One Dimensional Finite Element Model And Evaluation Method Of Shear Lag Effect Of Box Girder

Box girder are widely used in railway and road transportation because of their good mechanical properties.However,when the box girder is subjected to bending load,the deformation of normal section does not conform to the assumption of Euler beam’s flat section,resulting in uneven stress at the same section height,which is called shear lag.At present,many research universities and large transportation planning and design institutes at home and abroad have explored and studied the shear lag effect of box girder,and many achievements have been made.However,there are still some problems to be solved.This paper has done some research on the problem of shear lag effect,which is summarized as follows:(1)In this paper,the additional deflection of box girder is used to replace the shear lag warping displacement of box girder due to the unclear physical meaning of the shear lag warping displacement function in previous studies.The deflection of box girder is divided into two parts: deflection calculated by elementary beam and additional deflection.The differential equations of additional deflection and elementary deflection of the box girder are derived by using the new longitudinal displacement function and the total potential energy functional of the box girder.Based on the separation of deflection of elementary beam from additional deflection,the element displacement field is established,and the load matrix and stiffness matrix of the element are derived according to the total potential energy functional.(2)The analytical solutions of deflection and stress of the single box single room rectangular box girder with fixed ends under uniformly distributed load and concentrated load are derived by the variational method,and the results are compared with the one-dimensional discrete finite element model of the box girder.Meanwhile,the ANSYS finite element model under the same conditions is established to verify the accuracy of the above two theoretical methods.(3)According to the shear lag buckling displacement function of the trapezoidal box girder and the three-compartment box girder,the shear lag one-dimensional discrete finite element model of the box girder with different section types is derived,which is compared with the ANSYS finite element model and the experimental results,so as to verify the accuracy of the one-dimensional discrete finite element model of the box girder with different section types.The shear lag one-dimensional discrete finite element model of box girder considering shear deformation is derived,and the accuracy of the method is verified by taking the continuous beam with variable section as the research object.(4)The effects of different shear lag buckling displacement functions and different additional deflection shape functions on the calculated results are compared.The ratio of the total deflection second derivative to the deflection second derivative of the primary beam is used as the evaluation index of the shear lag effect.(5)In order to reflect the stress distribution of the box girder under moving load,the stress envelope of the box girder is proposed to evaluate the shear lag effect of the box girder.The stress envelope of the box girder with fixed ends and the continuous three-span beam with variable cross section under moving load is studied.