# Euler's Column Formula

## Buckling of columns

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Columns fail by buckling when their critical load is reached. Long columns can be analysed with the Euler column formula

*P = n π ^{2} E I / L^{2} (1) *

*where *

*P = allowable load (lb, N)*

*n = factor accounting for the end conditions*

*E = modulus of elastisity (lb/in ^{2}, kPa)*

*L = length of column (in, m)*

*I = moment of inertia (in ^{4}, mm^{4})*

### Factor Counting for End Conditions

- column pivoted in both ends :
*n = 1* - one end fixed, the other end rounded :
*n = 2* - both ends fixed :
*n = 4* - one end fixed, one end free :
*n = 0.25*

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