Theoretical Research On Torsional And Bending-torsional Buckling Of Thin-walled Box Girder Based On Plate-beam Theory

Thin-walled box girder is widely used in modern architecture,especially in bridge engineering,because of its advantages of light weight of thin-walled members and high utilization rate of materials,as well as large lateral stiffness and torsional stiffness.The torsional problem of thin-walled box girder is a complex mechanical problem.The traditional method to calculate the torsion problem of thin-walled box girder is to use Bredt free torsion theory and Wumanski constrained torsion theory respectively to carry out simple superposition.Wumanski constrained torsion theory uses Vlasov fan area law,which makes the actual calculation work very troublesome.Moreover,the concept of fan-coordinate limits the applicability of this theory only to components composed of a single material.The "plate-beam theory",which is a new set of combined torsion theory of thin-walled box girder established by Kirchhoff plate and Timoshenko beam mechanical model,quantitatively describes the free torsion,constrained torsion,secondary shear flow torsion and secondary warpage torsion of thin-walled box girder.The displacement,stress and strain are completed under the same theoretical framework.The torsional stiffness,torsion Angle and critical bending moment are calculated.Finally,the correctness of the theoretical analytical solution is verified by ANSYS finite element analysis software simulation.Therefore,this study is not only helpful for people to understand the torsion and buckling mechanism of thin-walled box girder based on the classical theory and method of plate and shell beam,but also has important theoretical value for further research and application of the torsion and bending and buckling theory of thin-walled box girder.In this paper,the combined torsion and bending-torsional buckling of singleaxisymmetrical thin-walled box girder and thin-walled box girder with cantilever plate are studied theoretically.The specific contents are as follows:（1）Based on the plate-beam theory,the energy variational model of combined torsion problem of thin-walled box girder is established,the total strain energy equation of combined torsion of box girder is derived,and the expressions of free torsional stiffness and constrained torsional stiffness of thin-walled box girder section are obtained.The differential equation model of combined torsion of thin-walled cantilever box girder under the action of concentrated end torque is established and the theoretical analytical solution of maximum torsion Angle of cantilever girder subjected to concentrated end torque is given.The combined torsion of a single axisy-symmetric box girder and a box girder with cantilever plate under the action of concentrated torque at the end is simulated by using ANSYS finite element analysis software.The finite element analysis results of the maximum torsion Angle are obtained,and the theoretical solution is compared with the finite element results.（2）Based on the plate-beam theory,the energy variational model for bending,torsion and buckling of thin-walled box girder is established,the total strain energy equation is derived,and the free torsional stiffness,constrained torsional stiffness and flexural stiffness around weak axis of thin-walled box girder are obtained.The initial stress potential energy equation of the bending,torsion and buckling problem of thin-walled box girder is derived,and the Wagner coefficient of uniaxial symmetric thin-walled box girder about strong axis is obtained.The exact solution of the critical moment of flexural,torsional and flexural buckling of a pure bent simply supported beam is obtained by using differential equation model.The finite element analysis software ANSYS was used to simulate the bending,torsion and buckling of simple supported steel beams with uniaxial symmetry box and cantilever plate box sections under the action of concentrated bending moments at both ends,and the finite element analysis results of critical bending moments were obtained,and the theoretical solution was compared with the finite element results.