Research On Analytical Theory And Application Of Transverse Internal Force Of Box Girder

As one of the widely used bridge,the thin-walled box girder bridge has the problems of distortion and transverse internal force under the action of eccentric load.The depth of research affects the reasonable and refined design of thin-walled box girder,otherwise,the bridge deck or other slab of box girder will crack,which will increase the maintenance cost in the later period.Based on the National Natural Science Foundation of China,this paper investigated the problems of transverse internal force and distortion of single box single-cell and single box double-cell box girder.Combined with the design and calculation of the box girder bridge deck,theoretical analysis and finite analysis were used to investigate the existing problems simultaneously.The results can be used as a reference for the design and calculation of thin-walled box girder.（1）In the calculation of the transverse internal force of the single box single-cell thin-walled box girder.Whether the lateral horizontal support should be set or not for the calculation model,formula considering the distortion for calculating transverse internal force of box girder with or without lateral horizontal supports was established.Combined with numerical examples,the influence of lateral horizontal supports on the transverse bending moment of box girder was analyzed when box girder parameters such as vertical load position,web inclination,aspect ratio and stiffness ratio changed.The results show that the transverse position of vertical load is the main factor which affect the transverse bending moment of box girder.The regular change of the web inclination,aspect ratio and stiffness ratio of the box girder can not make the lateral horizontal support produce an obvious and consistent change of transverse bending moment error at each corner of box girder,and the influence is not obvious.When the vertical load is within the range of the top slab,the lateral horizontal support has little influence on the transverse bending moment of the box girder with rectangular section,and the bending moment error is no more than 0.72%.（2）In the calculation of transverse internal force of the single box single-cell box girder with trapezoidal cross section,the influence of box girder distortion and frame shear increment on transverse internal force was considered simultaneously.Based on the decomposition of the eccentric vertical load,the energy variational method based on the minimum potential energy principle was used to analyze the transverse internal force of the rigid support frame.The variable shear increment of the top slab was used as an unknown quantity and the four-order governing differential equation was established.The transverse bending moment of frame under dissymmetrical loads was obtained by solving the shear increment through analogy method for the Beam on Elastic Foundation.Examples were used to verify the proposed method and analyze the differences of the results of the transverse internal force calculated by different methods.The results show that the analytical solution are in good agreement with the finite results,the maximum error is less than 9.68%.（3）Be aimed at the calculation of the transverse internal force of single box double-cell simply supported box girder.Based on the analysis of rigid support frame,considering the influence of box girder distortion and whether the calculation model needs to set up lateral horizontal support,the formula of transverse internal force was established.Combined with the numerical calculation example,the influence of the change of vertical load transverse position and width span ratio of box girder on the transverse internal force was investigated.The results show that the analytical solution are in good agreement with the finite element solution.When the vertical load within the range of the top slab,the calculation model without the lateral horizontal support of the box girder with rectangular section can be adopted for the transverse internal force calculation.When the width span ratio decreases to0.4,the change of the width span ratio has little effect on the transverse internal force.（4）Based on the box girder distortion theories investigated,the distortion transverse moment which one of the transverse internal force was calculated by the distortion angle.The distortion effect of box girder was analyzed by numerical examples,and verified the analytical solution with the shell-63 element of ANSYS.The numerical examples shows that the distortion analysis theory are different and the parameters of the distortion are different,but the distortion warping normal stress are equal.When the thickness of plate is small,the distortion deformation of the box girder is obvious,with the increase of the thickness,the distortion angle and bi-moment gradually decrease.The influence of the plate thickness on the distortion is greater than that of the web inclination and the width height ratio of the box girder.The distortion transverse bending moment calculated by the distortion analysis theory have a deviation with the frame analysis method,the maximum rate is 25.72%,and the calculation value of the frame analysis method is large.（5）Be aimed at the investigation of the distortion effect of single box double-cell equal height box girder,the governing differential equations of dissymmetric distortion and symmetric distortion were established by plate element analysis and energy variation method.According to the analysis of the symmetric distortion of the box girder,two parametersβ₁ andβ₂ were used to describe the distribution of the distortion warping normal stress on each plate.The finite element model was established used the shell-63 element of ANSYS,and the analytical solution of distortion effect of single box double-cell box girder was verified,the error is less than 8.71%.The distortion warping normal stress of single box double-cell box girder caused by dissymmetric distortion is 40.17%of that of single box single-cell box girder.The analytical solution and the finite element solution agree well when the dissymmetric distortion and the symmetric distortion are considered simultaneously.（6）Based on the research of transverse internal force and distortion of box girder,in order to solve the calculation of the design bending moment of the bridge deck accurately,taking the actual bridge as an example.Used the formula given in the highway code and the finite model of frame and the finite model of whole bridge calculated the bending moment of the mid-span and support of the top slab under the vehicle load,the coefficient range of calculating the moment of the top slab was given.For the calculation of the bending moment at the root of the cantilever of the box girder,according to the highway code formula,Baider Bahkt formula,the model of cantilever and the whole bridge of the plate-shell element were established.The influence of the rear axle and the middle axle and the front axle of the vehicle load were considered respectively.The results of various calculation methods were compared and analyzed.The results show that the bending moment at the root of the cantilever obtained by the whole bridge model is slightly smaller than that calculated by the cantilever finite element model and practical formula of the cantilever.The numerical error of the cantilever finite element model of ANSYS and the Baider Bahkt formula is only 0.7%.When the cantilever of long-span box girder is loaded with vehicle load,the contribution of the front axle and the middle axle load to the cantilever bending moment only increases by5.25%.