目录 第一章绪论1 1.1工程结构可靠性研究的缘起/1 1.2工程结构可靠度研究的发展史/3 1.2.1构件层次的可靠度分析/4 1.2.2整体结构的可靠度分析/5 1.2.3结构动力可靠度分析/7 1.3本书基本观点与内容/8 参考文献/10 第二章结构作用及其建模14 2.1结构作用的分类/14 2.2静力作用及其统计模型/14 2.2.1重力作用/15 2.2.2雪荷载/18 2.3动力作用的统计模型/20 2.3.1地震动的统计模型/20 2.3.2脉动风速的统计模型/23 2.4动力作用的随机物理模型/26 2.4.1地震动物理模型/26 2.4.2脉动风速物理模型/31 参考文献/34 第三章作用随机性在结构中的传播36 3.1统计矩及其传播/36 3.2静力作用分析/38 3.2.1弹性力学基本方程/38 3.2.2线弹性静力分析有限元基本方程/40 3.2.3静力分析中的二阶矩传递/41 3.3动力作用分析——随机振动/43 3.3.1动力方程及其解/43 3.3.2统计特征的传递/45 参考文献/48 第四章材料性质随机性在结构中的传播——构件抗力统计矩分析49 4.1引言/49 4.2材料性质的随机性及其统计分布/50 4.2.1钢材强度的统计矩与概率分布/50 4.2.2混凝土力学性质的统计矩与概率分布/51 4.3典型钢结构构件抗力的统计矩分析/53 4.3.1钢柱轴心受压/53 4.3.2钢梁受弯/54 4.4典型钢筋混凝土构件抗力的统计矩分析/55 4.4.1钢筋混凝土梁正截面抗弯强度/56 4.4.2钢筋混凝土梁斜截面抗剪强度/56 4.4.3混凝土构件抗力随环境作用的变化/58 参考文献/61 第五章结构构件可靠度分析——矩法63 5.1基本概念/63 5.2基于状态变量的分析/65 5.2.1结构可靠指标与失效概率/65 5.2.2可靠指标与安全系数的关系/69 5.3基于基本随机变量的分析/70 5.3.1基本随机变量、功能函数与一次二阶矩方法/70 5.3.2均值一次二阶矩方法/73 5.3.3设计验算点法/77 5.3.4相关随机变量/84 5.4概率分布信息的利用/85 5.4.1当量正态化——对边缘概率分布尾部信息的利用/86 5.4.2反函数变换——对边缘概率分布信息的利用/89 5.4.3Nataf变换——对边缘分布信息与变量相关信息的综合利用/91 5.4.4Rosenblatt变换——对联合概率分布函数的全息反映/94 5.5高阶直接矩法/95 5.5.1功能函数的一维近似表达/96 5.5.2功能函数的矩/97 5.5.3失效概率的计算/98 5.5.4高阶直接矩法的分析过程/101 5.5.5基本随机变量的分布估计/104 5.5.6拟正态变换及其应用/104 5.6关于矩法的评论/109 参考文献/110 第六章随机性在结构系统中的传播——概率密度演化理论113 6.1概率守恒原理/113 6.1.1一元随机函数概率分布的分析/113 6.1.2概率守恒原理的随机事件描述/114 6.1.3概率守恒原理的状态空间描述/116 6.1.4关于概率守恒原理的历史注记/117 6.2广义概率密度演化方程及其解/118 6.2.1物理力学方程及其解答/118 6.2.2广义概率密度演化方程/119 6.2.3广义概率密度演化方程的解析解/123 6.2.4广义概率密度演化方程的数值解/126 6.3概率空间剖分/128 6.3.1概率空间的Voronoi集合剖分/128 6.3.2点集的偏差/129 6.3.3初始点集的选取/133 6.3.4点集重整技术/135 6.4广义概率密度演化方程的数值求解/137 6.4.1有限差分法/137 6.4.2再生核配点法/144 6.5求解广义概率密度演化方程的群演化算法/151 6.5.1群演化方程/151 6.5.2子域标准差的估计/153 6.5.3加密点替代模型/155 参考文献/156 第七章结构整体可靠度分析158 7.1结构失效准则与结构整体可靠度/158 7.2结构整体可靠度分析方法/159 7.2.1吸收边界法/160 7.2.2等价极值事件法/161 7.2.3物理综合法/162 7.2.4分析实例/165 7.3经典结构体系可靠度分析方法/167 7.3.1结构的系统模拟/167 7.3.2结构失效概率的计算/170 7.3.3主要失效模式的搜索/171 7.3.4经典结构整体可靠度分析思想剖析：困境与局限性/174 7.4注记：经典可靠度多维积分的困境与出路/175 参考文献/176 第八章基于可靠度的结构设计178 8.1概率设计准则/178 8.1.1社会准则/179 8.1.2经济准则/179 8.1.3历史推定准则/179 8.2工程规范设计准则/181 8.2.1分项系数法/181 8.2.2分项系数的确定方法/184 8.3基于可靠度的结构构件设计/188 8.3.1结构功能可靠度验算/188 8.3.2结构构件设计/193 8.4基于可靠度的整体结构设计/194 参考文献/196 附录A平稳二项过程与复合泊松过程198 A.1平稳二项过程/198 A.2复合泊松过程/198 参考文献/199 附录B随机过程200 B.1随机过程的概率结构/200 B.2随机过程的数字特征/201 B.2.1时域数字特征/201 B.2.2频域数字特征/204 B.2.3数字特征的运算法则/206 参考文献/208 附录C随机场209 C.1基本概念/209 C.2随机场的相关结构/211 参考文献/212 附录D赋得概率计算213 D.1赋得概率的定义及其归一性/213 D.2赋得概率的计算/213 D.2.1局域覆盖法/214 D.2.2全域法/214 参考文献/215 附录E数论方法的生成向量217 参考文献/221 附录F论第三代结构设计理论（代后记)222 F.1认识结构设计理论的两个基本维度/222 F.2第一代结构设计理论/223 F.3第二代结构设计理论的发展/224 F.4第二代结构设计理论的局限性与基本矛盾/226 F.5第三代结构设计理论的基本特征与发展目标/227 F.6第三代结构设计的理论基础/229 F.6.1固体力学/229 F.6.2概率密度演化理论/231 F.7第三代结构设计理论的研究发展方向/233 F.8结语/235 参考文献/236 Contents Chapter 1Introduction1 1.1Origin of Reliability Analysis for Engineering Structures/1 1.2History of Reliability Analysis for Engineering Structures/3 1.2.1Reliability Analysis at the Level of Member Elements/4 1.2.2Global Reliability Analysis/5 1.2.3Dynamic Reliability Analysis/7 1.3Basic Viewpoints and Contents of This Book/8 References/10 Chapter 2Loads on Structures and Their Modelling14 2.1Classification of Loads on Structures/14 2.2Static Loads and Their Statistical Models/14 2.2.1Gravity Load/15 2.2.2Snow Load/18 2.3Statistical Models for Dynamic Loads/20 2.3.1Statistical Models for Seismic Ground Motion/20 2.3.2Statistical Models for Fluctuation Wind Speed/23 2.4Physical Models for Dynamic Loads/26 2.4.1Physical Models for Seismic Ground Motion/26 2.4.2Physical Models for Fluctuation Wind Speed/31 References/34 Chapter 3Propagation of Randomness Associated with Loads in Structures36 3.1Statistical Moments and Their Propagation/36 3.2Analysis for Static Loads/38 3.2.1Fundamental Equations of Elastic Mechanics/38 3.2.2Basic Finite Element Equations for Linear Elastic Static Analysis/40 3.2.3Transfer of Secondorder Moments in Static Analysis/41 3.3Analysis for Dynamic Loads: Random Vibration/43 3.3.1Dynamic Equation and Its Solution/43 3.3.2Transfer of Statistical Characteristics/45 References/48 Chapter 4Propagation of Randomness Associated with Material Properties in Structures： Statistical Moment of Structural Member Resistance49 4.1Introduction/49 4.2Randomness Associated with Material Properties and Their Statistical Distribution/50 4.2.1Statistical Moments and Probability Distribution of Steel Strength/50 4.2.2Statistical Moments and Probability Distribution of Mechanical Properties of Concrete/51 4.3Statistical Moment Analysis of Resistance for Typical Members of Steel Structures/53 4.3.1Steel Column under Axial Compression Load/53 4.3.2Steel Beam under Flexural Load/54 4.4Statistical Moment Analysis of Resistance for Typical Members of Concrete Structures/55 4.4.1Flexural Strength of Reinforcement Concrete Beams/56 4.4.2Shear Strength of Reinforcement Concrete Beams/56 4.4.3Variation of Resistance of Reinforcement Concrete Members under Environmental Loads/58 References/61 Chapter 5Reliability Analysis of Structural Members: Methods of Moments63 5.1Fundamental Concepts/63 5.2Analysis Based on State Variables/65 5.2.1Structural Reliability Index and Failure Probability/65 5.2.2Relationship between Reliability Index and Safety Factor/69 5.3Analysis Based on Basic Random Variables/70 5.3.1Basic Random Variables, Performance Function and First order second moment Method/70 5.3.2First order second moment Mean Value Method/73 5.3.3Design Point Method/77 5.3.4Correlated Random Variables/84 5.4Utilization of Probability Distribution Information/85 5.4.1Equivalent Normalization Method: Utilization of Tail Information of Marginal Probability Distribution/86 5.4.2Inverse Function Transformation: Utilization of Marginal Probability Distribution/89 5.4.3Nataf Transformation: Comprehensive Utilization of Marginal Probability Distribution and Correlated Information between Variables/91 5.4.4Rosenblatt Transformation: Global Reflection of Joint Probability Density Function Information/94 5.5Methods of High order Moments/95 5.5.1One dimensional Approximation of Performance Function/96 5.5.2Moments of Performance Function/97 5.5.3Calculation of Failure Probability/98 5.5.4Analysis Procedure of Direct Methods of High order Moments/101 5.5.5Estimation of Probability Distribution for Basic Random Variables/104 5.5.6Pseudo Normal Transformation and Its Applications/104 5.6Comments on Methods of Moments/109 References/110 Chapter 6Uncertainty Propagation in Structural Systems: Probability Density Evolution Theory113 6.1The Principle of Probability Preservation/113 6.1.1Analysis on Probability Distribution of One variable Random Function/113 6.1.2Random Event Description of the Principle of Probability Preservation/114 6.1.3State Space Description of the Principle of Probability Preservation/116 6.1.4Notes on the History of the Principle of Probability Preservation/117 6.2The Generalized Probability Density Evolution Equation and Its Solution/118 6.2.1The Physical Mechanical Equation and Its Solution/118 6.2.2The Generalized Probability Density Evolution Equation/119 6.2.3Analytical Solution of the Generalized Probability Density Evolution Equation/123 6.2.4Numerical Solution of the Generalized Probability Density Evolution Equation/126 6.3Partition of the Probability assigned Space/128 6.3.1Voronoi Cells of the Probability assigned Space/128 6.3.2Discrepancy of Point Sets/129 6.3.3Generation of Basic Point Sets/133 6.3.4Strategy for Point Sets Rearrangement/135 6.4Numerical Solution of the Generalized Probability Density Evolution Equation/137 6.4.1The Finite Difference Method/137 6.4.2The Reproducing Kernel Collocation Method/144 6.5Ensemble Evolution Method for Solution of the Generalized Probability Density Evolution Equation/151 6.5.1The Ensemble Evolution Equation/151 6.5.2Estimation of Standard Deviation of Subdomain/153 6.5.3The Surrogate Model Method for Densified Points/155 References/156 Chapter 7Structural Global Reliability Analysis158 7.1Structural Failure Criteria and Structural Global Reliability/158 7.2Structural Global Reliability Analysis Methods/159 7.2.1The Absorbing Boundary Condition Method/160 7.2.2The Equivalent Extreme value Event Method/161 7.2.3The Physical Synthesis Method/162 7.2.4Illustrative Examples/165 7.3Classical Structural System Reliability Analysis Methods/167 7.3.1Structural System Modelling/167 7.3.2Calculation of the Probability of Failure/170 7.3.3Identification of the Main Failure Modes/171 7.3.4Deficiency and Limitation of Classical Structural Global Reliability Analysis Methods/174 7.4Predicament and Outlet: Multi dimensional Integration in Classical Structural Reliability Analysis/ 175 References/176 Chapter 8Reliability based Structural Design178 8.1Criteria for Probabilistic Design/178 8.1.1Social Criteria/179 8.1.2Economic Criteria/179 8.1.3Criteria based on Historical Experimences/179 8.2Criteria for Structural Design Codes/181 8.2.1The Partial Factor Method/181 8.2.2Determination of the Partial Factors/184 8.3Reliability based Design at the Member Level/188 8.3.1Checking of the Structural Performance Reliability/188 8.3.2Design of Structural Members/193 8.4Reliability based Design at the Structure Level/194 References/196 Appendix AStationary Binomial Process and Compound Poisson Process198 A.1Stationary Binomial Process/198 A.2Compound Poisson Process/198 References/199 Appendix BStochastic Process200 B.1Probabilistic Structures of Stochastic Processes/200 B.2Statistical Characteristics of Stochastic Processes/201 B.2.1Statistical Characteristics in the Time Domain/201 B.2.2Statistical Characteristics in the Frequency Domain/204 B.2.3Operation Rules of Statistical Characteristics/206 References/208 Appendix CRandom Field209 C.1Basic Concepts/209 C.2Correlation Structures of Random Fields/211 References/212 Appendix DCalculation of Assigned Probability213 D.1Definition of Assigned Probability and Its Normalization Property/213 D.2Calculation of Assigned Probability/213 D.2.1Locally Covering Method/214 D.2.2Global Domain Method/214 References/215 Appendix EGenerator Vectors in Number Theoretical Method217 References/221 Appendix FOn the Third Generation of Structural Design Theory(Supplement)222 F.1Two Dimensions for Understanding Structural Design Theory/222 F.2The First Generation of Structural Design Theory/223 F.3Developments of the Second Generation of Structural Design Theory/224 F.4Limitations and Basic Contradiction in the Second Generation of Structural Design Theory/226 F.5Basic Characteristics and Targets of the Third Generation of Structural Design Theory/227 F.6Theoretical Foundation of the Third Generation of Structural Design Theory/229 F.6.1Solid Mechanics/229 F.6.2Probability Density Evolution Theory/231 F.7Development Tendency of the Research on the Third Generation of Structural Design Theory/233 F.8Conclusions/235 References/236
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