Contents lists available at ScienceDirect Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws Full length article Cross-aisle stifness analysis of industrial welded cold-formed steel rack upright frames Francesc Roure a,∗ , Teoman Peköz b , M. Rosa Somalo a , Jordi Bonada a , M. Magdalena Pastor a , Amadeu Segura a a RMEE, ETSEIB, Universitat Politècnica de Catalunya, Spain b Cornell University, USA ABSTRACT In general, industrial cold-formed steel pallet racks consist of upright frames and pallet beams. In the United States, typically, the upright frames are made welding the braces to the uprights. If the brace to upright joints are considered as rigid joints, the stifness of welded upright frames in the cross-aisle direction obtained numerically is very diferent from the stifness obtained experimentally (up to 300% higher). A method is proposed to improve the accuracy of the numerical determination of the stifness of the frames, by taking into account the semi-rigid behaviour of the brace to upright joints. The semi-rigid behaviour of the joints is analysed experimentally and by simulation with fnite elements. The method proposed uses linear behaviour approximation of the frame, and obtains a numerical stifness that difers only by 10% of the experimental stifness. 1. Introduction In general, industrial cold-formed steel pallet racks consist of up- right frames and pallet beams. Upright frames consist of uprights, up- right base plates and bracing members. In the United States, typically, base plates and braces are welded to the uprights. Usually the uprights are cold formed steel lipped channels. A typical example of frame is shown in Fig. 1. The stability of the rack is usually analysed in both directions: down-aisle and cross-aisle. In the down-aisle direction, stability relies on the beam to upright connections and the upright to foor connec- tions. Several authors have studied the nonlinear behaviour of beam- upright connections, as well as how to model them (See Refs. [1–11]). In the cross-aisle direction, stability relies on the stifness of the upright frames. In this type of frame, the axes of the uprights and the braces are all in the same plane, and a plane frame analysis may model correctly the behaviour of the frame, provided that the behaviour of the upright to brace joint is properly represented. S. Sambasiva et al. established a similar conclusion in 2004 [12]. In 2008, S.R. Sajja et al. [13] analysed the cross-aisle stifness of bolted rack braced frames, and have found that the local fexibility of the joints is very important when trying to build an FE model of the frame. The ANSI code MH 16.1: 2008 [14] developed by RMI for the design of rack structures, recommends also in paragraph 6.3.4 to take into con- sideration, for the analysis of joints, the deformation of the members legs, lips and stifening elements. In 2012 B P. Gilbert et al. [15] ana- lysed the shear behaviour of bolted rack braced frames experimentally and with FE models, with two diferent load schemes, and concluded that the transverse load method reproduces better the actual working behaviour of the frame, and that the local fexibility of the joints has great importance in the modelling of the frame. In 2015, F. Roure et al. [16] have also established the importance of local fexibility of the joints of the braces to uprights in an experimental and FE analysis of the down-aisle stifness of shelving structures with diagonal bracing. As shown by F. Roure et al. in Refs. [17,18], an analysis of welded rack braced frames, made using a rigid joint model, shows a stifness several times greater than the stifness of the actual frame, obtained experi- mentally. In 2017 H. Far et al. [19] have tested bolted rack braced frames, experimentally and with FE models, and have improved the FE models by reducing the axial stifness of the braces, to reproduce the efect of the fexibility of the joints. The semi-rigid nature of the joints results from the distortions of the column at the connections to the braces. Rotational fexibility at the joints does not have as signifcant efect as the stifness in the axial direction of the braces. However, the axial stifness of the braces is reduced signifcantly due to the distortions of the columns at the joints. https://doi.org/10.1016/j.tws.2019.04.041 Received 1 October 2018; Received in revised form 29 March 2019; Accepted 17 April 2019 ∗ Corresponding author. E-mail address: francesc.roure@upc.edu (F. Roure). Thin-Walled Structures 141 (2019) 332–344 0263-8231/ © 2019 Published by Elsevier Ltd. T