Study On The Space State Transfer Theory Of The Viaduct Structure Based On The Auxiliary System Theory

With the rapid development of china’s highways and urban roads, viaduct andinterchange project have come out increasingly, the long-span straight and curvedgirder bridges have been widely used. New code for seismic design of urban bridgeand guideline for seismic design of highway bridge have issued one after another,but calculation method and seismic theory of such bridge is not very mature andfurther research need to be done.On the basis of the previous study work of the research group, started from thebasic concepts of structure state transfer, based on the auxiliary system method, thespace state transfer theory of the viaduct structure is deepened and developed. Thecalculation formulas of static, dynamic, linear and elastic-plastic are deduced, andapplied to static calculation, dynamic calculation and seismic calculation of thelong-span viaduct. The example analysis and theoretical verification were carriedout. The main research contents are as follows:1. The exact solutions of space state transfer matrixes of straight and curvedgirder are deduced based on the auxiliary system method, considering the sheardeformation; the exact solutions of load items under12different loads are deduced;the spatial stiffness matrixes of straight and curved girder are deduced, according tothe relationship between the transfer matrix and the stiffness matrix; on the basis ofthe different situations of the supports, the dot matrixes of concentratedload(concentrated force, concentrated bending moment, concentrated torque),elastic support, rigid support and the middle hinge are deduced respectively. 2. The spatial elastic-plastic analysis of straight and curved girder is conductedbased on the auxiliary system method. The different models of bend-plastic hinge,shear-plastic hinge, torsion-plastic hinge as well as tension and compression-plastichinge model are put forward by the single component model, The transfer matrixesof different plastic hinge models are deduced; And on this basis the plastic regionmodel of chain plastic hinge is proposed, the exact solutions of the state transitivematrix of the plastic region is deduced.3. Types and forces of the support are analyzed, and the spatial state transitiverelations of upper and lower sections of the fixed hinge support and fixed supportare deduced respectively. According to the different types and mechanicalcharacteristics of the bridge piers, the exact solutions of spatial state transitivematrixes of uniform cross-section pier, variable cross-section circular pier andvariable cross-section rectangular pier are deduced by auxiliary system method. Thetotal spatial state transfer matrix of the whole bridge is comprised by connecting thestate transitive relation of girder, support and pier together.4. The auxiliary system theory of the structure spatial state transfer is appliedto the vibration characteristics analysis of the viaduct bridges. According to theboundary conditions, the natural frequency of the structure are got by frequencysearch method. Then each order vibration mode of the structure are obtained.5. The seismic state transfer matrix theory of viaduct is set up by combiningthe structural seismic analysis principle. The frequency domain auxiliary systemstate transfer matrix of the seismic response analysis of the viaduct bridge undermultiple input is put forward based on the Fourier transform, using a combinationthe auxiliary system transfer matrix method and the great mass method.6. Based on the above theory, the corresponding computer analysis program isdeveloped by using MATLAB, and the corresponding numerical examplecalculation is conducted.