[雙語翻譯]--橋梁工程外文翻譯--碳纖維增強復合材料（cfrp）筋預應力混凝土梁 時間依存性的特性（原文）

1、Time-dependent behaviour of concrete beams pretensioned by carbon fibre-reinforced polymers (CFRP) tendonsPatrick X.W. Zou a,*, Shouping Shang ba Faculty of the Built Environment, University of New South Wales, The Red C

2、entre, Room 3014, 3rd Floor, Sydney, NSW, Australia b Hunan University, Changsha, ChinaReceived 20 January 2005; received in revised form 24 May 2006; accepted 19 June 2006 Available online 22 August 2006AbstractDue to i

3、ts non-corrosive and high tensile strength properties, carbon fibre-reinforced polymers (CFRP) has attracted researchers’ interests worldwide to investigate the feasibility and effectiveness of using CFRP as reinforcemen

4、ts or prestressing tendons in concrete structures. However until now these studies have been mainly in the form of experimental tests and there is lack of theoretical framework provided. This paper first proposes an anal

5、ytical method to predict the time-dependent behaviour, including concrete strains, curvature and deflection as well as loss of prestress, of concrete beams prestressed by CFRP tendons, under sustained service load condit

6、ion. The paper then presents three illustrative examples of how to use this analytical method to calculate the time-dependent concrete strains, curvature and deflection of concrete beams pretensioned by CFRP tendons. It

7、is concluded that the proposed theoretical framework is suitable for analysis of the time-dependent performance of the concrete beams pretensioned by CFRP tendons and the behaviour of such beams are comparable to those w

8、ith steel and therefore CFRP can be effectively used as prestressing tendons in concrete beams. ? 2006 Elsevier Ltd. All rights reserved.Keywords: Carbon fibre reinforced polymer; Tendon; Time dependent behaviour; Concre

9、te beams; Deflection; Strain1. IntroductionIn prestressed concrete flexural members the prestress- ing force is applied to the concrete in order to reduce the curvature, the deflection and the extent of cracking. Over a

10、period of time the prestressing force in the member will progressively decrease due to creep and shrinkage of the concrete, as well as relaxation of the tendons, i.e., the loss of prestress increases with time. The loss

11、of prestress results in a gradual increase in the deflections which affects the ser- viceability of the member. If FRP tendons are to be used as alternatives to steel tendons in prestressed concrete, it is important to u

12、nder- stand the implications and effects on the time-dependent structural behaviour. The material properties of the ten- dons that most affect the serviceability performance of pre-stressed structures are the elastic mod

13、ulus Ep and the final percentage relaxation R (or creep coefficient, /p). Some FRP tendons may relax or creep more than prestressing steel tendons and the elastic modulus may be substantially lower than that of steel. Hi

14、gher creep in the tendons results in a greater loss of prestress (due to relaxation), whilst a lower elastic modulus means that the time dependent deformations of the concrete (due to creep and shrinkage) cause less loss

15、 of prestress. It may be noted at this point that this paper will focus on carbon fibre-reinforced poly- mers (CFRP) due its superior properties in terms of low creep (relaxation) and high tensile strength as well as mod

16、- erated elastic modulus. However the method presented in this paper is applicable to all types of FRP tendons. Many researchers have provided experimental results indicating that FRP in fact could be an effective altern

17、ative to steel for prestressing concrete beams [11,1,2,8,13–15,6] at service load level as well as at Ultimate limited state. However there is a gap in providing sound theoretical0950-0618/$ - see front matter ? 2006 Els

18、evier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2006.06.008* Corresponding author. Tel.: +61 2 9385 552 36. E-mail address: p.zou@unsw.edu.au (P.X.W. Zou).www.elsevier.com/locate/conbuildmatConstruction and Bui

19、lding Materials 21 (2007) 777–788Construction and BuildingMATERIALSN i ¼ ?P i ð7ÞMi ¼ Ms ? P idp ð8ÞThe initial concrete strain and stress at y below the top fi- bre areei ¼ e0i þ

20、yji ð9Þri ¼ Ecei ¼ Ecðe0i þ yjiÞ ð10ÞThe corresponding stresses in the tendons and the rein- forcement can be determined using the linear material properties for FRP prestress

21、ing tendon or reinforcement.2.3. Short-term analysis of a cracked pretensioned sectionAt any time t, if the applied moment at a section is greater than the cracking moment, cracking will occur and at each crack the concr

22、ete below the neutral axis is ineffective. The short-term behaviour of the cracked cross-section may be calculated using a simple elastic anal- ysis with the following three assumptions: (1) plane sec- tions remain plane

23、 and therefore the strain distribution is linear over the depth of the section; (2) perfect bond exists between the concrete and FRP tendons and reinforce- ments; (3) instantaneous material behaviour is linear-elastic fo

24、r concrete and FRP. The instantaneous strains and stres- ses on a cracked section are shown in Fig. 3. The horizontal equilibrium and moment equilibrium can be used in the cross-section to find the concrete strain at top

25、 fibre e0i and the depth of neutral axis dn, that isT p þ T s þ C þ Cs ¼ 0 ð11ÞMs ¼ T pdp þ T sds2 þ Cdz þ Csds1 ð12Þwhere C, Cs, Ts and Tp may be expressed as

26、functions of dn and e0i, as follows:C ¼ 12 Ece0ibdn ð13ÞCs ¼ Es1As1?e0iðdn ? ds1Þdn ð14ÞT s ¼ Es2As2?e0iðds2 ? dnÞdn ð15ÞT p ¼ EpAp epe þ jecej &

27、#254; ?e0iðdp ? dnÞdn? ?ð16Þwhereepe ¼ P e ApEp ð17Þece ¼ 1Ec ? P e Ag ? P ee2Ig? ?ð18ÞBy a trial and error procedure, the depth of neutral axis dn and the strain at top

28、fibre e0i can be found. Hence the cur- vature ji can be determined:ji ¼ ? e0i dn ð19ÞAfter dn is determined, the properties of the fully cracked transformed section with respect to the top reference sur- f

29、ace (A, B and I) may be calculated and the short-term strain at the top fibre, the curvature and hence the distribu- tion may be found by Eqs. (5) and (6), respectively. Fur- thermore, when dn and e0i are known, the stra

30、ins and stress in the tendons or reinforcements are also readily determined.2.4. Time-dependent analysis of cross-sectionIn pretensioned concrete beams, the bonded tendons and reinforcement provide restraint to the time-

31、dependent shortening of concrete caused by creep and shrinkage. The tendon and reinforcement are gradually compressed. Equal and opposite tensile forces are applied to the concrete at each level of the bonded tendon and

32、reinforcement, thereby reducing the compression caused by prestress. It is the ten- sile forces applied gradually at each level of bonded rein- forcement that result in significant time-dependent changes in curvature and

33、 deflection [10]. The sum of the time-dependent change of strain at any depth y below the top fibre of the cross-section (De) may be expressed in terms of the change in the top fibre strain (De0) and the change of curvat

34、ure (Dj):De ¼ De0 þ yDj ð20ÞThe time analysis of the cross-section considered here uses the age-adjusted effective modulus method (AEMM) to- gether with a relaxation approach. The application was prop

35、osed by Gilbert [9]. In the relaxation procedure, the strain state is assumed to be held constant throughout a gi- ven time interval. If the total strain is held constant and theDBAs1ApAs2Cs1TpσciStrain at different ages

36、 Cross section Stresses and stress resultants after loading At t0 (transfer) At t1 before loading At t1 after loading Ts2Ccσpσs1σs2dnε0iFig. 3. Distribution of strain and stress of a cracked section.P.X.W. Zou, S. Shan