Equivalent moment gradient factor for lateral- torsional buckling of web-tapered i-section beams

Introduction. This paper studies the stability of symmetrical web-tapered I-beams subjected to unequal end moments. Taper angle, which plays a main role in the lateral-torsional buckling behavior of web-tapered beams, is investigated through refinement of differential equations of the original Vlasov technical theory for thin-walled bars. Analytical solutions of refined differential equations are given based on the Bubnov – Galerkin method through the law of change of moment of inertia of the cross section of the beam along its axis. The final bifurcation equation of elastic critical moment contains new terms that includes reduction coefficients of cross-section. Equivalent moment gradient factor for the full range of values is determined and given in closed form with respect to taper angle. Comparative graphs show alignment between analytical and numerical solutions. These results can be used to formulate efficient buckling criteria for prismatic and non-prismatic I-section beams and can be integrated into the current design methods.

Aim. To develop a unified equation for the equivalent moment gradient factor. Refine Vlasov technical theory for web-tapered I-section members.

Materials and methods. Refined Vlasov technical theory and Bubnov – Galerkin method were used in the work.

Results. Based on given refinements, a closed form of elastic lateral-torsional buckling solution of a webtapered beam was obtained. Analytical calculation method is introduced.

Conclusions. The presented theoretical work introduces a unified design method for elastic critical moment and equivalent moment gradient factor determining for lateral-torsional buckling of web-tapered I-section beams. Results show an excellent agreement between numerical and analytical solutions. Equations are given in closed form similar to a constant cross-section but with additional factors and coefficients, that makes it possible to integrate the developed solution into existing calculation methods.

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