SOLVING LATERAL-TORSIONAL BUCKLING PROBLEMS IN THIN-WALLED BISYMMETRIC BEAM USING STODOLA-VIANELLO ITERATION METHOD
DOI:
https://doi.org/10.4314/njt.v44i1.1Keywords:
Lateral-Torsional Buckling, Stodola-Vianello Iteration Method, Critical Buckling Moment, Critical Buckling Load FactorAbstract
Thin-walled beams are susceptible to lateral torsional buckling (LTB) and can fail by LTB even when their material strengths have not been attained. The safe designs of thin-walled beams thus require LTB analysis to determine minimum LTB load. This paper aims to develop LTB load solutions of thin-walled bisymmetric beams using Stodola-Vianello iteration method (SVIM). The equations of LTB are differential equations derived from equilibrium conditions, incorporating bending, torsion, and warping effects. These equations are then transformed to more amenable iteration equations using SVIM. The SVIM uses successive integrations of the LTB equations to derive a system of iteration equations which is expressed for the arbitrary buckling mode, n. This work illustrates the use of the developed iteration equations to derive LTB solutions for simply supported thin-walled beams under constant end moment. Exact sinusoidal shape functions for the nth buckling mode derived from the governing equation for buckling are used for the two buckling displacement functions u(x), f(x) to derive the SVIM equations for the subsequent (n + 1)th iteration. Convergence at nth iteration is used for finding the stability equation that is solved for the eigenvalue which is used to find the buckling load. The method yielded closed form LTB solutions that were identical with previous solutions obtained using Ritz methods, finite Fourier sine transform method, least square weighted residual method and classical Navier series method.
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