Euler's Column Formula

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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 π² E I / L²    (1) 

where

P = allowable load (lb, N)

n = factor accounting for the end conditions

E = modulus of elastisity (lb/in², kPa)

L = length of column (in, m)

I = moment of inertia (in⁴, mm⁴)

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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