Date of Award


Document Type


Degree Name

Master of Science in Civil Engineering (MSCE)


Civil Engineering

First Advisor

Dr. Bilal EI- Ariss

Second Advisor

D r . Amr Sweedan

Third Advisor

D r. Khaled EI-Sawy


I-shaped steel members represent the basic structural element in the majority of steel structures. Perforated-web I-shaped steel sections have been used as structural members since the Second World War in an attempt to enhance the flexural behavior of traditional solid-webbed I-shaped steel sections without increasing the cost of the material. In general, two types of web perforations are commonly used in engineering practice; hexagonal and circular. Although, the main intent of the perforation process is to produce stiffer I-sections by increasing the web height and providing higher major-axis flexural capacity than solid-webbed members of the same weight, it also provides access to services and optimizes the use of the costly structural steel material. Moreover, the appealing aesthetical appearance of perforated-web members make them essential elements in construction of exposed steel structures. These advantages, combined with the significant development in computerized manufacturing equipments, have led to the wide spread use of perforated steel members with a variety of geometries suitable for various loading conditions in different structural applications.

Structural designs are always attracted by the fact that the augmentation of the cellular section height, compared to its original solid counterpart, enhances its in-plane structural characteristics. It should be noted, however, that the non-uniformity in the beam's cross section due to the presence of web perforations may have an adverse effect on the in-plane flexural capacity of cellular beams in case of instability failure before reaching their full flexural capacity. Web perforations are also expected to influence the response of these beams and the associated potential failure modes. The elastic lateral stability of cellular steel beams is typically a concern during the construction stage when lateral bracing elements are not yet installed. However, the inelastic lateral buckling behavior of cellular beams is more likely to be faced in practice, as a result of yielding in the outmost fibers of the beam before commencement of buckling. The load carrying capacity of these beams is influenced by its global buckling, local buckling of cross section elements and also by the discontinuities in the cross section due to the web perforations. Unfortunately, current design codes do not provide direct guidelines to address lateral torsional buckling of perforated steel beams.

The present research work is concerned with the lack of information pertaining to lateral stability of cellular steel beams subjected to flexure. This research presents a literature survey for experimental and numerical studies related to structural behavior of perforated steel beams with emphasis on the buckling response of castellated and cellular I-shaped steel beams. The study is carried out numerically using a detailed three dimensional finite element modeling using the general purpose software package ANSYS. The developed model takes into consideration material and geometrical non-linearities. The adopted mesh is selected to allow various deformations and rotations associated with global and local buckling modes of such beams to be captured (simulated). The developed model is validated by simulating various analytical and experimental case studies that have been reported in the literature. The validated finite element model is utilized to perform extensive buckling analyses of simply supported cellular steel beams subjected to equal end moments, mid-span concentrated load, and uniformly distributed load. Conducted buckling analyses cover a wide spectrum of practical geometrical dimensions and perforation patterns of I-shaped cellular beams.

A total of 11,340 cases of analyses are performed to investigate the influence of load application location on the elastic lateral torsional buckling of I-shaped cellular beams. Conducted analyses consider various cases of loading that are applied at the top and bottom flange levels of the modeled beams. The impact of various cross sectional dimensions, beam slenderness, and web openings size and spacing on the elastic buckling capacity is investigated under different types of loads. Results of conducted analyses are utilized to evaluate the variation of the moment gradient factor Cb relative to a non-dimensional factor ke that relates the warping rigidity to the torsional rigidity of cellular beams. Results are compared with those reported in the literature for loading at the shear center of beams. The comparison reveals a clear destabilizing effect for loads applied at the top flange level. On the contrary, loads applied at the bottom flange level enhance the lateral stability of cellular beams. Long span cellular beams are shown to buckle with pure lateral torsional buckling mode (LTB). Buckling of intermediate span beams is controlled by lateral distortional buckling (LDB) where web distortion occurs simultaneously with lateral deformations. Buckling of short span beams is dominated by a high level of web distortion due to the high shear stresses induced in the web. This particular behavior is shown to be consistently coupled with a significant reduction in the Cb value.

The study also covers the inelastic lateral buckling of cellular beams loaded at their shear center. A single steel material type is considered; namely A36 according to the American standards AISC 360-05. A comprehensive parametric study that includes 2,268 cases of analyses is conducted to evaluate the impact of various cross section dimensions, beam slenderness, different types of loads, and web openings size on the inelastic buckling capacity and their associated modes for cellular steel beams. Consistent with the case of elastic buckling, outcomes of the inelastic investigation are discussed by presenting the variation of the moment gradient factor Cb with respect to the non-dimensional factor ke. Similar to the observed elastic buckling response, long span cellular beams are shown to experience inelastic lateral buckling due to lateral torsional buckling (LTB) or lateral distortional buckling (LDB). Cellular beams with intermediate span length experience interaction between lateral buckling and local web shear deformations at buckling. The buckling of short span cellular beams is governed by high level of web distortion that results from the high shear stresses induced in the web. In such a case, no lateral buckling occurs and significant reduction in Cb values takes place. Several moment gradient factor Cb ranges that correspond to various buckling modes experienced by the wide range of dimensions considered in the simulation study are identified. This categorization takes into consideration possible interaction between global buckling modes and localized deformations of the cross section elements.