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The majority of the existing literature on the lateral stability of castellated beams deals with experimental and/or numerical studies. This paper presents a comprehensive analytical study of the lateral-torsional buckling of simply supported castellated beams subject to pure bending and/or a uniformly distributed load. Using the principle of total potential energy, analytical expressions for the critical buckling moments and loads are derived and applied for various beam lengths. The three different locations of the applied load are used: At the top flange, shear center and bottom flange. The results show that the influence of web openings on the critical buckling moments and loads are mainly due to the reduction of the torsional constant caused by the web openings. Web shear effects and web shear buckling become important only when the beam is short and the flange is wide. The critical moments and loads will be overestimated or underestimated if the full or reduced section properties are used. The accurate critical moment or load should be calculated based on the average torsional constant of the full and reduced sections rather than simply taking the average of the critical moments or loads calculated from the full and reduced section properties. The present analytical solutions are verified using 3D finite element analysis results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper an analytical model is presented to describe the lateral–torsional buckling behaviour of steel web tapered tee-section cantilevers when subjected to a uniformly distributed load and/or a concentrated load at the free end. To validate the present analytical solutions finite element analyses using ANSYS software are also presented. Good agreement between the analytical and numerical solutions is demonstrated. Using the present analytical solutions, the interactive buckling of the tip point and uniformly distributed loads is investigated and a parametric study is carried out to examine the influence of section dimensions on the critical buckling loads. It is found that web tapering can increase or decrease the critical lateral–torsional buckling loads, depending on the flange width of the beam. For a beam with a wide flange (width/depth=0.96) the critical buckling load is increased by 2% by web tapering, whereas for a beam with a narrow flange (width/depth=0.19) web tapering reduces the buckling load up to10% and 6% for the tip point loading and the uniformly distributed load respectively. [Copyright &y& Elsevier]

Abstract: This paper presents an analytical study of the flexural buckling and lateral–torsional buckling of cold-formed steel channel section beams subject to combined compression and bending about their major and minor axes. For channel section beams a bending about the minor axis creates a non-symmetric pre-buckling stress distribution, which has a significant influence on the lateral–torsional buckling of the beams. This kind of feature has not been discussed in the existing literature. The focus of this present study is the interaction between the compression load and the bending moments about the major and minor axes. It has been found that for a section subject to combined compression and the major-axis bending the bending moment will decrease the critical compression load, although the critical value of the largest compressive stress in the section actually increases with the applied bending moment. However, for a section subject to combined compression and the minor-axis bending the effect of the bending moment on the critical compression load depends on the direction of bending applied. For bending that creates a compressive stress in the lips the bending moment will reduce the critical compression load. However, for bending that creates a compressive stress in the web the bending moment has almost no influence on the critical compression load. [Copyright &y& Elsevier]