Pure torsion of circular shaft: Under a twisting moment, every cross-section of the shaft is primarily subjected to which type of stress?

Introduction / Context:
Shafts transmit torque in machines (motors, gearboxes, rotors). The dominant stress under pure torsion for circular shafts is shear, which defines the torsional strength and angle of twist.

Given Data / Assumptions:

• Solid or hollow circular shaft.
• Pure torque (no bending, no axial load).
• Linear elastic, isotropic material; Saint-Venant torsion holds.

Concept / Approach:
In circular shafts, warping is negligible and cross-sections remain plane. The shear stress varies linearly with radius: tau(r) = T * r / J where T is torque and J is polar second moment of area. Normal stresses (tension/compression) arise only if bending or axial loads are present.

Step-by-Step Solution:

Verification / Alternative check:
Mohr’s circle for pure shear shows principal normal stresses ±tau at 45°, but the applied stress state on the cross-section is shear.

Why Other Options Are Wrong:
Tension/Compression/Bending are not produced by pure torque in a circular shaft.Hydrostatic stress requires equal normal stresses in all directions, unrelated to torsion.

Common Pitfalls:
Confusing principal normal stresses at 45° with applied shear on the cross-section; applying noncircular-shaft concepts where warping matters.

Final Answer:

Shear stress