基于辅助体系法的高架桥梁空间性态传递理论研究

发布时间：2018-12-28 19:35

【摘要】：随着我国公路和城市道路的迅速发展，高架道路以及立体交叉工程日益增多，大跨径的直线梁桥与曲线梁桥应用广泛。尽管新的公路桥梁抗震设计细则和城市桥梁抗震设计规范已相继出台，但是这类桥梁的计算方法和抗震理论并不是很成熟，需要深入研究。本文从结构性态传递的概念出发，在课题组前期研究工作的基础上，基于“辅助体系法”深化和发展了高架桥梁结构空间性态传递的理论，推导了静力、动力、线性和弹塑性计算公式，应用于高架大跨桥梁的静力计算、动力计算和抗震计算，并进行了算例分析和理论验证。主要研究内容如下： 1.考虑剪切变形，基于“辅助体系法”推导了直线-曲线梁的空间性态传递场矩阵的精确解析公式；推导了12种不同荷载作用下的荷载项的精确解析公式；根据传递矩阵与刚度矩阵的关系推导了直线-曲线梁的空间刚度矩阵；根据支承的不同情况，，分别推导了集中荷载（包括集中力、集中弯矩、集中扭矩）、弹性支座、刚性支座和中间铰的点矩阵。 2.基于“辅助体系法”对直线-曲线梁进行了空间弹塑性分析。采用单分量模型，提出了弯曲塑性铰、剪切塑性铰、扭转塑性铰以及拉压塑性铰的不同模型。推导了不同塑性铰模型的传递矩阵；在此基础上，提出了“链式塑性铰”的塑性域模型，推导了塑性域的性态传递关系，使得传递矩阵的弹塑性分析更加合理。 3.分析了支座的类型以及受力情况，分别推导了固定铰支座、固定支座上下截面的空间性态传递关系；根据桥墩的不同类型及受力特点，基于“辅助体系法”推导了等截面墩、变截面圆形墩和变截面矩形墩的空间性态传递矩阵的精确解析公式，并将梁、支座与墩的性态传递关系联系到一起，共同组成整个桥梁的总空间传递关系。 4.将空间性态传递的辅助体系理论应用于高架桥梁的振动特性分析。根据边界条件的不同，运用频率搜索方法求得结构的自振频率，进而求得结构的各阶振型。 5.结合结构抗震分析原理，建立了高架桥的抗震性态传递理论。基于傅里叶变换，采用“辅助体系”传递矩阵法和底部大质量法相结合，提出了高架桥梁在多点输入下地震反应分析的频域辅助体系性态传递矩阵法。 6.基于以上理论，采用MATLAB研制了相应的计算机分析程序，并进行了相应的算例计算。
[Abstract]:With the rapid development of highway and urban road in our country, viaduct and crossing engineering are increasing day by day. The long-span linear girder bridge and curved beam bridge are widely used. Although new rules of aseismic design for highway bridges and codes for seismic design of urban bridges have been issued one after another, the calculation methods and seismic theory of these bridges are not very mature and need further study. Based on the concept of structural state transfer, based on the previous research work of the research group, the theory of spatial state transfer of elevated bridge structure is deepened and developed based on "auxiliary system method", and the static and dynamic forces are derived. The linear and elastic-plastic formulas are applied to static calculation, dynamic calculation and seismic calculation of long-span viaduct bridges. The main contents are as follows: 1. Considering shear deformation, an exact analytical formula of the spatial transfer field matrix of a straight-curve beam is derived based on the "auxiliary system method", and an exact analytical formula of the load term under 12 different loads is derived. According to the relation between transfer matrix and stiffness matrix, the spatial stiffness matrix of straight-curve beam is deduced. The point matrices of concentrated load (including concentrated force, concentrated moment, concentrated torque), elastic support, rigid support and intermediate hinge are derived according to the different conditions of support. 2. The spatial elastoplastic analysis of linear-curve beam is carried out based on the auxiliary system method. Different models of bending plastic hinge, shear plastic hinge, torsional plastic hinge and tension-compression plastic hinge are proposed by using single component model. The transfer matrix of different plastic hinge models is derived, and the plastic domain model of "chain plastic hinge" is proposed, and the behavior transfer relation in plastic domain is deduced, which makes the elastic-plastic analysis of transfer matrix more reasonable. 3. Based on the analysis of the type and force of the bearing, the spatial transfer relationship between the upper and lower sections of the fixed hinge bearing and the upper and lower section of the fixed hinge support is derived respectively. According to the different types of bridge piers and their stress characteristics, based on the "auxiliary system method", the exact analytical formulas of the spatial transfer matrix of the uniform section pier, the variable section circular pier and the variable section rectangular pier are derived. The relationship between the bearing and the piers is connected together to form the total spatial transfer relationship of the whole bridge. 4. The auxiliary system theory of spatial state transfer is applied to the analysis of vibration characteristics of elevated bridges. According to the difference of boundary conditions, the natural frequency of the structure is obtained by the method of frequency search, and then the vibration modes of each order of the structure are obtained. 5. The theory of seismic behavior transfer of viaduct is established based on the principle of seismic analysis. Based on Fourier transform, using the transfer matrix method of "auxiliary system" and the method of large mass at the bottom, a frequency-domain auxiliary system-state transfer matrix method for seismic response analysis of elevated bridges under multi-point input is proposed. 6. Based on the above theory, the computer analysis program is developed by MATLAB, and the corresponding calculation examples are given.
【学位授予单位】：西安建筑科技大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：U441

【参考文献】