Spring Shear Stress Formula
Compression-spring wire sees torsional shear: tau = 8FD/(pi*d^3), corrected for coil curvature by the Wahl factor Kw = (4C-1)/(4C-4) + 0.615/C. Use the working compression spring calculator to run it against the material allowable.
The formula
Uncorrected shear stress, then the curvature correction at spring index C = D/d:
tau = Kw * 8*F*D / (pi * d^3), Kw = (4C-1)/(4C-4) + 0.615/C
Why the correction matters
The inside of the coil carries both direct shear and the curvature concentration; at C = 6 the Wahl factor is about 1.25 - a quarter more stress than the naive formula.
Static vs cyclic
Compare against the material static allowable on the compression spring calculator; cyclic loads go to the fatigue screen instead.
Frequently asked questions
Is spring stress bending or shear?
Compression and extension spring bodies load the wire in torsional shear. Torsion-spring legs and extension hooks see bending - different formulas and pages.
What allowable should the stress stay under?
Customary static allowables run about 40-50% of the wire tensile strength depending on material; the working calculator carries the cited per-material values.
Related pages
- Compression spring calculator - rate, force and Wahl-corrected stress with material data.
- Spring fatigue life calculator - Goodman/Zimmerli cyclic screen.
- Wahl correction factor guide - where the correction comes from.
- Spring index calculator - C = D/d and what it implies.