Journal of Constructional Steel Research 67 (2011) 1115–1127 Contents lists available at ScienceDirect Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr Elastic local buckling of perforated webs of steel cellular beam–column elements Amr M.I. Sweedan * , Khaled M. El-Sawy Department of Civil and Environmental Engineering, UAE University, P.O. Box 17555, Al-Ain, United Arab Emirates article info Article history: Received 11 July 2010 Accepted 1 February 2011 Keywords: Steel Cellular Elastic local buckling Perforated web Finite element method abstract In this study, the finite element method is employed to determine the critical in-plane longitudinal load at which elastic local buckling of the web of cellular beam–column elements occurs. To simplify the simulation of the problem, the interaction between the flanges and perforated web is approximated by modelling the web only as a long plate having aspect ratio (L/h w ≥ 10) with multiple circular perforations. The utilized model incorporates restrained out-of-plane displacements along the four edges of the plate. Analyzed plates are subjected to linearly varying in-plane loads to simulate various combinations of axial and flexural stresses. The effect of different geometrical parameters on the elastic buckling load of perforated web plate is investigated. These geometrical parameters include the plate’s length and width, and the perforations’ diameter and spacing. Comprehensive finite element analyses are conducted to identify the behaviour of wide spectrum of perforated web plates at buckling under various combinations of axial compressive load and bending moment. Outcomes of the study are expected to enhance the understanding of the elastic local buckling of web plates of cellular beam–column elements. © 2011 Elsevier Ltd. All rights reserved. 1. Introduction and problem definition The elastic buckling problem of a rectangular plate panel of length L, width h, thickness t , and subjected to a uni-axial load in its longitudinal direction, was first studied by Timoshenko and Gere [1] in 1961 and modified later by Gerstle [2] in 1967. They considered the first order terms in the governing equations and expressed the critical elastic stress σ cr at buckling as σ cr = k π 2 E 12  1 - ν 2   t h  2 (1) where k is a dimensionless buckling coefficient of the plate that depends on the edge support conditions, and the plate’s aspect ratio L/h, while E and ν are the Young’s modulus and Poisson’s ratio of the plate’s elastic material, respectively. For the case of a solid rectangular long plate that is simply supported along its four edges and subjected to a uniform axial compression at the two opposite short edges, the value of k can be expressed as k =  1 m L h + m h L  2 , m = 1, 2, 3,..., etc. (2) where m corresponds to the number of half-waves that occur in the plate’s longitudinal direction at buckling (i.e. m defines the buckling mode of the plate). The value of m that produces the least * Corresponding author. Tel.: +971 50 2338970; fax: +971 3 762315. E-mail address: Amr.Sweedan@uaeu.ac.ae (A.M.I. Sweedan). buckling coefficient k (termed m cr ) is the one that defines the first buckling mode and the critical longitudinal half-wave length of the buckled plate. It should be noted that any value of m other than m cr will produce half-waves of length longer or shorter than the critical half-wave length leading to higher critical load [1]. The variation of the buckling coefficient k versus the plate’s aspect ratio (L/h) is presented graphically in many Ref. [1], and gives a minimum value of 4.0 for the buckling coefficient k. This minimum value occurs at integer aspect ratios of the plate; i.e., at L/h = 1 for m = 1, at L/h = 2 for m = 2, at L/h = 3 for m = 3,... etc. This implies that the lowest buckling stress in solid rectangular plates occurs when L/h is integer, and its value is independent of that integer number. This directed researchers to consider square plates (L/h = 1) to represent the buckling behaviour of rectangular plates with integer aspect ratio. The usage of cellular members (Fig. 1) in constructional steel applications has been spreading rapidly all over the world. A steel cellular member has circular web perforations and is produced from a standard I-shaped member by computerized-cutting it in a zigzag-like pattern along its longitudinal axis as shown in Fig. 2(a) and (b). The two halves are then separated, staggered, and welded together to form a cellular member (Fig. 2(c)). Despite the fact that the weight of a cellular member is slightly less than the original solid member, the cellular member geometry provides flexural stiffness and strength that are considerably higher than the original solid one. Moreover, web perforations reduce the cost of the material used in the fabrication, and also provide accessibility for piping, ducting, and other service systems. Due to the wide variety of perforation sizes and configurations and the different geometries of the web and flanges of cellular 0143-974X/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2011.02.004