Torsion of shafts in parallel:\nTwo shafts connected in parallel carry a common torque between a pair of rigidly connected flanges. Will the angle of twist of each shaft be the same?

Introduction / Context:
Multiple shafts in parallel are used to share torque between paths (e.g., multi-shaft drive lines). Understanding compatibility and equilibrium conditions in torsion helps determine torque distribution and shaft sizing.

Given Data / Assumptions:

• Two shafts connected in parallel between common rigid end plates/flanges.
• Total applied torque T is shared as T = T1 + T2.
• Linear elastic torsion (Saint-Venant), small angles.

Concept / Approach:
In parallel, both shafts experience the same end rotation because the end flanges remain plane and rotate together (compatibility). The torque splits according to each shaft’s torsional stiffness Kt = G * J / L. Stiffer shaft carries a larger share, but the twist angle θ is identical for both.

Step-by-Step Solution:

Verification / Alternative check:
Electrical analogy: torque ↔ current, angle of twist ↔ voltage, torsional stiffness ↔ conductance. Elements in parallel share the same “voltage” (θ), reinforcing the conclusion.

Why Other Options Are Wrong:

• “No” contradicts compatibility at the rigidly connected ends.
• Conditions on equal diameter/length are unnecessary; these affect torque split, not equality of θ.
• “Total torque zero” would trivially make θ = 0, but that does not define the general case.

Common Pitfalls:
Confusing series vs parallel: in series, torque is the same and twists add; in parallel, twist is the same and torques add.

Final Answer:
Yes