ANALYTICAL MODEL FOR CFRP SHEETS BONDED TO CONCRETE

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1 ANALYTICAL MODEL FOR CFRP SHEETS BONDED TO CONCRETE Brian Millr and Dr. Antonio Nanni Univrsity of Missouri Rolla Dpartmnt of Civil Enginring 5 ERL 1870 Minr Circl Rolla, MO 65401, USA Dr. Charls E. Bakis Pnnsylvania Stat Univrsity Dpt. of Engr. Scinc & Mchanics 7 Hammond Building Univrsity Park, PA 1680, USA KEYWORDS: bond, CFRP, composits, concrt, xtrnally bondd rinforcmnt, laminat, pling, rpair ABSTRACT Carbon Fibr Rinforcd Polymr (CFRP) shts ar usd as xtrnally bondd rinforcmnt for concrt structurs to improv flxural and shar strngth and confinmnt of concrt. Th bond btwn CFRP shts and concrt is important. It is th mans for th transfr of strss btwn th concrt and CFRP in ordr to dvlop composit action. An xprimntal invstigation was conductd in ordr to dtrmin th ffct of bondd lngth, concrt strngth, and numbr of plis (stiffnss) of CFRP shts on bond. An analytical modl was dvlopd using this xprimntal data. Th modl is brifly discussd in trms of its application to dsign. INTRODUCTION Th us of FRP for rinforcmnt for concrt structurs has mrgd as an xciting and promising tchnology in matrials and structural nginring. In particular, th us of CFRP shts as xtrnally bondd rinforcmnt has potntial in th ara of rpair/rhabilitation of concrt structurs (Nanni, 1997). Th bond btwn CFRP shts and concrt is an issu that must b addrssd in ordr achiv saf and proprly dsignd structurs. Th importanc of bond is that it is th mans for th transfr of strss btwn th concrt and CFRP in ordr to dvlop composit action. Th bond must b charactrizd by dtrmining th shap of th strain distribution in th CFRP sht and th factors that affct th strain distribution. It is known that whn using xtrnally bondd CFRP shts, prmatur failur known as pling can occur at lvls of strss much lowr than th ultimat strngth of th CFRP. Equations ar ndd to addrss this typ oailur in dsign. OUTLINE OF EXPERIMENT Tst spcimns wr prpard to addrss th factors that wr xpctd to affct th bond. In this projct, bondd lngth, concrt strngth, and numbr of plis (stiffnss) of CFRP wr addrssd. Th tsting in this projct was prformd on th spcimn shown in Figur 1. Th spcimn is a plain concrt bam with invrtd T-shap. It had a simply supportd span of 4 in (1067 mm) and a total lngth of 48 in (119 mm). A CFRP strip was bondd to th tnsion fac of th bam. Th sht was in (51 mm) wid and had a fibr thicknss of in (0.165 mm). Th modulus of lasticity of th fibr is ksi (8 GPa) and th tnsil strngth is 550 ksi (3.8 GPa). Tabl 1 shows th spcimns that wr tstd. For a mor dtaild dscription of th xprimntal program, rfr to (Millr, 1999). 1

2 (Both Sids) Hing 10 4 Saw Cut BL 4 4 UNBONDED MONITORED SIDE 48 Not: 1 in = 5.4 mm Figur 1: Tst Spcimn Sris Numbr Tabl 1: Dscription of Spcimns Spcimn Cod Concrt Class [f c ] (psi)* Numbr of Plis Bondd Lngth (in) I [6860] II [5900] III [3550] *Top numbr is class of concrt whil 8-day strngth is shown in brackts Not: 1 in = 5.4 mm; 1 psi = 6.89 kpa

3 EXPERIMENTAL RESULTS Tabl shows a sampl of th tst rsults. It was found that th ultimat load of th spcimns was th sam for all of th bondd lngths. Th rason th bondd lngth did not affct th ultimat load is th xistnc of an ffctiv bond lngth. Th lngth of sht from th point of maximum strss to th point whr th strss dcrass to zro is known as th ffctiv bond lngth. If th bondd lngth is gratr than th ffctiv bond lngth, th bondd lngth will hav no ffct on th ultimat load if th failur mod of th spcimns is by pling of th CFRP sht. In this projct, th pling bgins at midspan of th spcimn and is shown in Figur. Millr (1999) dscribs th mchanism of th pling failur mod in dtail. Sris I Spcimns Ultimat Load (lb) Tabl : Exprimntal Rsults Sris II Spcimns Ultimat Load (lb) Sris III Spcimns Ultimat Load (lb) Avrag 3613 Avrag 5438 Avrag 3668 Standard 94 Standard 60 Standard 757 Dviation Cofficint 8.14% of Variation Not: 1 lb = 4.45 N Dviation Cofficint of Variation 11.07% Dviation Cofficint of Variation 0.65% Strain in FRP (micro-strain) ASSUMED lb 000 lb 500 lb 3000 lb 3300 lb 3700 lb ASSUMED inch Bondd Lngth Distanc From Cntr (in) 3

4 Not: 1 in = 5.4 mm; 1 lb = 4.45 N Figur : Strain Distribution Th concrt strngth also did not affct th ultimat load of th spcimns. Th rason th concrt strngth had no ffct was bcaus th pling failur occurrd in th concrt-poxy intrfac. Th numbr of plis of CFRP sht did affct th ultimat load. It was found that th ultimat load incrasd whn th numbr of plis was incrasd. Basd on th chang of th numbr of plis (stiffnss), a modl was dvlopd to prdict th ultimat load of th spcimn. ANALYTICAL MODEL Th first stp in dvloping th modl was to quantify th ffctiv bond lngth of th sht. This was accomplishd by utilizing th linar shap of th strain distribution at th ultimat stag. Mada t al. (1997) and Brosns and Van Gmrt (1997) also notd th linar shap of th strain distribution at th ultimat stag. Exprimntally, for ach spcimn a valu of th slop (dε/dx) of th linar portion of th strain location curv was found. Th curvs usd to calculat th slops ar shown in Figur 3 and Figur 4 for Sris I and II rspctivly. Th curvs chosn wr th strain distributions just bfor pling occurrd. It should b notd that th valu of zro on th x-axis corrsponds to th start of th bondd rgion. Th valus of dε/dx ar shown in Tabl 3. As can b sn, th valu for dε/dx is largr for Sris I than Sris II. Also shown in ths two tabls is th load that corrsponds to th curv from which dε/dx was obtaind. Th strain was thn calculatd from th load using quation (1), and th ffctiv bond lngth, L, was thn calculatd by quation (). Th valus for wr not usd in th calculation for th avrag, standard dviation, and cofficint of variation for Sris I. Likwis, and wr not usd in th calculations for Sris II. Th rason for this was bcaus th valu of dε/dx for ths spcimns was considrably diffrnt as compard to th othr spcimns of th sris. Th valus of th cofficint of variation basd on th rmaining spcimns show that th rsults ar consistnt. It was found that th ffctiv bond lngth for Sris I and II ar clos to th sam. 4

5 9000 Strain in FRP (micro-strain) Sris I Thortical Location (in) Not: 1 inch = 5.4 mm Figur 3: Curvs Usd to Calculat dε/dx for Sris I Sris II Strain in FRP (micro-strain) Thortical Location (in) Not: 1 inch = 5.4 mm Figur 4: Curvs Usd to Calculat dε/dx for Sris II Tabl 3: Valus Usd to Find L Spcimn Load dε/dx ε max L Spcimn Load dε/dx ε max L 5

6 (lb) (µ/in) (µε) (in) (lb) (µ/in) (µε) (in) Avrag Avrag Standard Standard Dviation Cofficint of Variation 1.4% 11.1% 1.4% 1.1% Not: 1 lb = 4.45 N; 1 in = 5.4 mm Dviation Cofficint of Variation Not Considrd 1.1% 9.0% 1.1% 4.7% L xp = P ε = max 10 6 max (1) nt w E f ε max dε dx () ε max = Strain corrsponding to ultimat load (µε) P max = Ultimat load (kips or kn) n = Numbr of plis t f = thicknss of CFRP sht (in or mm) E f = Modulus of Elasticity (ksi or GPa) w f = width of CFRP sht (in or mm) L -xp = Effctiv bond lngth found xprimntally (in or mm) (dε/dx) = Slop of th strain distribution curv (µ/in or µ/mm) Th valus for L shown in Tabl 3 wr plottd vrsus th stiffnss of th CFRP sht and can b sn in Figur 5. Th axial stiffnss of a matrial is dfind as th cross-sctional ara multiplid by th tnsil modulus of th sht. Howvr, for FRP shts a unit width is oftn considrd and th stiffnss is considrd th thicknss multiplid by th tnsil modulus. An analytical modl dvlopd by Mada t al. (1997) is shown in quation (3). It was found that th rsults from Mada t al. (1997) dos not agr with th rsults prsntd by th currnt projct. Th rason for this is that Mada t al. (1997) considrd an avrag valu for dε/dx for all stiffnsss. From this thy calculatd th ffctiv bond lngth from quation (). Th problm with this approach is that sinc th maximum strain will dcras as th stiffnss incrass, th ffctiv bond lngth also dcrass. Howvr, th data from this projct sms to indicat that dε/dx dcrass as th stiffnss incrass. Sinc th strain dcrass also, th ffctiv bond lngth stays constant. Thrfor, it sms to b mor appropriat to st th ffctiv bond lngth to a constant and dvlop an quation for dε/dx. Until mor tsting can b conductd, th 6

7 consrvativ valu of L may b assumd to b 3 in (76 mm). Th valus of dε/dx ar plottd in Figur 6. A linar approximation is also plottd. Equation (4) is th quation for this lin. L M nt E xp ln 5.71 = 5.4 (3) L M = xp[ ln(nt E )] (3M) L -M = Effctiv bond lngth calculatd by Mada t al. (1997) (in or mm) dε dx dε dx =.915(nt E ) (4) = 0.654(nt E ) (4M) Not for quations (3) and (4), th units for t f is in. and E f is ksi. In quation (3M) and (4M), th units for t f is mm and E f is GPa. If th bond strss, τ, is takn as th avrag bond strss ovr th ffctiv bondd lngth, th forc P can b xprssd by quation (5). Also, quation (5) can b rwrittn in trms of strss as shown by quation (6). P = τ L w max f (5) p = pling strss of th FRP (ksi or GPa) τl f = fp (6) nt f Th shar strss, τ, can b found by quilibrium oorcs from Figur 7 as shown in quation (7). P P = τw dx 1 f (7) Th forc P can b xprssd in trms of strain as in quation (8). Equation (8) can b substitutd into quation (7) and noting that E f, t f, and w f ar constant givs quation (9). P = nt w ε E (8) (ε ε ) E nt w = τw dx 1 (9) (ε 1 -ε ) can b xprssd as shown in quation (10). Substituting (10) into (9) and solving for τ givs quation (11). 7

8 (ε 1 ε ) = ε = dε (10) dε τ = nt E 10 6 (11) dx τ = Avrag bond strss (ksi or GPa) Substituting quation (4) into quation (11) givs quation (1). Not that for quation (1) t f has units of in and E f has units of ksi, and for (1M) t f has units of mm and E f has units of GPa. τ = [.915(nt E ) + 304(nt E )] 10 6 (1) τ = [ 0.654(nt E ) (nt E )] 10 6 (1M) 3.5 Effctiv Bond Lngth (in) Currnt Projct Linar Approximation Stiffnss of CFRP Sht (ksi-in) Not: 1 inch = 5.4 mm; 1ksi-in = 5.71 GPa-mm Figur 5: Effctiv Bond Lngth vs. Stiffnss 8

9 dε/dx (µ/in) Stiffnss of CFRP Sht (ksi-in) Not: 1 inch = 5.4 mm; 1ksi-in = 5.71 GPa-mm Figur 6: dε/dx vs. Stiffnss τ P 1 P dx Figur 7: Fr-Body Diagram of Sht with Lngth dx To summariz th abov discussion, th ky quations of th modl ar shown blow. Sinc only a limitd rang of stiffnsss has bn tstd thus far, limits wr placd on th quations. Ths limits can b rmovd onc mor tsting has bn conductd. Using ths quations, th ultimat load was plottd vrsus th stiffnss of th sht (s Figur 8). Also shown on th graph ar th xprimntal valus of load vrsus stiffnss. It can b sn that th loads for th currnt rsarch ar highr than th valus shown by Mada t al. (1997). This can b xplaind by th rsults of rsarch by Horiguchi and Saki (1997). Thy rportd that th shar tst, which is th tst usd by Mada t al. (1997), producs lowr ultimat loads than th flxur tst. L = 3.0 in (00 ksi in < nt E < 450 ksi in) τ = [.915(nt E ) + 304(nt E )] 10 6 P = τ L w or max f 9 (00 ksi in < f = fp τl nt f nt E < 450 ksi in)

10 Ultimat Load (lb) Mada t al Currnt Projct Thortical (Proposd) Thortical (Mada t al.) Stiffnss of CFRP Sht (ksi-in) Not: 1 lb = 4.45 kn; 1ksi-in = 5.71 GPa-mm Figur 8: Ultimat Load vs. Stiffnss of CFRP Sht IMPLICATION ON DESIGN Th significanc of th quations is to account for pling in dsign. Using th proposd quations, th strss at which pling would occur can b calculatd. This strss would thn b usd as th ultimat strss in dsign quations. An xampl of th calculations is shown blow for a singl ply of matrial having a thicknss of in (0.165 mm), modulus of lasticity of ksi (8 GPa), and ultimat tnsil strngth of 550 ksi (3.79 GPa). L = 3.0 in τ =.915(nt E ) + 304(nt E ) τ =.915( in ksi) + 304( in ksi) = ksi f = fp τl nt f ksi 3.0 in f = = 37 ksi fp in It should b notd that du to rcnt findings, it is undrstood that this valu of pling strss is dpndnt on th surfac prparation of th concrt (Millr, 1999). Mor rsarch is ndd to addrss th influnc of th surfac prparation. 10

11 CONCLUSIONS Th bond btwn CFRP shts and concrt is a important issu whn using CFRP to rpair concrt structurs. A summary of an xprimntal projct that addrssd th bond along with th following conclusions wr prsntd. Th bondd lngth did not hav any affct on th ultimat load of th sht du to th xistnc of an ffctiv bond lngth. Th concrt strngth did not affct th ultimat load bcaus th failur occurrd in th concrt-adhsiv intrfac. Incrasd FRP stiffnss did incras th bond strngth, but not proportional to th numbr of plis. A modl was dvlopd from th xprimntal rsults. This modl was usd to prdict th strss at which pling occurrd. This strss can b usd in dsign as th ultimat strss. Limitations wr placd on th modl du to th rang of stiffnsss that wr tstd. Aftr mor rsarch has bn conductd, th limitations can b rmovd from th quations. ACKNOWLEDGEMENTS Th authors would lik to acknowldg NSF for th funding of this projct undr grant CMS and Mastr Buildrs Tchnologis for supplying matrial. REFERENCES Brosns, Kris and Van Gmrt, Dionys, (1997). Anchoring Strsss btwn Concrt and Carbon Fibr Rinforcd Laminats, Procdings of th Third Intrnational Symposium on Non-Mtallic (FRP) Rinforcmnt for Concrt Structurs, Vol 1, Japan Concrt Institut, Japan, pp Horiguchi, Takashi and Saki, Noboru, (1997). Effct of Tst Mthods and Quality of Concrt on Bond Strngth of CFRP Sht, Procdings of th Third Intrnational Symposium on Non-Mtallic (FRP) Rinforcmnt for Concrt Structurs, Vol 1, Japan Concrt Institut, Japan, pp Mada, Toshiya; Asano, Yasuyuki; Sato, Yasuhiko; Uda, Tamon; and Kakuta, Yoshio, (1997). A Study on Bond Mchanism of Carbon Fibr Sht, Procdings of th Third Intrnational Symposium on Non-Mtallic (FRP) Rinforcmnt for Concrt Structurs, Vol 1, Japan Concrt Institut, Japan, pp Millr, Brian, (1999). Bond Btwn Carbon Fibr Rinforcd Polymr Shts and Concrt, MSc Thsis, Dpartmnt of Civil Enginring, Th Univrsity of Missouri-Rolla, Rolla, MO, pp Nanni, Antonio, (1997). Carbon FRP Strngthning: Nw Tchnology Bcoms Mainstram, Concrt Intrnational: Dsign and Construction, Vol. 19, No. 6, pp