Columns are long slender members subjected to an axial compressive force. Lateral deflection on a column is called buckling.

The maximum axial load that a column can support when it is on the verge of buckling is called the critical load Pcr

From Euler's formula, define the first mode buckle as P1cr  = p2EI/(L)2, then P = n2Pcr     n = 1,2,3,4,...where

        L = the column length

        E = material Modulus

 

and n is the number of waves in the deflected shape of a column. Alternatively, if we define the effective length as the length of the column divided by n, then we can always substitute it into the first mode buckling formula, P1cr , defined above, to get the nth mode buckling load. For instance, if n=3, three waves appear in the buckled column, at the right of the animation and the column can support a critical buckling load that is 9 times the Pcr . It can only exist when the lateral braces support the column.