Engineering Structures 31 (2009) 2711–2722 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct Optimization of cold-formed steel pallet racking cross-sections for flexural–torsional buckling with constraints on the geometry M.M. Pastor a,∗ , M. Casafont a , E. Chillarón a , A. Lusa b , F. Roure a , M.R. Somalo a a Department of Strength of Materials and Structural Engineering, Escola Tècnica Superior d’Enginyeria Industrial de Barcelona (ETSEIB), Universitat Politècnica de Catalunya (UPC), Av. Diagonal, 647, 08028 Barcelona, Spain b Institute of Industrial and Control Engineering, Escola Tècnica Superior d’Enginyeria Industrial de Barcelona (ETSEIB), Universitat Politècnica de Catalunya (UPC), Av. Diagonal, 647, 08028 Barcelona, Spain article info Article history: Received 9 March 2009 Received in revised form 7 May 2009 Accepted 23 June 2009 Available online 8 July 2009 Keywords: Flexural–torsional buckling Optimization Upright sections abstract Starting from a comprehensive set of experimental test results of upright cross-sections in compression, this paper is focussed on how the section can be optimally designed to achieve the highest possible failure load in global buckling. The aim is to optimize a cross-section prototype shape with restrictions on its geometry attending to manufacturing feasibility and assembly constraints. The proposed scheme consists of maximizing the design strength with respect to flexural–torsional buckling, according to European Standard prEN 15512:2008 [European Standard prEN 15512:2008. Steel static storage systems - Adjustable pallet racking systems - Principles for structural design] / Fédération Européenne de la Manutention [Fédération Européenne de la Manutention (Section X): The design of static steel pallet racking. FEM 10.2.02; August 2000] design recommendations. This is a bicriteria optimization problem which is solved by formulating a nonlinear mathematical program. Optimization is performed prior to the finite element method (FEM) nonlinear analysis of the solution design. The procedure herein presented has two advantages: on the one hand it considerably reduces the number of nonlinear analyses, and on the other it ensures that the best design is achieved. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction The profiles used in storage pallet racking are characterized by their slenderness. They are typically mono-symmetrical cold- formed sections from a rectangular-sized steel sheet, which, in the case of uprights, contain arrays of perforations along the length, enabling beams to be clipped by connectors at heights that are not pre-determined prior to manufacture. In Part 1.3 of EC3 [1], rules for cold-formed member analysis are given, but in the case of perforated members they are not recommended. For these sections, carrying out tests is more appropriate. The relevant test procedures are given in Annex A of prEN 15512:2008 [2]. 1.1. Stub column test To find the effect of perforations and local buckling on a column subject to compression, testing is carried out on a short specimen, whose length must be more than three times greater than the longest dimension of the upright section, and more than five times the distance between perforations. From these tests the local ∗ Corresponding author. Tel.: +34 93 401 6532; fax: +34 93 401 1034. E-mail address: m.magdalena.pastor@upc.edu (M.M. Pastor). buckling strength is obtained, as well as the location of the effective centre of gravity. 1.2. Determining the buckling curve for the upright In order to establish the compressive strength for an effective range of upright lengths, taking into account all possible buckling modes and the restraining effects of beams and connectors, complete frames of different lengths are tested in compression. From these experimental tests the buckling curve is derived. It is implicit that the design of continuously perforated members requires testing; however, this is not intended to restrict the development of analytical procedures (e.g. using finite elements) for predicting the performance of members containing regular arrays of holes or slots. Where rational analysis can be shown to be sufficient, it may be used as an alternative to the use of the relevant test procedures. 2. Aim of the investigation The problem to be solved is to increase the axial load capacity of an upright section over the whole range of lengths used in practice by increasing its area, given certain manufacturing and assembly constraints. 0141-0296/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2009.06.017