Engineering Structures 26 (2004) 641–650 www.elsevier.com/locate/engstruct Rational definition ofthe flexural deformation capacity ofRC column sections Yu-Fei Wu a , Deric J. Oehlers b, , Michael C. Griffith b a Department of Building and Construction, City University of Hong Kong, Hong Kong, China b Department of Civil and Environmental Engineering, Adelaide University, Adelaide, SA 5005, Australia Received 16 July 2003; received in revised form 2 January 2004; accepted 6 January 2004 Abstract Traditionaldefinitions ofthe ultimate displacement ofRC structures are usually based on strength concerns in order to ma tain a substantial proportion ofthe initiaload-carrying capacity. This kind ofdefinition does not reflect the true deformation capacity ofstructures. This work reveals the qualitatively different deformation stages ofRC members through analytical and numerical studies,which is then used to define ultimate displacement and displacement ductility.The study provides a clear insight into the fundamental mechanism of concrete structural deformation and reveals the following three basic paramet affect the deformation capacity ofRC sections: ultimate strain ofconcrete material; axialload level;and cross-sectional depth. The longitudinal reinforcement is found to reduce the deformation capacity of RC sections at axial load levels that are low a criticalaxial load level, which is near to 30% ofconcrete crushing load, and to increase the deformation capacity at axial loa levels that are higher than the critical axial load. # 2004 Elsevier Ltd. All rights reserved. Keywords: RC columns; Flexuraldeformation; Concrete ultimate strain; Ultimate curvature; Deformation capacity; Ductility;Axial load level; Critical axial load 1. Introduction Structural calculationsand design involve both strength and displacement. The definition ofthe maximum or ultimate strength ofa structure is simple and clear,as a structural response curve usually has a peak, in terms ofstrength, at the junction ofthe ascending and descending (softening) branches ofthe response curve. The definition ofthe ultimate displace- ment is more controversial as there is usually no peak in a structural response curve in terms ofdisplacement. A popular way ofdefining the ultimate displacement, in assessing the ductility ofa structure, is to choose the maximum displacement ofa structure at which the structuralresistance isat a certain proportion ofits initial load-carrying capacity under the specified load pattern.For example, the ultimate curvature ofan RC memberis defined asthe curvature on the softening branch ofthe moment–curvature responsecurveat which the resistant momentofthe memberdropsto 80% ofthe maximum moment at the fourth cycle of load [8]. This kind ofdefinition is based on the strength concern ofthe structure and is widely accepted in the literature. However, this definition ofultimate displace- ment usually cannot reflect the true deformation capacity ofthe member and does not provide a uni- form benchmark to reflect the same degree of damage to the concrete structures. This work studiesthe fundamental mechanism of deformation ofRC members by relating the different stagesofmaterial damageofconcrete to different stagesofdeformation ofRC members.The different stages ofdeformation are shown to be qualitatively dis- tinctiveand the turning points ofthe deformation stages are used to define ultimate displacement ofRC members and displacement ductility.The study starts with a very simple model ofrectangular plain concrete cross-section and a triangular stress–strain model in Corresponding author. Tel.: +61-8-8303-4314; fax: +61-8-8303- 4359. E-mail address: doehlers@civeng.adelaide.edu.au (D.J. Oehlers). 0141-0296/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2004.01.001