Research On Multi-stage Mechanics Model And State Transfer Theory Of Curved Beam Bridge With High Piers

Curved beam bridge with high piers is widely used in high grade highways andurban overpasses because of its strong adaptability of topography and attractiveappearance. This type of bridge features in complex structure and stress, and is proneto structural damage and destruction under strong seismic excitations, but studies on itsdestruction process and damage mechanism are scant, the corresponding analysismethod is not mature, so it is in urgent need of further study.Based on the analysis on the configuration, mechanical characteristics ofsuperstructure, support, pier and pile foundation and cooperative work betweenstructure and pile foundation of curved beam bridge with high piers, a multi-stagecalculation model corresponding to elastic, elastic-plastic and collapsing stage ofcurved beam bridge was proposed. The state transfer theory compliance with themechanical transfer law was established to carry out the research work.(1) A mechanical calculation model was put forward for elastic system of thecurved bridge. Based on classic elastic theory, the explicit space transfer matrix ofcurved box girder bridge under three-dimensional uniformly-distributed forces,three-dimensional single forces, three-dimensional uniformly-distributed torques andthree-dimensional single torques was respectively derived by using Auxiliary SystemMethod. The calculation model takes into account of spatial bending, shear, torsion,tension and compression, warping and their coupling effects of cross section of boxgirder bridge, including the effect of non-coincidence of section s shear center and thecentroid. Then a calculation programme was compiled and verified by an example.(2) The Cayley-Hamilton Transfer Matrix Method was proposed. In combination with Cayley-Hamilton theorem, the continuous model and discrete model was derivedseparately based on stress-strain relationship, geometric equation and motion equationof curved beam and lumped mass, considering spatial bending, shear, torsion, tensionand compression, warping and their coupling effects. Then a calculation programmewas compiled and verified by an example.(3) A Cayley-Hamilton Discrete Time Transfer Matrix Method was put forward.Using step-by-step integration method, the velocity and acceleration was linearized.On this basis, in combination with Cayley-Hamilton theorem, the special transfermatrix of undamped continuous/discrete model and damped discrete model underseismic excitation was derived separately based on stress-strain relationship, geometricequation and motion equation of curved beam and lumped mass, considering spatialbending, shear, torsion, tension and compression, warping and their coupling effects.Then a calculation programme was compiled and verified by an example. Theproposed method expands the application range of the transfer matrix method to thedynamic, nonlinear, time-varying fields, and avoids establishing the overall systemdynamic equation which the traditional method requests. The order of the system stotal transfer matrix is low, which only depends on the highest order of the elementmatrix. The equation of motion is available to be calculated in time domain, and thecomplex process of Fourier transform can be avoided. The method requests smallamount of calculation, which makes a fast calculation speed and a flexible modeling.So the calculation process is concise and highly stylized.(4) Considering spatial bending, torsion, shear, tension and compression of pierstud, the explicit space transfer matrix of pier stud under no external loads,three-dimensional uniformly-distributed forces, three-dimensional single forces,three-dimensional uniformly-distributed torques and three-dimensional single torqueswas respectively derived by using Auxiliary System Method. Then a calculationprogramme was compiled and verified by an example. Then the various possible formsof supporting and connecting hinge of curved bridge are discussed, and the transfermatrix was deduced. The calculation method of the unknown quantity for theconnected components was expounded respectively taking chain rod bearing, hinge and fixed hinge bearing as an example. The spatial transfer matrix of bearing unit wasdeduced. The various possible boundary conditions of the curved beam system werediscussed. Combined with transfer matrix method and m method, the calculationtheory for pile foundation is given in the single soil layers and different soil layers, andthe transfer matrix was deduced.(5) A calculation model for elastic-plastic curved bridge system was presented. Byusing Auxiliary System Method, the spatial transfer matrix of pier stud under p-?effect is deduced. Based on the inner link between stiffness matrix and transfer matrix,the spatial transfer matrix of pier stud under both p-? and p-? effects is deduced. Aplastic domain model was established for the elastic-plastic pier considering the plastichinge length. And the plastic field distribution pattern of vertical and horizontaldirection is discussed for different bridge pier systems. The calculation method ofplastic hinge length is studied. The plastic transfer matrix for bridge piers underdifferent stress states was deduced.(6) The mechanical calculation model for collapsing curved bridge system wasput forward. Based on the damage theory of plastic hinge, the possible collapse failuremodes of the piers under different stress states were analyzed, and transfer matrix forpiers under different failure stage. The spatial transformation matrix between the localcoordinate system and integral coordinate system are deduced. According toequilibrium equation and the displacement compatibility condition at the pier-beampoint, the whole transfer matrix was deduced respectively for rigid bridge system,simply-supported bridge system, and the continuous beam bridge system. Then acalculation programme was compiled and verified by an example. The possiblecollapse failure modes were discussed for rigid bridge system, simply-supported bridgesystem, and the continuous beam bridge system under seismic excitations. The wholetransfer matrixes set up for various bridge systems under different damage stages.Based on the shaking table test, the collapse failure modes and failure process werediscussed for C-shaped, S-shaped and herringbone curved bridge.