Development of consistent buckling curves for torsional and lateral‐torsional buckling

The stability design of beams and columns for lateral‐torsional and torsional buckling is generally treated in the new Eurocode 3‐1‐1 [1] by using the same buckling curves used for flexural buckling. These buckling curves are expressed mathematically in terms of a function χ( $ \bar \lambda $ ), which was derived in [2] and [3] by combining a first‐yield strength criterion with a second‐order analysis of a geometrically imperfect column. Since the basic idea of this approach was originally presented by Ayrton and Perry [4], their names are often quoted in reference to this type of representation of buckling curves. In this paper, analytical Ayrton‐Perry‐type formulae are developed for the lateral‐torsional and torsional buckling modes of profiles with doubly symmetrical open I‐sections. The similarities and differences to the flexural buckling mode are highlighted. As a first step, the analytical background of the current code regulations is discussed and compared to the actual behaviour in lateral‐torsional and torsional buckling of open sections as shown by geometrically and materially non‐linear FEM calculations (GMNIA). Then, both the numerically derived buckling curves and the current code regulations (Eurocode 3) for these modes are compared to the Ayrton‐Perry‐type formulae developed.