Question

If \( \sigma_1 \) and \( \sigma_2 \) are two principal stresses, then the radius of Mohr’s circle is

• A. \( \sigma_1 + \sigma_2 \)
• B. \( \sigma_1 - \sigma_2 \)
• C. \( \dfrac{\sigma_1 + \sigma_2}{2} \)
• D. \( \dfrac{\sigma_1 - \sigma_2}{2} \)

Hint:

In Mohr’s circle, diameter represents principal stresses, and radius gives the maximum shear stress.

Answer 1

The Correct Option is D

Step 1: Understanding Mohr’s circle.
Mohr’s circle is a graphical representation of the state of stress at a point. The principal stresses \( \sigma_1 \) and \( \sigma_2 \) lie at the extreme ends of the diameter of Mohr’s circle.
Step 2: Determining the center of Mohr’s circle.
The center of Mohr’s circle lies at the average of the principal stresses: \[ \text{Center} = \frac{\sigma_1 + \sigma_2}{2} \]
Step 3: Calculating the radius.
The radius of Mohr’s circle is half the difference of the principal stresses: \[ \text{Radius} = \frac{\sigma_1 - \sigma_2}{2} \]
Step 4: Conclusion.
Hence, the radius of Mohr’s circle is \( \dfrac{\sigma_1 - \sigma_2}{2} \).