Euler buckling length

According to the equation developed by L.P. Euler (1707-1783), the relation Critical load (Feuler) versus buckling length (Leff) is defined by:


Relation between Critical load (Feuler) and buckling length (Leff)


There are several ways to determinate Feuler or Leff:

  • Analytical calculation: Solving the derivative
  • Simplified methods: Using alignment charts, standard (braced) situations, standard solutions for cantilevers or arches, etc.
  • Numerical calculations: FEM or FDM


Actually, Feuler or Leff could be calculated according to:

  • Global instability mode: Feuler (Fcr) for the total structure
  • Partial instability mode: Leff for each element


The purpose of the 1st way (Global) is to distinguish the possibility to perform Linear Elastic analysis (LE) or necessity to perform Geometric Non-linear analysis (GNL), as required by the National codes, like EN1993 art. 5.2.1

Another purpose of the Global instability mode is the generic way Leff could be calculated, as the Partial instability mode needs boundary conditions and is less suitable for non-standard situations. The appropriate method for Global instability mode is the Euler Buckling Stability analysis by FEM.