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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: The majority of the existing literature on castellated members is focused on beams. Very little work has been done on the stability of castellated columns although they have been increasingly used in buildings in recent years. This paper presents a new analytical solution for calculating the critical buckling load of simply supported castellated columns when they buckle about the major axis. This analytical solution takes into account the influence of web shear deformations on the buckling of castellated columns and is derived using the stationary principle of potential energy. The formula derived for calculating the critical buckling load is demonstrated for a wide range of section dimensions using the data obtained from finite element analyses published by others. It was found that the influence of web shear deformations on the critical buckling loads of castellated columns increased with the cross-sectional area of a tee section and the depth of web opening, but decreased with the length and the web thickness of the column. It is shown that the inclusion of web shear deformations significantly reduces the buckling resistance of castellated columns. Neglecting the web shear deformations could overestimate the critical buckling load by up to 25%, even if a reduced second moment of area is used. [Copyright &y& Elsevier]