Study On Shear Lag Effect Thin Walled Box Girder With Cosine Function As Warping Displacement Function

With the development of transportation industry in our country,big span, wing margin wide-body box girder is widely used in modern bridge construction,but the shear lag of box girder question can not be ignored,if don't take these problems seriously,it is likely to cause local cracking, local instability and even more serious consequences of box girder.So it has important theoretical and engineering significance to study the shear lag effect of thin walled box girder,based on the thin wall structure theory and the energy variational principle, this paper has carried on the following research to the single room and double room box girder:(1)Based on single room straight web box girder with cantilever plate equals top plate,selected the cosine function as the shear lag warping displacement function and the difference of the same maximum shear angle for each wing plate is the generalized displacement of shear lag,by using the energy variational principle to deduce the governing differential equation of section,combined with the boundary conditions of simply supported and cantilever to give the stress solution in the vertical concentrated force and uniform force under the box girder.A case study of a typical single room box girder,the numerical solution and the solution of this paper are used to study the distribution law of shear lag coefficient in the transverse and longitudinal direction.results show,selected the cosine function as the shear lag warping displacement function of shear lag effect has good accuracy,the solution and numerical solution are in good agreement in this paper.(2)For general single room trapezoidal cross section box girder, from the nature of each wing plate with different longitudinal warping,considering the same maximum shear angle difference and the difference of the maximum shear angle as the generalized displacement of shear lag,using energy variational principle to deduce the governing differential equation of box beam,combined with simply supported boundary conditions to give the solution of the longitudinal stress of each wing plate under the concentrated force and uniform force.Using the solution and numerical of the same and different maximum shear angle difference to analysis the effect on shear lag effect,results show,the longitudinal stress solution with different maximum shear angle is better than that of the same maximum shear angle difference and it can correctly reflect the difference between the shear lag warping of the wing plates;Secondly, analysis the effect of the height-span ratio on the shear lag effect coefficient in the middle section,research shows,the negative coefficient of shear lag decreases and the positive coefficient of shear lag increases with the increase of the height span ratio;the effect of the high span ratio on the shear lag coefficient is similar to the linear distribution under theconcentrated force,under the uniform force,it is the curve distribution.(3)For the twin-celled single box girder,each wing plate to choose the different maximum shear angle difference as the shear lag generalized displacement,based on the energy variational principle to deduce the governing differential equations of the cross section is considered or is not considered the shear deformation,according to the boundary conditions of simply supported to deduce the longitudinal stress solution and the solution of the vertical deflection.By using the paper solution and numerical solution to analysis the effect shear deformation on the longitudinal stress and the vertical deflection,results show,shear deformation does not affect the longitudinal stress, but has a significant effect on the deflection,the greatest for considering the shear deformation,the second for not considering the shear deformation and the least for elementary beam theory.In addition,analysis on the longitudinal distribution of the shear lag effect coefficient and the effect the height-span ratio on shear lag effect coefficient in the middle section,the results of the study are similar to the single room box girder,the shear lag effect of the side plate is slightly larger than that of the shear lag effect in the medium web.(4)For the twin-celled single box girder without cantilever plate,there is difference in the longitudinal displacement of the top plate and the bottom plate when lateral load lateral symmetry movement,therefore, the top plate and the bottom plate adopt shear lag generalized displacement,At the same time, the influence of the lateral position of the load should be considered when calculating the potential energy of the external force,using the energy variational principle to deduce the governing differential equation of box girder section under the load lateral movement,combining with the boundary conditions of simply supported under uniformly distributed load are given longitudinal stress solution of the top and bottom plates.By using the paper solution and numerical solution to analysis the laws of the shear lag lateral distribution in the mid-span section and the height-span ratio influenced the changing of the shear lag effect coefficient in the middle section,research shows,with the symmetrical loading on the top plate moving from side webs to the center of single room,the shear lag effect on the top plate near the webs change from positive to negative,and the shear lag effect on the bottom plate near the webs rarely changes basically remain positive;the area near the load is shown as the positive shear lag effect,far from the place, it is shown as negative shear lag effect.