Conceptual
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Stress and Deflection in Open Coil Helical Springs

Open coil helical springs, in which the wire helix is wound at a pitch large enough that successive turns do not lie in a single plane, transmit an axial load as four internal force resultants — axial tension, transverse shear, torsion (twisting moment), and bending moment — resolved from the applied load and its moment through the helix angle, rather than the pure direct-shear-plus-torsion state of a closed coil spring. This belongs to the mechanics-of-materials theory of springs (a subtopic of strength of materials), and the resulting normal and shear stress components are combined via principal-stress transformation (Mohr's circle) to obtain maximum stress, while castigliano/strain-energy-style integration of the torsional and bending rotations over the wire length yields the axial deflection and angular rotation of the spring.