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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 概率极限状态法概率极限状态法 1.4.4 Design Expre
2、ssion 设计表达式设计表达式1.4.1LimitStatesofSteelStructure钢结构的极限状态钢结构的极限状态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钢结构的极限状态分为承载力极限状态承载力极限状态和和正常使正常使用极限状态用极限状态两大类。两大类。 1. Limit State of load-bearing cap
3、acity 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 system or the excessive p
4、lastic deformation occurs. 承载力极限状态承载力极限状态对应于结构或构件达到对应于结构或构件达到最大承载最大承载力力或出现不适于继续承载的或出现不适于继续承载的变形变形，包括倾覆、强度破，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坏、疲劳破坏、丧失稳定、结构变为机体或出现过度的的塑性变形塑性变形。 2. Limit State of the regular usage corresponds to the situation that the structure or the member reach the certain allowable v
5、alue for the regular usage or endurance, including: the deformation for regular usage(or appearance), vibration and the part damage. 正常使用极限状态正常使用极限状态对应于结构或构件达到正常使对应于结构或构件达到正常使用或耐久性能的用或耐久性能的某项规定限值某项规定限值，包括出现影响正常使，包括出现影响正常使用（或外观）的变形、振动和局部破坏。用（或外观）的变形、振动和局部破坏。 1.4.2 Load effect analysis of the structur
6、e 结构的荷载效应分析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 force analysis.设计钢结构需要处理两个方面的因素：设计钢结构需要处理两个方面的因素：一是一是结构和构件的抗力结构和构件的抗力；
7、二是二是荷载施加于结构的效应荷载施加于结构的效应(荷载效应通过荷载效应通过内内力分析力分析来解来解)。Considering of the effect of deformation or not, the inner force analysis is divided into: one rank analysis and two rank analysis;内内力力分分析析根根据据是是否否考考虑虑变变形形影影响响分分为为：一一阶阶分析和二阶分析；分析和二阶分析；Considering of the plastic performance of steel material or not,
8、the inner force analysis is divided into: elastic analysis and inelastic analysis.内力分析根据是否考虑内力分析根据是否考虑钢材塑性性能钢材塑性性能分为：分为：弹性分析和非弹性分析。弹性分析和非弹性分析。 1.4.3TheLawofProbabilityLimitStates概率极限状态法概率极限状态法The fundamental problem for structure design to solve is to choose an optimum equilibrium between the reliab
9、ility and economy，and make the structure constructed 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
10、Limit States.结构设计要解决的根本问题是在结构的结构设计要解决的根本问题是在结构的可靠可靠和和经济经济之间选择一种最佳的平衡，使由之间选择一种最佳的平衡，使由最经济最经济的途径的途径建成的结构能以建成的结构能以适当的可靠度适当的可靠度满足各种满足各种预定的功能预定的功能要求。要求。结构的可靠性理论已进入以结构的可靠性理论已进入以概率理论概率理论为基础的为基础的极限状态设计方法，简称极限状态设计方法，简称概率极限状态设计法概率极限状态设计法。 The performance function of structure is:结构的结构的功能函数功能函数为：为：Z = R SR sta
11、nds for the resistance of the structure, S stands for the synthetical effect of load to the structure.R代表结构的代表结构的抗力抗力，S代表荷载对结构的综合代表荷载对结构的综合效应效应。 When the value of this function is positive, the structure may meet the performance demand, and the structure is in the reliable state；When the value of th
12、is 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. 这这一一函函数数为为正正值值时时，结结构构可可以以满满足足功功能能要要求求，结结构构处处于于可可靠靠状状态态；为为负负值值时时，结结构构则则不不能能满满足足功功能能要要求求，结结构构处处于于失失效效状状态态；为为零零时时，结结构构达达到
13、到极极限状态限状态。Z = R SThe definition of structural reliability is: in stated time, under stated conditions, the probability of scheduled performance to be fulfilled by the structure. 结构的可靠度结构的可靠度定义为：结构在规定的定义为：结构在规定的时间时间内，在内，在规定的规定的条件条件下，完成下，完成预定功能预定功能的的概率概率。 WithpSmeaningthestructuralreliability,thenthee
14、xpressionofthedefinitionis: 以以pS表示结构的表示结构的可靠度可靠度，则定义的表达式为：，则定义的表达式为：pS=P（Z0）Theprobabilityoffailureispf：结构的结构的失效概率失效概率为为pf：pf=P（Z0）thenpS=1pfHence, the calculation of structural reliability is converted to the calculation of probability of failure. Whether the structure is reliable or not, is to see
15、 whether the structural probability of failure pf is small enough to be accepted. 因此，因此，结构可靠度结构可靠度的计算转换为的计算转换为结构失效概率结构失效概率的计算。的计算。结构是否可靠就看结构是否可靠就看结构失效概率结构失效概率pf是否小到可是否小到可以以接受的程度接受的程度。 The structural reliability is affected by loading, material property, geometrical parameter and the accuracy of the
16、formula, etc. These factors, with randomicity, are called 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 n
17、ormal distribution. Hence, Z = RS also is the normal random variable. 结构的可靠度通常受结构的可靠度通常受荷载荷载、材料性能材料性能、几何参几何参数数和和计算公式精确性计算公式精确性等因素的影响。这些具有随机等因素的影响。这些具有随机性的因素称为基本变量。性的因素称为基本变量。对于一般建筑结构，可以归并为对于一般建筑结构，可以归并为荷载效应荷载效应S和和结结构抗力构抗力R两个基本变量，并设二者都服从两个基本变量，并设二者都服从正态分布正态分布。因此，因此，Z=R-S 也是正态随机变量。也是正态随机变量。 For a equa
18、tion 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 have certain one-one correspondence. The more increases, decreases , the more reliable the structure is. 对于一个对于一个结构状结构状态方程态方程，其
19、平均值，其平均值 与其标准差与其标准差 的比值的比值 ，称为结构或构件的，称为结构或构件的目标可靠指标目标可靠指标 。与与 有确定的一有确定的一一对应关系。一对应关系。 增大，增大，减小，结构也就减小，结构也就越可靠。越可靠。Per Unified standard for reliability design of building structures, the reliability target value for steel structure member is 3.2 , for steel structure connection is 4.5. 根据根据建筑结构可靠度设计统一
20、标准建筑结构可靠度设计统一标准, 钢结钢结构构件构构件设计的目标可靠指标为设计的目标可靠指标为3.2 ，钢结构连接钢结构连接的的目标可靠指标推荐用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. 根据根据建筑结构可靠度设计统一标准建筑结构可靠度设计统一标准，结构设，结构设计的计的设计基准期设计基准期为为50年。年。 For fatigue calcula
21、tion, allowable stress design is still used in codes. 规范对规范对疲劳计算疲劳计算仍采用仍采用容许应力法容许应力法。 1.4.4 Design Expression 设计表达式设计表达式The design expression for structurememberinlimitstates:结构构件结构构件极限状态极限状态设计表达式设计表达式：Structural importance coefficient. 结构重要性系数结构重要性系数;separate coefficient of member resistance; 构件抗力分
22、项系数；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；永久荷载效应的标准值；the nominal value of variable load effect; 可变荷载效应的标准值可变荷载效应的标准值;separate coefficient of permanent load; 永久荷载分项系数永久荷载分项系数separate coefficient of variable load; 可变荷载分项系数；可变荷载分项系数； Building structures are divided into three
23、safe grades according to the seriousness of the damage results: the ordinary industrial and civil buildings are in the 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,
24、 and take =0.9; 建筑结构根据其破坏后果的严重性，分为建筑结构根据其破坏后果的严重性，分为三个安全等级：三个安全等级：一般工业与民用建筑列为一般工业与民用建筑列为二级二级，取，取 =1；影剧院、体育馆和高层建筑等宜按重要性影剧院、体育馆和高层建筑等宜按重要性为为一级一级考虑，取考虑，取 =1.1；次要和临时建筑物为次要和临时建筑物为三级三级，取，取 =0.9； Per Unified standard for reliability design of building structures, separate coefficients of permanent load and
25、 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建筑结构可靠度设计统一标准对对永久荷载永久荷载和和可变荷载可变荷载的的分项系数分项系数分别取为定值。分别取为定值。在在一般情况一般情况下下 =1.2， =1.4；在在异号异号的情况下则取的情况下则取 =1.0， =1.4。 More than one variable load are exerted on the structure,
26、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.施加在结构上的施加在结构上的可变荷载可变荷载不止一种，这些荷不止一种，这些荷载不可能同时达到各自的载不可能同时达到各自的最大值最大值。因此，还要根。因此，还要根据据组合荷载效应组合荷载效
27、应的概率分布来确定荷载的的概率分布来确定荷载的组合系组合系数数，加入式，加入式1-11。 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.除永久荷载和除永久荷载和第一第一可变荷载外，其他可变荷载的可变荷载外，其他可变荷载的效应都乘以不大于效应都乘以不大于1的的组合系数组合系数。 Thenexpression1-
28、11istransformedto：则式则式1-11转换为：转换为： （1-17）where式中Thisformulaisbasiccombinationofthelimitstateofload-bearingcapacity.此公式是承载能力极限状态的基本组合. 、 Theith and the firsteffectsofvariableload.第第i个和第一个可变荷载的效应。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
29、design of building structuresGB500092001. 第第i个可变荷载的组合值系数个可变荷载的组合值系数,应按应按建筑结建筑结构荷载规范构荷载规范GB500092001的规定采用。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
30、 most disadvantageous combination.设计时应把设计时应把效应最大效应最大的可变荷载取为的可变荷载取为第一个第一个；如；如果何者效应最大并不明确，则需把不同的可变荷载作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，找出为第一个来进行比较，找出最不利组合最不利组合； nAs for bent frame and skeleton frame, formula 1-17 can be simplified, S can be instead by:对于对于排架排架和和框架框架,公式公式(1-17)可以简化可以简化, S可以被替可以被替换为换为:Th
31、eformulaarebasiccombinationofthelimitstateofload-bearingcapacity.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.钢结构设计规范钢结构设计规范(GB50017)对对R和和S都取为都取为应力应力。 For example, the strength check for member are in terms of : 例如构件例如构件强度验算强度验算都采用以下形式：都采用以下形式： wher
32、e式中式中fdesignvalueofmaterialstrength;材料的材料的强度设计值强度设计值; combinated stress of themember under the design value ofloads. 构件在构件在荷载荷载设计值组合下的设计值组合下的应力应力。 Take a tensile member in an ordinary steel roof truss for example, when it only carries permanent load and snow load, the left end of the expression (1-1
33、7) should be: 例如，对于一般钢屋架的受拉构件，当屋架只例如，对于一般钢屋架的受拉构件，当屋架只承受承受永久荷载永久荷载和和雪荷载雪荷载且雪荷载效应比永久荷载大且雪荷载效应比永久荷载大时，公式时，公式(1-17)左端为左端为: （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永久荷载作用下杆件的应力设计值应力设计值、杆件、
34、杆件轴线轴线拉力拉力的的设计值设计值和和标准值标准值； 、 、 whenmemberisunderthesnowload,designvalueofstress,designvalueofaxistension,nominalvalueofaxistension; 雪荷载作用下杆件的雪荷载作用下杆件的应力设计值应力设计值、杆件轴线、杆件轴线拉力拉力的的设计值设计值和和标准值标准值； net area of the member. 杆件净截面面积。杆件净截面面积。 As for limit state of the regular usage, when check whether the de
35、formation exceed the stated value or not, the separate 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
36、in limit state of the regular usage. However, quasi-permanent combination should be considered for steel-concrete composite beam. 对于对于正常使用极限状态正常使用极限状态：当验算当验算变形变形是否超过规定限值时，是否超过规定限值时，不考虑不考虑荷载分项系数荷载分项系数；荷载效应的组合分为标准组合、频遇组合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。和准永久组合三类。钢结构钢结构的正常使用极限状态一般只考虑的正常使用极限状态一般只考虑标标准组合准组合。 Ho
37、mework课后作业：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钢结构的极限状态分为哪两大类?2.In the performance function of structure， What do R and S stand for？ 结结构构的的功功能能函函数数Z = R S中中，R和和S各各代表什么？代表什么？3. Write down the definition of structural reliability，the expressions of th
38、e 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、写下结构的可靠度定义、结构的可靠度和失结构的可靠度和失效概率表达式，效概率表达式， 以及可靠度和失效概率关系以及可靠度和失效概率关系的表达式。的表达式。4. Considering the combination coefficient, write down t
39、he design expression for structure member in limit states and the definitions for each letter in the formula. 考虑组合系数考虑组合系数, 写下结构构件极限状态设写下结构构件极限状态设计表达式及式中各字母的定义。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 reference period for structure design is ye
40、ars. The reliability target value for steel structure member is , for steel structure connection is .根据根据建筑结构可靠度设计统一标准建筑结构可靠度设计统一标准，结，结构设计的设计基准期为构设计的设计基准期为 年。年。 钢结构构件钢结构构件设计的目标可靠指标为设计的目标可靠指标为 ，钢结构连接的，钢结构连接的目标可靠指标推荐用目标可靠指标推荐用 。 6. Limit State of load-bearing capacity corresponds to the situation that
41、 the structure or the member reach the maximum bearing capacity, or the deformation disallow them to carry more force, including: _, _ 、_、_ 、_ or _. 承载力极限状态承载力极限状态对应于结构或构件达到最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，包括大承载力或出现不适于继续承载的变形，包括_、_、_、_、_或或_。 7. Limit State of the regular usage corresponds to the situat
42、ion that the structure or the member reach the certain allowable value for the regular usage or endurance, including: _ for regular usage (or appearance), _ and _. 正常使用极限状态正常使用极限状态对应于结构或构件达到正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）的现影响正常使用（或外观）的_、_和和_。8. For fatigue calculation,
43、 _ is still used in codes. 规范对规范对疲劳计算疲劳计算仍采用仍采用_。 Answer答案：答案：1. 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. 钢钢结结构构的的极极限限状状态态分分为为承承载载力力极极限限状状态态和和正正常常使使用用极限状态两大类。极限状态两大类。2 R stands for the resistance of
44、the structure, S stands for the synthetical effect of load to the structure.R代表结构的抗力，代表结构的抗力，S代表荷载对结构的综合效应。代表荷载对结构的综合效应。3.Thedefinitionofstructuralreliabilityis:Instatedtime,understatedconditions,theprobabilityofscheduledperformancetobefulfilledbythestructure.结构的可靠度定义为：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
45、预定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。功能的概率。WithpSmeaningthestructuralreliability,thentheexpressionofthedefinitionis:以以pS表示结构的可靠度，则定义的表示结构的可靠度，则定义的表达式为：表达式为：pS=P（Z0）Theprobabilityoffailureispf：结构的失结构的失效概率为效概率为pf：pf=P（Z0）Theexpressionoftherelationshipofthestructuralreliabilityandtheprobabilityoffailureis:pS=
46、1pf4.where式中式中: Structural importance coefficient；结构重结构重 要性系数要性系数; Separate coefficient of permanentload；永久荷载分项系数永久荷载分项系数 The nominal value of permanentloadeffect；永久荷载效应的标准值；永久荷载效应的标准值；、 Theithandthefirsteffectsofvariableload；第第i个个和和第第一一个个可可变变荷荷载载的分项系数；的分项系数；、 Theithandthefirsteffectsofvariableload；
47、第第i个个和和第第一一个个可可变变荷荷载载的的效应；效应； The combination coefficient of the i th variable load； 第第i个可变荷载的组个可变荷载的组合值系数合值系数; Theresistanceofthestructure；结构的抗力；结构的抗力；Thenominalvalueoftheresistanceofthestructure；结结构构的的抗抗力标准值；力标准值； Separate coefficient of member resistance. 构件抗力分项系数。构件抗力分项系数。 5.PerUnifiedstandardfo
48、rreliabilitydesignofbuildingstructures,thedesignreferenceperiodforstructuredesignis50years.Thereliabilitytargetvalueforsteelstructurememberis3.2,forsteelstructureconnectionis4.5.根据根据建筑结构可靠度设计统一标准建筑结构可靠度设计统一标准，结，结构设计的设计基准期为构设计的设计基准期为 50 年。年。 钢结构构钢结构构件设计的目标可靠指标为件设计的目标可靠指标为 3.2 ，钢结构连，钢结构连接的目标可靠指标推荐用接的目
49、标可靠指标推荐用 4.5 。 6. Limit 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 tu
50、rns into the changeable system or the excessive plastic deformation occurs. 承载力极限状态承载力极限状态对应于结构或构件达到最大承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，包括载力或出现不适于继续承载的变形，包括倾覆倾覆、强强度破坏度破坏、疲劳破坏疲劳破坏、丧失稳定丧失稳定、结构变为机体结构变为机体或或出出现过度的塑性变形现过度的塑性变形。 7. Limit State of the regular usage corresponds to the situation that the structur
51、e 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. 正常使用极限状态正常使用极限状态对应于结构或构件达到正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）的现影响正常使用（或外观）的变形变形、振动振动和和局部破坏局部破坏。8. For fatigue calculation, allowable stress design is still used in codes. 规范对规范对疲劳计算疲劳计算仍采用仍采用容许应力法容许应力法。
