Study On State Transfer Theory Of Curved Box Bridges

With the process of western development and the building of high-grade highway, many kinds of curved bridge have been used, Curved bridge can not only is adapt to bridge site that is limited by the terrain and surface features, and also because the curve lines of the structure is smooth, crisp, lively mood, it can give people enjoyment. The design of the curved structure can enable the architectural beauty and the environment coherence,and coordinated with people's aesthetic demands. considering whether from the point of geometric, aesthetics nor economics,the curved bridge has important practical significance and good prospect.The curved bridge not only has the coupling of bending and torsion out plane,but also has the bending and axis deformation in plane.The characteristics mechanic and dynimic are very complex. Although the literature researching curved beam are too numerous to mention, but, because the complexity of mechanical and dynamic properties and the difference in the approach as well as the inconsistency of starting point,there is no comprehensive and accurate analysis on complex characteristics of curved bridges. With the progress of science and technology and the development of the mechanization construction, the span of curved bridge is increasing.seismic response analysis is an important method for studying seismic ability and guiding safe design of bridges. When do the seismic design of the long-span bridges, considering multi-support seismic impact has become the consensus of the engineering and academic at home and abroad.Thus,The paper is attampt to establish a analysis calculation method which is simple,easily understand, clear, high precision and strongly applicable to provide a theoretical basis and computational methods for curesd structural analysis.In this paper,some specific tasks have been done as follows:In chapter 1,generalizes and summarizes the research progress of the analysis methods of curved bridges and the research status of transfer matrix method and its application,and find out the disadvantages of the transfer matrix method.In chapter 2,based on transfer matrix theory, with the closed-form solution of the deformation differential equation of curved beams, the transfer matrix of curved bridges have been derivated seriously and perfectly. the specific expression of field transfer matrix of curved box girder has been provided, and in accordance with the vibration theory the curved girder bridge, the vibration transfer matrix theory is established, the corresponding calculation program has been worked out with Matlab.combining the seismic analysis principles of structure, sesponse spectrum is introduced to the transfer matrix method,the seismic transfer matrix theory of curved girder bridge is established. and the corresponding calculation program has been worked out with Matlab. provides an effective way for the application of the transfer matrix method in static and dynamic analysis of the curved girder bridge.In chapter 3,the traditional transfer matrix method based on the precise answer of the structural differential equations.This method is simple and feasible to simple strut structure of. But to complex curved beam structure it is very difficult to solve,and its application is extremely inconvenient. Based on the precise algorithm of exponential matrix and transfer matrix theory, proposes a Precise Transfer Matrix Method (PTMM)for struture analysis of curved bridge.Perfectly derives the precise transfer matrix of curved bridges in detail,and establishse a complete theory of transfer matrix. Based on the numerical integration calculation program has been worked out with Matlab,and some comprehensive analysises and numerical validations and comparisons of PTMM are conducted.This method is general, can be used for any structural mechanical analysis. For complex structures, the advantage of the transfer matrix method becomes more apparent.In chapter 4,for the statically determinate structure, internal forces is not caused by the temperature change.Deformation and displacement result to free expansion and contraction of the material. But to statically indeterminate structure, the temperature change not only cause the deformation and displacement, but also caused structural internal force.The curved beams as one of the bridge structure are generally designed as statically indeterminate structure, under the action of variable temperature the mid-span transverse displacement of curved bridge is too large leading to destruction is a common failure mode. Based on the thermal expansion deformation of the curved structures,a precise transfer matrix format for solving internal forces and displacements of curved beams in-plane with pinned-pinned ends are derived explicitly. The corresponding calculation program has been worked out with Matlab, This method is theoretically possible to solve internal force and deformation of the beam under an arbitrary temperature field. It will expand the use of this method to the solution of multi-span curved bridge, and obtains the transfer matrix format for solving the internal force and displacement of the multi-span curved beams under the co-moderated action of the variable temperature and pier at the top surface.In chapter 5,natural vibration characteristics of the structure is an important performance, which determines the seismic response behavior and seismic performance of the structure. combining the precise integration method which is high-precision and transfer matrix method which is clear mechanical concept, Based on the theory of differential equations and matrix analysis, a new precise transfer matrix form is provided by combining the high-precision precise integration and the clear concept transfer matrix method.The calculation formulas of the method are derivated.The natural frequencies of the curved box bridge are solved with the method. Compared with the traditional transfer matrix method, it no need to solve the differential equations, just follows the iterative formula, the necessary transfer matrixes are obtained. According to the boundary condition,the natural frequency of the structure can be get use by the search method of the frequency. The corresponding calculation program has been worked out with Matlab. The method applies to a continuous structure also applies to discrete structures, but also can be applied to analysis the vibration characteristics of hybrid structure which is combined with discrete and continuous structure, provides a convenient and effective way for precise analysis of the dynamic properties of complex structures.In chapter 6,based on the FFT and FTMM,derives the power transfer matrix of curved in horizontal and vertical directions,and provides the FTMM for resolving the earthquake response of the curved box bridge in frequency domain.The corresponding calculation program has been worked out with Matlab,and some examples are analyzed, and the results indicate the accuracy and efficiency of this method. Not only enrich the seismic analysis of curved box girder bridges, but also the analysis platform of transfer matrix method extended from the time domain to the frequency domain, which would apply the possibility of the application of wavelet transform in the transfer matrix theory.In chapter 7,the multi-point incentive analysis model of large-span structure is more realistic and more reasonable than uniform input model.Based on the FFT and pseudo-static displacements,proposes a precise transfer matrix method for long-span curved box bridges seismic response analysis under multi-support excitations in frequency domain.Takeing the dynamic response of curved box bridge in curvature plane as a example,gives the solving thinking of pseudo-static displacement matrix.Derives the transfer matrix of the point unit focused on quality under multi-support excitations in frequency domain.In chapter 8,the dynamic analysis of structures under acceleration of bearing input is studied by the combination of precise transfer matrix method and great mass method. At first,according to the basic principle of great mass method,a great mass is attached to the bearing.Then,applying the precise transfer matrix method,the overall transfer matrix is set up in frequency domain.The equations are obtained and solved with the boundary conditions, and the dynamic reaction of the structure is obtained. And based on the above theory, the corresponding Matlab calculations program has been established.This method is more in line with the actual force situation of the structure,it can be regarded as an effective way to analysis dynamic response under multi-support excitations.In chapter 9,the conclution and outlook are obtained,in which the major work and innovative points of dissertation are summarized,including some suggestions and prospect for the research in the future.