Contents lists available at ScienceDirect Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws Full length article An improved method for analyzing shear lag in thin-walled box-section beam with arbitrary width of cantilever ﬂange Xiayuan Li a , Shui Wan a,∗ , Y.L. Mo b , Kongjian Shen a , Tianmin Zhou b , Yuze Nian a a School of Transportation, Southeast University, Nanjing, 210096, China b Department of Civil and Environment Engineering, University of Houston, Houston, TX, 77204-4006, USA ARTICLEINFO Keywords: Thin-walled box-section beam Shear lag phenomenon Initial shear rotation Designed procedure Theoretical analysis method Finite element method ABSTRACT The shear lag eﬀect can signiﬁcantly aﬀect the performance of wide-box structures, and even becomes one of the most important inﬂuencing factors endangering structural safety. This paper develops a theoretical analysis method, which is designated as PM analysis for analyzing shear lag phenomenon in thin-walled box-section beam with arbitrary width of cantilever ﬂange. In this method, the introduction of initial shear rotation (or initial shear strain) γ 0i , due to the eﬀect of web restraint on ﬂanges, is innovatively proposed and further em- ployed in describing the additional warping displacement in top lateral cantilever ﬂanges, and a practical and straightforward procedure of coeﬃcient α 3 is designed (DP) based on the proposed assumptions. In addition, a modiﬁed method to PM-DP analysis is developed for improving the defects of the hypothesis of shear-lag warping displacements in top lateral cantilever ﬂanges, that is, PM-DP(M) analysis. The diﬀerential equations for generalized displacement w(x) and the standard magnitude of shear-lag warping displacement U(x) of the beam are deduced by means of the principle of minimum potential energy (MPE) and solved with the given boundary conditions. Numerous models of thin-walled box-section with arbitrary width of top lateral cantilever ﬂanges under distributed load are chosen and built through a software program (ABAQUS). The results obtained from PM analysis (PM-LB, PM-DP and PM-DP(M)) are summarized into a series of curves indicating the distribution of normal stress and the displacements for various examples, and compared to those obtained from the ﬁnite element method (FEM). The study widely demonstrates the strong applicability and high precision of PM-DP(M) analysis, which can be considered as an ideal solution in predicting shear lag eﬀect for thin-walled box-section beam with arbitrary width of cantilever ﬂange and, possibly, be adopted as valuable reference for the design of related thin-walled structures. 1. Introduction The shear lag eﬀect of thin-walled box-section beam, especially in engineering structure design, has received enormous investigation due to several catastrophic events happened before. Owing to the shear lag eﬀect, the structural performance can be diﬀerent from those predicted by the elementary beam theory, where the normal stress distribution along ﬂanges is assumed to be non-uniform and the deﬂection of the beam is much larger [1–8]. Therefore, for safety's sake, the shear lag coeﬃcient [9,10] and eﬀective-width [11,12] should be introduced in structure design, which, strictly speaking, requires the accurate normal stress distribution over the cross-section of thin-walled box-section beam. Numerous literature published are concerned with the experimental tests [9,18], theoretical analysis [19–27] and numerical analysis [13–18,28,29]. Reisnner [1], Kuzmanovic and Graham [2], and Dezi and Mentrasti [3] were one of the earliest pioneers to investigate the shear lag eﬀect for thin-walled box-section beam on the basis of the principle of minimum potential energy (MPE), and the quadratic parabolic curve was suggested to describe the distribution of the ﬂex- ural normal stress in the ﬂange plate of girders. Subsequently, to de- termine which expression of shear-lag warping displacement function in ﬂanges is appropriate, much research work have been done, such as quadratic parabolic curve by Zhang [4–6], cubic parabolic curve by Guo and Fang [9], and Chang [22], biquadratic parabolic curve by Chang [23], and cosine curve by Qian and Ni [7,24], etc. Gan and Zhou [31] studied the precision selection of expression of shear-lag warping displacement function for thin-walled box-section beam. However, some critical factors are left unconsidered; for instance, equilibrium condition of internal force of cross section, the relationship between the https://doi.org/10.1016/j.tws.2019.03.026 Received 15 July 2018; Received in revised form 24 January 2019; Accepted 12 March 2019 ∗ Corresponding author. E-mail addresses: lixiayuan123@163.com (X. Li), lanyu421@163.com (S. Wan), yilungmo@central.uh.edu (Y.L. Mo). Thin-Walled Structures 140 (2019) 222–235 Available online 27 March 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved. T