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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]

This paper presents an analytical study on the thermal buckling analysis of axially loaded columns of thin-walled open section with nonuniform sectional properties. Obtained herein are critical loads related to flexural, torsional and flexural-torsional buckling of an I-section column subjected to an axial compressive load applied at the geometric centroid, and under linearly varied non-uniform temperature distribution scenarios. The analysis is accomplished using traditional energy methods. The influences of thermal strain, nonuniform distribution of pre-buckling stresses, and variation of pre-buckling stresses along the longitudinal axis of the column on critical buckling loads are examined. The present results highlight the importance of nonuniform sectional properties in the buckling analysis of columns of doubly symmetric section. [ABSTRACT FROM AUTHOR]