Analysis On Finite Segment Method Of Shear-lag Effect Of Box Girders Based On Flange-slab Shear Deformation Law

The research on the shear-lag effect in the traditional concrete box girder and the new type of composite box-girder with corrugated steel webs was made in this paper.On the basis of the variational principle for analyzing shear lag effect in box girders,a finite segment method corresponding to beam element for analyzing shear lag effect in box girders was proposed.Different from the traditional finite element method,two shear-lag degrees of freedom are employed at each node of the element in the method,which purpose is to adapt to different shear lag boundary conditions.Finite segmental method provides an effective method for the study of shear lag effect.This article mainly study the following areas:(1)Derivation of shear lag warp displacement function of traditional concrete box girder.On the one hand,according to the distribution law of the shear flow,the longitudinal displacement of the box girder?s upper and lower wing plate is the two parabola distribution along the width direction of the wing plate,on the other hand,the ratio of shear flow between various wing plates is obtained according to the size of the shear flow of the wing plate,the function of the shear lag warping displacement of the traditional concrete box girder is obtained in the two aspects.The effect of the additional axial force is neglected here.(2)Based on the obtained function of shear lag warping displacement,the governing differential equations of the shear lag effect are established by the energy variation method for the traditional concrete box girders.The expression of stress,deflection,additional bending of the simple supported beam under concentrated load or uniformly distributed load and cantilever beam under concentrated force at free end or uniformly distributed are obtained.With the help of numerical examples,the shear lag effect of the box girder under the external load is analyzed,and the correctness and reliability are analyzed.(3)On the basis of the variational principle for analyzing shear lag effect in box girders,a finite segment method corresponding to beam element for analyzing shear lag effect in box girders was proposed.In the method,two shear-lag degrees of freedom are employed at each node of the element.A series of matrix formulations for the finite segments including the shear lag coefficient matrix and generalized load vector are deduced and the corresponding finite element analysis formula is obtained.The shear lag effect of different beam bridge forms and different load forms is analyzed and compared with the relevant literature.(4)Combined with the structure characteristics of composite box-girder with corrugated steel webs,on the basis of the function of shear lag warping displacement of the traditional concrete box girder,the effect of the additional axial force is considered here.A uniform axial displacement is introduced in the full section,the function of shear lag warping displacement of composite box-girder with corrugated steel webs is formed.(5)The governing differential equations of the shear lag effect and boundary conditions considering the shear deformation of the web are established by the energy variation method for the composite box-girder with corrugated steel webs.The deflection equation of simply supported box girder with the composite box-girder with corrugated steel webs is obtained based on the elementary beam theory,the shear effect of corrugated steel web and the shear lag effect of box girder under the action of mid span concentrated load or full span uniform load.And a numerical example is used to analyze the proportion of the total deflection of each part and the midspan deflection of simply supported box girder with corrugated steel webs when shear span ratio varieties.(6)Using finite segmental method to analyze the shear lag effect of composite box-girder with corrugated steel webs under three different load conditions,compare the results with the results of the finite element method and analyze the distribution of shear lag effect under three loading conditions.(7)Using finite segmental method to analyze influence of the mid-span section shear lag effect of composite box-girder with corrugated steel webs due to the change of the geometrical parameters of the structure.The main factors and non-sensitive factors affecting the shear lag effect of the box girder are obtained.On the basis of the ratio of the cantilever plate to the roof is equal to 1,an empirical formula for the maximum shear lag coefficient of a composite box girder under external load when the width to span ratio change or comprehensive considerate the simultaneous variation of the cantilever plate to the wing plate ratio and the width to span ratio is proposed.