Keywords: thin-walled steel beams, thin-walled steel frames, generalised beam theory, buckling analysis, effect of the load point of application, localised buckling.

The structural efficiency of a given slender steel structure can only be adequately assessed after acquiring in-depth information concerning its buckling behaviour, a task involving (i) the identification of the relevant buckling modes and (ii) the evaluation of the associated bifurcation stresses. However, since these structures are typically built from thin-walled open-section members, which exhibit a very low torsion stiffness and are highly susceptible to global, local, distortional and localised buckling phenomena, the assessment of their structural response constitutes a very complex task that involves performing either (i) costly and carefully planned experimental tests or (ii) complex, time-consuming and computer-intensive shell finite element analyses. A very promising alternative is using one-dimensional models (beam finite elements) based on generalised beam theory (GBT).

The authors have recently developed and numerically implemented GBT-based beam finite elements that make it possible to analyse the local, distortional and global buckling behaviour of continuous beams and frames. However, such finite elements are only valid for transverse loads acting at cross-section shear centres. In spite of the undeniable practical interest in such loadings, one must recognise that structural members are often subjected to loads applied at various cross-section points.

This paper presents the development, finite element implementation and application of a GBT formulation intended to analyse the localised, local, distortional and global buckling behaviour of thin-walled continuous beams and frames subjected to transverse loads applied at various cross-section points (away from the shear centre). In order to take into account the effects caused by the transverse load position, the GBT buckling formulation must incorporate geometrical stiffness terms stemming from either (i) the internal work of the pre-buckling transversal normal stresses ("exact" formulation) or (ii) the external work of the applied transverse loads (approximate/simplified formulation). After presenting the main concepts and procedures involved in developing the above "exact" and simplified formulations, the paper addresses the corresponding numerical implementations. Then, in order to illustrate their application and capabilities (as well as the limitations of the simplified formulation), various numerical result sets are presented and discussed. They concern (i) strip (thin rectangular) beams, (ii) hat-section cantilevers, (ii) two-span I-beams and (iv) "L-frames" with I-section members, all acted by transverse loads applied at two different locations. The accuracy of the GBT-based results is assessed through the comparison with "exact" values, yielded by rigorous ANSYS shell finite element analyses.

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