【作者】 李杰；

【导师】 郑凯锋；

【作者基本信息】 西南交通大学 ， 桥梁与隧道工程， 2007， 博士

【摘要】 随着城市桥梁向美观、大跨的方向发展，自锚式悬索桥的建造逐渐增多，这种桥梁的结构力学行为和性能成为研究热点，论文对自锚式悬索桥地震响应的研究正是基于这样的背景。考虑作为生命线工程的桥梁结构，在地震灾害发生后所造成的严重后果，同时现有设计规范不能适用于此类桥型的抗震分析，论文全面分析自锚式悬索桥动力特性和地震响应的研究现状，详细研究自锚式悬索桥地震分析方法，总结并概括自锚式悬索桥动力特性和地震响应研究的最新成果。针对自锚式悬索桥自由振动特性和地震激励下结构响应，详细推导了自锚式悬索桥自由振动微分方程，对多种激励方式下自锚式悬索桥非线性时程响应进行深入研究，提出自锚式悬索桥地震响应的简化计算方法。论文主要开展了以下几方面的研究工作：（1）应用广义泛函变分原理，采用经典解析方法推导自锚式悬索桥自由振动微分方程。考虑到自锚式悬索桥不同于普通地锚式悬索桥的特点，综合考虑大缆纵向变形、加劲梁压弯耦合效应、剪切和垂跨比等多种因素影响，根据Hamilton原理，应用广义泛函变分方法推导三跨连续自锚式悬索桥自由振动微分方程，针对常见自锚式悬索桥的结构特征，对微分方程进行简化，推导这类桥梁的纵向振动频率计算公式、竖向振动频率计算公式以及自由扭转振动的振型计算公式和简化后的横向振动简化微分方程，研究加劲梁和桥塔与边墩之间约束强弱等边界条件对自由振动特性的影响。（2）推导自锚式悬索桥考虑几何非线性和初始内力等因素的加劲梁单元刚度矩阵和缆索单元刚度矩阵表达形式。论文研究分析了采用有限元方法计算自锚式悬索桥地震响应时加劲梁单元和缆索单元的刚度矩阵的构成。考虑自锚式悬索桥加劲梁承受轴向压力的结构受力特点，推导加劲梁单元刚度矩阵的表达式；忽略大变形刚度矩阵，计入线刚度矩阵和几何刚度矩阵，推导缆索单元刚度矩阵表达式；研究整体坐标系下缆索单元刚度矩阵的转换方法。在地震响应分析中，针对缆索支撑结构的单元刚度矩阵不同于一般结构的特点，对由于荷载作用下的结构大位移、缆索自重垂度和缆索初始内力等因素产生自锚式悬索桥的几何非线性，采用Newton-Raphson迭代法、Ernst公式和叠加初始内力产生的几何刚度项分别考虑。（3）采用二维相干函数模型和三角级数法编制人工地震波生成程序，利用大质量法详细研究不同激励方式下自锚式悬索桥非线性时程响应。基于二维相干模型，假定静力非线性平衡状态为桥梁结构地震响应分析的初始状态，详细研究人工地震波功率谱模型和部分相干函数模型后，选择Hao二维相干函数模型，考虑垂直地震波传播方向各支点影响，编制出可综合考虑频率对视波速影响以及不同支点间非平稳调制函数差异等因素的人工地震波生成程序，并合成实桥的六个支点的地震加速度时程。分别研究考虑几何非线性、行波效应和部分相干效应的多点激励，应用大质量法和所生成的人工地震波，详细分析结构在强地震荷载作用下桥塔、墩柱地震响应特性，最后考虑材料非线性、几何非线性等因素，对自锚式悬索桥在多维一致激励、多维非一致激励下的结构响应进行分析。分析研究表明：在静力非线性平衡状态下，几何非线性对自锚式悬索桥地震响应影响较小；行波效应会使弯矩极值滞后，加劲梁跨中位移随着地震波传播速度而增大，考虑行波效应时桥塔、加劲梁的弯矩均比考虑一致激励的弯矩大；考虑垂直地震波传播方向各支点间的二维相干效应对塔、梁交接处和塔底弯矩和位移有一定影响，但二维相干效应不显著，故对于自锚式悬索桥地震响应仅考虑一维相干效应，二维相干影响可忽略；材料塑性使能量耗散，对结构地震响应峰值的有一定影响。（4）归纳总结出影响自锚式悬索桥地震响应的4个无量纲参数，研究加劲梁参数与垂跨比参数的基准值和塔梁参数、桥塔参数的设计计算曲线与表格。详细研究自锚式悬索桥加劲梁的主跨长度、宽度、高度、桥塔高度、桥塔根部单柱截面尺寸、垂跨比和阻尼比等结构参数对自锚式悬索桥地震响应的影响，分析总结上述各个结构参数的影响趋势和相关性，进一步优选并将相关结构参数组合为4个无量纲参数：加劲梁参数k₁、塔梁参数k₂、桥塔参数k₃和垂跨比k₄。充分考虑桥梁主要尺寸的变化范围和不同地震激励模式，通过大量的结构地震响应计算分析，在确定加劲梁参数基准值为0.037和垂跨比基准值0.125的基础上，详细计算分析塔梁参数和桥塔参数，得到自锚式悬索桥与这两个结构参数相关数值曲线和表格，可供结构方案设计或初步设计参考使用。（5）研究自锚式悬索桥加劲梁参数和垂跨比的计算修正系数，提出自锚式悬索桥地震响应的简化计算方法，并验证其可行性。研究加劲梁参数和垂跨比对自锚式悬索桥地震响应的影响，通过对这两个结构参数的修正，即加劲梁宽度修正系数k_β和垂跨比修正系数k_λ，给出加劲梁宽度修正系数和垂跨比修正系数相关图表。基于弹性概念采用根据应力和位移评价地震响应的原则，提出采用加劲梁参数、塔梁参数、桥塔参数和垂跨比4个参数的自锚式悬索桥地震响应的简化计算方法，由此可简便地计算恒载应力和地震荷载总应力与恒载应力的比率（塔根应力放大因子）、塔加劲梁交接处桥塔恒载应力与地震荷载产生总应力与恒载应力的比率（塔梁交接处桥塔应力放大因子）、地震作用下加劲梁跨中最大竖向位移和塔顶最大水平位移。论文通过对5座实桥计算比较，初步验证自锚式悬索桥地震响应简化计算方法的可行性。更多还原

【Abstract】 As the development of city bridge is changing to beautiful and long, the construction of self-anchored suspension bridge is more and more. To study on structure mechanics behavior and performance of this bridge structure is becoming hot point and the thesis that studies on seismic response of self-anchored suspension bridge is based on this background. Considering bridge structure as life-line and disastrous consequence after seismic and the current specified criteria to be not fit for analysis seismic of this style bridge, the thesis roundly analyzes current situation research of dynamic feature and seismic response and studies on resistance seismic analysis method of self-anchored suspension bridge in detail, and it summarizes recently-researched achievement of self-anchored suspension bridge free vibration and seismic response. Aimed at free vibration and structure response under seismic excitation of self-anchored suspension bridge, the thesis achieves differential equation of self-anchored suspension bridge free vibration, and under different excitation deep analyzes response of non-linear time-history, and brings forward simplified approach that analyzes seismic response of self-anchored suspension bridge. The chief research works of the thesis are as follows:（1） Application of generalized variation principle and classic analytical method, the thesis presents differential equation of self-anchored suspension bridge free vibration, and studies on boundary constraint conditions （such as connection of stuffiness girder, tower and side pier each other） affection to free vibration. Considering self-anchored suspension bridge characteristic, which is different to ordinary suspension bridge, synthetically taking into account longitudinal displacement of cable, coupling effect of stiffness girder axial and flexural action, shearing and ratio of rise to span etc., according to Hamilton principle, the thesis applies of generalized variational principle to present differential equation of self-anchored suspension bridge free vibration. Aimed at structural feature of usual three-span continual self-anchored suspension bridge, simplified differential equation, free vibration frequency formulas of longitude and vertical is achieved, and the thesis still presents formula of torsional vibration style and simplified differential equation of transverse vibration.（2） Considering geometric non-linearity and initial load, the thesis presents element stiffness matrix expression of stiffness girder and cable. When based on FEA to analyze seismic response of self-anchored suspension bridge, it studies on stiffness girder and cable element stiffness matrix’s component. Taking into account structural characteristic that stiffness girder bears axial compression, it presents expression of girder element stiffness matrix. Neglecting large-displacement stiffness matrix, considering linear and geometric stiffness matrix, it presents expression of cable element stiffness matrix. The thesis still studies on conversion of cable element stiffness matrix under global coordinates. In the analysis of seismic response, aimed at structural element stiffness matrix’s characteristic that the structure to be supported by cable is different to others, for geometric nonlinear factors which is brought forth by structural large-displacement, self-load’s rise to span of cable and initial load etc., the thesis applies to Newton-Raphson’s iterative method, Ernst’s formula and addition geometric stiffness matrix which is brought forth by initial load to take into account, respectively.（3） Based on 2D-coherence function model and triangular series method, the thesis programs to produce artificial seismic wave, and under different seismic excitations to apply of great mass method, it analyzes nonlinear time-history response of self-anchored suspension bridge in detail. Based on 2D-coherence model, assumed static nonlinear balance to be as initial state of bridge structure seismic response analysis, after studying on PSD （power spectral density） function model of artificial seismic wave and incoherence function model, considering effect of vertical seismic wave promulgating direction to other supported points, selecting Hao’s 2D-coherence model, applying of triangular series method and MATLAB the thesis achieves artificial seismic wave program and produces six points artificial seismic acceleration waves of the actual bridge. Considering geometric non-linearity, wave passage effect and incoherence effect, it studies on multi-support excitation. Applying of great mass method and artificial seismic wave, under strong shock, the paper analyzes seismic response character of towers and piers in detail. At last, considering material and geometric nonlinear, it analyzes self-anchored suspension bridge structural response under multi-dimension uniform and non-uniform excitation. Under static nonlinear balance state, it shows that the effect of geometric nonlinear is little to seismic response; the time that the moment occurs to crest value can be lagged and the girder mid-span displacement will increase as seismic wave promulgating velocity increase; comparing with uniform excitation, when taking into account wave passage effect, moment of tower and girder is larger than that of uniform excitation; considering every support point’s coherence effect each other which their connecting lines are vertical with seismic wave promulgating direction, it will affect moment of tower bottom and girder tower’s interface and displacement, but 2D coherence effect is not obvious, so 2D coherence effect may be neglected and only considered 1D coherence effect in the seismic response analysis; plastic material may disseminate energy, and it can affect structural crest value of seismic response.（4） Summarizing four dimensionless parameters which affect seismic response of self-anchored suspension bridge, studying on reference value of girder and ratio of rise to span parameters, presenting design curves and tables which corresponding tower girder parameter and tower parameter. Studying on effect of parameters, which include main-span, girder’s width and height, tower’s height, area of single tower bottom, ratio of rise to span and damping ratio etc. parameters. Through analyzing those parameters’ affection current and relativity and furthermore optimum seeking to constitute, the thesis presents four dimensionless parameters, which are girder parameter k₁, tower girder parameter k₂, tower parameter k₃ and ratio of rise to span ratio k₄. Adequately considering variation range of bridge’s dimension and different seismic excitation model, based on girder parameter and ration of rise to span parameter to be 0.037 and 0.125 respectively, through enough analyzing, calculating tower girder and tower parameters in detail, the thesis achieves curves and tables that are correlation with the above-mentioned two parameters, and the curves and tables may be used in structural plan design or initial design.（5） Studying on amended parameters correlation with girder and ration of rise to span, presenting simplified approach to analyze seismic response of self-anchored suspension bridge and checking its feasibility. Analyzing affection of girder and ration of rise to span parameters to seismic response, through two structural amended parameters, that is, girder width amended parameter k_B and ration of rise to span amended parameter k_λ, the thesis achieves correlation tables. Based on elastic concept and applied of stress and displacement to estimate seismic response, presenting simplified approach that applies of girder, tower girder, tower and ration of rise to span parameters to analyze seismic response of self-anchored suspension bridge. The approach may expediently calculate amplification factor of tower bottom that is specific value total stress to be produced by dead-load stress and seismic stress with dead-load stress, and amplification factor of tower and girder interface that is specific value total stress to be produced by dead-load stress and seismic stress with dead-load stress, and under seismic effect it may still calculate maximal vertical displacement of mid-span and maximal horizontal displacement on the tower top. Through five actual self-anchored suspension bridges to check, it may draw a conclusion that simplified approach is feasible to analyze seismic response of self-anchored suspension bridge.更多还原