Question

A solid circular shaft is subjected to a constant torque. Which statement is correct about shear stress?

• A. Maximum at center and zero at surface
• B. Uniform across cross-section
• C. Maximum at outer surface and zero at center
• D. Varies linearly and is maximum at center

Hint:

Shear stress due to torsion in a solid circular shaft always varies linearly} from the center to the surface, with the maximum value at the outermost fiber.

Answer 1

The Correct Option is C

Step 1: Shear stress distribution in circular shafts under torsion
In a solid circular shaft subjected to torque \( T \), the shear stress \( \tau \) varies linearly from the center (zero) to the outer surface (maximum). The formula for shear stress is: \[ \tau = \frac{T r}{J} \] Where:
- \( \tau \) = shear stress at radius \( r \)
- \( T \) = applied torque
- \( J \) = polar moment of inertia
- \( r \) = radial distance from center (0 at center, \( R \) at surface)
Step 2: Analysis of stress distribution
- At the center of the shaft (\( r = 0 \)), \( \tau = 0 \)
- At the outer surface (\( r = R \)), \( \tau \) is maximum Step 3: Final Answer
Hence, shear stress is maximum at the outer surface and zero at the center.