Conclusion and Future Developments

After an extremely brief overview of the concepts/procedures involved in a “conventional” GBT analysis, the paper reported on the GBT formulations/applications recently developed at the TU Lisbon, namely:

(i) The use of “conventional GBT” to derive approximate analytical formulae to estimate dis – tortional buckling stresses in lipped channel, zed-section and rack-section cold-formed steel members.

(ii) Extensions of the conventional GBT to cover members with (ii1) arbitrary open/closed branched cross-sections and (ii2) made of orthotropic linear elastic and non-linear elastic-plastic materials.

(iii) A GBT formulation to analyse the vibration behaviour of loaded folded-plate members made of orthotropic linear elastic materials.

(iv) A geometrically non-linear GBT formulation to analyse the post-buckling behaviour of folded – plate members made of orthotropic linear elastic materials.

To illustrate the application and provide an idea of the capabilities of the GBT approach to solve structural analysis problems, a few numerical results were presented and very briefly commented. For validation purposes, some of these results were also compared with values yielded by shell finite element analyses, performed in the commercial codes ADINA and ABAQUS.

Because a very rich research activity on GBT formulations, implementations and applications is still under way at the TU Lisbon, further developments are to be expected in the near-to-intermediate future. For instance, the topics being currently investigated include:

(i) GBT formulations to analyse the buckling behaviour of thin-walled members made of ortho­tropic linear elastic or non-linear elastic-plastic materials that exhibit arbitrary closed/branched cross-sections.

(ii) GBT formulations to analyse the vibration behaviour of thin-walled members made of orthotropic linear elastic materials and exhibiting arbitrary closed/branched cross-sections.

(iii) GBT formulations to analyse the buckling and vibration behaviour of isotropic linear elastic thin-walled members exhibiting arbitrary closed/branched cross-sections and subjected to non­uniform internal force and moment diagrams (i. e., under stress gradients).

(iv) GBT formulations to analyse the first and second-order behaviour of isotropic elastic-plastic thin-walled members with unbranched open cross-sections.

(v) A GBT formulation to analyse the post-buckling behaviour of orthotropic linear elastic thin – walled members with open branched and arbitrary closed/branched cross-sections.

(vi) The influence of local-plate/distortional and local/global mode interaction effects on the elastic post-buckling behaviour of cold-formed steel members.

(vii) The development of GBT-based beam finite elements intended to enable the performance of elastic first-order and buckling analyses of plane and spatial frames made of thin-walled steel members.