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CivilComp Proceedings
ISSN 17593433 CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 247
LateralTorsional Buckling of Tapered ThinWalled Beams: 1D Formulation vs. Shell FE Analysis A. Andrade+, D. Camotim* and P.B. Dinis*
+Department of Civil Engineering, Faculty of Science and Technology, University of Coimbra, Portugal
A. Andrade, D. Camotim, P.B. Dinis, "LateralTorsional Buckling of Tapered ThinWalled Beams: 1D Formulation vs. Shell FE Analysis", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 247, 2004. doi:10.4203/ccp.79.247
Keywords: lateraltorsional buckling, webtapered beams, buckling analysis, onedimensional variational formulation, prebuckling deflections, Isection cantilevers, RayleighRitz method, shell finite element analysis.
Summary
In recent years, the use of thinwalled tapered structural members (i.e., non
prismatic members with a continuous crosssection variation) has gained an increasing
popularity in the steel construction industry, mainly because of their efficiency and
aesthetics. Opensection flexural members, either prismatic or tapered, are prone to
lateraltorsional buckling (LTB) and, therefore, it would be most convenient, for the
sake of uniformity and easeofuse, to have design methodologies that are valid for
both prismatic and tapered beams. In order to achieve this goal, the most "natural"
approach consists of extending the prismatic beam rules and procedures already
available in the current steel design codes, making them also valid for the design of
tapered beams. Indeed, this was precisely the approach followed in the most recent
"preliminary version" of the upcoming EN version of Eurocode 3. Hence, the need
arises to develop efficient and accurate methods to evaluate the elastic critical load
parameter (i.e., the load parameter associated with the first bifurcation point) of a
given tapered beam, a necessary step towards the determination of its slenderness.
Very recently, the first two authors derived a onedimensional (1D) formulation to analyse the elastic LTB behaviour of singly symmetric tapered thinwalled open beams, which (i) is able to account for the influence of the prebuckling deflections and (ii) clearly shows that, in general, the behaviours of prismatic and tapered beams are qualitatively different. This 1D formulation is based on a number of a priori assumptions (which, in fact, are an extension of the classical Vlassov's hypotheses of prismatic thinwalled beam theory) and was only validated through the comparison with LTB results reported by other researchers, also relying on more or less similar a priori assumptions. Therefore, it becomes necessary to further (i) validate these assumptions and (ii) assess the merits of the 1D model that they bring about. This is precisely the central objective of this work, in which a comparison is made between (i) the global performance of the above 1D formulation (numerically implemented by means of the RayleighRitz method) and (ii) the results yielded by shell finite element analyses (FEA). The latter are performed in the code ABAQUS and their results are deemed "exact". The FEA are also used to check the validity of one of the kinematical assumptions underlying the 1D model (the one stating that the crosssections remain undeformed in their planes). This comparative study concerns Isection cantilevers (i) with equal/unequal uniform flanges and uniform/linearly tapered webs, which (ii) are acted by point loads applied at various locations of the free end section. The paper begins with a brief review of the 1D formulation. Next, the most relevant aspects involved in the LTB shell FEA of (prismatic and tapered) beams are addressed, including (i) the adequate discretisation of the beams, (ii) the numerical procedure used to solve the eigenvalue problem arising in the linear stability analysis (prebuckling deflections neglected) and (iii) the approach devised to account for the prebuckling deflections. Finally, the results of the comparative study are presented and discussed. They consist of (i) 1D and FEAbased linear (i.e., obtained by neglecting the prebuckling deflections) and nonlinear critical loads, and (ii) the associated critical buckling modes  Figure 1(a). Also shown is the free end section web distortion appearing in the FEAbased critical modes, which makes it possible to assess how much the web "true" deformed shape deviates from the one generated by an inplane rigid body rotation  Figure 1(b). On the basis of this study, it is possible to say that, as long as the cantilevers are not too short, the onedimensional formulation leads to reasonably accurate estimates of the critical loads and buckling mode shapes, regardless of whether the prebuckling deflections are taken into account or not. Moreover, the accuracy of these estimates gradually increases with the cantilever length, a trend that reflects the decreasing relevance of the web distortion taking place near the free end section. To a certain extent, this fact validates one of the a priori assumptions incorporated in the onedimensional model. As for the considerable differences between the 1D and shell finite element models recorded for the shorter cantilevers, they are mainly due either to (i) significant web distortion or (ii) a localised web buckling phenomenon, which occur in the neighbourhood of the load point of application. Obviously, none of these local effects can be captured by the 1D formulation.
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