In mechanics of materials, a closed-coiled helical spring under axial load develops shear stress in its wire from a combination of direct (transverse) shear and torsional shear induced by the twisting moment produced by the load acting at the coil's mean radius; the resulting maximum shear stress is corrected by a stress concentration factor (a function of the spring index, the ratio of coil diameter to wire diameter), with a more precise correction given by an empirically derived factor accounting for coil curvature. Axial deflection of such a spring is derived by integrating the angular twist along the wire length, yielding a relation among the applied load, coil geometry, shear modulus, and number of coils, from which a spring constant (load per unit deflection) characterizes the spring's stiffness.
In mechanics of materials, a closed-coiled helical spring under axial load develops shear stress in its wire from a combination of direct (transverse) shear and torsional shear induced by the twistin…