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1、Bond Stress–Slip Relationship between FRP Sheet and Concrete under Cyclic LoadHunebum Ko1 and Yuichi Sato2Abstract: Fifty-four bond specimens were subjected to cyclic bond tests to obtain the bond stress–slip relationshi

2、ps between the fiber reinforced polymer ?FRP? sheets and concrete. The specimens were prepared in accordance with Japan Concrete Institute recommenda- tions ?in 1998?. The tests were conducted using three experimental va

3、riables: ?1? type of FRP ?aramid, carbon, and polyacetal?; ?2? sheet layers ?single layered and double layered?; and ?3? loading hysteresis. The bond stress–slip model was developed on a Popovics base envelope and consis

4、ted of seven empirical parameters: The maximum bond stress ?max, the corresponding slip smax, the curve characteristic constant a, the unloading stiffness K, the ultimate slip su, the friction stress ?fp, and negative fr

5、iction stress ?fn. Numerical analyses using the model compared well overall to the experimental cyclic responses of the specimens.DOI: 10.1061/?ASCE?1090-0268?2007?11:4?419?CE Database subject headings: Concrete; reinfor

6、ced; Fiber reinforced polymers; Slip; Bond stress; Cyclic loads.IntroductionFiber reinforced polymer ?FRP? sheets have been successfully used to retrofit a number of existing concrete buildings and struc- tures because o

7、f the FRP sheets’ excellent properties ?strength, lightness, and durability?. One of the most promising uses of FRP is strengthening concrete buildings that have been damaged by earthquakes or have insufficient bearing c

8、apacity by the external application of FRP sheets. Bond characteristics between FRP sheets and concrete should be verified to be an effective retrofit- ting system. During the past several years, a number of FRP bond tes

9、ts have been carried out using various methods. These research efforts discovered that bond characteristics are influenced by bond length, concrete strength, and concrete surface condition ?Brosens and Van Gemert 1999; H

10、origuchi and Saeki 1997; Maeda et al. 1997; Nakaba et al. 2001; Lorenzis et al. 2001; Harmon et al. 2003?. Then the researchers proposed bond stress–slip relation ??–s? models including the linear cutoff model, bilinear

11、model, tri-linear model, and Popovics formula ?Maeda et al. 1997; Brosens and Van Gemert 1999; Ueda et al. 1999; Nakaba et al. 2001?. These models, however, considered only the monotonic response of the bond behaviors; c

12、yclic bond behavior has not been considered.Research SignificanceRC structures strengthened with FRP sheets are often subjected to cyclic load ?traffic, seismic, temperature, etc.?. Analytical and ex- perimental investig

13、ations of the FRP-strengthened structures therefore demand essentially cyclic local bond models. This paper addresses the formulation of a local bond stress–slip relationship model under cyclic loading conditions for the

14、 FRP–concrete interface. Fifty-four specimens prepared according to Japan Concrete Institute recommendations ?JCI 1998? were subjected to double shear tests, on which three types of FRP sheets ?aramid, carbon, and polyac

15、etal? had been applied. The developed cyclic bond stress–slip model was verified through numerical analyses.Experimental ProgramThe tests were conducted with three experimental variables: ?1? type of FRP ?aramid, carbon,

16、 and polyacetal?; ?2? sheet layers ?single layered and double layered?; and ?3? loading hysteresis ?monotonic, cyclic 1, and cyclic 2?. Fig. 1 shows the specimen geometry. Each specimen consisted of a 600 mm long concret

17、e block with a 100 mm by 100 mm cross section. The same layers of FRP sheets, which were 50 mm in width, were bonded with epoxy resin on two opposite sides of the concrete block. The same kind of the resin was used for t

18、he aramid sheet and the carbon sheet while a resin of a higher viscosity was applied for the poly- acetal sheet according to each manufacturer’s process specifica- tion. Each specimen was double notched at the middle lin

19、e on the other two opposite surfaces, to which a crack would be induced before loading. A deformed steel bar with a 19 mm diameter was embedded in the block to apply tension. The bar was cut at the middle so that the ext

20、ernal force was then balanced by the inter- facial shear between the FRP sheets and the concrete. Table 1 presents the elastic modulus, tensile strength, and average thick- ness of the FRP sheets. Table 2 shows the confi

21、guration of the fiifty-four specimens. The first alphabet of the specimen name refers to the type of FRP ?i.e., A=aramid, C=carbon, and P=polyacetal?, whereas the next number indicates the FRP layer1Associate Professor,

22、Dept. of Architecture, Inha Technical College, 253 Yonghyun-dong, Nam-ku, Incheon, 402-752 Korea. E-mail: hbko@ inhatc.ac.kr 2Assistant Professor, Dept. of Urban and Environmental Engineering, Kyoto Univ., Kyoto 615-8540

23、, Japan. E-mail: satou@archi.kyoto-u.ac.jp Note. Discussion open until January 1, 2008. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be fil

24、ed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and pos- sible publication on April 3, 2006; approved on June 22, 2006. This paper is part of the Journal of Composites for Constru

25、ction, Vol. 11, No. 4, August 1, 2007. ©ASCE, ISSN 1090-0268/2007/4-419–426/$25.00.JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / JULY/AUGUST 2007 / 419J. Compos. Constr. 2007.11:419-426.Downloaded from asceli

26、brary.org by Sultan Qaboos University on 04/10/15. Copyright ASCE. For personal use only; all rights reserved.Table 2. Specimens and Test ResultsLoad Specimen Sheet layer tFEF ?kN/mm? Pmax kNUltimate displacement ?mm? Gf

27、 ?kN/mm? ?max ?MPa? Smax ?mm?Monotonic A1-1 1 10.4 14.10 4.51 0.95 1.85 0.06A1-2 10.4 14.49 5.51 1.01 2.47 0.20A1-3 10.4 13.75 5.09 0.91 2.45 0.46A2-1 2 20.9 17.10 3.20 0.70 2.07 0.06A2-2 20.9 20.32 3.37 0.99 2.69 0.02A2

28、-3 20.9 20.22 3.57 0.98 2.01 0.03C1-1 1 43.5 20.65 1.56 0.49 3.24 0.20C1-2 43.5 21.18 1.78 0.52 2.28 0.08C1-3 43.5 19.58 1.52 0.44 2.03 0.30C2-1 2 87.0 29.83 1.33 0.51 3.71 0.05C2-2 87.0 31.16 1.25 0.56 3.93 0.05C2-3 87.

29、0 28.28 1.32 0.46 4.65 0.16P1-1 1 12.4 9.70 7.84 0.38 2.54 0.81P1-2 12.4 8.70 7.48 0.31 1.95 0.52P1-3 12.4 8.79 7.77 0.31 1.99 0.67P2-1 2 24.7 15.91 6.71 0.51 6.67 0.62P2-2 24.7 16.39 7.14 0.54 3.40 1.09P2-3 24.7 15.30 6

30、.26 0.47 2.71 0.84Cyclic 1 A14 1 10.4 12.18 3.42 0.71 1.65 0.04A15 10.4 12.42 4.57 0.74 1.60 0.04A16 10.4 11.89 3.02 0.68 2.07 0.13A24 2 20.9 17.86 2.71 0.76 1.63 0.07A25 20.9 20.05 3.56 0.96 1.72 0.04A26 20.9 16.28 2.71

31、 0.64 1.76 0.04C14 1 43.5 21.00 2.13 0.51 2.93 0.11C15 43.5 18.32 1.62 0.39 2.87 0.11C16 43.5 15.84 1.29 0.29 2.81 0.17C24 2 87.0 29.02 1.03 0.48 1.32 0.04C25 87.0 24.50 0.98 0.34 2.83 0.09C26 87.0 26.60 1.27 0.41 4.03 0

32、.03P14 1 12.4 9.34 7.70 0.35 3.16 0.38P15 12.4 8.24 6.86 0.27 2.48 0.56P16 12.4 9.20 7.77 0.34 1.87 1.24P24 2 24.7 13.21 5.45 0.35 3.30 0.73P25 24.7 12.73 6.04 0.33 4.25 0.50P26 24.7 14.49 6.05 0.43 2.79a 0.12aCyclic 2 A

33、17 1 10.4 12.42 3.02 0.74 2.18 0.10A18 10.4 15.27 1.95 1.12 1.77 0.05A19 10.4 10.79 2.02 0.56 1.72 0.19A27 2 20.9 17.91 2.05 0.77 2.32 0.04A28 20.9 17.26 2.37 0.71 2.47 0.05A29 20.9 15.06 2.04 0.54 1.93 0.12C17 1 43.5 19

34、.86 1.06 0.45 3.25 0.06C18 43.5 14.10 0.83 0.23 0.36 0.16C19 43.5 17.02 1.61 0.33 3.07 0.07C27 2 87.0 29.01 0.81 0.48 3.55 0.06C28 87.0 27.31 1.10 0.43 5.42 0.09C29 87.0 26.57 0.97 0.41 1.76 0.07P17 1 12.4 15.11 9.84 0.9

35、2 0.21a 0.04aP18 12.4 15.95 10.25 1.03 0.43a 0.52aP19 12.4 15.74 10.88 1.00 1.27a 0.06aP27 2 24.7 19.67 7.19 0.78 0.50a 0.57aP28 24.7 18.74 6.66 0.71 4.36a 0.47aP29 24.7 20.54 7.20 0.85 5.24 0.28aCalculating for the valu

36、e was limited because some strains were over 30,000.JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / JULY/AUGUST 2007 / 421J. Compos. Constr. 2007.11:419-426.Downloaded from ascelibrary.org by Sultan Qaboos Universit

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