| As a new type of structure,compared with full-section concrete box girder,waveform steel web combined box girder has the advantages of higher load-bearing capacity,good seismic performance,lighter dead weight and higher material utilization rate,and has been widely used in bridge engineering.Due to the uneven distribution of bending stresses in the thin-walled box girder wings,there is a shear hysteresis phenomenon.In order to prevent structural damage,the structural shear hysteresis problem should be properly and reasonably considered in the preliminary design stage.China’s research on the shear hysteresis effect of waveform steel webs combined box beam started late,although many results have been achieved,but the theoretical calculation methods are relatively few compared to finite element analysis and experimental research,and mainly based on the energy variation method.In this context,this thesis combines the structural characteristics of corrugated steel webs,takes Hamiltonian mechanics as the theoretical basis,selects the appropriate generalized displacement as the unknown function,and introduces dual variables according to Legendre transformation.The Hamiltonian canonical equation of shear lag effect analysis of structure is derived,and the stress and deformation of upper and lower flanges of box girder are calculated by MATLAB software programming.This thesis further enriches the theoretical calculation method for shear hysteresis effect analysis of this type of structure,which can be used to evaluate the structural stability in the preliminary design stage.The main tasks are as follows:(1)By consulting relevant literature and collecting data,we can understand the development history and research status of composite box girder bridges with corrugated steel webs at home and abroad,and describe the shear lag phenomenon.Summarize the current research methods of shear lag effect of this kind of structure,review the development of Hamiltonian mechanics and the solution process of precise integration method;(2)Considering the shear deformation and longitudinal warping displacement of box girder when it is bent.Different longitudinal displacement difference functions are assumed for cantilever plate,bottom plate and top plate of box girder,and quadratic parabola is selected to describe the shear lag and warping displacement of wing plate.The total potential energy of the structure and the corresponding Lagrangian function are established,and the Hamiltonian canonical equations of the bending problems of single box,two chambers,one box,three chambers and two boxes and one chamber are derived.Compared with the results of literature examples and finite element numerical results,the accuracy is verified and analyzed,and the causes of errors are deeply analyzed and explained.Analyze and summarize the distribution law of shear lag of multi-chamber corrugated steel web composite box girder;(3)Derive the longitudinal elastic modulus of the waveform steel webs based on the second theorem of the Carpenter.Based on the Hamiltonian dual system,a linear interpolation function is used to obtain the matrix expression of the structure’s Lagrangian function,and the solution of the matrix expression containing the elements of the linear interpolation function is the error-prone point.In this thesis,the solution process of these elements is illustrated by taking a single-box double-cell waveform steel web composite box girder as an example.(4)Linear interpolation function is used to describe the longitudinal warping displacement of the cross section of multi-chamber corrugated steel web composite box girder under bending-torsion coupling load.The Hamiltonian canonical equation of structural bending-torsion coupling problem is derived and solved by precise integration method of two-terminal boundary value problem.The accuracy analysis and convergence verification of the calculation results of this method are carried out with specific examples. |
PDF Full Text Request