Elastic buckling of elliptical tubes subjected to generalised linearly varying stress distributions J.M. Abela, L. Gardner n Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, United Kingdom article info Article history: Received 2 March 2012 Accepted 24 April 2012 Available online 18 May 2012 Keywords: Biaxial bending Combined bending and axial compression Cross-sectional classification Elastic buckling Elliptical hollow sections Instability Oval hollow sections abstract The structural behaviour of elliptical hollow sections has been examined in previous studies under several loading conditions, including pure compression, pure bending and combined uniaxial bending and compression. This paper examines the elastic buckling response of elliptical hollow sections under any linearly varying in-plane loading conditions, including the most general case of combined compression and biaxial bending. An analytical method to predict the elastic buckling stress has been derived and validated against finite element results. The predictive model first identifies the location of the initiation of local buckling based on the applied stress distribution and the section geometry. The critical radius of curvature corresponding to this point is then introduced into the classical formula for predicting the elastic local buckling stress of a circular shell. The obtained analytical results are compared with results generated by means of finite element analysis. The comparisons between the analytical and numerical predictions of elastic buckling stress reveal disparities of less than 2.5% for thin shells and, following an approximate allowance for the influence of shear, less than 7.5% for thick shells. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction Research activity in the area of elliptical sections has increased in recent years due to their emergence as hot-rolled structural products. Elliptical hollow sections (EHS) combine the elegance of circular hollow sections (CHS) with the improved structural efficiency in bending associated with sections of differing flexural rigidities about the two principal axes. This behaviour has been exploited in a number of recent projects that have adopted EHS as structural elements, such as the Honda Central Sculpture in Good- wood, UK, the Society Bridge in Braemar, UK [1] and the airport at Barajas in Madrid, Spain [2]. EHS were also included in the latest edition of the European product standard EN 10210 [3] and in the BCSA/SCI Eurocode member resistance tables [4]. A review of research into the structural behaviour of elliptical hollow sections, together with a description of recent practical applications, may be found in [5]. Further subsequent work on the buckling response of EHS members has also been performed [6–12]. 2. Literature review The focus of the present study is the elastic buckling response of elliptical tubes under linearly varying in-plane stress distributions, including the most general case of combined axial compression plus biaxial bending. First, previous investigations of the elastic buckling response of EHS under isolated loading cases, as well as compression plus uniaxial bending, are reviewed. 2.1. Compression Marguerre [13] made the first attempt at representing the buckling behaviour of cylindrical shells of variable curvature under compression. The work was later continued by Kempner [14] and Hutchinson [15]. Kempner’s work [14] concluded that the elastic buckling stress of an oval hollow section (OHS) could be accurately predicted as the buckling stress of a circular hollow section (CHS) with a radius equal to the maximum radius of curvature of the OHS. This solution was shown to be a lower bound. Hutchinson [15] found that this approach could also be applied to elliptical hollow sections (EHS), provided that the shell is sufficiently thin. The proposals were later confirmed by experiments carried out by Tennyson et al. [16]. Further investigations have been carried out by Zhu and Wilkinson [17], Chan and Gardner [18], Ruiz-Tera ´ n and Gardner [19] and Silvestre [20]. These studies confirmed that Kempner’s approach [14] of basing the elastic buckling stress of an EHS on that of a CHS with a radius equal to the maximum radius of curvature of the ellipse is acceptable but with increasing errors for higher aspect ratios and thicker sections. Analyses of the Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/tws Thin-Walled Structures 0263-8231/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tws.2012.04.016 n Corresponding author. Tel.: þ44 207 594 6031. E-mail address: leroy.gardner@imperial.ac.uk (L. Gardner). Thin-Walled Structures 58 (2012) 40–50