Euler's Column Formula

Buckling of columns

euler column

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

F = n π2 E I / L2    (1) 


F = 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

Example - A Column Fixed in both Ends

A square aluminum column with length 5 m is fixed in both ends. The Moment of Inertia of the column is 4 108 mm4 (4000 10-8 m), the Modulus of Elasticity of aluminum is 69 GPa (69 109 Pa) and the factor for the column fixed in both ends is 4.

The Euler buckling load can be calculated as

F = 4 π2 (4000 10-8 m4) (69 109 Pa) / (5 m)2 

 =  4354 N

Related Topics

  • Beams and Columns - Deflection and stress, moment of inertia, section modulus and technical information of beams and columns

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