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Spring Index

Leaf Spring Design

More details on Spring design are to be found in the links below the table.


Leaf Springs are widely used in the automobile and railway industries for suspension applications.  The simplest variation is the single beam spring.  The more normal application is the laminated (multiple) leaf spring which provides a more efficient stress distribution..

Single Leaf Springs have the following characteristics.

  • They are suitable for low and medium load forces
  • They have reasonably linear working characteristics
  • They have relatively low spring constant
  • They are long items with relatively low cross section
  • They are relatively low cost items

Laminated leaf springs have the following characteristics

  • They are suitable for higher loading forces
  • They have theoretically linear working characteristics (friction between the leaves causes hysteretic pattern of the working curve)
  • Compared to single leaf springs they have relatively high spring constants (stiffness)
  • Laminated spings have high space requirements compared to single leaf springs
  • They require regular maintenance (lubrication and cleanness)

E = Young's Modulus (N/m2)
F = applied Force (N)
t = thickness of leaf (m)
b = width (m)
L = length (m)
t = thickness of leaf (m)
δ = deflection (m)
σ = Bending stess <σ(N/mm2
k = spring rate (stiffness) F/δ (N/m

Single leaf springs

There are two primary variations the cantilever spring and the simply supported beam..

Cantilever spring

Simply supported spring

Multiple leaf springs

Considering a cantilever type leaf spring, the stress distribution is related to the distance from the load point.

σ = 6Fx / bt2

If (x/b) is constant along beam, of constant thickness t, then the stress level will be constant and the most efficient spring will result.  If x/b is constant then a triangular shaped spring results.   The multileaf spring is designed to provide a constant stress level along the spring length as it is designed to be equivalent to a triangular spring as shown below.

For this spring the maximum stress( which ideally is constant along the spring) is and the stiffness are as follows..

These equations apply to the quarter elliptic spring as shown below

The relevant equations for the semi-elliptic spring as shown below are

Links to Spring Design
  1. Diracdelta.co.uk ...Leaf Spring Formulae and calculator

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Last Updated 21/02/2008