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