中英文翻译(20211121222009).pdf

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1、1、绪论在过去的十年，纤维增强聚合体筋作为预应力钢筋的使用已经被提议，并且已经用 FRP筋建造了一些混凝土桥。与传统的预应力钢筋相比，FRP筋有许多优点，其中包括它们有无腐蚀性和绝缘性的良好性能，质轻，还有较高的抗拉强度。大多数关于用 FRP筋的预应力混凝土梁的研究工作都集中在预应力构件的短期行为；在文献里面关于配有FRP筋的混凝土构件的长期行为的研究成果是缺乏的。最近 ACI 委员会在关于用 FRP筋的预应力混凝土结构的报告中指出“关于预应力的长期损失和随时间变化的弯曲度和变形的研究是必要的,。”混凝土结构中大多数的 FRP筋的研究和应用要么是碳纤维增强聚合体或者是芳族聚酸胺纤维增强的聚合体

2、。玻璃纤维增强聚合体的应用大多数都局限在传统的配筋中，因为它的抗拉强度相对较低，而且抵抗徐变的能力差。因此，这篇论文集中在 CFRP 和 AFRP 筋的预应力构件的研究上。混凝土的徐变和收缩以及预应力筋的松弛引起混凝土结构长期的变形。虽然承认长期的损失不会影响预应力混凝土构件的极限承载力，然而为了确保混凝土结构在使用期间能正常的工作，对这些损失给出一个合理的、准确地推测是重要的。如果低估了预应力损失，在全负荷的情况下会超出混凝土的抗拉强度，引起开裂和料想不到的过度变形。另一方面，高估了预应力损失会导致过渡的拱曲和不经济的设计。在预测长期的预应力损失发生错误可能是因为以下几个方面的原因：（1）在

3、评估材料长期的特性上不准确（如：混凝土的徐变和收缩以及预应力筋的松弛）；（2）使用的分析方法不正确。本篇论文的目的是通过对用FRP筋制作的预应力混凝土构件中随时间而定的应变和应力的评估这样一个简单的分析法来强调错误的第二来源。这种方法满足了平衡性和兼容性的要求，避免了经验公式的使用，一般来说精确的表明了损失。所用的材料特性的错误可以通过改变输入的材料参数和确定分析结果的上下限来减轻。为了避免这篇论文产生混淆，采用协定的一致的符号。轴力 N当它受拉时为正。弯矩 M当使横截面的纤维底部受拉时为正，与其相应的曲率也为正。当受拉时应力 为正，当拉长时应变 为正。向下的变形为正。由此得出结论，收缩时应变

4、 为负值。由于松弛或者是由于徐变，收缩，和松弛的联合作用引起的预应力钢筋内拉力的损失为负值。这里所考虑的分析集中在钢筋混凝土截面在垂直方向混凝土纤维和钢筋层从给定的参考点向下测量的y 坐标。2.FRP 预应力筋的松弛与混凝土和钢筋相似，AFRP 预应力筋当遭受到持续的应变时会显示出徐变。CFRP 筋表现出的徐变是可以忽略的，在大多数实际应用中都被忽略。当预应力筋在两点之间被拉长时，它将会产生持续的应变。因为徐变，随着时间的推移筋内的应力会减少以保持恒定的应变。这种应力的减少被认为是固有松弛pr。当钢筋受到的应力低于屈服应力的50%时，不会呈现出可感知的松弛，对AFRP筋的测试表明在很低的应力作

5、用下它们会产生松弛。AFRP 筋的松弛水平取决于许多因素，包括周围环境的温度，外界因素（例如，空气，碱度，酸度或者是盐含量），初应力 p0与极限强度 fpu的比，还有初始应力之后的时滞。基于对 AFRP筋的松弛特性的广泛的实验，Saadatmanesh和 Tannous两人表明它们的关系如下：(1)，在这里，=p1/fpu，p1是应力释放 1 小时后钢筋内的应力。在测试中 p1/p0的比值在 0.91 和 0.96 之间变化，平均值是 0.93。表中变量 a 和 b 的数值提供了在=0.4 和 =0.6及不同温度水平和溶解类型下的变量a 和 b 的数值。在空气温度为25 摄氏度的条件下，AFR

6、P筋中 a 和 b 的关系建议如下：(2)。在钢筋混凝土构件中，预应力筋的两端由于混凝土的徐变和收缩经常向彼此靠近，因此要减少钢筋中的张拉应力。这种应力的减少于钢筋受到较小的初始应力有相似的效果。因此，松弛的减少量应该采用预应力构件长期效应的分析值，因此(3)，其中 r是无量纲系数决不一致。以下是之前Ghali 和 Trevino建议的估算预应力钢筋 r的一种方法，AFRP 筋的 r可以这样计算(4)，其中A(dMogf)AnA-0,27u=A0.03；b=23)U=(1I3C)(A(aViAr=X=ZreTpr又(l-QC)-(V-(5)，是无量纲的时间函数，定义了钢筋的应力与时间关系的曲线

7、的形状。随着从初始预应力时间t0变化到最后时间 t，的数值从 0 增加到 1。是总的预应力损失与固有松弛的差和初始应力的比，表达式为 (6)。表示的是在 p0/fpu=0.4,0.5,和 0.6 的情况下,r随 的变化，这描绘了初始配筋率的公值。正如以后部分所述，在实际用途中假定 在 0.1 和 0.2之间变化，r=0.95 3.分析的理论方法这种分析遵循了 Ghali 等人提议的一般的四个步骤。示意性的描述如图2。考虑到由简单的混凝土组成的任意截面，在t0处受到预应力和永久荷载这种程序能够进一步发展。这种方法将会得出一个一次方程，容易被实践工程师运用，而不是冗长的矩阵分析法只能用于特殊用途的

8、计算机程序。除了横截面的初始应力外，这个方程仅仅是四个容易计算出的无因次系数，徐变系数和收缩的函数。3.1.初始步骤步骤 1：瞬时应变。在任何的纤维层，由于永久荷载和预应力的效应下，能计算出在时间 t0处的应变和曲率。眼下，设计者可能已经决定在t0时刻的应力分布没有超过允许应力。在这种情况下，可以通过t0时刻混凝土的土的弹性模量来划分应力的值进而得到在t0时刻应变的图表。步骤 2：混凝土自由的徐变和收缩。在 t0到 t 的时间内由于徐变和收缩引起的混凝土应变的分布式通过混凝土净截面区域质心处的值(cc)free来表示，Ac代表总面积减去 FRP筋的面积，在后张拉的情况下，Af是总面积减去预张拉

9、管道的面积或者是减去 FRP筋的面积，是在先张拉的情况下。当y=ycc时，关系如图 3所示，因此(cc)free=cc(t0)+cs，(7)这儿的 ycc是混凝土净截面质心处的y坐标，是 t0到 t 时间内的徐变系数，cs是在相同时间内的收缩，cc(t0)是在混凝土净截面质心处的应变，它们的关系如下cc(t0)=1(t0)+(ycc-y1)(t0)(8)，其中 y1是在 t0时刻换算面积处的质心，(t0)是在 t0时的曲率。所以，free=(t0)(9)。-AI=o(m-i1/=(3V)lvI(7V-xOV(29)，其中(M)i是每个截面处弯矩的变化。所以有(M)A=(M)B=F1/2 和MB

10、=F1。大多数桥梁的一般参数考虑时注意的事项显示出p(con是很小的，相对于忽略弯矩的变化而分析得到的p来说。5.辅助设计的发展几何系数kA,kI,kcc和kp取决于截面的几何形状和材料的参数Ef/Ec(t0),Ep/Ec(t0)，。大多数配有 FRP筋的梁的横截面都是单一或是双T梁，因此取代了 18 中的 Eq。典型的后张拉DT截面的几何系数的辅助设计如图6a,6b,6c,7a,7b,7c,7d分别是配有 CFRP 筋和 AFRP 筋。在这些数字里，边缘 FRP筋的配筋率是 f=Af/(bhf)，预应力钢筋的面积与总面积的比是p=Ap/(hbw)。表中没有的数据可以用线性内插法得到。1.In

11、troduction The use of fiber reinforced polymer(FRP)tendons as prestressing reinforcements have been proposed in the past decade and a few concrete bridges have already been constructed utilizing fiber reinforced polymer(FRP)tendons.Compared to conventional steel prestressing tendons,FRP tendons have

12、 many advantages,including their noncorrosive and nonconductive properties,lightweight,and high tensile strength.Most of the research conducted on concrete girders prestressed with FRP tendons has focused on the short-term behavior of prestressed members;research findings on the long-term behavior o

13、f concrete members with FRP tendons are scarce in the literature.The recent ACI Committee report on prestressing concrete structures with FRP tendons(ACI 440.4R-04 1)has pointed out that:“Research on the long-term loss of prestress and the resultant time-dependent camber/deflection is needed”Most of

14、 the research and applications of FRP tendons in concrete structures have adopted either carbon fiber reinforced polymer(CFRP)or aramid fiber reinforced polymer(AFRP)tendons.The use of glass fiber reinforced polymers(GFRP)has mostly been limited to conventional reinforcing bars due to their relative

15、ly low tensile strength and poor resistance to creep.Therefore,this paper focuses on prestressed members with either CFRP or AFRP tendons.Creep and shrinkage of concrete,and relaxation of prestressing tendons,cause long-term deformations in concrete structures.While it is generally accepted that lon

16、g-term losses do not affect the ultimate capacity of a prestressed concrete member,a reasonably accurate prediction of these losses is important to ensure satisfactory performance of concrete structures in service.If prestress losses are underestimated,the tensile strength of concrete can be exceede

17、d under full service loads,causing cracking and unexpected excessive deflection.On the other hand,overestimating prestress losses can lead to excessive camber and uneconomic design.The error in predicting the long-term prestress losses can be due to:(1)inaccuracy in estimation of the long-term mater

18、ial characteristics(creep and shrinkage of concrete and relaxation of prestressing tendons);and(2)inaccuracy of the method of analysis used.The objective of this paper is to address the second source of inaccuracy by presenting a simple analytical method to estimate the time-dependent strains and st

19、resses in concrete members prestressed with FRP tendons.The method satisfies the requirements of equilibrium and compatibility and avoids the use of empirical equations,which in general show loss in accuracy to enable generality.The inaccuracy in the material characteristics used can be mitigated by

20、 varying the input material parameters and establishing upper and lower bounds on the analysis results.For the purpose of this paper,and to avoid confusion,a consistent sign convention is used.Axial force N is positive when it is tensile.Bending moment,M,that produces tension at the bottom fiber of

21、a cross section and the associated curvature are positive.Stress,and strain,are positive for tension and elongation,respectively.Downward deflection is positive.It follows that shrinkage,cs,is negative quantity.The loss in tension in prestressing reinforcement due to relaxation pr or due to the comb

22、ined effects of creep,shrinkage,and relaxation,p,is negative quantity.The analysis considered herein focuses on a prestressed concrete section with its centroidal principal y-axis in vertical direction with the coordinate y of any concrete fiber or steel layer being measured downward from a given re

23、ference point.2.Relaxation of FRP prestressing tendons Similar to concrete and steel,AFRP prestressing tendons exhibit some creep if subjected to sustained strains.CFRP tendons typically display insignificant amount of creep,which can be neglected for most practical applications.When a prestressing

24、tendon is stretched between two points,it will be subjected to a constant strain.Because of creep,the stress in the tendon decreases(or relaxes)with time to maintain the state of constant strain.This reduction in stress is known as intrinsic relaxation pr.While steel tendons subjected to stresses le

25、ss than 50%of the yield stress do not exhibit appreciable amount of relaxation,tests on AFRP tendons have shown that they display relaxation under very low stresses.The level of relaxation of AFRP tendons depends upon many factors,including ambient temperature,environment(e.g.,air,alkaline,acidic,or

26、 salt solutions),ratio of initial stress,p0,to its ultimate strength,fpu,and time t lapsed after initial stressing.Based on extensive experimentation on relaxation properties of AFRP tendons,Saadatmanesh and Tannous 2 suggested a relationship of the form:(1)where =p1/fpu.p1 is the stress in the tend

27、on 1 h after stress release.Ratios of p1/p0 in their tests varied between 0.91 and 0.96,with an average of 0.93.Tabulated values of the variables a and b were provided for =0.4 and =0.6,and for different temperature levels and solution types.For AFRP tendons in air at a temperature of 25 C,relations

28、hips for a and b were proposed 2 as(2)In a prestressed concrete member,the two ends of the prestressing tendon constantly move toward each other because of creep and shrinkage of concrete,thereby reducing the tensile stress in the tendon.This reduction in tension has a similar effect to that when th

29、e tendon is subjected to a lesser initial stress.Thus,a reduced relaxation value,should be used in the analysis of long-term effects in prestressed members,such that(3)where r is a dimensionless coefficient less than unity.Following an approach previously suggested by Ghali and Trevino 3 to evaluate

30、 r for prestressing steel tendons,r for AFRP tendons can be calculated as(log t in Eq.(1)is taken equal to 5 for 100,000 h):(4)A（ijAld)_50a=X6,03;b=2iOprAffpr=yrAffprr1M-QC、U)(l-flCHA-(-SA)Jtr=FcL=.AhA-0.27where(5)and is a dimensionless time function defining the shape of the tendon stress time curv

31、e.The value of increases from 0 to 1 as time changes from initial prestress time t0 to final time t.is the ratio of the difference between the total prestress loss ps(t)and intrinsic relaxation pr(t)to the initial stress p0,expressed as(6)Fig.1 shows the variation of r with for p0/fpu=0.4,0.5,and 0.

32、6,which represents the common values of initial prestressing ratios 1.As will be shown in a later section,typically varies between 0.1 and 0.2 and a value of r=0.95 can be assumed for practical purposes.3.Proposed method of analysis The analysis follows the four generic steps proposed by Ghali et al

33、.4 and depicted schematically in Fig.2.The procedure can be developed considering an arbitrary section consisting of a simple type of concrete,subjected at time t0 to both prestressing and dead loads.The method will result in a simple equation that is easy to use by practicing engineers instead of l

34、engthy matrix analysis that could only be used in special-purpose computer programs.In addition to the initial strain profile of the cross section,the equation is only a function of four dimensionless coefficients that can be easily calculated(or interpolated from graphs)and the creep coefficient an

35、d 3.1.Initial steps Step 1:Instantaneous strains.At any fiber,the strain and the curvature at time t0 due to the dead load and prestressing effects(primary+secondary)can be calculated.Alternatively,at this stage,the designer may have determined the stress distribution at 义1-以卜0.27=A(1-QQ-0.03;if23/-

36、Afr?Xf)Q=t0 to verify that the allowable stresses are not exceeded.In this case,the strain diagram at t0 can be obtained by dividing the stress values by the modulus of elasticity of concrete at t0,Ec(t0).Step 2:Free creep and shrinkage of concrete.The distribution of hypothetical free change in con

37、crete strain due to creep and shrinkage in the period t0 to t is defined by its value(cc)free at the centroid of the area of the net concrete section,Ac(defined as the gross area minus the area of the FRP reinforcement,Af,minus the area of the prestressing duct in the case of post-tensioning,or minu

38、s the area of the FRP tendons,Ap,in case of pretensioning)at y=ycc as shown in Fig.3,such that(cc)free=cc(t0)+cs(7)where ycc is the y coordinate of the centroid of the net concrete section,is the creep coefficient for the period t0 to t,and cs is the shrinkage in the same period and cc(t0)is the str

39、ain at the centroid of the net concrete section given by cc(t0)=1(t0)+(ycc-y1)(t0)(8)where y1 is the centroid of the transformed area at t0,and (t0)is the curvature(slope of the strain diagram)at t0.Also free curvature is free=(t0)(9)Step 3:Artificial restraining forces.The free strain calculated in

40、 Step 2 can be artificially prevented by a gradual application of restraining stress,whose value at any fiber y is given by(10)where is the age-adjusted modulus of concrete 5 and 6,used to account for creep effects of stresses applied gradually to concrete and is defined as P，&、+少ftrcVA=Ic(11)The ar

41、tificial restraining forces,N at the reference point O(which is the centroid of the age-adjusted transformed section),and M,that can prevent strain changes due to creep,shrinkage and relaxation can be defined as(12)and(13)where Ic,yp,and are the second moment of Ac about its centroid,y coordinate of

42、 the centroid of the FRP tendons,and the reduced relaxation stress between times t0and t.It should be noted that if the section contains more than one layer of prestresssing tendons,the terms containing Ap or ypAp should be substituted by the sum of the appropriate parameters for all layers.Step 4:E

43、limination of artificial restraint.The artificial forces N and M can be applied in reversed direction on the age-adjusted transformed section to give the true change in strain at O,O,and in curvature,such that(14a)(14b)where is the second moment of about its centroid and is the area of age-adjusted

44、transformed section defined as(15)&N=-E1ACM+AOTXAdpfA=-AM/网A=AM/(EJ)A=AeAfAM=-cicAfnc-从)+0AA(l)+where Ef and Ep are the moduli of elasticity for the FRP reinforcement and tendons,respectively,and the is as defined in Eq.(11).Substituting Eqs.(12)and(13)into Eqs.(14a),(14b)and(15)gives(16)and(17)wher

45、e(18)The time-dependent change in strain in prestressing tendons p can then be evaluated using Eq.(19)and the time-dependent change in stress in prestressing tendons(described by Eq.(20)is the sum of Ep p and the reduced relaxation.p=O+yp(19)(20)Substitution of Eqs.(16)and(17)into Eq.(20)gives an ex

46、pression for the long-term prestress loss,p,due to creep,shrinkage,and relaxation as(21)It should be noted that the last term in Eq.(21),is zero in the case of prestressed members using CFRP tendons.5cA?AffwA%=柄一h=令；ki=yjtec=卞*；-_+)pAffp=p(Aite+ypA)+AP(Afe)+yr卜Al+&AffpkwMOVpAtfp,1必=*/Afrflc+(AKCCJ-h

47、+pAapr(23)(24)4.Application to continuous girders Prestressing of continuous beams or frames produces statically indeterminate bending moments(referred to as secondary moments).As mentioned previously,1(t0)and (t0)(Eqs.(7),(8)and(9)represent the strain parameters at a section due to dead load plus t

48、he primary and secondary moments due to prestressing.The time-dependent change in prestress force in the tendon produces changes in these secondary moments,which are not included in Eq.(21).This section considers the effect of the time-dependent change in secondary moments on the prestress loss.Step

49、 1:Considering a two-span continuous beam,as shown in Fig.4(a)where the variation of the tendon profile is parabolic in each span,the statically indeterminate beam can be solved by any method of structural analysis(such as the force method)to determine the moment diagram at time t0 due to dead load

50、and prestressing.Step 2:The time-dependant sectional analysis can be performed as shown previously for each of the three sections shown in Fig.4(b)an d determine()i for each section,where i=A,B and C.Step 3:Use the force method to determine the change in internal forces and displacements in the cont