Lateral-torsional buckling checks of steel frames using second-order analysis

This article summarizes the rules given in EN 1993-1-1 [2] for using second-order analysis to check the flexural and lateral-torsional buckling of members and systems loaded in the strong plane of their cross-section which may not fail due to out-of-plane instability.
The rules relevant in EN 1993-1-1 [2] are those for equivalent geometrical imperfections resulting from the elastic buckling modes with amplitudes derived from column buckling tests according to EN 1990 Annex D [1] plus those for the linear superposition of utilization rates in the strong and weak planes as used for evaluating tests to determine the amplitude of imperfections and the partial factors.
Computer assistance is generally required for determining the elastic buckling modes; the computer outputs gives both modal out-of-plane displacements and modal out-of-plane bending moments for the relevant flanges of the sections. The use of out-of- plane bending moments makes the assessment clear and simple. It leads to a magnification factor for the in-plane-utilization rate that allows the design point x = xd to be found along the length of the member or system where the cross-sectional check is relevant. It also shows that the results of the second-order analysis for this design point and the use of buckling curves for member checks at this design point are identical.
The assessment procedure with second-order analysis is generic and applicable to all design cases, whereas the member checks with buckling curves as specified in EN 1993-1-1 [2] are intended to be valid for specific loadings and boundary conditions only (object-oriented rules). They should be consistent with the generic rules. In this respect, this article is a contribution towards the further evolution of EN 1993-1-1 [2].