Torsion of shafts in parallel: Two 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?
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AYes
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BNo
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COnly if both shafts have equal diameter
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DOnly if total torque is zero
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EOnly if both shafts have equal length
Answer
Correct Answer: Yes
Explanation
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:
Angle of twist: θ = T1 * L / (G1 * J1) = T2 * L / (G2 * J2) for common end rotation.Equilibrium: T = T1 + T2.Solve for T1 and T2 using stiffnesses; θ emerges identical for both shafts.Hence, in parallel systems, twist compatibility enforces the same θ.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