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? 
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?
Show Hint
- 90
- 60
- 45
- 120
The Correct Option is C
Solution and Explanation
Step 2: In this problem, we are dealing with a situation where the plane PQ in the infinitesimal element is in a state of pure shear. Pure shear refers to a condition where the normal stress is zero (\( \sigma = 0 \)) and only shear stress (\( \tau \)) exists.
Step 3: When the material is subjected to pure shear, the Mohr’s circle will show that the shear stress acts at an angle of \( \theta \) from the x-axis, and the circle will be centered at the origin. The maximum shear stress is represented as the radius of the Mohr’s circle.
Step 4: The key idea here is that the state of pure shear corresponds to the case where the shear stress is at its maximum and acts at an angle of \( 45^\circ \) to the principal axes. This is a well-known property of Mohr's circle.
Step 5: In Mohr’s circle, the shear stress reaches its maximum when the angle \( \theta \) corresponds to \( 45^\circ \). This angle is the one at which the shear stress is fully transformed into the maximum shear component and is geometrically represented by the diameter of the Mohr’s circle.
Step 6: Based on this understanding of Mohr's circle, the correct angle for pure shear is \( \theta = 45^\circ \), which corresponds to the option (C).
Step 7: Therefore, the correct answer is (C) 45 degrees. This value of \( \theta \) aligns with the condition of pure shear, where the shear stress is at its maximum, and the normal stress is zero.
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