Elastic Flexural-torsional Buckling Of Monosymmetric Web-tapered I-beams

Tapered beams are widely used in steel structures, especially in portal frames. In a tapered beam, the size of the cross-section changes along the length of the beam which happens to coincide with the distribution of the moment in the same direction, so the application of tapered beams can efficaciously help saving materials and thus reduce the deadweight of the structure, making it more reasonable and economical. Therefore, it is of great theoretical value and practical significance to study on tapered beams.This paper is an advanced study which bases on the theory by Genshu Tong, focusing on elastic flexural-torsional buckling of monosymmetrical web-tapered I-beams. It consists of four parts as follows:Firstly, on the basis of Vlasov's thin-walled beam assumptions, the normal stresses, shear stresses and transverse stresses of web-tapered I-beams are figured out. The total potential for flexural-torsional buckling of thin-walled members is composed of linear strain energy and nonlinear strain energy while no nonlinear load potential is included. In order to calculate the non-linear strain energy of the web, the directions of stresses are converted so that the coordinate system of stresses can consist with that of strains. 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 including both elastic and geometric stiffness matrices is achieved using variational principles.Thirdly, any thin-walled member is comprised of some planes or shells. Since Shell theory is more prevalent than thin-walled theory, the elastic flexural-torsional buckling critical load based on shell buckling theory, which would later be used as a reference, is calculated using FEA software ANSYS. Afterwards, a comparative study about the critical load calculated respectively 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 monosymmetrical web-tapered I-beams.Fourthly, a formulation of critical load is obtained using energy method in this paper, considering the effects of taper ratio. And the coefficient which reflects the changes of cross-sections along the direction of length is introduced into the formulation too. In order to adjust the coefficients in the formulation, the elastic flexural-torsional buckling of simply supported web-tapered I-beams with monosymmetrical cross-sections under moment gradient is investigated by FEA method so that a mimic fomula of the coefficients can be derived from the FEA results. Finally, a formulation formally similar to that for beams of constant cross-sections is obtained, with clear physical meaning and nice practicability.