Question

The Mohr’s circle corresponding to an infinitesimal element is shown in the figure. The plane PQ in the infinitesimal element, at an angle of \(\theta\) from the x-axis, is in a state of pure shear.

Which one of the following values of \(\theta\) (in degrees) is CORRECT?

• A. 90
• B. 60
• C. 45
• D. 120

Hint:

For Mohr’s circle, always remember: an angle \(\theta\) in the physical plane corresponds to a rotation of \(2\theta\) on Mohr’s circle. Pure shear planes are located at 45° from principal planes.

Answer 1

The Correct Option is C

Step 1: Mohr’s circle basics.
- Each point on Mohr’s circle corresponds to a plane at some physical angle \(\theta\). - On Mohr’s circle, angle \(2\theta\) is measured from the x-axis in physical space.

Step 2: Condition for pure shear.
Pure shear means normal stress = 0, only shear stress acts. On Mohr’s circle, this corresponds to points on the vertical axis (top or bottom of circle).

Step 3: Location of pure shear points.
The circle center is at 0, radius = \(\sigma_0\). At top of circle: \((\sigma=0, \tau=\sigma_0)\). At bottom: \((\sigma=0, \tau=-\sigma_0)\).

Step 4: Relation to angle \(\theta\).
These points correspond to rotation of \(2\theta = 90^\circ\). So, \[ \theta = 45^\circ \] Final Answer:
\[ \boxed{45^\circ} \]