Moment gradient factor of cellular steel beams under inelastic flexure Khaled M. El-Sawy, Amr M.I. Sweedan ⁎, Mohammad Iqbal Martini Department of Civil and Environmental Engineering, UAE University, P.O. Box 15551, Al-Ain, Abu Dhabi, United Arab Emirates abstract article info Article history: Received 7 August 2013 Accepted 17 February 2014 Available online 18 March 2014 Keywords: Steel beam Lateral torsional buckling Elasto-plastic Buckling Finite element The flexural capacity of cellular steel beams is influenced by both local and global instabilities. In the current paper, the finite element method is employed to investigate the inelastic behavior of cellular steel beams under combined buckling modes. A three-dimensional non-linear finite element model, that takes into consideration possible interaction between lateral torsional/distortional buckling modes and localized de- formations of the cross section is developed and validated against available results in the literature. The study considers simply supported beams subjected to three different load configurations; mid-span load, uniformly distributed load and end moments. An extensive parametric analysis is conducted to assess the impact of various geometrical parameters on the inelastic stability of cellular steel beams. These parameters include the dimensions of the beam cross-section; flange width and thickness, web height and thickness, and hole size and spacing. The moment gradient factors that correspond to various buckling modes experi- enced by the wide range of dimensions considered in the simulation study are reported. The outcomes of the this study are expected to provide more insight into the behavior of cellular steel beams and enable accurate prediction of the moment gradient factor and consequently the flexural capacity of this special type of steel beams. © 2014 Elsevier Ltd. All rights reserved. 1. Introduction Perforated–web I-shaped non-composite steel sections have been used as structural members since the Second World War in an attempt to enhance the flexural behavior without increasing the cost of the ma- terial. In general, two types of web perforations are commonly used in engineering practice; hexagonal and circular. The hexagonal perforation pattern occurs during the typical manufacturing of castellated members by cutting the web of a typical I-shaped member longitudinally in a zigzag pattern and then re-assembling the resulting parts by welding. Cellular beams are the modern style of the traditional castellated beams. The manufacturing process of cellular beams (Fig. 1) increases the overall depth to be up to 1.6 times deeper than that of the root (parent) solid section. The diameter of the openings may reach 80% of the total height of the beam and it is possible to leave only a small distance between the openings which allows for a high level of trans- parency. The flexural behavior of solid-web I-shaped steel beams is complicated due to its susceptibility to several failure and instability modes. Failure modes include flexural and shear failures while buckling modes comprise local web and local flange instabilities, lateral, torsional and distortional buckling or combination thereof. For the particular case of perforated-web beams, the non-uniformity in the cross section properties due to the existence of web openings increases the level of complexity in the flexural behavior and the associated failure and insta- bility modes. 1.1. Elastic lateral torsional buckling The critical value of the uniform bending moment, at which elastic lateral torsional buckling (LTB) occurs in an I-shaped beam, is well established [Timoshenko and Gere [22]] and is defined as M cr ¼ π L b ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EI y GJ þ π E L b   2 I y C w s ð1Þ where L b is the laterally unbraced length of the beam's compression flange, I y is the cross-sectional moment of inertia about an axis perpendicular to the axis of bending, J is the torsional moment of inertia of the cross-section, C w is the warping constant, and G and E are the elastic shear and Young's moduli of the beam's material, respectively. In practical situations beams are subjected to non-uniform bend- ing moment between the points of lateral supports and, therefore, have greater flexural strength than the value estimated by Eq. (1) for the case of constant bending moment. This is reflected in the Journal of Constructional Steel Research 98 (2014) 20–34 ⁎ Corresponding author. Tel.: +971 50 2338970; fax: +971 3 7134997. E-mail address: amr.sweedan@uaeu.ac.ae (A.M.I. Sweedan). http://dx.doi.org/10.1016/j.jcsr.2014.02.007 0143-974X/© 2014 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect Journal of Constructional Steel Research