Question

When a shaft is subjected to torsion, the shear stress induced in the shaft varies from ---- at the centre and ---- at the circumference.

• A. minimum, maximum
• B. maximum, minimum
• C. zero, maximum
• D. maximum, zero

Hint:

Shear stress in torsion varies linearly from the center to the outer surface of the shaft.

Answer 1

The Correct Option is C

Step 1: Understanding torsion in a circular shaft.
When a circular shaft is subjected to torsion, shear stress develops due to twisting.
Step 2: Variation of shear stress.
The shear stress \( \tau \) at a distance \( r \) from the center is given by: \[ \tau = \frac{Tr}{J} \] where \( T \) is torque and \( J \) is polar moment of inertia.
Step 3: Evaluating stress at centre and surface.
At the centre (\( r = 0 \)): \[ \tau = 0 \] At the circumference (\( r = R \)): \[ \tau = \tau_{\max} \]
Step 4: Conclusion.
The shear stress varies from zero at the centre to maximum at the circumference.

Answer 2

Under torsion, each material fibre parallel to the shaft's axis at radius \( r \) is sheared by an amount proportional to its distance from the centre, since the relative twist between two cross-sections increases linearly with radial distance. Checking the options against this behaviour:

1. Minimum, maximum: This is imprecise: the shear stress at the very centre is not merely a "minimum" among nonzero values, it is exactly zero, since a fibre lying exactly on the axis experiences no relative sliding at all when the shaft twists.
2. Maximum, minimum: This reverses the actual trend. Fibres farther from the axis undergo more relative angular displacement for the same twist, so stress must increase, not decrease, moving outward from the centre.
3. Zero, maximum: A fibre on the axis itself does not move sideways relative to its neighbours during twisting, so it carries no shear stress there. The stress increases linearly with radius and is greatest at the outer surface, matching both ends of this description.
4. Maximum, zero: This would require the shaft's centre to twist more than its outer surface, which contradicts the fact that outer fibres travel a greater arc for the same angle of twist and hence experience more shear.

Since shear stress in torsion grows linearly from the axis outward, it must be zero at the centre and maximum at the outer surface.

Therefore, the correct answer is zero, maximum.