Pure torsion — identify the statement that is NOT an assumption Which one of the following statements is NOT an assumption of the elementary (pure) torsion theory for a uniform circular shaft?

Introduction / Context:Elementary torsion theory underpins the design of shafts. It relies on a set of assumptions that lead to the familiar torsion formula tau = T r / J and angle-of-twist relation.

Given Data / Assumptions:

• Uniform circular shaft subjected to pure torque.
• Saint-Venant torsion conditions.
• No warping for circular sections.

Concept / Approach:The correct assumptions include material linearity and isotropy, plane circular sections remaining plane, straight radial lines, and (for constant T and constant GJ) a constant rate of twist. However, the shear stress is not uniform over the section; it varies linearly with radius: tau(r) = T r / J, being zero at the axis and maximum at the surface.

Step-by-Step Solution:

Verification / Alternative check:The torque equilibrium integral T = ∫(tau * r) dA requires tau ∝ r for circular shafts to satisfy compatibility.

Why Other Options Are Wrong:

• Options a, b, c, and e are standard assumptions or results for a prismatic circular shaft under constant torque.

Common Pitfalls:Confusing uniform shear stress (false) with uniform rate of twist (true) for prismatic shafts under constant torque.

Final Answer:Shear stress is uniform over the cross-section at a given torque