英文原文 - 随时间变化的钢筋混凝土抵抗力分析

浙江工业大学毕业设计 杭州某宾馆77Random Time Dependent Resistance Analysis on ReinforcedConcrete Structures*GUAN Chang-sheng1) WU Ling2)1) Wuhan University of Technology 2) Wuhan University of Science and Technology(Received :Aug. 20 ,2001)Abstract : The analysis method on random time dependence of reinforced concrete material is introduced , the effect mechanism on reinforced concrete are discussed , and the random time dependence resistance of reinforced concrete is studied. Furthermore , the corrosion of steel bar in reinforced concrete structures is analyzed. A practical statistical method of evaluating the random time dependent resistance , which includes material , structural size and calculation influence , is also established. In addition , an example of predicting random time dependent resistance of reinforced concrete structural element is given.Key words random analysis ; time dependent resistance ; reinforced concrete1 IntroductionReinforced concrete is one of the most useful materials in civil engineering for its suitability and inexpensive price. Therefore , a large number of this kind material is used. However ,in tradition- al design of construction structure and material research of reinforced concrete , litte attention to the time dependent strength of reinforced concrete is paid , especially the random properties of the various effects on the materials are hardly studied1 ,2 . Until recent year there are a few resea-rches that mention the problem about the random time dependence of reinforced concrete in engineering structures. Li and Melchers3 have studied the failure probability of reinforced concrete columns under stochastic loads ,and given a technique to calculate the time-variant failure probability. Li and Liu4 have studied the durability of concrete structure considering the effect of reinforced corrosion.Leng5 et al have discussed the status and problem of study on thestress corrosion of concrete. Also Lu6 et al have discussed the state of reinforcement corrosion. Generally speaking , reinforced concrete resistance 浙江工业大学毕业设计 杭州某宾馆78obviously decrease , which depends on different factors7 . To evaluate the safety of concrete structure ,a basic theory for analyzing durability of reinforced concrete should be proposed. It is necessory to study random time dependent properties of reinforced concrete structures.2 Time Dependent Effect Mechanisms of Reinforced ConcreteThere are many factors affecting the resistance of reinforced concrete. More than 50 kinds of chemical corrosion factors exist only in the area of water basin ,water works and water conditioning. The practical method to obtain a time dependent model of reinforced concrete is aMulti-factor comprehension technique. In general ,for single-factor ,many results have been shown that if only concrete carbonization is considered ,a formula of predicting carbonization thick can be written as :D ( t) = K t (1)where D ( t ) , K and t are thick , speed coefficient and time of carbonization ,respectively.Up to now many predicting models are used in steel corrosion , fatigue damage , and chemical erosion , but no common recognized results unanimously exist . Generally speaking , the decreasing resistance function of reinforced concrete includes some variables that can express as steel bar ,concrete ,geometric size ,environment condition nearby , and properties of random and time dependence of resistance1 ,5 . Obviously , reinforced concrete resistance is a function of random process or variable of series of materials and structures. Reinforced concrete carbonization in air is called neutralization ,which is a complex and slow neutralization process of CO2 in the air and alkaline material in reinforced concrete. In air it will take several decades to completely carbonize the protective coating of steel bar in dense concrete ,but only take a few years in non-dense concrete. If fineness of carbonized materials is higher , its strength is lower and carbonization process is faster in decreasing cross section of structure. Carbonization makes 浙江工业大学毕业设计 杭州某宾馆79alkalinity lower and steel bar corrosion2 .Steel bar corrosion is a process that iron in steel bar surface losses electron continually and dissolves in water under the condition of oxygen and water interaction. Therefore , the volume of eroded materials is expended several times , which can make the protective coating of reinforced concrete crack , drop , and cohesion damage between steel bar and concrete along steel bar direction so that reinforced concrete structure losses bearing capability. Recent researches show that the steel bar gets into a serious corrosion state when non-carbonized protective coating is only 15mm thick. On the other hand , the start time of corro-sion may be in advance due to incomplete coating and crack in concrete , also corrosion velocity may increase greatly. When steel stress is less than yielding point , the corrosion velocity is stable , but increases several times if the corrosion velocity passes over the yielding point . The latter is called stress corrosion , which is of brittleness and more dangerous. Steel corrosion can make bearing area of steel bar decrease , cohesion damage , and lose structure effectiveness. Erosion air and liquid all have strong effect on reinforced concrete , which can make reinforced concrete erosion ,decrease protective coating of concrete , and finally accelerate steel corrosion. When bearing dynamic load , reinforced concrete structure can undergo fatigue damage ,leading strength and rigidity to decreasing , forming crack and expansion. Usually fatigue damage can be divided into determine and random models , the former deals with determine period loading , and the latter is relative to the random of material and load. Besides all mentioned above , there are many otherfactors , such as temperature (including high or low ,and cyclic temperature ,freezing damage) ,humidity , (including cyclic of dry and humid) ,and the amplitude of loading , which can result in resistance decreasing of reinforced concrete structure.3 Random Time Dependence AnalysisUnder the condition that every random variable of structure is independent on each other , and considering time dependence characteristic of material , the random time dependent function of reinforced concrete material characteristic can be written as8 :浙江工业大学毕业设计 杭州某宾馆80KM ( t) = k - 10 K0 ( t) K f (2)where K0 ( t) is a random variable indicating property difference of structural material and testing material ; k0 is a coefficient of property difference of structural and testing material ,and Kf is a random variable of testing material . As statistics theory , the mean value and standard deviation coefficient of KM ( t) are as follows respectively : KM( t) = k - 10 k0( t) Kf (3) KM( t) = 2K KM0( t) + 2Kf (4)where k0( t) and K KM0( t) respectively are mean value and standard deviation coefficient of random process. K0( t) , Kf and Kf are the mean value and standard deviation coefficient of testing material property and random variable Kf ,respectively. By the same way the similar random analytical model may be set up for studying the randomness and time dependence to geometric parameters and calculation methods of reinforced concrete structure. The resistance of reinforced concrete can be expressed by resistance function R ( x1 , x2 , , xn ) , in which xi denotes the parameters of materials , geometry and calculation procedure of structural material . If random and time dependence are applied simultaneously to resistance and relative variables , xi can be dealt with as a random process. Moreover , considering fatigue mechanics , calculation model and initial conditions , time dependent resistance model can be written as :R ( R0 , t) =R0 KpR ( x 1 , x2 , , xn) (5)where R ( R0 , t) is resistance random process , R0 is initial resistance , is a 浙江工业大学毕业设计 杭州某宾馆81random process of fatigue damage , and Kp is an undeterminable parameter of calculation model , xi denotes a random process of material parameters . Many experiments on steel corrosion indicate thatsteel erosion process accords with normal random process. By separation procedure , random time dependent resistance R ( R0 , t) can simply be expressed as :R ( R0 , t) = R ( t) R0 (6)where R ( t ) is a determining time dependent function , and R0 is random initial resistance.In addition , some other undetermined conditions should be employed , such as undetermined resistance of actual material , geometric size and calculation model . As to a simple structure , resistance function of random process also can be simplified as :R ( t) = g ( t) Kp ( y) Rp ( t ) (7)where g ( t) is time dependent function , Kp ( t ) is undeterminable parameter of calculation model ,and Rp ( t ) is structure resistance determined by calculating model .To a single structural element equation (7) can be written as :R ( t) = Kp ( t) KM ( t) KA ( t) RK( t) (8)where Kp ( t ) , KM ( t ) ,and KA ( t ) are respectively time dependent parameter of calculation ,geometry and material characteristic of reinforced concrete structural element . RK( t) is standard value of material resistance. The mean value and standard deviation of equation(8) are respectively as follows : R ( t) = KP( t) KM( t) KA( t) RK( t) (9) R ( t) = 2KP( t) + 2KM( t) + 2KA( t) 1/ 2 (10)In engineering application , decreasing function random process of concrete structural resistance can be expressed by :浙江工业大学毕业设计 杭州某宾馆82R ( t) = ( t) (11)where R ( t ) is random process of concrete structural resistance ,is relative random variable ,and ( t ) is time dependent determining function.Based on durability grade of designed concrete structure , equation (11) can be established as : cu ( t) = cu (1 - 1 t) (12) cu ( t) = cu (13) y ( t) = y (1 - 2 t) (14) y ( t) = y (15)where cu ( t) and y ( t) are respectively resistance mean value of concrete and steel bar when reinforced concrete is used up to time t ; cu ( t) and y ( t) are standard deviation coefficients of concrete and steel bar of reinforced concrete at time t respectively ; cu , y , cu , y are initial values of various variables ; 1 and 2 are resistance decrease coefficients of concrete and steel respectively , which relate to structural material and can be obtainedfrom material experiment .4 Engineering ApplicationA structural element of reinforced concrete bearing axial pressure is tested , some statistical data of structural resistance is calculated. Consider initial values : C30 concrete ,the mean value cu = 1. 41 and standard deviation cu = 0. 19 ;20MnSi steel bar ,mean value y = 1. 14 andstandard deviation y = 0. 07 ; initial section size is 1m2 . There are 0. 02 variation on each side of the structural element. Resistance decrease coefficients of 浙江工业大学毕业设计 杭州某宾馆83concrete and steel obtained from Ref . 4 are respectively1 = 8 10 - 7 and 2 = 2. 2 10 - 6 . Under these conditions the random time dependent resistance of the reinforced concrete structure bearing axial load can be obtained.According to design theory of reinforced concrete structures , resistance function can be formed by R = AcuRcu + AyRy ,in which Rcu and Ry are initial resistance of concrete and steel bar respectively , and then using the theory suggested in this paper , the random time dependent resistance can be calculated. Some statistical data are listed in Table 1. From the results it is seen that the resistance change of reinforced concrete is obvious ( decreasing with time) . This phenomenon is significant and not to be ignored for evaluating the safety of reinforcedconcrete.Table 1 Random Time Dependent Resistance of Reinforced Concrete Structural Element Bearing Axial Loadt/ year 0 10 20 30 40 50Mean value/ KN 7625. 20 7323. 95 7136. 56 6885. 75 6517. 44 5987. 32Standard deviation/ KN 1248. 63 1193. 80 1164. 73 1129. 49 1080. 28 1011. 05Variation coefficient 0. 1637 0. 1629 0. 1632 0. 1640 0. 1657 0. 16885 ConclusionsThe characteristic of reinforced concrete structures is important for research ,design and construction of civil engineering. The study of random and time dependence of reinforced concrete material is necessary for structural testing , maintaining and safety evaluation of reinforced concrete structures. For structural reliability design , a practical random and time dependent resistance should be established. In this paper random time dependent