Beam Section Finite Element Method And Its Application For Constrained Torsional Analysis Of Continuous Box Girder With Variable Cross-section

At present,there are many ways to study the torsion of box section beam.The method used in the analysis of variable section continuous box girder is mainly differential method.Based on the second theory of the torsional analysis of box beam constraint,it is solved by the initial parameter,and the differential equation is four order.In the solution of the differential equation,it is divided into two two order equations,and the four order differential equation is obtained through the solution of the two order equation.Solution.The difference method is very complicated,so it is not widely applied.With the development of science and technology,the three-dimensional finite element model can be established by computer to analyze the constrained torsion problem of thin-walled box girder.However,the preparation of the three-dimensional finite element model is not only time-consuming and laborious,but also higher in the computer,and the result of calculation is integrated with various factors,so the result is not very ideal.In view of the restrained torsion phenomenon of thin-walled box girder under torsional load,based on thin-walled rod theory and finite element method,the basic theoretical deduction is first introduced,and the generalized displacement function(twist angle ?)and warpage function representing the warping degree(??)are defined.The relationship between the warpage positive stressw? and the constrain torsional shear stress? and the generalized bis torque B and torque are established by theoretical deduction T.Then the basic differential equation is established,and the internal force and displacement of any section of the box beam can be solved by solving the initial parameter method and combining the boundary conditions.Finally,according to the finite element knowledge of box beam is derived in unit constraint torsion stiffness matrix and equivalent nodal force,general idea and reference member structure finite element analysis,the calculation program for the analysis of one-dimensional discrete beam constrained torsion box is programmed in Fortran language.By comparing the calculation results of the program with the analytical solution of an example,it is proved that the program is feasible and has high precision.The Lao Wan Fu River Bridge as the engineering background in this paper,the program calculates the torsional stress constraint under the different loading conditions of box girder,and obtained the conditions under the constraint of box girder torsional stress ratio of positive bending stress.Through the study of this paper,the main conclusions are:(1)The method of calculating the stress of arbitrary section by discrete section continuous box beam into one dimensional section element with equal section is very reliable.Moreover,there are warped double moments along the span direction of the beam.Although they are very large in some parts,they have fast attenuation characteristics.These locations are mainly located at the action of concentrated torque and the supporting section of beams,and the torque torque has a sudden change in the action of concentrated torque.(2)Under different load conditions,the ratio of warping stress to bending stress is different.The ratio of the ratio is larger in the middle span of the 1/4 cross section and in the working condition four(the whole bridge is distributed only by uniform load)at the middle span of the 1/4 cross section.Under the condition of the 1/2 cross section,the ratio is large at the side span of the 1/2 cross section.Under the condition of six(both left span layout and middle span arrangement of concentrated load),the ratio is larger in the middle span of 1/2cross section,and in working condition seven(only on both sides).When the load is eight and the load is uniformly distributed on the left side,the ratio is larger at the pivot section.(3)Under the same load condition,the ratio of warping stress to bending stress under two lane is smaller than that under single lane action.(4)Through the analysis of the total torque of each control section under the action of a single lane,it can be seen that the free torque calculated by the free torsion theory is larger than the ratio of the total torque.