General formulation of equivalent moment factor for elastic lateral torsional buckling of slender rectangular sections and I-sections

In the past decades, great progress has been made in analyzing lateral torsional buckling of slender beams. The phenomena has been accurately described by differential equations, closed form solutions are available for specific cases and the solution for any load and any boundary condition can be obtained by finite element analysis. Timber and steel design standards provide a procedure based on equivalent moment factors. With this procedure, beams can be designed straightforwardly. However, modern designers continue to push the envelope and more irregular load patterns are found, on which the design standards do not provide solutions. Consequently, designers are forced to determine the equivalent moment factors based on case-specific literature and/or conservative assumptions. Unfortunately, this makes many challenging modern designs uneconomical. Furthermore, significant inconsistencies between the different design procedures are found. For that purpose, this paper proposes a solution in the form of a general formulation to determine equivalent moment factors for any loading on a single-span beam for both free and restrained lateral bending and/or warping at the supports, for both I-sections and rectangular slender sections loaded in the shear center. It is shown that the obtained moment factors are accurate and in good agreement with design standards and literature, and a wide range of irregular load patterns is considered