A closely coiled helical spring is subjected to an axial load. Predominantly, the wire of the spring is under which type of action?
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ABending
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BDirect shear only
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CTorsion (resulting in shear stress in the wire)
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DCrushing
Answer
Correct Answer: Torsion (resulting in shear stress in the wire)
Explanation
Introduction / Context:Helical compression and tension springs are ubiquitous in machines. Understanding how an axial load translates into stresses within the spring wire is vital for sizing and fatigue analysis.
Given Data / Assumptions:
- Closely-coiled helical spring (helix angle small).
- Axial load applied along the spring axis.
- Standard thin-wire spring theory (Wahl, curvature effects ignored for first order).
Concept / Approach:In a closely-coiled spring, the axial load primarily produces a twisting moment in the wire. Hence, the wire experiences torsion, which induces shear stress. There is a small direct shear component, but torsion dominates the stress state and governs design.
Step-by-Step Solution:
Model the coil as a curved beam subjected to axial force.Resolve the axial load into a torque about the wire’s centreline.Compute maximum shear using τ_max ≈ 16 W R / (π d^3) with curvature factors as needed.Note direct shear W/(π d^2/4) is secondary compared to torsional shear.Verification / Alternative check:Energy methods and Castigliano’s theorem yield the same deflection when torsional strain energy dominates, confirming torsion as the primary action.
Why Other Options Are Wrong:Bending and crushing do not represent the principal action in closely-coiled springs; “direct shear only” ignores the dominant torsion.
Common Pitfalls:Neglecting curvature correction (Wahl factor) and stress concentration at the inner fibre in detailed design.
Final Answer:
Torsion (resulting in shear stress in the wire)