The Research On Stability And Vibration Of Cable-arch Structure

Arch bridge is a basic bridge structure, and the cable-stayed arch bridge is a new type of composite bridge, which combines the cable-stayed bridge and the arch bridge harmoniously. To ensure arch bridges and cable-stayed arch bridges safty during construction and service, and to make its design more economical and reasonable, the research on mechanical model, stability and vibration of cable-stayed arch bridge is developed in this paper based on construction of arch bridges and cable-stayed arch bridge—the Xiangtan Xiangjiang 4th bridge in Xiangtan city, Hunan province. The main contents and achievements are as following:1. Modeling of cable-stayed arch bridges and comparative study of basic theory of stability and vibration are developed. According to modeling methods of mathe and mechanics, mechanical model of cabe-arch structure is introduced by systematic analysis of mechanical behavior of cable-stayed arch bridge, based on the Xiangtan Xiangjiang 4th bridge. Comparative study of definitions, mechanical theories, modeling methods and solving means of stability and vibration is presented, and the conclusion that stability and vibration belong to eigenvalue problem is obtained.2. The static performance of arch and cable-arch structure is investigated. The stress tensor and deformation of cable are considered. Based on cable-arch model of cable-stayed arch bridge, geometric equation and physical equation of arch, the formula for calculation and analysis of cable-arch structure is established. Furthermore, the program is developed to calculate the structure members and mechanical behavior of arch and cable-arch structure under dead load and live load is studied, which has the same structural parameters3. Co-rotational formulation is proposed and used to solve the in-plane stability of cable-arch structure. The tangent stiffness matrices of plane beam element and plane bar element are derived, which can be used for resolving the geometrical nonlinear ploblem for a structure with a large displacement and rotation. Then, in response to the mixed finite element method and the tangent stiffness matrix, the nonlinear finite element program is developed to investigate the eigenvalue buckling and the limit load-carrying capacity of cable-arch structure under all sorts of loads.4. The approximate formulae for calculating lateral-torsional buckling critical load and in-plane buckling critical load are deduced respectively by studying the mechanical behavior of arch and cable-arch structure and applying the minimum potential energy principle in conjunction with Rayleigh-Ritz method. Moreover, Furthermore, the influence on stable performance for cable-arch of structural parameters, such as, number, position, length, cross-section area, dead load intensity of cable and open-angle, radius of arch is also studied.5. Neglecting the effects of shear deformation and warping, the relationship of strain and displacement for spatial arch is given in this thesis. The nonlinear dynamic differential equations, which have three displacement freedoms and a torsion freedom, are erected according to Hamilton principle with consideration of the effect of cable. At the same time, out-of-plane free vibrtion differential equations, which are consistent with those simplified from the nonlinear dynamic differential equations, are developed by using static balance method.6. A transfer matrix method is used to analyze in-plane free vibration and out-of-plane free vibration of cable-arch structure, and Gear method is also used to solve the differential equations. Additionally, the computer program are designed to explore the influence on dynamic characters for cable-arch of structural parameters, such as, number, position, length, cross-section area of cable and open-angle, radius of arch. Some conclusions for engineering are drawn.7. The approximate formulae for calculating basic frequency of in-plane vibration of cable-arch structure are established by using the minimum potential energy principle and Rayleigh-Ritz method. In addition, the approximate formulae for calculating basic frequency of out-of-plane vibration of cable-arch structure are also established according to out-of-plane free vibrtion differential equations, Galerkin method and Rayleigh-Ritz method, respectively.