# Buckling Coefficient

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Buckling coefficient, abbreviated as $$k_{cr}$$, a dimensionless number, is an instability that leads to a failure mode.  When a structure is subjected to compressive stress, buckling may occure.  Buckling is characterized by a sudden sideways deflection of a structural member.

## Buckling coefficient formula

 $$\large{ k_{cr} = \left( \frac{ n \; w }{ l } \;+\; \frac{ l }{ n \; w } \right)^2 }$$

### Where:

$$\large{ k_{cr} }$$ = buckling coefficient

$$\large{ n }$$ = number of half sine curvatures that occure lengthwise (dimensionless)

$$\large{ l }$$ = length of member

$$\large{ w }$$ = width of member