Advance Design computes the elastic critical moment, Mcr, according to NF EN 1993-1-1/NA, with the formula:

Formula used by Advance Design to compute the elastic critical moment  (1)

Where the buckling is considered by means of the buckling coefficients, kz and kw, which are defined in the Lateral-torsional buckling area:

Steel design assumptions - Buckling settings

Figure 1- Steel design assumptions - Buckling settings 

Mcr is computed in all the five points of each mesh of the linear element. The one resulted in the Unfavorable case (on a specific mesh and point) is given on the element stability check.
As for the buckling lenghts Lfy and Lfz, they are computed based on rigidity distribution factors, η1 and η2, at both ends of the element (braced or unbraced), according to CM66 or EC3 ENV:

Properties list – Lateral-torsional buckling settings

Figure 2 - Properties list – Lateral-torsional buckling settings

Also, you can peform a more thorough and precise stability analysis by means of the Advance stability (2nd order) solver. It considers multiple effects in an eigen value stability problem, without using standard buckling data (length, coefficients). This feature is implemented since the Advance Design 2019 version.

Properties list - Advance stability tool settings

Figure 3 - Properties list – Advance stability tool settings 

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