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.

Laminated leaf springs have the following characteristics

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

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