In torsion of circular shafts, the shear stress distribution is maximum at which location within the shaft cross-section?

Introduction / Context:
Torsion in circular shafts creates a shear stress distribution that is linear from the centre to the outer surface. Knowing where maximum shear occurs is important for safe shaft design in machines and structures.

Given Data / Assumptions:

• Solid circular shaft.
• Radius = r.
• Torque applied = T.

Concept / Approach:
Shear stress in torsion is given by: τ = (T * r) / J where J is the polar moment of inertia. Since τ ∝ radius, maximum occurs at r (outer surface).

Step-by-Step Solution:
At centre (r = 0), τ = 0.At half radius (r/2), τ = 0.5 τmax.At full radius (r), τ = τmax.Thus maximum shear occurs at the surface.

Verification / Alternative check:
Finite element torsion models confirm that shear stress is linear from axis to circumference.

Why Other Options Are Wrong:

• Centre: stress = 0.
• r/2: stress is half maximum.
• 3/4 r: stress is 0.75 τmax, not maximum.
• None: incorrect, since maximum is clearly at surface.

Common Pitfalls:

• Assuming uniform shear across section; in torsion it is linear.

Final Answer:
at the top of the surface