A Theory Of Stability For Thin-Walled Members Considering The Effects Of Transverse Stresses And Its Applications

A vast amount of research was focused on the flexural-torsional buckling theory of thin-walled members in the past decades, but diversities existed among different theories, which led directly to the differences on predicting the critical loads of beams among codes for design of steel structures in different nations and some well-known monographs. This thesis presented a critical review and analysis on the current theories on thin-walled members, based on the variational theorem on buckling problem in the classical mechanics of the solid and continuum.For the linear theory of thin-walled members, this thesis studied the transverse stresses in the thin-walled members using the equilibrium condition of a plate element in the tangential direction of a cross-section. And the explicit expressions were derived. The analyses of a simply supported I-beam under uniform distributed loads by FEA using shell elements showed that the proposed formulae were accurate in assessing the transverse stresses in thin-walled members. Some examples showed that attentions should be paid to the adverse effects of transverse stresses at supports, beam-column connections and where the concentrated forces acting.Analyses on the buckling of monosymmetric I-sectional simply supported beams, using shell elements of FE software ANSYS, were carried out in this thesis, and compared with the traditional theory and a newer theory indicated that the traditional theory was closer to the shell buckling analysis than the newer theory was. The newer theory shared a general popularity in China, but the shell buckling theory is more correct than thin-walled members' for its buckling theory using fewer assumptions.Based on the variational principle on stability of solids, no nonlinear load potential should be introduced into the total potential of the stability problem of thin-walled members. This thesis discarded the nonlinear load potential, which was included in most current theories on buckling of thin-walled members, but introduced the nonlinear strain energy of transverse stress into the total potential. A new theory for flexural-torsional buckling of thin-walled beams was thus obtained. For simply supported beams, this new theory was the same as the traditional theory.Using the proposed theory, the stabilities of simply supported beams and cantilevers under different loadings were studied. These analyses showed that the proposed theory eliminated all the problems existed in current available theories, and was suitable for buckling analysis of beams under any boundary conditions and loadings.Using the traditional theory, the newer theory and the proposed theory, this thesis investigated the buckling of cantilevered thin-walled beams. When cantilevers under uniform bending, the newer theory and the proposed theory is the same, but the traditional theory is not correct because it not allow the moment rotating at the free end of a cantilever. While for cantilevers under transverse loads, the newer theory is not correct. Comparisons between the test results from the literature, the results of the newer and the proposed theory suggested that the proposed theory has an excellent agreement with the test results, while the newer theory predicted either higher or lower critical loads than the test.Beams with doubly symmetrical sections under uniform moment, uniformly distributed load and concentrated load at the free end were analyzed, new approximate formulae for the critical moment were presented which are more accurate, yet much simpler than currently available formulae.A general theory for the buckling and nonlinear analysis of thin-walled members with any cross-section was derived using the energy method and the Fictitious Load Method. In the Fictitious Load Method, the fictitious loads from the shear stress and the transverse stress on two longitudinal sides are included, which is necessary for the Fictitious Load Method to include the same nonlinear effects as in the energy method. Formulation of shell theory was also used to develop the new general theory.