Contents lists available at ScienceDirect Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws Probabilistic estimation of the buckling strength of a CFS lipped-channel section with Type 1 imperfection Hashmi S.S. Ahmed a , Siddhartha Ghosh a, ⁎ , Mohit Mangal b a Structural Safety, Risk & Reliability Lab, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India b Department of Civil and Environmental Engineering, Hong Kong University of Science & Technology, Kowloon, Hong Kong ARTICLE INFO Keywords: Cold-formed steel Uncertainty Imperfection Local buckling Post-buckling Lipped channel ABSTRACT Local geometric imperfections in a cold-formed steel (CFS) member can significantly alter the force-carrying capacity of the member. These are the dents and undulations which occur during cold-rolling, handling, transportation and erection of CFS members. The buckling strength of a lipped channel section with Type 1 local imperfection is obtained and characterised statistically using finite element analyses and Monte Carlo simula- tions. The reduction in strength due to these imperfections are found to be significant. The quantification of reduction in strength due to these imperfections is found for different values of non-dimensional slenderness ratio. Based on the statistical analysis, design equations and strength curves are recommended for the buckling strength of geometrically imperfect members. Legitimacy of using a generalised statistics of imperfection, in the case of unavailability of specific data for a particular section, is also verified. 1. Geometric imperfections in cold-formed steel sections Cold-formed steel (CFS) sections are fabricated from thin steel sheets using either press-braking or roll-forming process, by passing the sheet through a number of dies. The characteristic that differentiates CFS sections from hot-rolled ‘structural’ steel sections is that the shape of the cross-section, instead of the thickness of the section, is used for carrying loads [1]. The force carrying capacity of CFS sections depends largely on the shape achieved through a cold-forming process. Devia- tions from the target shape may affect a CFS section's capacity sig- nificantly. However, due to a multiplicity of reasons it is almost im- possible to maintain the perfection in the cross-sectional dimensions of a CFS section that is finally used in construction. One major reason is that cold-rolling mills do not adhere to a very strict quality in the cold- rolling process, which results in geometrically imperfect sections coming out of these mills. The other significant reason is the loads during handling, transportation, and erection (those loads, for which the section is not typically designed), which cause visible deformations in these thin members. Geometric imperfections (GIs) in CFS sections include global and local deviations. Whereas global behaviours, such as bow, camber and twist, are categorised under global GI, local devia- tions are characterised by dents and undulations in the member ele- ments (flange, web etc.). As mentioned earlier, these deviations can significantly alter the force-carrying capacity of a section. CFS sections are characterised by the presence of different instability modes, such as local, distortional and global buckling, prior to the ultimate ‘failure’ of the member. The design of these sections is generally governed by the ‘post-(local/distortional) buckling’ behaviour. The strength limit states are defined by ‘overall’ buckling, which includes flexural, torsional and torsional-flexural modes. Owing to typical proportions of CFS member elements, these buckling modes (in real structures) are usually elastic [2]. However, some stocky members fail by inelastic (overall) buckling as well. Design standards, such as AISI S100 [3] or AS/NZS 4600 [4], include the effect of inelasticity in the post-(local) buckling behaviour of CFS mem- bers. In this article, we focus on the effects of Type 1 local geometric im- perfections on the buckling strength of a lipped channel (‘C’) section, in a statistical sense. A lipped C section is considered for this study because these are the most commonly used sections in structures made of cold- formed steel, other than ‘Z’ sections. 2. Previous studies on geometric imperfections in CFS sections A local (or, cross-sectional) GI is understood as local unevenness or undulation in the elements of cross-section distributed over the length of the member, which is generally referred as local geometric im- perfection or cross-sectional geometric imperfection [5]. Schafer and Peköz [6] categorised the local GIs into two groups: 1. Type 1: Maximum local imperfection in a stiffened element, such as a web http://dx.doi.org/10.1016/j.tws.2017.07.001 Received 19 October 2015; Received in revised form 7 June 2017; Accepted 1 July 2017 ⁎ Corresponding author. E-mail address: sghosh@civil.iitb.ac.in (S. Ghosh). Thin-Walled Structures 119 (2017) 447–456 0263-8231/ © 2017 Elsevier Ltd. All rights reserved. MARK