{\tau_y}{E} \cdot (1 + \mu) \] where \( \mu \) is Poisson's ratio and \( E \) is Young's modulus.
Thus, the maximum value of the principal strain is given by \( \frac{(1 + \mu)\tau_y}{E} \). The correct answer is (B).
Final Answer: (B) \( \frac{(1 + \mu)\tau_y}{E} \)