# Buckling Coefficient

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

$$\large{ k_{cr} = \left( \frac{ n \; w }{ l } \;+\; \frac{ l }{ n \; w } \right)^2 }$$
Symbol English Metric
$$\large{ k_{cr} }$$ = buckling coefficient $$\large{dimensionless}$$
$$\large{ n }$$ = number of half sine curvatures that occure lengthwise $$\large{dimensionless}$$
$$\large{ l }$$ = length of member $$\large{in}$$ $$\large{mm}$$
$$\large{ w }$$ = width of member $$\large{in}$$ $$\large{mm}$$