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

There are several ways to determinate F_{euler} or L_{eff}:

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, F_{euler} or L_{eff} could be calculated according to:

Global instability mode: Feuler (F_{cr}) for the total structure

Partial instability mode: L_{eff} 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 L_{eff} 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.