7/23/2019 Gardner 2010 http://slidepdf.com/reader/full/gardner-2010 1/12 Proceedings of the Institution of Civil Engineers Structures and Buildings 163 December 2010 Issue SB6 Pages 391–402 doi: 10.1680/stbu.2010.163.6.391 Paper 900095 Received 30/11/2009 Accepted 22/07/2010 Keywords: codes of practice & standards/reviews/steel structures Tak Ming Chan Assistant Professor, School of Engineering, University of Warwick, UK Leroy Gardner Reader, Department of Civil and Environmental Engineering, Imperial College London, UK Kwan Ho Law PhD student, Department of Civil and Environmental Engineering, Imperial College London, UK Structural design of elliptical hollow sections: a review T. M. Chan MSc, DIC, PhD, L. Gardner MSc, DIC, PhD, CEng, MICE, MIStructE and K. H. Law MSc, DIC, CEng, MIStructE Tubular construction is synonymous with modern architecture. The familiar range of tubular sections – square, rectangular and circular hollow sections – has been recently extended to include elliptical hollow sections (EHSs). Due to differing ﬂexural rigidities about the two principal axes, these new sections combine the elegance of circular hollow sections with the improved structural efﬁciency in bending of rectangular hollow sections. Following the introduction of structural steel EHSs, a number of investigations into their structural response have been carried out. This paper presents a state-of-the-art review of recent research on EHSs together with a sample of practical applications. The paper addresses fundamental research on elastic local buckling and post-buckling, cross-section classiﬁcation, response in shear, member instabilities, connections and the behaviour of concrete-ﬁlled EHSs. Details of full- scale testing and numerical modelling studies are described, and the generation of statistically validated structural design rules, suitable for incorporation into international design codes, is outlined. NOTATION A gross cross-section area A c cross-section area of the concrete within a concrete- ﬁlled steel tube A eff effective cross-section area A s cross-section area of a steel tube A v shear area a half of the larger outer diameter of an EHS b half of the smaller outer diameter of an EHS D e equivalent diameter D e1 equivalent diameter (Kempner, 1962) D e2 equivalent diameter (Ruiz-Teran and Gardner, 2008) D e3 equivalent diameter (Zhao and Packer, 2009) E Young’s modulus f coefﬁcient dependent on thickness and larger outer diameter of an EHS f ck compressive concrete strength f y material yield stress L 0 perimeter M el,Rd elastic moment resistance M el, z ,Rd elastic moment resistance about the minor (z–z ) axis M pl,Rd plastic moment resistance M pl, y ,Rd plastic moment resistance about the major ( y – y ) axis M u ultimate bending moment M y ,Ed design bending moment about the major ( y – y ) axis M z ,Ed design bending moment about the minor (z– z ) axis N b,Rd member buckling resistance N c,Rd cross-section compressive resistance N CFT cross-section compression resistance of a concrete- ﬁlled EHS N cr elastic ﬂexural buckling load N Ed design axial force N u ultimate axial load N y plastic yield load R rotation capacity r radius of curvature r 0 radius of a circular section with the same perimeter as the corresponding oval r cr critical radius of curvature r max maximum radius of curvature r min minimum radius of curvature s coordinate along the curved length of an oval t thickness of shell V pl,Rd plastic shear resistance V u ultimate shear force W eff effective section modulus W el elastic section modulus y coordinate along the major ( y – y ) axis y – y cross-section major axis z coordinate along the minor (z– z ) axis z– z cross-section minor axis coefﬁcient dependent on the material yield stress º non-dimensional member slenderness Poisson’s ratio eccentricity of an oval 1 , 2 end stresses cr elastic buckling stress y yield stress in shear ł ratio of end stresses 1. INTRODUCTION The opening of Britannia Bridge in the UK in 1850 (Collins, 1983; Ryall, 1999) heralded a new era for structural hollow sections. It was the ﬁrst major civil engineering application to adopt rectangular hollow sections (RHSs) in the main structural skeleton. Behind the scenes, viable design options involving circular hollow sections (CHSs) and elliptical hollow sections (EHSs) were also considered during the conceptual design Structures and Buildings 163 Issue SB6 Structural design of elliptical hollow sections: a review Gardner et al. 391