Spring Shear Stress Calculator

Related Resources: calculators

Shear Stress Helical Linear Spring Calculator

This calculator will determine the shear stress in a helical spring as well as maximum allowable torsional stress

shear stress in a helical linear spring
Eq. 1
τ = K_s 8 F D / ( π d³ )

where

d = wire diameter, (in, mm)
F = applied force, (lbs, N)
D = mean spring diameter, (in, mm)
K_s = (2C + 1)/(2C),
C = D/d.

The deflection and force are related by F = kx where the spring rate (spring constant) k is given by

Eq. 2
k = d⁴ G / ( 8 D³ N )

where

G = shear modulus of elasticity, (N/mm², lbs/in²)
N = number of active coils, #

Spring Material: The minimum tensile strength of common spring steels may be determined from

Eq. 3
S_ut = A / d^m

where

S_ut = tensile strength in MPa,
d = wire diameter in millimeters,

A and m are listed in the table

Maximum allowable torsional stress for static applications may be approximated as

S_sy = τ = 0.45 S_ut cold-drawn carbon steel (A227, A228, A229)

S_sy = τ = 0.50 S_ut hardened and tempered carbon and low-alloy steel (A232, A401)

Source

Fundamentals of Engineering Supplied Reference Handbook, Fifth Edition
National Council of Examiners for Engineering and Surveying