Lateral torsional buckling of rectangular beams using variational iteration method

Abstract

Lateral torsional buckling is the main failure mode that controls the design of “slender” beams; that is, the beams which have greater major axis bending stiffness than minor axis bending stiffness or the beams which have considerably large laterally unsupported lengths. Since the buckling equations for beams are usually much more complex than those for columns, most of the analytical studies in literature on beam buckling are concentrated on simple cases. This paper shows that complex beam buckling problems, such as lateral torsional buckling of narrow rectangular cantilever beams whose minor axis flexural and torsional rigidities vary exponentially along their lengths, can successfully be solved using variational iteration method (VIM). The paper also investigates the effectiveness of three VIM algorithms, two of which have been proposed very recently in solving lateral torsional buckling equations. Analysis results show that all iteration algorithms yield exactly the same results in all studied problems. As far as the computation times and spaces are concerned, however, one of these algorithms, called variational iteration algorithm II, is found to be superior than the others especially in lateral torsional buckling problems where the beam rigidities vary along the beam length. Key words: Lateral torsional buckling, narrow rectangular beam, tapered beam, variable rigidity, variational iteration algorithms, variational iteration method.