Introduction:

One of the earliest mathematical explanation of the phenomenon of buckling was given by Euler (1759) who proposed the Euler's theory.

Description:

Euler's formula:

where

f_E = Euler’s critical stress,

P_E = Euler’s critical load,

A = Area of cross section,

I = Moment of inertia of the section,

Radius of gyration,

Slenderness ratio of the element, and

k = A coefficient which depends upon the end condition of the column.

Also various empirical formulae, e.g. Rankine’s, Johnson’s and Perry’s are available for estimating the buckling load of columns.