Question

For plane stress, Mohr’s circle has:

• A. Radius equal to maximum normal stress
• B. Radius equal to maximum shear stress
• C. Centre at origin
• D. No radius

Hint:

Mohr's circle radius always equals the maximum shear stress in plane stress conditions. The center lies at the average normal stress.

Answer 1

The Correct Option is B

Mohr’s circle is a graphical method used to determine the state of stress at a point and to find principal stresses and maximum shear stress.
In the case of plane stress, the circle is plotted using normal stress \( \sigma \) on the x-axis and shear stress \( \tau \) on the y-axis.
The radius of the Mohr’s circle is equal to the maximum shear stress, which is calculated as:
\[ R = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \]
Thus, the radius represents the magnitude of the maximum shear stress acting on the element.
- Option (1) is incorrect because the maximum normal stress is a function of the center and radius, but not equal to radius.
- Option (3) is incorrect as the center is at \( \left(\frac{\sigma_x + \sigma_y}{2}, 0\right) \), not at the origin.
- Option (4) is incorrect because the circle always has a radius unless all stresses are zero.