Buckling

Columns are long slender members subjected to an axial compressive force. Lateral deflection on a column is called buckling.

The maximum axial load that a column can support when it is on the verge of buckling is called the critical load P_cr

From Euler's formula, define the first mode buckle as P1_cr = π²EI/(L²), then P = n²P_cr , n = 1,2,3,4,... where

L = the column length

E = material Modulus

and n is the number of waves in the deflected shape of a column. Alternatively, if we define the effective length as the length of the column divided by n, then we can always substitute it into the first mode buckling formula, P1_cr, defined above, to get the nth mode buckling load. For instance, if n = 3, three waves appear in the buckled column, at the right of the animation and the column can support a critical buckling load that is 9 times the P_cr. It can only exist when the lateral braces support the column.

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This material is based upon work supported by the National Science Foundation under Grant No. 0633602. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

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