Elastoplastic Finite Element Analysis Of Thin-walled Steel Box Girders With Rectangular Section

This dissertation studies the method of finite element analysis of thin-walled box girderwith rectangular cross section. With considering the effect of vertical shear deformation ofweb and the shear lag in the flanges under axial and vertical loads, a new accurate element isproposed and its efficiency is demonstrated by some numerical examples.Firstly, the beam theory of vertical shear deformation and shear lag effect are introducedconsidering the mechanical characteristics of thin-walled box girders. Based on theassumption of deformation of thin-walled box girder under axial and vertical loads, thedisplacemet model is introducticed and the energy functional is constituted, and then,governing differential equations and boundary conditions are derived using the variationalprinciple. After that, the closed-form solution of these equations are obtained. The superiorityof the proposed method is illustrated with an example of cantilever beam.Secondly, the element shape functions are constructed using the general solution of thegoverning differential equation of the thin-walled box girders, and an accurate element forlinear elastic analysis of thin-walled box girder, is developed following the standardprocedure of the finite element formulation. Then, considering the effect of load alongelement, which is subjected by uniformly distributed vertical load, the displacement andstrain-stress fields of element are solved. In the end of this part, numerical examples arepresented to illustrate the effectiveness in calculation of the displacement filed and stressfiled.Thirdly, in order to investigate the effect of material nonlinearity, new elastoplasticelement is developed to get the mechanical response of steel box girder in elastic-plastic range.Based on the element shape functions and strain-displacement matrix in the elastic analysisand the plastic strain theory of thin-walled steel box girder, the energy functional ofthin-walled box girder in the elastic-plastic range is constituted. Followed by that, the integralexpressions of element tangent stiffness matrix and element resistant force of thin-walled boxgirder are derived using the potential energy variational principle. Again the shear lag effectof the flanges and the vertical shear deformation of the web are considered as well as thematerial nonlinearity. An incremental-iterative analysis algorithm is proposed and implemented. Numerical examples are presented to illustrate the effectiveness of the proposedelement and algorithm.Finally, all the work in this dissertation is summarized and the outlook is presented.