Spring Wire Stress (Wahl), Solid Height, and Buckling
Three helical-spring checks beyond the rate: wire shear stress, solid height, and buckling.
Example
You enter
- Wire diameter d (in) 0.08
- Mean coil diameter D = OD - d (in) 0.75
- Spring force F (lb) 5
- Total coils Nt 10
- Free length L0 (in) 2
- End condition squared-ground
You get
- Spring index 9.375
- Wahl correction factor Kw 1.155
- Uncorrected torsional stress 18651 psi
- Corrected wire shear stress 21545 psi
- Solid height Ls 0.800 in
- Max travel to solid 1.200 in
Details, formula, and sources
Wire shear stress tau = Kw x 8 F D / (pi d^3), where the Wahl factor Kw = (4C - 1)/(4C - 4) + 0.615/C corrects the plain torsional stress for wire curvature and direct shear; solid height Nt d with ground ends, (Nt + 1) d unground, and the travel left before the spring stacks solid; and a slenderness screen L0/D against the 5.26 limit for squared-and-ground ends on flat plates. A 0.080 in wire on a 0.75 in coil at 5 lb runs 18,651 psi uncorrected but 21,545 psi with Kw = 1.155, and a tight index bites hard: Kw is 1.40 at C = 4 against 1.12 at C = 12. The allowable stress by material and duty is the spring maker's. Companion to the helical spring rate.
C = D/d; Kw = (4C - 1)/(4C - 4) + 0.615/C; tau_uncorrected = 8 F D / (pi d^3); tau = Kw x tau_uncorrected; Ls = Nt d (ground ends) or (Nt + 1) d (unground); travel = L0 - Ls; slenderness = L0/D, stable under 5.26 for squared-and-ground ends on parallel flat plates.
The standard round-wire helical-compression-spring wire shear stress with the Wahl correction factor, the Shigley end-condition solid-height table, and the absolute-stability slenderness limit, per Machinery's Handbook and Shigley's Mechanical Engineering Design, by name.
The Wahl factor, the torsional-stress relation, and the solid-height and stability criteria are public machine-design results.
Estimate. AHJ and licensed professional govern.
Field names used by the API: wire_diameter_in, mean_coil_diameter_in, force_lb, total_coils, free_length_in, end_type, spring_index, wahl_factor, tau_uncorrected_psi, tau_psi, solid_height_in, max_deflection_in
- Wahl correction Kw = (4C - 1)/(4C - 4) + 0.615/C applied to 8 F D / (pi d^3); round wire, axial loadMachinery's Handbook / Shigley
- Solid height Nt d for ground ends, (Nt + 1) d for ungroundShigley end-condition table
- Stability absolute stability while L0/D < 5.26 for squared-and-ground ends on parallel flat platesShigley spring-buckling criterion
- Allowable not included the permissible stress by material, wire size, and duty is the spring maker's; fatigue and set removal are separatespring-design practice