Static Analysis Of Box Girder Considering Shear Lag Effect

In recent years,box-shaped beams have been widely used in bridges due to their own advantages.Based on the energy variational method,a calculation method of shear lag with quadratic parabola as the warping displacement function was proposed.Combined with the finite element method,the influence of shear deformation on bending normal stress,the calculation method of shear lag,distribution law of shear lag,and influencing factors of shear lag were studied.The specific work is as follows:(1)By analyzing the distribution law of shear flow and the shear deformation of the flange plate,the quadratic parabolic is deduced as the warpage displacement function,and the governing differential equations and boundary conditions of box section girders are established by using the energy variation method.The differential equations of the shear lag of typical simply supported box girders and cantilever box girders under different loading conditions were proposed.(2)The longitudinal and transverse shear lag coefficients of simple box girder are calculated by energy variational method and finite element method,and the variation law of the shear lag coefficients of longitudinal and transverse section of box girder and the influence of load position,width-span ratio 2b/ L,width-height ratio 2b/ h,web spacing,load types,cantilever length on the distribution of shear lag were studied.It the results showed that when the box girder is subjected to the concentrated load,the maximum longitudinal shear lag coefficient of the top plate and floor appears at the place where the load is applied,and the influence area of the shear lag is narrow.When the load position changes from the top of the web to the center of the top plate,the roof experiences a process from "positive shear lag" to "negative shear lag".The larger the 2b/ L and the 2b/ h,the greater the shear lag coefficient.The larger the ratio of flange width A to half of roof width B,the smaller the shear lag coefficient above the rib,the larger the shear lag coefficient at the middle of the roof,and the smaller the shear lag coefficient at the flange position.When the box girder is subjected to a uniform load,the maximum shear lag coefficient occurs at the support position,which is smaller than the shear lag coefficient at the support position when the box girder is subjected to a concentrated load,and the shear lag coefficient curve has a small change.When the length of the cantilever plate is less than half of the roof,the variation range of the shear lag coefficient is not obvious.When the length of the cantilever plate is more than half of the roof,the variation of the shear lag coefficient is larger.(3)Based on the superposition method,the dismemberment method,and the finite element method,through the calculation of the shear lag coefficient of typical continuous beams,the applicable conditions of the two theoretical solution methods and the reasons for the errors in the calculation results are studied,the shear lag distribution law and the influencing factors of the shear lag distribution law of the continuous beam section are analyzed.The results show that the calculation results of the shear lag coefficient of the superposition method and the dismemberment method have very small errors,and the main reason for the error is that the dismemberment method does not consider the deflection at the inflection point.The smaller the2b/ L and the 2b/ h,the smaller the shear lag coefficient,and the shear lag coefficient does not change with the 2b/ L at the inverse bending point.The shear lag coefficients of the roof and floor under uniform load are smaller than those between the two spans of continuous beam under concentrated load.The inclination angle of the web affects the distribution of the shear lag at the edge of the wing plate,and the variation range is 8.20%.When the continuous beam is subjected to concentrated load,the longitudinal influence area of the shear lag effect is narrow.The distribution law of the shear lag near the loading point is the same as that of the uniform load on the continuous beam.The closer the loading position is to the support,the more significant the shear lag effect is,and the shear lag coefficient at the support position is the largest.(4)By comparing the results of finite element and analytical method,it is concluded that the analytical method is suitable for the calculation of shear lag coefficient of multispan continuous beam,which has little error with the calculation result of the finite element method.