GBT-BASED STRUCTURAL ANALYSIS OF THIN-WALLED MEMBERS:. OVERVIEW, RECENT PROGRESS AND FUTURE DEVELOPMENTS

D. Camotim1, N. Silvestre1, R. Gonsalves2 and P. B. Dinis1

1 Civil Engineering Department, ICIST/IST, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisboa, Portugal E-mail: dcamotim@civil. ist. utl. pt 2EST Barreiro, Polytechnical Institute ofSetdbal, Rua Stinville 14, 2830-114 Barreiro, Portugal

Abstract

This paper provides an overview of the Generalised Beam Theory (GBT) fundamentals and reports on the novel formulations and applications recently developed at the TU Lisbon: the use of con­ventional GBT to derive analytical distortional buckling formulae and extensions to cover (i) the buckling behaviour of members with (i1) branched, closed and closed/branched cross-sections and (i2) made of orthotropic and elastic-plastic materials, and (ii) the vibration and post-buckling be­haviours of elastic isotropic/orthotropic members. In order to illustrate the usefulness and potential of the new GBT formulations, a few numerical results are presented and briefly discussed. Finally, some (near) future developments are briefly mentioned.

1. Introduction

Generalised Beam Theory (GBT) was first proposed by Richard Schardt in 1966 and has, since then, fostered a vast amount of theoretical and applied research activity at the University of Darmstadt. However, due to the fact that practically all publications originating from this research group were available exclusively in German (including the book published by Schardt in 1989), GBT had vir­tually no impact for non-German-speaking researchers up until the early 90s. This situation was altered by J. M. Davies, who learnt about GBT in the mid 80s and, almost single-handed, dissem­inated it among the English-speaking technical and scientific communities together with his Ph. D. students Leach and Jiang, Davies employed GBT to perform in-depth investigations on the buckling behaviour of cold-formed steel members and, in particular, showed that this approach is a valid and often advantageous alternative to finite element or finite strip analyses (Davies, 1998, 2000). Moreover, it appears that Davies can also be credited with encouraging Schardt to start publishing in English (Schardt, 1994a, b).

Although GBT has recently attracted considerable attention from several researchers around the world (e. g., Rendek and Balaz, 2004; or Simao and Silva, 2004), it seems fair to say that the vast majority of the novel formulations and applications originated from the Technical University of Lisbon – this can be attested by the review paper recently published by the authors (Camotim et al., 2004), which summarises the work carried out prior to 2004. Therefore, the objective of this work is to provide a follow-up of that paper, by (i) reporting on the research activity concerning GBT undertaken in the last couple of years and (ii) addressing the developments expected for the foreseeable future. At this stage, it should be pointed out that, due to space limitations, it is only possible (i) to provide a brief overview of the new findings, (ii) to present a very small number of illustrative examples and (iii) to mention the main references, where the interested reader may find much more detailed accounts of all these topics dealt with in this paper.

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M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 187-204 © 2006 Springer. Printed in the Netherlands.

Figure 1. Thin-walled member (a) geometry, axes/displacements; (b) cross-section discretisation.