Analysis On Torsional Effect Of Continuous Box Girder Bridge Based On New Generalized Displacement

With the development of society,the demand of highway transportation for bridge construction is increasing day by day,and the box-girder bridge is particularly concerned because of its advantages of large stiffness and good stability.In order to improve the rigid torsion analysis theory of continuous box girder bridges with variable section,firstly,the box girder bridge with variable section is discretized into beam segment elements with equal section,a novel torsion generalized displacement is proposed for box girder with constant section.On this basis,the constrained torsion governing differential equation is established and the initial parameter solution is given.A torsion beam element with 2-nodes and12-DOFs is proposed.Based on the initial parameter solution,the element stiffness matrix and the equivalent node load array are established.By referring to the finite element analysis idea of plane truss structure,the torsion analysis program is written by using Fortran language,and the correctness of the girder segment element and analysis program is verified by numerical examples.The increasing stress coefficient is introduced to characterize the increasing effect of eccentric load on longitudinal bending stress.Finally,a continuous rigid frame box girder bridge with variable section is analyzed.The main work and conclusion of this paper are as follows:(1)The total torsion angle of box girder section is divided into two parts.According to the definition of different torsion angles,the expression of longitudinal warpage displacement of section with definite physical meaning is obtained from shear deformation.Then,based on the longitudinal balance of the micro-element and considering the influence of the cantilever plate on the shear flow in the closed chamber,the basic calculation formula of the constrained torsional deformation of the cantilever plate and the closed chamber is established respectively.The torsional governing differential equation is obtained by superimposing the torsional torques and the initial parameter solutions of torsional internal forces and displacements of box girder under different loads are given.When Bredt torque is 0,the above theory can be reduced to torsion analysis theory of thin-walled open member.The correctness of the theory in this section is verified by using the finite element software ANSYS to calculate a numerical example,and the influence law of geometric parameter variation on the buckling normal stress,each torque component and torsion angle coefficient is analyzed in detail.The results show that the two torques corresponding to the constrained shear torsion angle only occur in the area near the section under concentrated load.With the increase of the height and size of the box girder,the position where the maximum normal stress occurs tends to the end of the cantilever plate.(2)The increasing coefficient of normal stress and shear stress is defined to reflect the increasing effect of shear lag and rigid torsion on the longitudinal bending stress.Aiming at the bending of arbitrary thin-walled structures,the formulas for calculating the normal stress and shear stress of bending are established.When the symmetry axis of the structure is calculated,it can be reduced to the longitudinal bending theory established in the mechanics of materials.In view of the shear lag effect caused by the shear deformation of the flange plate of box girder,the governing differential equation was established by taking the additional deflection as the generalized displacement,and the shear lag effect was analyzed as an independent deformation state separated from the longitudinal bending.The correctness of the theory in this section is verified by numerical examples.(3)For the proposed 2-nodes and 12-DOFs beam segment element,the stiffness matrix and the equivalent node load array of the element were derived from the initial parameter solutions of the governing differential equations of longitudinal bending,shear lag and constraint torsional effect and the boundary conditions.The example is studied and analyzed by the program and found that the calculated results are in good agreement with the theoretical values.The reliability of the beam element in this paper is verified.(4)A continuous rigid frame box girder bridge with variable section was analyzed,and the specific values of concentrated load and uniform load in different lane loading were calculated respectively,so as to determine the two kinds of lane loads with different effects.Using the program,the bending moment and the influence line of the double moment of each control section of the bridge(the left cross midspan,the mid-span rigid joint,right cross midspan)are obtained.Combined with the two kinds of lane loads,six load conditions of the normal stress and shear stress of the section are defined,and the bending and torsional effects of the box girder bridge under different working conditions are studied.The results show that the distribution of generalized internal forces corresponding to the normal stress of shear lag and the constraint torsion are similar.The maximum value of the coefficient appears in the upper flange plate under each working condition,which proves that the upper flange plate is the reasonable location for the value of the stress increasing coefficient.The section with large stress increase coefficient has the characteristic of small bending stress,however,the total stress value of this section is still at a low level,so it is not suitable to be used as a reference section for the value of stress increase coefficient.