The main aspects concerning an orthotropic second order generalised beam theory (GBT), previously developed by the authors to enables the structural analysis of thin-walled members displaying special orthotropy, are briefly presented and discussed in the first part of the paper. Special attention is paid to the symbolic and numerical computational aspects related to the implementation of the GBT equations to perform member linear stability analyses. For this purpose, a finite element formulation is developed, validated and applied to solve the eigenvalue problem associated with the GBT system of differential equilibrium equations. Then, the second order orthotropic GBT is employed to investigate the buckling behaviour of pultruded fiber reinforced plastic lipped channel members, namely columns, beams and beam-columns. In particular, with the objective of illustrating the concepts and procedures involved in the performance of a GBT analysis, a detailed in-depth study of simply supported lipped channel columns is presented, in which the relevant (local and global) buckling modes are identified and the corresponding bifurcation stress values are determined. In addition, the results of an investigation concerning the influence of the applied stress distribution, cross-section geometry, material properties and end support conditions on the member buckling behaviour are presented, which required the completion of a number of parametric studies. In these investigations, careful consideration was given to the occurrence and characterisation of local-plate, distortional and mixed flexural–distortional buckling modes.
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