Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct Fibre beam element models for nonlinear analysis of concentrically loaded circular CFT columns considering the size effect Siqi Lin a , Yan-Gang Zhao a,b , Zhao-Hui Lu a, ⁎ a Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China b Dept. of Architecture and Building Engineering, Kanagawa Univ., Kanagawa 2218686, Japan ARTICLE INFO Keywords: Fibre beam element model Concrete-filled steel tube columns Size effect ABSTRACT The fibre beam element (FBE) method has been widely used to investigate the behaviors of concrete-filled steel tube (CFT) columns for its high efficiency and accuracy. The existing models were generally developed or ca- librated by using specimens with relatively small size, in which the size effects were ignored or poorly in- corporated. Additionally, most existing FBE models focused on CFT stub columns. In this paper, a new FBE model for nonlinear analysis of concentrically loaded stub and slender columns was proposed, in which the size effects on the effective stress-strain relationships of steel tube and core concrete were well incorporated. The proposed FBE models were then used to develop an ultimate strength model for the design of both stub and slender columns. A total of 1029 specimens assembled from 72 previous studies were used to verify the proposed models. The results suggested that the proposed FBE model performs quite well for both small- and large- size CFT stub columns and predicts the behaviors of slender columns with reasonable accuracy. Moreover, the ul- timate strength model developed based on the proposed FBE models was found to make satisfying prediction of test results. 1. Introduction Concrete-filled steel tube (CFT) columns, as composite structures, combine the advantages of the constituent steel and concrete materials [1], leading to excellent performance of high strength, stiffness and ductility [2]. To understand the behaviours of CFT columns, many ex- perimental tests have been done in previous studies. Although experi- mental tests are important for the investigation of CFT columns, they are generally expensive and time-consuming. The finite element method is an alternative way to investigate the behaviours of CFT columns. Detailed three-dimensional (3D) finite-element (FE) models using commercial software, e.g. ABAQUS, allow direct modelling of the composite action between the steel and concrete components, with local and global imperfections, residual stresses and boundary condi- tions considered [3]. In general, 3D FE models can precisely predict the behaviour of composite structures, which, however, are tedious and complicated to build and impractical for the analysis of large structural systems or for routine design [4]. To achieve a balance between effi- ciency and accuracy, the fibre beam element (FBE) method was widely used for its accuracy and high computational efficiency [5]. For the FBE method, effective stress-strain models of steel tube and concrete, accounting for the composite effects, are necessary. Several effective stress-strain models have been available in previous studies for nonlinear analysis of concentrically loaded CFT columns, which were mainly developed based on experimental test results, e.g., the models of Neogi et al. [6],Sato [7],Tang et al. [8], Susantha et al. [9], Han et al. [10], Sakino et al. [11], Chen et al. [12], Hatzigeorgiou [13], and De- navit [5], or based on regression analysis of the effective stress-strain curves generated using 3D FE models, e.g., Shams et al. [14], Lai et al. [15], and Katwal et al. [4]. For the models developed based on ex- perimental tests, their accuracy was generally limited to the range of tests used. Using 3D FE method to develop FBE models, i.e., the effec- tive stress-strain models of steel tube and concrete, is considered more reliable and scientific [4]. Among existing FBE models, Katwal et al.’s, developed based on Tao et al.’s 3D FE model [3], was one of the most sophisticated for that the strain softening or strain-hardening behaviour of steel tube and concrete were well simulated. Generally, the results predicted by Katwal et al.’s model agreed well with experimental re- sults. However, the specimens they used to verify their model generally had relatively small size, which is a common issue for all existing FBE models. It is well known that the CFT columns in practical structures are of large size, and their behaviours have been found to differ from those of small-size specimens [16–18]. Thus, the applicability of ex- isting FBE models to large-size CFT columns is doubtful. Although some https://doi.org/10.1016/j.engstruct.2020.110400 Received 17 September 2019; Received in revised form 16 January 2020; Accepted 17 February 2020 ⁎ Corresponding author. E-mail address: luzhaohui@bjut.edu.cn (Z.-H. Lu). Engineering Structures 210 (2020) 110400 0141-0296/ © 2020 Elsevier Ltd. All rights reserved. T