土木工程外文文獻(xiàn)翻譯--決定用frp筋制作的預(yù)應(yīng)力混凝土構(gòu)件的長(zhǎng)期行為的方法（英文）-

1、An approach to determine long-term behavior of concrete members prestressed with FRP tendonsSamer A. Youakim, Vistasp M. Karbhari *Department of Structural Engineering, MC-0085, University of California, San Diego, La Jo

2、lla, CA 92093-0085, USAReceived 8 August 2005; received in revised form 23 January 2006; accepted 6 February 2006 Available online 6 May 2006AbstractThe combined effects of creep and shrinkage of concrete and relaxation

3、of prestressing tendons cause gradual changes in the stresses in both concrete and prestressing tendons. A simple method is presented to calculate the long-term prestress loss and the long-term change in concrete stresse

4、s in continuous prestressed concrete members with either carbon fiber reinforced polymer (CFRP) or aramid fiber rein- forced polymer (AFRP) tendons. The method satisfies the requirements of equilibrium and compatibility

5、and avoids the use of any empirical multipliers. A simple graph is proposed to evaluate the reduced relaxation in AFRP tendons. It is shown that the prestress loss in FRP tendons is significantly less than that when usin

6、g prestressing steel, mainly because of the lower moduli of elasticity of FRP tendons. The long-term changes in concrete stresses and deflection can be either smaller or greater than those of comparable girders prestress

7、ed with steel tendons, depending on the type of FRP tendons and the initial stress profile of the cross-section under consideration. ? 2006 Elsevier Ltd. All rights reserved.Keywords: Creep; FRP; Long-term; Prestress los

8、s; Prestressed concrete; Relaxation; Shrinkage1. IntroductionThe use of fiber reinforced polymer (FRP) tendons as prestressing reinforcements have been proposed in the past decade and a few concrete bridges have already

9、been con- structed utilizing fiber reinforced polymer (FRP) tendons. Compared to conventional steel prestressing tendons, FRP tendons have many advantages, including their non- corrosive and nonconductive properties, lig

10、htweight, 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 behav

11、ior of 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

12、-term loss of pre-stress and the resultant time-dependent camber/deflection is needed . . .’’ Most of the research and applications of FRP tendons in concrete structures have adopted either carbon fiber reinforced polyme

13、r (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 relatively low tensile strength and poor

14、 resistance to creep. Therefore, this paper focuses on prestressed members with either CFRP or AFRP tendons. Creep and shrinkage of concrete, and relaxation of pres- tressing tendons, cause long-term deformations in conc

15、rete structures. While it is generally accepted that long-term losses do not affect the ultimate capacity of a prestressed concrete member, a reasonably accurate prediction of these losses is important to ensure satisfac

16、tory performance of concrete structures in service. If prestress losses are under- estimated, the tensile strength of concrete can be exceeded under full service loads, causing cracking and unexpected excessive deflectio

17、n. On the other hand, overestimating0950-0618/$ - see front matter ? 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2006.02.006* Corresponding author. Tel.: +1 858 534 6470; fax: +1 858 534 6373. E-mai

18、l address: vkarbhari@ucsd.edu (V.M. Karbhari).www.elsevier.com/locate/conbuildmatConstruction and Building Materials 21 (2007) 1052–1060Construction and BuildingMATERIALSwhere k = rp1/fpu. rp1 is the stress in the tendon

19、 1 h after stress release. Ratios of rp1/rp0 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 k = 0.4 and k = 0.6, and for different temper

20、ature levels and solution types. For AFRP tendons in air at a temperature of 25 ?C, relation- ships for a and b were proposed [2] asa ¼ k ? 0:03; b ¼ k ? 0:2723 ð2ÞIn a prestressed concrete member, th

21、e two ends of the pres- tressing 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 t

22、hat when the tendon is subjected to a les- ser initial stress. Thus, a reduced relaxation value, D? rpr, should be used in the analysis of long-term effects in pre- stressed members, such thatD? rpr ¼ vrDrpr ð3

23、Þwhere vr is a dimensionless coefficient less than unity. Fol- lowing an approach previously suggested by Ghali and Trevino [3] to evaluate vr for prestressing steel tendons, vr for AFRP tendons can be calculated as

24、 (log t in Eq. (1) is taken equal to 5 for 100,000 h):vr ¼Z 10kð1 ? XfÞ ? ða0 ? 5b0Þð1 ? XfÞðk ? ða ? 5bÞÞ df ð4Þwherea0 ¼ kð1 ? XfÞ ? 0:03;

25、 b0 ¼ kð1 ? XfÞ ? 0:2723 ð5Þand f is a dimensionless time function defining the shape of the tendon stress–time curve. The value of f increases from 0 to 1 as time changes from initial prestress

26、time t0 to final time t. X is the ratio of the difference between the total pre- stress loss Drps(t) and intrinsic relaxation Drpr(t) to the ini- tial stress rp0, expressed asX ¼ ? DrpsðtÞ ? Drprðt

27、22;rp0 ð6ÞFig. 1 shows the variation of vr with X for rp0/fpu = 0.4, 0.5, and 0.6, which represents the common values of initial prestressing ratios [1]. As will be shown in a later section, X typically varies

28、between 0.1 and 0.2 and a value of vr = 0.95 can be assumed for practical purposes.3. Proposed method of analysisThe analysis follows the four generic steps proposed by Ghali et al. [4] and depicted schematically in Fig.

29、 2. The procedure can be developed considering an arbitrary0.850.90.9510 0.1 0.2 0.3rp 0 /f pu = 0.6= 0.5= 0.4Fig. 1. Reduced relaxation coefficient vr for AFRP.y= ycc AfAp Occ (t0)(t0)Step 1: Instantaneous strainshrink

30、age(t0)cc (t0)Step 2: Free shrinkageand creepcreepcsM N(t,t0)O (t,t0)Step 4: Restraining forcesapplied in reverseddirectionsr ResultantsStep 3: Artificial restraint of concrete deformationsN M O AxisCentroid of AcFig. 2