Close-coiled helical spring under an applied couple M about the helix axis: what happens to the internal action and geometry?

Introduction / Context:
A close-coiled helical spring can be loaded either by an axial force (causing twisting of the wire) or by a torque/couple about the spring’s axis (causing bending of the wire). This question distinguishes these two classic loading cases in strength of materials and spring design.

Given Data / Assumptions:

• Close-coiled helical spring (helix angle small).
• An external couple M is applied about the helix (spring) axis, not an axial force.
• Linear elastic behavior, small deformations, uniform wire and constant coil diameter.

Concept / Approach:

For close-coiled springs: an axial force P produces torsion of the wire (primary) and slight direct shear, while a torque M applied about the helix axis produces pure bending of the wire (primary). The distinction follows from resolving the external load into actions along the wire centerline: torque about the spring axis leads to a uniform bending moment in the wire’s local plane; no twisting moment acts about the wire’s own axis in this idealization.

Step-by-Step Solution:

Verification / Alternative check:

Textbook spring theory tables list: “Axial force → torsion of wire; Axial couple → bending of wire.” This is a standard result used in spiral spring and clock spring calculations.

Why Other Options Are Wrong:

Mean diameter decrease (option b) and “increase in number of coils” (option c) are not intrinsic outcomes of the elastic analysis; they are misleading. “All of the above” (option d) is therefore incorrect.

Common Pitfalls:

Confusing the axial force case (wire in torsion) with the axial couple case (wire in bending).

Final Answer:

It is subjected to pure bending of the wire