资格考试哈工大年夜荷载与结构设计方法.pptx

ContentsChapter 1 IntroductionChapter 2 Basic Concepts of Structural Reliability TheoryChapter 3 Component Reliability Analysis of StructuresChapter 4 System Reliability Analysis of StructuresChapter 5 Statistical Analysis of LoadsChapter 7 Reliability-Based Design Methods of Structures Chapter 6 Statistical Analysis of Structural Member Resistance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1IntroductionChapter 1Introduction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1IntroductionChapter 1:IntroductionChapter 1:Introduction1.2 Objectives and Tasks of Structural Design1.3 Development of Structural Design Method1.1 Uncertainties in Structural Engineering1.5 Probability Foundations for Structural Reliability TheoryContents1.4 Probability Levels of Structural Design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1IntroductionChapter 1 Introduction1.1 Uncertainties in Structural Engineering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1Introduction1.1 Uncertainties in Structural Engineering 1.1 Uncertainties in Structural Engineering 1 1There are three kinds of uncertain information in Structural Engineering,which includeRandom InformationProbability Theory,Statistics,Random Process Theory,Random Field TheoryFuzzy InformationFuzzy Mathematics,Fuzzy System TheoryUnascertain or Incomplete InformationUnascertain Mathematics,Grey Mathematics,Rough Set Theory,Evidence Theory,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1Introduction1.1 Uncertainties in Structural Engineering 1.1 Uncertainties in Structural Engineering 2 2We can divide the above three uncertainties into two categories Objective UncertaintyRandomnessSubjective UncertaintyFuzzinessUnascertainty or Incompleteness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1Introduction1.1 Uncertainties in Structural Engineering 1.1 Uncertainties in Structural Engineering 3 3The uncertainties in structural engineering can also be put into two major categories with regard to causes Natural causes of uncertaintyLoad uncertainties such as wind,earthquake,snow,ice,water pressure,or live load.Resistance uncertainties such as material strength,geometry,fabrication error,etc.Human causes of uncertaintyIntended human errorsUnintended human errors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1Introduction1.1 Uncertainties in Structural Engineering 1.1 Uncertainties in Structural Engineering 4 4There are three types of uncertainties as to the randomness in structural engineeringPhysical UncertaintyVariation of load and resistance that is inherent in the quantity being consideredStatistical UncertaintyUncertainty arising from estimating parameters based on a limited sample sizeModel UncertaintyUncertainty due to simplifying assumptions,unknown boundary conditions,and unknown effects of other variables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1Introduction1.1 Uncertainties in Structural Engineering 1.1 Uncertainties in Structural Engineering 5 5Conclusions Many sources of uncertainty are inherent in structural planning,designconstruction,and operation.The parameters of the loading and the load-carrying capacities of structural members are not deterministic quantities,they are random variables,and therefore absolute safety of structures cannot be achieved.Due to uncertainty,structures must be designed to serve their function with a finite probability of failure.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1IntroductionChapter 1 Introduction1.2 Objectives and Tasks of Structural Design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1Introduction1.2 Objectives and Tasks of Structural Design 1.2 Objectives and Tasks of Structural Design 1 11.2.1 Main Objectives of Structural DesignThe main objectives of structural design is to satisfy the specified function requirements with the optimal economic waysThe specified function requirementsTo carry all kinds of actions during the stage of proper construction and operationTo have the favorable working performance during the stage of proper operationTo have the adequate durability during the stage of proper maintenanceTo keep the essential integrity when encountered occasional actions such as earthquakes,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1Introduction1.2 Objectives and Tasks of Structural Design 1.2 Objectives and Tasks of Structural Design 2 2As to the above four items of requirementsThe items 1 is called structural safetyThe item 2 is called structural serviceabilityThe item 3 is called structural durabilityThe items 4 is called structural integrityStructural reliabilityStructural safetyStructural serviceabilityStructural durabilityStructural integrity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1Introduction1.2 Objectives and Tasks of Structural Design 1.2 Objectives and Tasks of Structural Design 3 31.2.2 Basic Tasks of Structural DesignStructural loading and load effectStatistical analysis of loadLoad effect calculation(material mechanics,structural mechanics,elastic mechanics,plastic mechanics,etc)Structural resistanceStructural testing of resistanceStatistical analysis of resistanceBalance between load effect and structural resistanceStructural designStructural reliability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1IntroductionChapter 1 Introduction1.3 Development of Structural Design Method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1Introduction1.3 Development of Structural Design Method 1.3 Development of Structural Design Method 1 1Method of Allowable Stress Design(ASD)elastic theorydesign formula:where,is the stress of an arbitrary point of structural element under the standard load;is the allowable stress of material.where,is the ultimate stress of material;is the factor of safety.all uncertainties in both load and resistance are all considered by a single factorthe factor of safety is estimated by designers experience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1Introduction1.3 Development of Structural Design Method 1.3 Development of Structural Design Method 2 2Method of Damage Phase Design(DPD)plastic theoryalso named Load Factor Design(LFD)design formula:all uncertainties in both load and resistance are all considered by a single load factorthe factor of safety is also estimated by designers experiencewhere,is the load effect of the critical section of structural element under the standard load;is the load-carrying of structural element when it reaches the state of damage;is the load factor.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1Introduction1.3 Development of Structural Design Method 1.3 Development of Structural Design Method 3 3Method of Multiple Factor Limit State Design(MFLSD)the concept of Structural Limit State is proposedthe partial factor of safety is adoptedMultiple factor limit state design formula:where,is the load effect of dead load and live load which are calculated by the standard value;is the member resistance;andis the standard value of material strength;is the partial factor of loads;andis the partial factor of material strength;is the partial factor of member resistance.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1Introduction1.3 Development of Structural Design Method 1.3 Development of Structural Design Method 4 4Single factor limit state design formula:where,is the member resistance;is the member strength factor;is the additional safety factor considering structural importance.is the load effect;is the load factor,;is the basic safety factor,which is determined by both load factor and member strength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1Introduction1.3 Development of Structural Design Method 1.3 Development of Structural Design Method 5 5Method of Probabilistic Limit State Design(PLSD)based on structural reliability theorythe load and resistance factor design(LRFD)safety-checking format is usedthe partial factor of safety is determined by structural reliability theoryrepresents the direction of structural design developmenthas four levels of probabilitylevel:semi-probability and semi-experiencelevel：approximate probabilitylevel：full probabilitylevel：optimal probability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1IntroductionChapter 1 Introduction1.4 Probability Levels of Structural Design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1Introduction1.4 Probability Levels of Structural Design 1.4 Probability Levels of Structural Design 1 1Level 0:Empirical Designallowable stress design(ASD)load factor design(LFD)Level:Semi-Probability Designmultiple factor limit state design(MFLSD)single factor limit state design(SFLSD)Level:Approximate Probability Designload and resistant factor design(LRFD)first order and second moment(FOSM)methodusing reliability index as the measure of reliabilitydetermining target reliability index by way of calibrating the level codes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1Introduction1.4 Probability Levels of Structural Design 1.4 Probability Levels of Structural Design 2 2Level:Full Probability Designusing failure probability as the measure of reliabilityexact probability analysis of the overall structural systemdirectly using reliability checking as design formatLevel:Optimal Probability Designreliability based optimum design(RBOD)using the total life-cycle cost(LCC)minimization as the optimization criterionusing reliability as the global constraintthe optimal target reliability is determined by the utility analysis or cost-effect analysis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1IntroductionChapter 1 Introduction1.5 Probability Foundations forStructural Reliability Theory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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 1 11.5.1 Definition of Random VariablesDefinition:random variableLet be a random experiment,is its sample space,for,there exists a real single-value function .If for ,is a random event on event field,then we can call a random variable.random variablediscrete random variablecontinuous random variableor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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 2 21.5.2 Description of Random Variables1.Probability Mass Function(PMF)for discrete random variableThere are three kinds of functions for description of random variables as follows:2.Cumulative Distribution Function(CDF)for discrete random variablefor continuous random variable3.Probability Density Function(PDF)for continuous random variable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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 3 31.Probability Mass Function(PMF)The probability mass function(PMF)is defined for discrete random variables as follows:represents probability that a discrete random variable is equal to a specific value ,where is a real number.Mathematically,2.Cumulative Distribution Function(CDF)represents the total sum(or integral)of all probability functions(continuous and discrete)corresponding to values less than or equal to .Mathematically,The cumulative distribution function(CDF)is defined for both discrete and continuous random variables as follows: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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 4 43.Probability Density Function(PDF)For continuous random variables,the probability density function(PDF)is defined as the first derivative of the cumulative function .Mathematically,Properties of CDF,PDF and PMFThe CDF is a positive,nondecreasing function whose value is between 0 and 1:If ,then ,For continuous random variable,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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 5 51.5.3 Moments of Random Variables1.Mean or Expected Value(First Moment)The mean value of a random variable is denoted byFor a continuous random variable,the mean value is defined asFor a discrete random variable,the mean value is defined asThe expected value of is commonly denoted by and is equal to the mean value of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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 6 6For a discrete random variable,the nth moment is defined asThe expected value of is called the nth moment ofFor a continuous random variable,the nth moment is defined asThe mathematical expectation of an arbitrary function of the random variable is defined as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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 7 7The standard deviation of is defined as the positive square root of the variance:An important formulaThe variance of a random variable is a measure of the degree of randomness about the mean value:2.Variance and Standard Deviation(Second Moment)continuous variablediscrete variable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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 8 8If a set of n observations are obtained for a particular random variable ,then The nondimensional coefficient of deviation is defined as the standard deviation divided by the mean:3.Moments of Samplethe true mean can be approximated by the sample meanthe true standard deviation can be approximated by the sample standard deviation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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 9 91.5.4 Standard Form of Random VariablesLet be a random variable.The standard form of ,denoted by ,is defined asthe mean value of is calculated as follows:the deviation of is calculated as follows: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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 10101.5.5 Common Random Variables1.Uniform Random Variables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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 11112.Normal Random VariablesFor a standard normal RV UFor a general normal RV X The PDF of U is denoted by The CDF of U is denoted by 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1Introduction1.5 Probability Foundations for Structural Reliability Theory 1.5 Probability Foundations for Structural Reliability Theory 1212Standard Normal Random VariablesRelationship between general normal RV X and standard normal RV U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1Introduction1.5 Probability Foundat