**Related Resources: calculators**

### Spring Shear Stress Calculator

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 d^{3} )*

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 = d ^{4} G / ( 8 D^{3} N )
*

where

G = shear modulus of elasticity, (N/mm^{2}, lbs/in^{2})

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

Material | ASTM |
m |
A |

Music wire |
A228 |
0.163 |
2060 |

Oil-tempered wire |
A229 |
0.193 |
1610 |

Hard-drawn wire |
A227 |
0.201 |
1510 |

Chrome vanadium |
A232 |
0.155 |
1790 |

Chrome silicon | A401 |
0.091 |
1960 |

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)*

Related:

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- Compression Spring "k" Constant Calculator
- Axial Tension or Compression Springs Stiffness Constant Equations and Calculator
- Compression Spring Assembly Operating Life and Reliability Equations and Calculator
- Constant Force Spring Design & Equations
- Helical Compression Springs Engineering and Design
- Extension Spring "k" Constant Calculator
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- Extension Spring Normal Load Tolerances load / force Specifications
- Helical Compression Spring Critical Frequency Formula and Calculator Helical springs, such as those used in the valve trains of internal combustion engines, can fail if the frequency of loading coincides with the natural, or critical, frequency of the spring, called resonance.
- Helical Spring Fatigue Loading and Factor of Safety Formula and Calculator Rarely are helical springs not subjected to fatigue loading. The number of cycles may only be in hundreds or thousands, but usually they must be designed for millions and millions of cycles such that an infinite life is desired.
- Series and Parallel Spring Rate Formula and Calculator
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Source

Fundamentals of Engineering Supplied Reference Handbook, Fifth Edition

National Council of Examiners for Engineering and Surveying