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?
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AMaximum at the centre and zero at the circumference
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BZero at the centre and maximum at the circumference
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CUniform across the section
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DMinimum at the centre and maximum at mid-radius
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ENone of these
Answer
Correct Answer: Zero at the centre and maximum at the circumference
Explanation
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:
Write torsion formula: tau = T r / J.At r = 0 (shaft axis), tau = 0.At r = R (outer fibre), tau = T R / J (maximum value).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