The paper began by describing the main concepts involved in a GBT formulation to analyse the buckling behaviour of thin-walled composite members. Then, a beam finite element is derived in order to solve the system of differential equations. For validation purposes, some GBT-based results are compared with experimental and theoretical values available in literature. Finally, in order to illustrate the application and capabilities of the above formulation, the results of a study concerning the local and global buckling behaviour of fully fixed I-section columns is presented and discussed. Among the several conclusions drawn from this study, the following ones deserve to be specially mentioned: (i) In the context of linear (first order) analyses of I-section beams characterized by material couplings, the GBT-based results agree very well with the experimental and theoretical estimates. (ii) In the context of stability analyses of an I-section column characterized by material couplings, it is found that local buckling modes might be critical. Unlike columns made of isotropic materials, columns characterized by material couplings exhibit buckling modes with very unusual deformed configurations. In fact, it is unveiled that the shear modes play a relevant role in the mechanics of coupling between the different conventional modes (all shear undeformable). (iii) It is found that the incorporation of both matrices H and F, accounting for the modal couplings, is indispensable to achieve reliable results. Thus, neglecting these matrices may lead to nonconservative buckling load values (up to 25%) and to very different buckling mode shapes, as it can be observed from figures 1(a) (buckling mode from the exact analysis) and 1(b) (buckling mode from the analysis without matrices H and F).
Buckling mode configuration: (a) exact and (b) approximate (analysis without matrices