Eurocode lateral torsional buckling capacity is calculated per equations in Annex F in the ENV 1993-1-1:1992. This calculation uses variables C1, C2 and C3. Since there is no generic formula in the Eurocode to calculate the moment gradient factor, C1, RISA will use the widely accepted López, Yong and Serna method by default.
The method proposed by López, Yong and Serna in their paper “ Lateral-Torsional Buckling of Steel Beams: A General Expression for the Moment Gradient Factor” to determine the moment gradient factor takes into account both the moment diagram and support conditions.
The general proposed closed form expression presented by López et al is the following:
Where k is,
A1 and A2 are given by,
The contribution of the support conditions are considered in the k1 and k2 terms. When lateral bending and warping are free, k1 or k2 is equal to 1.0 for the corresponding support. When lateral bending and warping are prevented, k1 or k2 is taken as 0.5.
The values rendered using this closed form expression have been shown to match closely with numerical results in comparison to methods proposed by AISC and BS 5950-1. However, the user can always override this value within the Design tab on the Member Information dialog.
Alternatively, this override is also in the Hot Rolled tab of the Members spreadsheet.