Analysis On Restrained Torsion Of Continuous Box Girder Bridge With Variable Cross-Section

With the country’s large investment in infrastructure projects,box girder bridges have been widely used due to their good mechanical performance.This paper mainly studies the restrainted torsion problem of box girder.First,the variable cross-section continuous box girder was discretized,that is,it becomes the beam segment element with constant cross-section,and the differential equation was established by using the energy variation method,and the constraint conditions of the boundary were determined.Then the initial parameter method is used to solve the differential equation,and the internal forces and displacements of arbitrary section of the box girder were obtained.According to the general definition of stiffness coefficient,the element stiffness matrix and equivalent nodal load were derived.Then,by referring to the general finite element analysis method of plane frame structure,the torque and double torque of arbitrary section of box girder were calculated by using the self-programmed program of FORTRAN language.Finally,combined with the main bridge of Tuanjie River Bridge,the bending stress,warping normal stress and restrained torsional shear stress were calculated by using the the self compiled program,and the stress amplification factor was further calculated.Compared with the finite element software,the internal force of the whole section of the beam can be calculated by self programming,while the finite element software can only calculate the local stress of the beam.Combined with numerical examples,the main conclusions of this paper are as follows:(1)The practical formulas for calculating torsion centre,principal sector coordinate and static moment were derived considering different depth of cantilever plate and top plate.Shear stress coefficient was introduced to study the influence of the secondary shear stress on the total shear stress.The warping normal stress and shear stress of a simply supported box girder were calculated by applying the analytic method and ANSYS solid element.The influence of variation of cantilever plate width and box cell depth on the generalized sector static moment,secondary shear stress,and shear stress coefficient was studied in detail.It was shown that the analytical solution was in good agreement with the ANSYS solution,which verifies the correctness of the formula.The shear stress coefficient at the maximum point of the webs can reach the maximum value of 2.4 when the width ratio of cantilever plate is approximately 0.3.As the box cell depth width ratio increase,the secondary shear stress at the characteristic point decreases gradually.As the cantilever plate width ratio and the box cell depth width ratio increase,the generalized sector static moment at the midpoint of the top and bottom plate shows completely different variation rule.(2)By studying the torsion effect under three different load conditions,the distribution law of the warping double moment,torque and torsion angle can be obtained as follows: the warping double moment reaches the maximum at the support section and the concentrated torque.The torque will have a sudden change at the concentrated torque.The torsion angle reaches the maximum at the concentrated torque and is zero at the support point.(3)Under the same load condition,the stress amplification factor of double lane was generally smaller than that of single lane.Under different load conditions,the position of maximum normal stress amplification factor was not fixed.In the first working condition,there is a maximum value at the 1/4 section of the mid-span.In the second working condition,there is a maximum value at the 3/4 section of the mid-span.In the third working condition,there is a maximum at the left support section.(4)The shear stress amplification factor reaches the maximum at the intersection of the top plate and the web on the bearing section.In the first working condition: single lane(1.6022),double lane(1.4127).In the second working condition: single lane(2.1741),double lane(1.8046).In the third working condition: single lane(1.6919),double lane(1.4741).