Solid circular shaft in torsion — radial variation of shear stress In a solid circular shaft subjected to a torque (pure torsion), how does the shear stress vary from the centre to the outer surface?

Introduction / Context:
Torsion of circular shafts is a cornerstone topic in machine and structural design. Correctly recalling the shear stress distribution is essential for sizing shafts and checking combined stress states.

Given Data / Assumptions:

• Solid circular shaft of radius R under torque T.
• Material is homogeneous and linear-elastic; Saint-Venant torsion applies.

Concept / Approach:
For a solid circular shaft, the shear stress varies linearly with radius:
tau(r) = (T * r) / Jwhere J is the polar moment of inertia. Therefore, tau = 0 at r = 0 and tau = tau_max at r = R.

Step-by-Step Solution:

Verification / Alternative check:
The angle of twist formula theta = T L / (G J) also relies on J; using the linear tau–r law integrates to the correct torque–stress relationship.

Why Other Options Are Wrong:

• Maximum at centre: contradicts tau = T r / J.
• Uniform: only true for thin-walled tubes under special approximations, not solid shafts.
• Maximum at mid-radius: incorrect; linear variation peaks at the surface.

Common Pitfalls:
Confusing solid and hollow shafts; misremembering that stress is linear (not parabolic) in torsion for circular shafts.

Final Answer:
Zero at the centre and maximum at the circumference