Question

Maximum shear stress in a circular shaft under torque is at:

• A. Center
• B. Surface
• C. At radius/2
• D. At neutral axis

Hint:

For torsion in circular shafts, the maximum shear stress occurs at the outer surface, not at the center or any other point within the shaft.

Answer 1

The Correct Option is B

The maximum shear stress (\(\tau_{{max}}\)) in a circular shaft under torsion occurs at the surface of the shaft. This is due to the fact that shear stress in a shaft is a function of the radial distance from the center. The shear stress varies linearly from the center to the surface, where it reaches its maximum value.
The shear stress at a point in a shaft under torque is given by the formula: \[ \tau = \frac{T r}{J} \] Where:
- \(T\) is the applied torque,
- \(r\) is the radial distance from the center,
- \(J\) is the polar moment of inertia of the shaft's cross-sectional area.
The shear stress is directly proportional to the distance from the center, which means that at the center of the shaft, the shear stress is zero, and at the surface, it is maximum. Therefore, the maximum shear stress occurs at the surface of the shaft.
Thus, the correct answer is that the maximum shear stress occurs at the surface of the shaft.