To underpredict or to overpredict an LBA or MNA, that is the question (a brief note on the LBA-MNA design method of EN 1993-1-6:2025)

The semi-computational LBA-MNA buckling design method of EN 1993-1-6 intended for metal shells requires an accurate execution of a linear bifurcation analysis (LBA) and a materially nonlinear analysis (MNA). Both analyses are almost invariably performed using an implementation of the finite element method which, together with analyst judgment, introduces a number of potential pathologies that can lead to either reference resistance being over- or underpredicted, to the detriment of the final buckling resistance obtained from the design method. Because the MNA resistance in particular is combined in a nonlinear manner to obtain the final buckling resistance via the so-called ‘capacity curve’, it is not immediately clear whether an overprediction of the MNA resistance (due to, e.g., ill-applied strain hardening or an excessively coarse mesh) or its underprediction (due to, e.g., ill-applied early termination) is the bigger sin. This paper presents a first-order algebraic perturbation theory exploration of the consequences of computationally over- or underpredicting either reference resistance ( R c r from the LBA or R p l from the MNA) on the final buckling resistance R k obtained from the LBA-MNA design method. It is demonstrated algebraically that an overprediction of the LBA resistance is never conservative, while an overprediction of the MNA resistance is likely unconservative under most circumstances of practical interest. For more slender, more imperfect but still elastic-plastic shells, however, an underprediction of the MNA resistance can be unconservative. The moral of this paper is thus that either MNA bias can become a sin, and that this analysis should be established as accurately as possible under all circumstances.