The Dynamic Analysis About Curved Thin-walled Box-girder

With a lot of high grade highway and urban ramp built, all kinds of curved girderstructure were widely used. Curved girder can well meet the requirements of the terrainand landmark, to make the arrangement of traffic lines tend to be more reasonable andscientific. Because of its large torsional stiffness, beautiful appearance, goodadaptability and other advantages, the box section was widely used in the curved girderbridge. However, due to the presence of curvature and the characteristics of thin-walledstructure, the vibration of curved thin-walled box-girder would be with some complexissues, such as the spatial bending-torsion coupling, cross section warping and so on.With reference to the research achievements of predecessors, this paper considered thetension and compression, bending, torsion and warping, to get the dynamic analysis ofcurved girder. In this paper, main works were as follows:①A three-dimensional curvilinear orthogonal coordinate system that wassuitable for the variable-curvature and variable-height curved box-girder wasestablished. With reference to the existing research results, the variable-curvature andvariable-height curved box-girder were analyzed in bending and torsion, to obtain therelationships between normal strain and shear strain at any point in the section anddisplacement of global sections of box-girder under the action of bending and torsion.Relative to the general analysis of curved girder in which axis curvature was studied asthe whole girder curvature, this paper considered the effect of the curvature changewith transverse in the actual curved box-girder structure in the derivation process.②An isoparametric curved beam element that had three nodes, seven degrees offreedom each node was established. The curved beam element fully considered thecharacteristics of curved box-girder, both can effectively model the variation ofcurvature and the girder height, and can apply to the trapezoidal cross section ofbox-girder, considering the tension and compression, bending, and the torsion, warp.On the basis of the relationships between normal strain and shear strain at any point inthe section and displacement of global sections of box-girder when under the action ofbending and torsion, the element stiffness matrix was derived. According to therelationships between speed at any point in the section and speed of global sections, bymeans of kinetic formulas, the element mass matrix was deduced. Rayleigh damping matrix which had a linear relation with the stiffness matrix and mass matrix wasestablished. The natural vibration characteristics of the structure were obtained bymeans of solving a generalized eigenvalue problem of the undamped vibrationequation. The equation of motion of the structure established, the dynamic response ofthe structure was obtained by modal superposition method.③On the basis of the above research results, the FEM calculation program waswritten by using MATLAB computer language. The program can calculate the naturalvibration characteristics of the variable-curvature and variable-height curvedbox-girder when under several common bridge support conditions, and also cancalculate the dynamic response of several typical load of curved box-girder. Throughsome examples, it can verify the effectiveness and superiority of calculation methodproposed in the paper, and prove the correctness of the written program.