Analytical Study On Shear Lag Effect Of Thin-walled Box Girder Based On Energy-Variational Principle

With the rapid development of transportation industry in our country, thin-walled box girder is widely used in all kinds of large span or width bridge structures, the shear lag problem of which is indispensable, if not taking these problems seriously, it’s more likely to cause local cracking or buckling or even more serious consequences. Therefore intensive study on the shear lag effect in thin-walled box girder is of great significance in the respect of theory and engineering. This article mainly does the following research on single-cell and multi-cell box girders based on the theory of thin-walled structure and the energy variational principle:1. The shear lag effect analysis of single-cell box girder by using energy variational method with varying transverse load position.The laws of the longitudinal displacements’distribution functions used k-degree parabola in order to analyze the precision of different warping displacement functions, the wings of box girder were set with different longitudinal displacement difference functions separately in order to reflect the change range of different wings’warping displacements, the potential energy of external force considered the influence of transverse load position, both shear lag effect and shear deformation were considered, then the governing differential equations and their solutions were derived with variational method and the results of the presented method were compared with those of the finite element model. Finally the theoretical formulas of shear lag coefficient and effective width ratio were derived and the analysis theory of box girder’s shear lag effect with varying transverse load position was optimized.2. Study on influencing factors of the single-cell box girder’s shear lag effect with varying transverse load position.The shear lag effect of simply supported and cantilever box girders was calculated with energy variational method, the influence relation between effective width ratio and influencing factors was summarized and compared with the current code, finding that the conclusion that effective width ratios of all wings use one curve in the code is unreasonable and unsafe, the transverse load position should be considered to choose corresponding curve based on the conclusions of this article.3. The shear lag effect analysis of single-cell box girder by using finite segment method with varying transverse load position. The homogeneous solutions of the shear lag differential equations were used as the displacement patterns of the finite segment method, and the displacement field functions were formed. The element stiffness matrix and equivalent nodal loads vector were derived, and then the finite segment model of single-cell box girder for analyzing shear lag was built. Taking continuous girder with variable section as an example, the results of variational method, finite element method and model test were compared, which verified the correctness of the proposed analysis method.4. The superposition principle for shear lag effect analysis was proposed.The shear lag effect of box girder under complex force state was solved with that under decomposed simple force state, and the superposed results were compared with those of finite element method to verify the accuracy of this article’s method. The shear lag theory can be used in the engineering practice with this method.5. The shear lag effect analysis of multi-cell box girder by using energy variational method with varying transverse load position.The laws of the longitudinal displacements’distribution functions used k-degree parabola, the wings of box girder were set with different longitudinal displacement difference functions separately, and self-balance of the whole cross-section’s axial force was considered, then the governing differential equations and their solutions were derived with variational method and the results of the presented method were compared with those of the finite element method to verify the correctness of all assumptions and theoretical derivation.6. The influence study of parabola’s degree on computational accuracy.For single-cell box girder, cubic parabola is closer to the finite element solution than quadratic parabola when the load locates on top of web, and quadratic parabola is closer when the load locates other positions. For the multi-cell box girder, cubic parabola is closer to the finite element solution than quadratic parabola for top and bottom plate, quadratic parabola is closer for cantilever plate. Although parabola’s degree affects the computational accuracy, the accuracy can meet the requirements of practical engineering.