Elastic Flexural-torsional Buckling Of Doubly Symmetric Web-tapered I-beams

This paper is composed of the following three parts.Firstly, based on Vlasov's thin-walled beam assumptions, normal stresses, shear stresses and transverse stresses of web-tapered I-beams are derived. Genshu Tong [2] has pointed out the total potential for flexural-torsional buckling of thin-walled members is composed of linear strain energy and nonlinear strain energy, no nonlinear load potential is included. Thus, the total potential for flexural-torsional is derived.Secondly, a cubic displacement field is adopted for the transverse displacement and twisting rotation. A matrix is achieved by use of variational principles, which comprises elastic and geometric stiffness matrices.Thirdly, any thin-walled member is comprised of some planes or shells. Shell theory is more prevalent than thin-walled theory. Thus, the elastic flexural-torsional buckling critical load based on shell buckling theory are calculated using FEA software Ansys, which is taken as reference. A comparative study about the critical load by the one-dimensional model and two-dimensional shell finite element analysis is presented and discussed. The comparison shows that the theory in this paper can lead to accurate predictions of elastic flexural-torsional buckling of doubly symmetric web-tapered I-beams.Considering the effects of taper ratio, the elastic flexural-torsional buckling of simply supported web-tapered I-beams with doubly symmetrical cross-sections under moment gradient is investigated by FEA method. Using the formulation obtained by Genshu Tong [2] through energy method, but adjusting the coefficients in this formulation based on the results of FEA, we obtaine a new formula for the critical moment. It has a similar formulation as those for beams of constant cross-sections, with clear meaning and easy to application in practice.