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1、1.4 Limit States and the Law of Probability Limit States of Steel Structure钢结构的极限状态和概率极限状态法,1.4.1 Limit States of Steel Structure 钢结构的极限状态 1.4.2 Load Effect Analysis of the Structure 结构的荷载效应分析 1.4.3 The Law of Probability Limit States 概率极限状态法 1.4.4 Design Expression 设计表达式,1.4.1 Limit States of Steel
2、 Structure 钢结构的极限状态,Limit States of Steel Structure is divided into two types:the limit State of load-bearing capacity and the limit State of the regular usage.钢结构的极限状态分为承载力极限状态和正常使用极限状态两大类。,1.Limit State of load-bearing capacity corresponds to the situation that the structure or the member reach th
3、e maximum bearing capacity,or the deformation disallow them to carry more force,including:overturn,strength damage、fatigued damage、failure of stability、the structure turns into the changeable system or the excessive plastic deformation occurs.承载力极限状态对应于结构或构件达到最大承载力或出现不适于继续承载的变形，包括倾覆、强度破坏、疲劳破坏、丧失稳定、结
4、构变为机体或出现过度的塑性变形。,2.Limit State of the regular usage corresponds to the situation that the structure or the member reach the certain allowable value for the regular usage or endurance,including:the deformation for regular usage(or appearance),vibration and the part damage.正常使用极限状态对应于结构或构件达到正常使用或耐久性能的
5、某项规定限值，包括出现影响正常使用（或外观）的变形、振动和局部破坏。,1.4.2 Load effect analysis of the structure 结构的荷载效应分析,Designing the steel structure need to handle two factors：One is the resistance of the structure and member；the second is the load effect exerted on the structure.Load effect can be got by means of the inner forc
6、e analysis.设计钢结构需要处理两个方面的因素：一是结构和构件的抗力；二是荷载施加于结构的效应(荷载效应通过内力分析来解)。,Considering of the effect of deformation or not,the inner force analysis is divided into:one rank analysis and two rank analysis;内力分析根据是否考虑变形影响分为：一阶分析和二阶分析；Considering of the plastic performance of steel material or not,the inner for
7、ce analysis is divided into:elastic analysis and inelastic analysis.内力分析根据是否考虑钢材塑性性能分为：弹性分析和非弹性分析。,1.4.3 The Law of Probability Limit States 概率极限状态法,The fundamental problem for structure design to solve is to choose an optimum equilibrium between the reliability and economy，and make the structure co
8、nstructed per the most economic method meet the desired performance demands per proper degree of reliability.Limit States design method,which is based on probability theory,has been used in structural reliability theory,is called the Law of Probability Limit States.,结构设计要解决的根本问题是在结构的可靠和经济之间选择一种最佳的平衡
9、，使由最经济的途径建成的结构能以适当的可靠度满足各种预定的功能要求。结构的可靠性理论已进入以概率理论为基础的极限状态设计方法，简称概率极限状态设计法。,The performance function of structure is:结构的功能函数为：Z=R SR stands for the resistance of the structure,S stands for the synthetical effect of load to the structure.R代表结构的抗力，S代表荷载对结构的综合效应。,When the value of this function is posi
10、tive,the structure may meet the performance demand,and the structure is in the reliable state；When the value of this function is negative,the structure can not meet the performance demand,and the structure is in the failure state.When the value is zero,the structure reaches the limit State.这一函数为正值时，
11、结构可以满足功能要求，结构处于可靠状态；为负值时，结构则不能满足功能要求，结构处于失效状态；为零时，结构达到极限状态。,Z=R S,The definition of structural reliability is:in stated time,under stated conditions,the probability of scheduled performance to be fulfilled by the structure.结构的可靠度定义为：结构在规定的时间内，在规定的条件下，完成预定功能的概率。,With pS meaning the structural reliabi
12、lity,then the expression of the definition is:以pS表示结构的可靠度，则定义的表达式为：pS=P（Z 0）The probability of failure is p f：结构的失效概率为p f：p f=P（Z 0）then pS=1 p f,Hence,the calculation of structural reliability is converted to the calculation of probability of failure.Whether the structure is reliable or not,is to s
13、ee whether the structural probability of failure pf is small enough to be accepted.因此，结构可靠度的计算转换为结构失效概率的计算。结构是否可靠就看结构失效概率pf是否小到可以接受的程度。,The structural reliability is affected by loading,material property,geometrical parameter and the accuracy of the formula,etc.These factors,with randomicity,are cal
14、led basic variable.As to ordinary building structure，they can be reduce to two basic variables:the resistance of the structure“R”,the synthetical effect of load to the structure“S”.And this two basic variables are considered to obey the normal distribution.Hence,Z=RS also is the normal random variab
15、le.,结构的可靠度通常受荷载、材料性能、几何参数和计算公式精确性等因素的影响。这些具有随机性的因素称为基本变量。对于一般建筑结构，可以归并为荷载效应S和结构抗力R两个基本变量，并设二者都服从正态分布。因此，Z=R-S 也是正态随机变量。,For a equation of the structural state,its ratio of the average to the standard deviation is,called the reliability target value of structure or member.Figure 1-16 indicates and ha
16、ve certain one-one correspondence.The more increases,decreases,the more reliable the structure is.,对于一个结构状态方程，其平均值 与其标准差 的比值，称为结构或构件的目标可靠指标。与 有确定的一一对应关系。增大，减小，结构也就越可靠。,Per Unified standard for reliability design of building structures,the reliability target value for steel structure member is 3.2,fo
17、r steel structure connection is 4.5.根据建筑结构可靠度设计统一标准,钢结构构件设计的目标可靠指标为3.2，钢结构连接的目标可靠指标推荐用4.5。,Per Unified standard for reliability design of building structures,the design reference period for structure design is fifty years.根据建筑结构可靠度设计统一标准，结构设计的设计基准期为50年。,For fatigue calculation,allowable stress desig
18、n is still used in codes.规范对疲劳计算仍采用容许应力法。,1.4.4 Design Expression 设计表达式,The design expression for structure member in limit states:结构构件极限状态设计表达式：,Structural importance coefficient.结构重要性系数;separate coefficient of member resistance;构件抗力分项系数；the nominal value of permanent load effect;永久荷载效应的标准值；the nom
19、inal value of variable load effect;可变荷载效应的标准值;separate coefficient of permanent load;永久荷载分项系数separate coefficient of variable load;可变荷载分项系数；,Building structures are divided into three safe grades according to the seriousness of the damage results:the ordinary industrial and civil buildings are in th
20、e second grade,take=1;Theatre、Gymnasium and high-rise building etc.should be considered as the first grade,take=1;the secondary and temporary buildings are in the third grade,and take=0.9;,建筑结构根据其破坏后果的严重性，分为三个安全等级：一般工业与民用建筑列为二级，取=1；影剧院、体育馆和高层建筑等宜按重要性为一级考虑，取=1.1；次要和临时建筑物为三级，取=0.9；,Per Unified standar
21、d for reliability design of building structures,separate coefficients of permanent load and variable load are fixed values.Normally,=1.2，=1.4；when and are in unlike signed situation,then take=1.0，=1.4.建筑结构可靠度设计统一标准对永久荷载和可变荷载的分项系数分别取为定值。在一般情况下=1.2，=1.4；在异号的情况下则取=1.0，=1.4。,More than one variable load
22、are exerted on the structure,however they can not reach the maximum at same time.Hence,the combination coefficient must be decided from the probability distribution of the combinated load effect,and be added into the expression 1-11.施加在结构上的可变荷载不止一种，这些荷载不可能同时达到各自的最大值。因此，还要根据组合荷载效应的概率分布来确定荷载的组合系数，加入式1
23、-11。,Except for permanent load and the first variable load,the other effect of variable load must to be multiplied the combination coefficient,which are more than value 1.除永久荷载和第一可变荷载外，其他可变荷载的效应都乘以不大于1的组合系数。,Then expression 1-11 is transformed to：则式1-11转换为：（1-17）where式中 This formula is basic combina
24、tion of the limit state of load-bearing capacity.此公式是承载能力极限状态的基本组合.,、The i th and the first effects of variable load.第i个和第一个可变荷载的效应。,The combination coefficient of the i th variable load,which is chose per Load code for the design of building structuresGB500092001.第i个可变荷载的组合值系数,应按建筑结构荷载规范GB500092001
25、的规定采用。,The greatest effect of variable load must be the first;when it is not clear which is the greatest one,the comparisons must be taken by putting the variables to the first place to get the most disadvantageous combination.设计时应把效应最大的可变荷载取为第一个；如果何者效应最大并不明确，则需把不同的可变荷载作为第一个来进行比较，找出最不利组合；,As for ben
26、t frame and skeleton frame,formula 1-17 can be simplified,S can be instead by:对于排架和框架,公式(1-17)可以简化,S可以被替换为:The formula are basic combination of the limit state of load-bearing capacity.此公式也是承载能力极限状态的基本组合.,Code for design of steel structures(GB50017)takes stresses for both R and S.钢结构设计规范(GB50017)对R和
27、S都取为应力。For example,the strength check for member are in terms of:例如构件强度验算都采用以下形式：,where式中 f design value of material strength;材料的强度设计值;combinated stress of the member under the design value of loads.构件在荷载设计值组合下的应力。,Take a tensile member in an ordinary steel roof truss for example,when it only carrie
28、s permanent load and snow load,the left end of the expression(1-17)should be:例如，对于一般钢屋架的受拉构件，当屋架只承受永久荷载和雪荷载且雪荷载效应比永久荷载大时，公式(1-17)左端为:（1-19）,where式中、when member is under the permanent load,design value of stress,design value of axis tension,nominal value of axis tension;永久荷载作用下杆件的应力设计值、杆件轴线拉力的设计值和标准值
29、；,、when member is under the snow load,design value of stress,design value of axis tension,nominal value of axis tension;雪荷载作用下杆件的应力设计值、杆件轴线拉力的设计值和标准值；net area of the member.杆件净截面面积。,As for limit state of the regular usage,when check whether the deformation exceed the stated value or not,the separate
30、 coefficients should not be considered.The combinations of load effect include three types:nominal combination,frequent combination and quasi-permanent combination.For steel structure,generally,nominal combination is only to be considered in limit state of the regular usage.However,quasi-permanent c
31、ombination should be considered for steel-concrete composite beam.,对于正常使用极限状态：当验算变形是否超过规定限值时，不考虑荷载分项系数；荷载效应的组合分为标准组合、频遇组合和准永久组合三类。钢结构的正常使用极限状态一般只考虑标准组合。,Homework课后作业：,1.Which two types are divided for Limit States of Steel Structure?钢结构的极限状态分为哪两大类?2.In the performance function of structure，What do R
32、 and S stand for？结构的功能函数Z=R S中，R和S各代表什么？,3.Write down the definition of structural reliability，the expressions of the structural reliability and the probability of failure，and the expression of the relationship of the structural reliability and the probability of failure.写下结构的可靠度定义、结构的可靠度和失效概率表达式，以及
33、可靠度和失效概率关系的表达式。,4.Considering the combination coefficient,write down the design expression for structure member in limit states and the definitions for each letter in the formula.考虑组合系数,写下结构构件极限状态设计表达式及式中各字母的定义。,5.Per Unified standard for reliability design of building structures,the design referenc
34、e period for structure design is years.The reliability target value for steel structure member is,for steel structure connection is.根据建筑结构可靠度设计统一标准，结构设计的设计基准期为 年。钢结构构件设计的目标可靠指标为，钢结构连接的目标可靠指标推荐用。,6.Limit State of load-bearing capacity corresponds to the situation that the structure or the member reac
35、h the maximum bearing capacity,or the deformation disallow them to carry more force,including:_,_、_、_、_ or _.承载力极限状态对应于结构或构件达到最大承载力或出现不适于继续承载的变形，包括_、_、_、_、_或_。,7.Limit State of the regular usage corresponds to the situation that the structure or the member reach the certain allowable value for the r
36、egular usage or endurance,including:_ for regular usage(or appearance),_ and _.正常使用极限状态对应于结构或构件达到正常使用或耐久性能的某项规定限值，包括出现影响正常使用（或外观）的_、_和_。,8.For fatigue calculation,_ is still used in codes.规范对疲劳计算仍采用_。,Answer答案：1.Limit States of Steel Structure is divided into two types:the limit State of load-bearin
37、g capacity and the limit State of the regular usage.钢结构的极限状态分为承载力极限状态和正常使用极限状态两大类。2R stands for the resistance of the structure,S stands for the synthetical effect of load to the structure.R代表结构的抗力，S代表荷载对结构的综合效应。,3.The definition of structural reliability is:In stated time,under stated conditions,th
38、e probability of scheduled performance to be fulfilled by the structure.结构的可靠度定义为：结构在规定的时间内，在规定的条件下，完成预定功能的概率。With pS meaning the structural reliability,then the expression of the definition is:以pS表示结构的可靠度，则定义的表达式为：pS=P（Z 0）The probability of failure is pf：结构的失效概率为pf：pf=P（Z 0）The expression of the r
39、elationship of the structural reliability and the probability of failure is:pS=1 pf,4.where 式中:Structural importance coefficient；结构重 要性系数;Separate coefficient of permanent load；永久荷载分项系数 The nominal value of permanent load effect；永久荷载效应的标准值；,、The i th and the first effects of variable load；第i个和第一个可变荷
40、载的分项系数；、The i th and the first effects of variable load；第i个和第一个可变荷载的效应；The combination coefficient of the i th variable load；第i个可变荷载的组合值系数;,The resistance of the structure；结构的抗力；The nominal value of the resistance of the structure；结构的抗力标准值；Separate coefficient of member resistance.构件抗力分项系数。,5.Per Un
41、ified standard for reliability design of building structures,the design reference period for structure design is 50 years.The reliability target value for steel structure member is 3.2,for steel structure connection is 4.5.根据建筑结构可靠度设计统一标准，结构设计的设计基准期为 50 年。钢结构构件设计的目标可靠指标为 3.2，钢结构连接的目标可靠指标推荐用 4.5。,6.L
42、imit State of load-bearing capacity corresponds to the situation that the structure or the member reach the maximum bearing capacity,or the deformation disallow them to carry more force,including:overturn,strength damage、fatigued damage、failure of stability、the structure turns into the changeable sy
43、stem or the excessive plastic deformation occurs.承载力极限状态对应于结构或构件达到最大承载力或出现不适于继续承载的变形，包括倾覆、强度破坏、疲劳破坏、丧失稳定、结构变为机体或出现过度的塑性变形。,7.Limit State of the regular usage corresponds to the situation that the structure or the member reach the certain allowable value for the regular usage or endurance,including:the deformation for regular usage(or appearance),vibration and the part damage.正常使用极限状态对应于结构或构件达到正常使用或耐久性能的某项规定限值，包括出现影响正常使用（或外观）的变形、振动和局部破坏。,8.For fatigue calculation,allowable stress design is still used in codes.规范对疲劳计算仍采用容许应力法。,
