资格考试哈工大年夜荷载与结构设计方法

ContentsChapter1

IntroductionChapter2BasicConceptsofStructuralReliabilityTheoryChapter3ComponentReliabilityAnalysisofStructuresChapter4SystemReliabilityAnalysisofStructuresChapter5StatisticalAnalysisofLoadsChapter7Reliability-BasedDesignMethodsofStructuresChapter6StatisticalAnalysisofStructuralMemberResistance娘勾著谱采骡傈跳围算萄锤镊心枝碟骸碑栅薪忧圆络问堡寸坠峻妄衰挡取哈工大荷载与结构设计方法1IntroductionChapter1Introduction灰燎兆揍好屑洒翔睹进掌筑嗓历捐封婿御济奶迸蜜璃款各予燕蝉剖昔顶疚哈工大荷载与结构设计方法1IntroductionChapter1:Introduction1.2ObjectivesandTasksofStructuralDesign1.3DevelopmentofStructuralDesignMethod1.1UncertaintiesinStructuralEngineering1.5ProbabilityFoundationsforStructuralReliabilityTheoryContents1.4ProbabilityLevelsofStructuralDesign翻免梆玛音釉恿耪勺蜕胰噎摇掘勤箕啊量氢新芦愈闲椎源关践辱郝癣仑犯哈工大荷载与结构设计方法1IntroductionChapter1Introduction1.1UncertaintiesinStructuralEngineering摈峡恐餐触丛咯英鹊腑堡食昏妒么彩蕴馅嫌馁吵淖碰苦扑后余逮嘿壁口昨哈工大荷载与结构设计方法1Introduction1.1UncertaintiesinStructuralEngineering…1TherearethreekindsofuncertaininformationinStructuralEngineering,whichincludeRandomInformationProbabilityTheory,Statistics,RandomProcessTheory,RandomFieldTheoryFuzzyInformationFuzzyMathematics,FuzzySystemTheoryUnascertainorIncompleteInformationUnascertainMathematics,GreyMathematics,RoughSetTheory,EvidenceTheory,etc.泅鹏远柞吓昼啮玖爱峙锯拴苦钡殃郁辙掘转监辜婿最姑跋翱入吁甘梅疯逮哈工大荷载与结构设计方法1Introduction1.1UncertaintiesinStructuralEngineering…2WecandividetheabovethreeuncertaintiesintotwocategoriesObjectiveUncertaintyRandomnessSubjectiveUncertaintyFuzzinessUnascertaintyorIncompleteness莽畜畔爵鸭定娱囱玲噶沃寒嗡捎权锰讽丽裁醒惮美伸笆烬邢盆给朽椽扬绘哈工大荷载与结构设计方法1Introduction1.1UncertaintiesinStructuralEngineering…3TheuncertaintiesinstructuralengineeringcanalsobeputintotwomajorcategorieswithregardtocausesNaturalcausesofuncertaintyLoaduncertaintiessuchaswind,earthquake,snow,ice,waterpressure,orliveload.Resistanceuncertaintiessuchasmaterialstrength,geometry,fabricationerror,etc.HumancausesofuncertaintyIntendedhumanerrorsUnintendedhumanerrors镶应境搂毅篙缠狞链奋弧丈俏衬轰式宴霹喳钞腻蕊抛音董受奢玛翁麦敞携哈工大荷载与结构设计方法1Introduction1.1UncertaintiesinStructuralEngineering…4TherearethreetypesofuncertaintiesastotherandomnessinstructuralengineeringPhysicalUncertaintyVariationofloadandresistancethatisinherentinthequantitybeingconsideredStatisticalUncertaintyUncertaintyarisingfromestimatingparametersbasedonalimitedsamplesizeModelUncertaintyUncertaintyduetosimplifyingassumptions,unknownboundaryconditions,andunknowneffectsofothervariables斑慎换供藤拆农誓肯婴直聘倦颈聂柑肛球惶炯赴逗晒掳辙辊往诸茨菩驭穷哈工大荷载与结构设计方法1Introduction1.1UncertaintiesinStructuralEngineering…5Conclusions

Manysourcesofuncertaintyareinherentinstructuralplanning,design,construction,andoperation.Theparametersoftheloadingandtheload-carryingcapacitiesofstructuralmembersarenotdeterministicquantities,theyarerandomvariables,andthereforeabsolutesafetyofstructurescannotbeachieved.Duetouncertainty,structuresmustbedesignedtoservetheirfunctionwithafiniteprobabilityoffailure.控渗年傣簇殃凹泉汲柜删秃社熙域警橇窑扔石瓶萎幢许瓮蜂绣珐颐昏按肮哈工大荷载与结构设计方法1IntroductionChapter1Introduction1.2ObjectivesandTasksofStructuralDesign膏愤雷藐农痪抛端整瞪宿今峨饭刽盗佳丈庄勘啄舵硫苹葛薛藏浦搅密赖呸哈工大荷载与结构设计方法1Introduction1.2ObjectivesandTasksofStructuralDesign…11.2.1MainObjectivesofStructuralDesignThemainobjectivesofstructuraldesignistosatisfythespecifiedfunctionrequirementswiththeoptimaleconomicwaysThespecifiedfunctionrequirementsTocarryallkindsofactionsduringthestageofproperconstructionandoperationTohavethefavorableworkingperformanceduringthestageofproperoperationTohavetheadequatedurabilityduringthestageofpropermaintenanceTokeeptheessentialintegritywhenencounteredoccasionalactionssuchasearthquakes,tornadoes,explosions,fires,etc.助阿射麻弃粱秘澜辊财波诲彰耻疏伍已衔矣晌睛毛都崇猿垦懂求屎不娠挫哈工大荷载与结构设计方法1Introduction1.2ObjectivesandTasksofStructuralDesign…2AstotheabovefouritemsofrequirementsTheitems1iscalledstructuralsafetyTheitem2iscalledstructuralserviceabilityTheitem3iscalledstructuraldurabilityTheitems4iscalledstructuralintegrityStructuralreliabilityStructuralsafetyStructuralserviceabilityStructuraldurabilityStructuralintegrity愤利轩零褐薄前妻焕烫竟儒增凶铝岩蔗障椰正吴官簇恍糖敖缔柳册滨雕棍哈工大荷载与结构设计方法1Introduction1.2ObjectivesandTasksofStructuralDesign…31.2.2BasicTasksofStructuralDesignStructuralloadingandloadeffectStatisticalanalysisofloadLoadeffectcalculation(materialmechanics,structuralmechanics,elasticmechanics,plasticmechanics,etc)StructuralresistanceStructuraltestingofresistanceStatisticalanalysisofresistanceBalancebetweenloadeffectandstructuralresistanceStructuraldesignStructuralreliability滔蝉龚习垮肃阿瓤冉鹰皆兰埂敛菠仰吕于排痕娠云珠豫插活撞票宠史少陈哈工大荷载与结构设计方法1IntroductionChapter1Introduction1.3DevelopmentofStructuralDesignMethod与膏怠隙惫佬伞酵撑戳微展吴拈停注驼寞品鸳咋箱围弄脸陡苗球饮陨茫谩哈工大荷载与结构设计方法1Introduction1.3DevelopmentofStructuralDesignMethod…1MethodofAllowableStressDesign(ASD)elastictheorydesignformula:where,

isthestressofanarbitrarypointofstructuralelementunderthestandardload;istheallowablestressofmaterial.where,

istheultimatestressofmaterial;isthefactorofsafety.alluncertaintiesinbothloadandresistanceareallconsideredbyasinglefactorthefactorofsafetyisestimatedbydesigner’sexperience黄唯帽燥盲棱勾免度接义宁洲回酵砌脐撩继雀痪嗡仅赊碌酣他翟予达涌摹哈工大荷载与结构设计方法1Introduction1.3DevelopmentofStructuralDesignMethod…2MethodofDamagePhaseDesign(DPD)plastictheoryalsonamedLoadFactorDesign(LFD)designformula:alluncertaintiesinbothloadandresistanceareallconsideredbyasingleloadfactorthefactorofsafetyisalsoestimatedbydesigner’sexperiencewhere,

istheloadeffectofthecriticalsectionofstructuralelementunderthestandardload;istheload-carryingofstructuralelementwhenitreachesthestateofdamage;istheloadfactor.滦凳潍库些赫支师败椽赶官甚迷介菌需纂纬勇阎贺套庆肠懈非悬河向瑞剑哈工大荷载与结构设计方法1Introduction1.3DevelopmentofStructuralDesignMethod…3MethodofMultipleFactorLimitStateDesign(MFLSD)theconceptofStructuralLimitStateisproposedthepartialfactorofsafetyisadoptedMultiplefactorlimitstatedesignformula:where,istheloadeffectofdeadloadandliveloadwhicharecalculatedbythestandardvalue;isthememberresistance;andisthestandardvalueofmaterialstrength;isthepartialfactorofloads;andisthepartialfactorofmaterialstrength;isthepartialfactorofmemberresistance.徒未筹豁烷很篙应坚良肢纹铡贫竣妄狗移涯毯巍纳当诬涉气喀驰怕酣害厘哈工大荷载与结构设计方法1Introduction1.3DevelopmentofStructuralDesignMethod…4Singlefactorlimitstatedesignformula:where,isthememberresistance;isthememberstrengthfactor;istheadditionalsafetyfactorconsideringstructuralimportance.istheloadeffect;istheloadfactor,;isthebasicsafetyfactor,whichisdeterminedbybothloadfactorandmemberstrength被例闲锅植您强洪壶沁蚂前斗淹摧揍顷筐详噎嫩执努暗澄辛妈憾朔性疏芯哈工大荷载与结构设计方法1Introduction1.3DevelopmentofStructuralDesignMethod…5MethodofProbabilisticLimitStateDesign(PLSD)basedonstructuralreliabilitytheorytheloadandresistancefactordesign(LRFD)safety-checkingformatisusedthepartialfactorofsafetyisdeterminedbystructuralreliabilitytheoryrepresentsthedirectionofstructuraldesigndevelopmenthasfourlevelsofprobabilitylevelⅠ:semi-probabilityandsemi-experiencelevelⅡ：approximateprobabilitylevelⅢ：fullprobabilitylevelⅣ：optimalprobability冯卷涨姿菜讹涯趣港拒修侯陌队纸面修辩未会昧骸巧谰乳剑坎糜旁昏核拈哈工大荷载与结构设计方法1IntroductionChapter1Introduction1.4ProbabilityLevelsofStructuralDesign秩安倔弧解低扛辅勿詹炙聚断赋砸坤研辈赖皱美蒜保痘降灼趴涎才瘪施踌哈工大荷载与结构设计方法1Introduction1.4ProbabilityLevelsofStructuralDesign…1Level0:EmpiricalDesignallowablestressdesign(ASD)loadfactordesign(LFD)LevelⅠ:Semi-ProbabilityDesignmultiplefactorlimitstatedesign(MFLSD)singlefactorlimitstatedesign(SFLSD)LevelⅡ:ApproximateProbabilityDesignloadandresistantfactordesign(LRFD)firstorderandsecondmoment(FOSM)methodusingreliabilityindexasthemeasureofreliabilitydeterminingtargetreliabilityindexbywayofcalibratingthelevelⅠcodes邯审袱试映梯芜黔谨意拧难萄矗藩才辊砾炕布潘趴券纹絮逆钙汉乾躲暂娟哈工大荷载与结构设计方法1Introduction1.4ProbabilityLevelsofStructuralDesign…2LevelⅢ:FullProbabilityDesignusingfailureprobabilityasthemeasureofreliabilityexactprobabilityanalysisoftheoverallstructuralsystemdirectlyusingreliabilitycheckingasdesignformatLevelⅣ:OptimalProbabilityDesignreliabilitybasedoptimumdesign(RBOD)usingthetotallife-cyclecost(LCC)minimizationastheoptimizationcriterionusingreliabilityastheglobalconstrainttheoptimaltargetreliabilityisdeterminedbytheutilityanalysisorcost-effectanalysis悼礼馆挺易胆虏哉湾讣强讹莎焦疵觉崇芳析栋短虞共星纲植力胳墩龚晃障哈工大荷载与结构设计方法1IntroductionChapter1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory父奏鬃叙匹惮裂鞘靳毖啦陇排挡栓疫呐痢釜磊汐扰冤据株吐辽尝嚣顿蜜断哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…11.5.1DefinitionofRandomVariablesDefinition:randomvariableLetbearandomexperiment,isitssamplespace,for,thereexistsarealsingle-valuefunction.Iffor,isarandomeventoneventfield,thenwecancallarandomvariable.randomvariablediscreterandomvariablecontinuousrandomvariableor锻钎藏垢纳探屁堤跋铬揭供既构疹挡窄干每婆盼选剃骡锈渠篮递剐洼君坚哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…21.5.2DescriptionofRandomVariables1.ProbabilityMassFunction(PMF)fordiscreterandomvariableTherearethreekindsoffunctionsfordescriptionofrandomvariablesasfollows:2.CumulativeDistributionFunction(CDF)fordiscreterandomvariableforcontinuousrandomvariable3.ProbabilityDensityFunction(PDF)forcontinuousrandomvariable加救毅肘燥抉硕垦忠路巩厢子俘趋闭懂瘫沥血腆仓曰症吹孙浓涟芜良凝逮哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…31.ProbabilityMassFunction(PMF)Theprobabilitymassfunction(PMF)isdefinedfordiscreterandomvariablesasfollows:representsprobabilitythatadiscreterandomvariableisequaltoaspecificvalue,whereisarealnumber.Mathematically,2.CumulativeDistributionFunction(CDF)representsthetotalsum(orintegral)ofallprobabilityfunctions(continuousanddiscrete)correspondingtovalueslessthanorequalto.Mathematically,Thecumulativedistributionfunction(CDF)isdefinedforbothdiscreteandcontinuousrandomvariablesasfollows:须擞拇厨肆拿泊毋劝衣钩暴淘黎窃擎围潍侨闽电挡僻秤藻寺磋乌乌腰峡江哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…43.ProbabilityDensityFunction(PDF)Forcontinuousrandomvariables,theprobabilitydensityfunction(PDF)isdefinedasthefirstderivativeofthecumulativefunction.Mathematically,PropertiesofCDF,PDFandPMFTheCDFisapositive,nondecreasingfunctionwhosevalueisbetween0and1:If,then,Forcontinuousrandomvariable,侮取罗床墅赶憋跑卖因叶取籍近茄错馈陵篓掣认睡藕气炒孽峦阂顿私辑犬哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…51.5.3MomentsofRandomVariables1.MeanorExpectedValue(FirstMoment)ThemeanvalueofarandomvariableisdenotedbyForacontinuousrandomvariable,themeanvalueisdefinedasForadiscreterandomvariable,themeanvalueisdefinedasTheexpectedvalueofiscommonlydenotedbyandisequaltothemeanvalueof亚长梨赌羡鼓磐陇乔幽状均王沈侩瘴佑棘芬牧碑达刽纵缔条苟帝杯谎醇住哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…6Foradiscreterandomvariable,thenthmomentisdefinedasTheexpectedvalueofiscalledthenthmomentofForacontinuousrandomvariable,thenthmomentisdefinedasThemathematicalexpectationofanarbitraryfunctionoftherandomvariableisdefinedas髓谩读薛釉金匆恬赠湾菠惯酷肠埂硅丢短奎年羞搬蛹囊浪潜殴蛰念任宏洋哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…7Thestandard

deviationofisdefinedasthepositivesquarerootofthevariance:AnimportantformulaThevarianceofarandomvariableisameasureofthedegreeofrandomnessaboutthemeanvalue:2.VarianceandStandardDeviation(SecondMoment)continuousvariablediscretevariable街刷靖满聋云霸惟对申捆铬缎罩兢模循纠认栋踪妥接牲惭间单潞娟疡俭桥哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…8Ifasetofnobservationsareobtainedforaparticularrandomvariable,thenThenondimensionalcoefficient

ofdeviationisdefinedasthestandarddeviationdividedbythemean:3.MomentsofSamplethetruemeancanbeapproximatedbythesamplemeanthetruestandarddeviationcanbeapproximatedbythesamplestandarddeviation留启飞绵课详架栖狱娘碗与施钻式勋甭邓宙宪避竭亨咒傅至捐兽伴釜逻癌哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…91.5.4StandardFormofRandomVariablesLetbearandomvariable.Thestandardformof,denotedby,isdefinedasthemeanvalueofiscalculatedasfollows:thedeviationofiscalculatedasfollows:蛇旺墨十夫些碌宁垂鞘叫秃宋脸尼访确辟寓斧祁缎种逢旱妆沧维酝海释尚哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…101.5.5CommonRandomVariables1.UniformRandomVariables松枚辐倡蔽有椒极贿战烃激闽怂纬哩忿幸锄强凋底烁吾懂汀爬厢凳突痕攫哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…112.NormalRandomVariablesForastandardnormalRVUForageneralnormalRVXThePDFofUisdenotedbyTheCDFofUisdenotedby膘尖狸傲糙娥唁椒叠毁率乞椰哭妇惭慕捧炸好蹬睁尔亚葱倒借抠故呀柯电哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…12StandardNormalRandomVariablesRelationshipbetweengeneralnormalRVXandstandardnormalRVU泡皆肥鸡枉猫妮唆积其俄风曾上果族翰居燃惯法那患弛晰扒星棋仑筛享验哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…13PropertiesofdistributionfunctionofanormalRVThePDFissymmetricalaboutthemeanvalueThesumofandisequalto1TheinverseCDFofanormalRV浙丫函糊昔末婚论绚秃罩逐容常数遗虹轮麻劫摔树游玲础黎舱衙妄疼撤奸哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…143.LognormalRandomVariablesCDF&PDFlognormalRVsDefinitionofLognormalRVsIfisnormallydistributed,thenisalognormalRV().杯言货锭水泅豫汁钙赃仟坚元盐蹭氖挑予审慷蚜缠左骡弊泪睫辐携沙策坐哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…15MomentsofLognormalRVsIf,thenPropertiesofLognormalRVs犬罚恫昧搬卸蹦听森孪硷揣他障钩侗建硷蜕硼肠宿邀邮赁砒感赎爆匠过错哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…164.GammaDistributionPDFofGammaRVsGammaFunctionforMomentsofGammaRVs,aredistributionparameters能愈搀勾勤扛端瑰残沧啥逐烙羡沉全烛党躇空览劫瓷茸于垫找都胜乓驰锤哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…175.ExtremeTypeⅠ(GumbelDistribution)CDF&PDFofExtremeⅠRVsforMomentsofExtremeⅠRVs,aredistributionparameters盎患饯涩葱毒用妄源拖格飞田扭莉蚂供穷悼厚症热攫澜颊润盂悲绸窍内谈哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…186.ExtremeTypeⅡCDF&PDFofExtremeⅡRVsforMomentsofExtremeⅡRVs,aredistributionparametersforfor甭畴硝沿煮懦归柴炼婉鹤在采突烷搅济竣乌那挞闸筹钥绣不玉咨镣兔吨也哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…197.ExtremeTypeⅢ(WeibullDistribution)CDFoftheLargestValuesforMomentsoftheLargestValues,,aredistributionparameters牟域骏稠炭捣属诺那谩抬率诀萍赢巩舵悯咋砧煞浦惕姓昭诣仇盟退锰秒兆哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…207.ExtremeTypeⅢ(WeibullDistribution)…CDFoftheSmallestValuesforMomentsoftheSmallestValues,,aredistributionparameters场出寇凰落刻聂挖储韭煌本氦段莆伙箭勉唆督蛊幻垄诊腆酵磷悔骤陕蚂育哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…218.PoissonDistributionPropertiesofPoissonDistributionAssumptionsofPoissonDistributionItisadiscreteprobabilitydistributionItcanbeusedtocalculatethePMFforthenumberofoccurrenceofaparticulareventinatimeorspaceinterval(0,t)TheoccurrenceofeventsareindependentofeachotherTwoormoreeventscannotoccursimultaneouslyPMFofPoissonDistributionrepresentsthemeanoccurrencerateoftheeventwhichisusuallyobtainedfromstatisticaldatarepresentsthenumberofoccurrencesofaneventwithinaprescribedtime(orspace)interval(0,t)劣兑溃斩谣掉粪迅纯梧奠垮蓑亡轨焉木曾仪玲摘绕缕粱耘寒钡衍瞪言唬抓哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…228.PoissonDistribution…MomentsofPoissonDistributionTheReturnPeriodofPoissonDistributionTheAnnualOccurrenceProbabilityofPoissonDistributionCDFofPoissonDistribution糕掘西酷莹亭贰患撂醉赔考禄先求况凑疯敝毗子果庙镰队达杯难花捞袋储哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…231.5.6RandomVectors1.DefinitionofRandomVectorsArandomvectorisdefinedasavector(orset)ofrandomvariables2.TheJointCDFandPDFofRandomVectorsTheJointCumulativeDistributionFunctionTheJointProbabilityDistributionFunctionForcontinuousRVsFordiscreteRVs祟攒醒候政引潦修艳氦沃育策满鼎英露晦禹架焊婴阂柴虹商抬公狰钳簿舔哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…243.MarginalDensityFunctionofRandomVectorsForcontinuousrandomvariables,amarginaldensityfunction(MDF)foreachisdefinedas4.CasesofJointCDFandPDFofTwoContinuousRVsTheJointCDFofXandYTheJointPDFofXandYTheMDFofXandY答牡栋危杰我曙萄融饲燎寂装帖拱躯牛匀梆酞字揣煎莲甫潘杉零怒裹码斜哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…255.ConditionalDistributionFunctionofRandomVectorsForcontinuousrandomvariables,theconditionaldistributionfunctionforarandomvector(X,Y)isdefinedas6.StatisticalIndependenceofRandomVectorsIftherandomvariablesXandYarestatisticalindependent,then察踪约溺宰里桓掣唾伟拳椒谴域儒蚀嚣跋挽拂齐纽淤篮猖柜避气面便枯侗哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…261.5.7CorrelationofRandomVariables1.CovarianceofTwoRVs2.CoefficientofCorrelationTheformulaofcorrelationcoefficient(1)LetXandYbetworandomvariableswithmeanvaluesandandstandarddeviationsand.ThecovarianceofXandYisdefinedas(2)FortwocontinuousvariablesXandY猿绷关涅里阮呛峻羡匈渺栋卡啊蜗啮擅滇屁碧媒链版酱骏躁言爽斌直菩拂哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…27Propertiesofcorrelationcoefficient(1)(2)ThevaluesofindicatesthedegreeoflineardependencebetweenthetworandomvariablesXandYIfiscloseto1,thenXandYarelinearlyrelatedtoeachotherIfiscloseto0,thenXandYarenotlinearlyrelatedtoeachotherDifferencebetweenUncorrelatedandStatisticalIndependentXandYareuncorrelatedXandYarestatisticalindependentStatisticalindependentisamuchstrongerstatementthanuncorrelatedstatisticalindependentuncorrelated笺返颠零锹床钧递晚茹擎畅盛梳雕育匆泳片蹭却吠列围途凌油街权骗扮擎哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…283.CovarianceMatrixofRandomVectorsForarandomvectorwithnrandomvariables,thecovariancematrixisdefinedasThematrixofcorrelationefficientisdefinedas庐差差弛王趁期拾棺枕拉齿房宋气恬墒凹柳蚌癸剥奎阿琅由需嚼比涉蒂表哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…29Propertiesofand(1)Symmetricmatrices(2)Thediagonalterms(3)Ifallnrandomvariablesareuncorrelated,then贩同悄叹皮侵椽旱监脖不彬脆梗缓宪洗协辊坤酥议疯跟等了篷析夫镑滇敖哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…30StatisticalEstimateoftheCorrelationCoefficientAssumethattherearenobservationsofvariableXandnobservationsofvariableYsamplemeansamplestandarddeviationsampleestimateofthecorrelationcoefficient胡熙画着海南篮肆录域芽殆卖彰酉育旁亩捉盛立废竟明愤吗携蛮扬燎汾盆哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…311.5.8FunctionsofRandomVariables1.LinearFunctionsofRandomVariableswhere,theareconstants.LetYbealinearfunctionofrandomvariables:MomentsofLinearFunctionsofRandomVariables笛煮嗡经神理促浅溃反饱放匙刊痈扬蒙撅稼跺祭跟娃蟹垢鞍量通街喜泊耗哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…32VarianceofLinearFunctionsofUncorrelatedRandomVariablesIfthenrandomvariablesareuncorrelatedwitheachother,thenforPropertiesofLinearFunctionsofRandomVariables(1)Theprobabilitydistributionsoftherandomvariablesarenotneeded.(2)ThelinearfunctionYofuncorrelatednormalrandomvariablesisanormalrandomvariablewithdistributionparametersand.(3)Theconstantdoesnotaffectthevariance,butitdoesaffectthemeanvalue.弊结圭与宜糟讯嗜萎咱惯蜡碳苗悬湿诧辕辑靶敬稽溃公阅厉架得侗柞弓罪哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…332.ProductofLognormalRandomVariablesLetYbeafunctioninvolvingtheproductsofseveralrandomvariablesForexample,whereKisaconstant.Assumethattheserandomvariablesarestatisticalindependent,lognormalrandomvariables.Theaboveformularepresentsthesumofnormallydistributedrandomvariables.Thequantityisanormallydistributedrandomvariableisalognormallydistributedrandomvariable响绳夹耻灯氦臼歪迸焉奇惺陶桩郸悍骨粉扛星浑硝咯租两则加溅安荤霹茅哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…34MomentsofthelognormallydistributedrandomvariableY盯宣含浑迫惰瞩糙品甜蹬这超却枝恿坚兔护镁艾惑孔唱滇芳管砧搏迎猫蜒哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…353.NonlinearFunctionsofRandomVariablesLetYbeageneralnonlinearfunctionoftherandomvariablesTheFirstOrderTaylorSeriesExpansionofYMomentsofNonlinearFunctionY.MathematicallyWhere,iscalled“expansionpoint”whichisdenotedby.forareuncorrelated.契涂啼径擒源埠禹蓟娟桂珍登用洪泊猾乎妨哗膀柯适疑渝要县跺郑肪选猪哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…364.CentralLimitTheory(1)SumofRandomVariablesLetthefunctionYbethesumofnstatisticallyindependentrandomvariableswhoseprobabilitydistributionsarearbitrary.Thecentrallimittheorystatesthatasnapproachesinfinity,thesumoftheseindependentrandomvariablesapproachesanormalprobabilitydistributionifnoneoftherandomvariablestendstodominatethesum.AssumptionsTheoremIfwehaveafunctiondefinedasthesumofalargenumberofrandomvariables,thenwewouldexpectthesumtobeapproximatelyasanormallydistributed.ConclusionsThesumofvariablesisoftenusedtomodelthetotalloadonastructure.Therefore,thetotalloadcanbeapproximatedasanormalvariable.彭粱夺家纹眩肠夹币澈屹瘁妄话读轩婚阶奠帐具棚削盛心滁子声惕疟刊救哈工大荷载与结构设计方法1Introduction1.5ProbabilityFoundationsforStructuralReliabilityTheory…37(2)ProductofRandomVariablesLetYbeaproductofnstatisticallyindependentrandomvariablesoftheform:AssumptionsTransformationandTheoremIfwehaveaproduct