Chapter 3 Design method
Design method
3.1 Functions which should be satisfied during design Reliability The properties of a structure or part of it will perform its intended function for a specified period of time under required condition
Reliability The properties of a structure or part of it will perform its intended function for a specified period of time under required condition
Intended function Safy(安全性) 正常施工、正常使用条件下，能承受各种可能出现的 外界作用而不发生破坏。偶然事件发生后，保持必要 的整体稳定性 Serviceability(适用性) 正常使用条件下，有良好的使用性能。如吊车梁变形 过大、水池开裂不能蓄水，虽然不引起倒塌，但已丧 失使用功能。 ·Durability(耐久性) The ability of structures to fulfill its intended function during its intended life span. (在预定的时间内完成预定的功能的能力)
l Safety(安全性） 正常施工、正常使用条件下，能承受各种可能出现的 外界作用而不发生破坏。偶然事件发生后，保持必要 的整体稳定性 l Serviceability （适用性） 正常使用条件下，有良好的使用性能。如吊车梁变形 过大、水池开裂不能蓄水，虽然不引起倒塌，但已丧 失使用功能。 l Durability （耐久性） The ability of structures to fulfill its intended function during its intended life span. (在预定的时间内完成预定的功能的能力)
Design purpose To achieve acceptable probabilities(概率) that a structure will not become unfit for its intended use.ie,will not reach a limit state
To achieve acceptable probabilities (概率） that a structure will not become unfit for its intended use. i.e, will not reach a limit state
3.2 Uncertainties in reliability assessment 。Random variables(随机变量) Loads(作用)，material strength,geometry of section, Location of rebars,calculating methods,human errors Design use the concept of probability and apply the methods of statistics
l Random variables (随机变量) Loads(作用), material strength, geometry of section, Location of rebars, calculating methods, human errors Design use the concept of probability and apply the methods of statistics
3.3 Review of probability theory 。Random variable A random variable is a variable whose values vary randomly and cannot be predicted precisely in advance 。Probability distribution function(分布函数) The probability distribution function of a random variable is probability for the random varible being smaller than or equal to a variable Fx(x)=P(X≤x)
l Random variable A random variable is a variable whose values vary randomly and cannot be predicted precisely in advance l Probability distribution function(分布函数) The probability distribution function of a random variable is probability for the random varible being smaller than or equal to a variable F (x) P(X x) X
Probability density function(概率密度函数) fx(x)= dFx(x) dx Moment(矩)： 1st moment Mean value(Mathematical expectation(数学期望) E(X)=xP(x)dx=ux 2nd moment E(X2)=[x2P(x)dx
l Probability density function(概率密度函数) l Moment（矩）: 1st moment Mean value (Mathematical expectation(数学期望) 2nd moment dx dF x f x X X ( ) ( ) d X E(X ) xP(x) x E(X ) x P(x)dx 2 2
Variance(方差) Variance=E[(X-E(X)2]=E[X2]-[E(X)]2= Standard deviation(标准差)OX Coefficient of variation 1(变异系数) 6= E(x) Lx
l Variance （方差） Variance= Standard deviation（标准差） Coefficient of variation （变异系数） 2 2 2 2 [( ( ) ] [ ] [ ( )] E X E X E X E X X X X X X E x ( )
3.4 Classification of design methods 水准川全概率法 水准川近似概率法 水准！半概率法 多系数极限状态设计法 两个极良状态 M(∑n,9k)≤mMn(k∫，k.fc,a,…) 多安全系数 材料强度考虑统计特性 基于可靠性理论的极限状态设计法
容许应力法 破坏阶段设计法 多系数极限状态设计法 弹性 单一安全系数（经验） 极限承载力计算 塑性 单一安全系数（经验） 两个极限状态 多安全系数 材料强度考虑统计特性 基于可靠性理论的极限状态设计法 M (n q ) mM (k f ,k f ,a,.......) i ik u s s c c k M M u k f 水准I 半概率法 水准II 近似概率法 水准III 全概率法
3.5 Limit state design Two principal types of limit state: Ultimate limit state:The whole structure or its components should not collapse,overturn or buckle when subjected to design loads. Serviceabilitiy limit state:The structure should not become unfit for use due to excessive deflection, cracking or vibration
l Two principal types of limit state: Ultimate limit state: The whole structure or its components should not collapse, overturn or buckle when subjected to design loads. Serviceabilitiy limit state: The structure should not become unfit for use due to excessive deflection, cracking or vibration