FEuler calculation performing calculation of factor a_{cr} by which the design loads would have to be increased to cause elastic instability in a global mode. Theoretical case a_{cr} is calculating by meaning:
a_{cr} = F_{cr} / F_{ed}
where:
F_{cr}  the elastic critical buckling load for global instability mode based on initial elastic stiffnesses
F_{ed}  the design loading on the structure
Calculation of FEuler stability is based on two stages. On the first stage linear calculation of entire system is performed. As result all the forces and displacements including axial forces as Nx is calculated. Using this calculation of FEuler is starting.
For the calculation on FEuler is presumed, that axial force in the elements is changing proportionally the parameter a>0. Changing in potential energy of entire system taken in to account influence of axial forces aN is analyzed:
(1)
where:
P – potential energy of an element taking in to account influence of axial force
E – Youngs modulus
I_{2}, I_{3} – Moments of inertia (I_{2} = I_{z}, I_{3} = I_{y})
u = (u_{1}, u_{2}, u_{3}), v = (v_{1}, v_{2}, v_{3}) – displacements:
u_{1}, v_{1} – displacements in Х direction
u_{2}, u_{3}, v_{2}, v_{3} – displacements in main directions of cross section
l – element length
Derivatives in Х' direction:
Let define H as set of functions U for that potential energy P(u) could be estimated and that satisfy kinematic determined boundary conditions. Also for such a boundary conditions on u v H, following requirement should be stated as true:
a(u, u) > 0 (2)
Inequality (2) in fact is describing geometrically stable system. Taking in to account (1), entire system is stable, in case for all u v H following inequality is true:
P(u, a) > 0 (3)
And entire system is unstable, in case for all u v H, U ≠ 0:
P(u, a) < 0 (4)
Loss of stability is met for l_{0}, u_{0} v H, u_{0} ≠ 0:
P(u_{cr}, a_{cr}) = 0 (5)
Also for all a < a_{cr} inequality (3) should be satisfied as true.
Factor a_{cr} > 0, is satisfying (5), is called "Stability criterion". Stability criterion a_{cr} is used for Steel code check (NENEN 199311, EN 199311 chapter 5.2.1).
Example
Single project file calculating different structural parts – columns:
 Calculating single column loaded by F=1500kN:

a_{cr} = 7.14 < 10  GNL calculation is needed (NENEN 199311 chapter 5.2.1) 
 Calculating single column loaded by F=100kN:

a_{cr}= 107.16 > 10  LE is sufficient (NENEN 199311 chapter 5.2.1) 
 Single project calculating two structural elements – columns:
a_{cr} = 7.14 < 10  GNL calculation is needed (NENEN 199311 chapter 5.2.1) 
Conclusion:
Conservative approach is taken. In case of separate structures, the decisive structure part determines a_{cr}.
For current example the whole structure should be calculated GNL :
 Otherwise the structure should be split in separate projects to calculate some parts GNL and others LE;
 GNL approach is always better then LE in case of steel code checking, only calculation is more time consuming.