Mpt cong thiPC mai CILF doan do vong cua dam be tdng cot sgi thuy tinh
A new formula for estimation of deflection of GFRP reinforced concrete beams
Ngay nhan bai: 15/9/2014 Ngay site bai: 5/11/2014 Ngay chap nhan dang: 10/12/2014
Tom l a t
Bai bao de xu5t mpt cong thilc mdi xac djnh m o men quan tinh tiet di^n tilctng ditdng va dp vdng cua dam be long cot GFRP, trong do, CO xet them i n h hddng cua h a m ld(?ng va mo-dun dan hoi cua cot doc GFRP. Cong thilc de xuSt dd<?c kiem chiing va so sanh v6i cac c6ng thilc trong c4c hii6ng cian thi^t k l hign hanh va cac nghien cilu triJdc d^y dUa tren ckc kit qud thv(c nghi?m.
Tinh chinh xac va on dinh cua cong thilc de xuat tren mien khao sat tilOng d6i rong cho thay cong thdc de xuat co dp tin ciy cao, vl v^y, hoan t o i n co the dUijc sil dung d^ di^ doan d^ vong cho dam be tong cot FRP.
Tii k h 6 a : dp vong; m 6 - m e n qudn tinh tilt d i | n qui doi; c6t GFRP; cong thilc; dim.
Abstract
t h i s paper proposes a new formula for calculation of effective moment of inertia that is used for estimation of deflection of GFRP reinforced concrete beams considering effects of ratio and elastic modulus of GFRP rebars. The proposed formula is evaluated and compared to those in current design codes and previous researches by testing results. The evaluation show high accuracy and stability ofthe proposed formula within the entire range of investigated parameters, therefore, it could be used to estimate deflection of GFRP reinforced concrete beams in practice design.
Keywords: deflection; effective moment of inertia; GFRP rebars;
formula; beams.
I h S . Cd Thi H o n g Yen
Khoa Ky thuat Xay dilng, D^i hpc Bach Khoa Tp. HCM, E-mail:
ThS. V 6 U Ngpc Di^n
Khoa xay Di^ng, TnJdng Dai hpc T i l n Giang, Tiln Giang, E-mail: [email protected]
TS. NguySn M i n h Long
Khoa Ky thu4t Xay d i ^ g , Dai hpc Bach Khoa Tp. HCM, E-mail:
minhlongsk@gmaiLcom
Cu Thj Hong Y e n , Vo Le Ngoc Dfen Nguyen Minh Long
l.GIC3iTHl£U
Ben canh cac ket cau be tong c6t thep (BTCT) truyen thong, viec tlrr kiem n h u i i g gi^i phap cong nghg, vSt lieu mdi, tien tien, vh than thler moi tri/dng nh5m tao ngn nhCmg dang ket cau mcri co tfnh nang tot va tuoi t h o cao luon la van de cap thiet. Bfii voi cac c6ng trinh BTCT, sir an mon cot thep la m g t trong nhQng nguydn nhan quan trong lam giam chat lu'ong va tuoi t h o cOa cong trinh. NgoSi ra, si/an mon cot thep eo the dan den sif ph5 hoai k^t du n l u khong duoc siia chua kip th6i. Cot soi thCiy tinh GFRP (Glass-Fiber-Reinforced-Polymer) v6i uXi d i l m khong bi an m o n co the giup gISi quyet triSt 64 van de an mon cCia c6t thep. Them vao do, n h d co cUdng do chiu k^o cao, trpng Itfpng bcin than nhe, khong nhiem tj^ va n h i l m di§n, c6t FRP dang r\6i l l n nhif la m o t lua chon hap dSn cho cac cong trinh xay dung hISn nay.
Viec xac dinh do vong cOa dam bi tfing cot FRP hien nay deu dila tren cac cong thu'c cCia d i m BTCT du'oc d i l u chinh nhSm xet den sir khde biet ve cac dac tfnh ea \^ ciia cdt FRP. Theo 06,66 vong dim hi tfing cdt FRP duoc x^c dinh theo mo hlnh do cOng khSng u6n trung binh vh d f l cdng nay duoc xac dinh du'a tren dai lifOng mo-men quin tinh t i l t d i f n tUiAig du'Ong (1^ do Branson [1] de xuSt cho dam BTCT. Thitctl,ceic cong thu'c xac dinh 1^ hign cd, d o ddac xiy dung dUa tren m o t so lupng mau thCr han che, thucfng dan den k i t qu3 dU doan ve dp vong chua duoc chfnh xac ([2], [3], [4], [5], [6]). Ngoai ra, mo hlnh tfnh l^do Branson de xual chUa phan anh hop If SLT l^m vigc cCia cdc dam cd h^m luong cdt doc chju keo nho hon 1 % khi 6 trang thSi da nijft [7]. Thifc te nay doi hfii can co mol sU hieu chinh cho mfi hlnh Branson hodc thay ddi m d hinh tfnh nhSm du doan chinh xac hOn d o vdng dam bi tfing cdt FRP.
Bai bao kiem chiJng dc cdng thiJc t i n h toan d o vong dSm b e t o n g col FRP trong cac hudng dan t h i l t k l hign hhnh va cac nghien cilu trudc dSj dUa tren cac k i t qui thUc nghlem.Tren CO sdcCia k i t qu3 kiem chiing, hh bao d l xuat cdng thdc mdi xac djnh md-men qu^n tfnh tiet dign tUdng duong, trong dd, cd xet them linh hUdng cila ham luong vh mo-dun dar hdi cCia cdt dpc, de phuc vu cho vl&c tinh todn dp vdng dam be tong cdi FRP duoc chfnh xac hon.
2. CAC CONG THl^C T I N H T O A N IV16-IV1EN Q U A N T ( N H T I ^ T D I E N QU D 6 i H I E N CO
Hai phuong phdp xdc djnh md-men qudn tfnh tiet dien qui ddi (le!
cLia dam hign nay gom: phuong phdp trung binh d d ciJng va trung binh d d cong; dUOc xac djnh trdn cd sd thUc nghigm npl suy giCfa 2 trang tha nut va khdng niJt cOa t i l t dign dSm. Phu'dng phdp xdc dinh I, dUa trgr trung binh dp cimg dUdc de xuKt bdi Branson [1] vli dUOC sCrdung rfinc rai de xac dinh dp vdng cho cau kien BTCT chju udn.Trong khi dd, phu'onc phdp xdc djnh 1^ dUa tren trung binh dfi cong duoc s i i d u n g trong cdc t i g i chuan tfnh toan cCia cac ni/dc chSu Au, n h i / CEB FIP MC 2010 [8] va E C : 19].
Rieng vdi cau kien chju uon b l t d n g cdt FRR m d t sd cdc cdng thdt tfnh 1^ di/oc xay difng t r l n phuong phSp trung binh d o cijfng n h u cdt
Hinh 1 , Quan he mo men - 36 vong thiic nghiem va ly thjyet di;a tren mot so mau dam thiic nghldm (Sen htnh ciia [21, [18]
cdng thdc ciia Benmokrane [10], Al-Sayed [11], Toutanji va Saafi [12], Yost va cdng sU[2], Sunna vd cpng sif (4], ACl 4401R [13], va Rafi vi Nadjai [6]. Ben canh dd, mdt sd cdng thifc xdc dinh 1^ duoc xay difng dua trgn phu'ong phdp t f u n g binh d p cong n h u ciia Faza va Gangarao {14], Farve va Charif [15], Hall vd Ghali [16], ISIS Canada [17], va BIschoff [7]. Dac diem chung cua cdc cdng thiJc da ngu la deu dUpc xay d u n g dua trgn 1;^ thuyet tinh ciia dam BTCT, k i t hop vdi higu chinh dUa trgn cdc nghien cdu thuc nghiem. Vigc hieu chinh nay nhSm k l d i n su khde bigt ve dac tfnh bdm dfnh va mo d u n dan hfii giCra cdt FRP vi cdt thep bSng each: (i) gidm dp ldn cua md-men qudn tinh tiet dien dam cho ca hai trang thdi d^n hdi va sau khi ndt t h d n g qua cdc he sd thifc nghigm; (2i) thay ddi tdc dp chuyen doi tCf giai doan ddn hoi sang giai doan sau khi ndt t h o n g qua viec dieu chinh he sd m u cda ti sd M ^ M ^ ; hodc (31) k i t hpp ddng thdi cd hai phuong phap vCfa neu.
3. KlflW C H Q N G V A N H A N X E T T I N H C H I N H XAC CCiA C A C C O N G THtfC H I E N CO
3.1. K i l m chdng va nhan xgt cac cdng thCrc tfnh d(>vfing dua tren 1^
Quan he mfl men - dp vfing theo thuc nghiem vd theo tfnh toan ly thuyet t i f m d t sd cdng thdc hien cd dua tren k i t qua t h i nghiem cCia mdt sd tac gid ([2], [18]) duoc the hien trgn (Hinh 1). Cd the thay, cdc cdng thdc deu cho kgt qud chfnh xac trong giai doan trUdc khi v l t ndt xuat hien.Tuy nhign, d giai do^n sau khi vet nut xuat hign, cac cdng thdc deu dif doan dp vong Idn hon nhieu so vdi thdc nghigm. Cang gan v l glai doan pha hoai, gia t n d d dodn cang xa gia tri thdc nghiem. Ngodi ra, cdc cdng thdc
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Ifinh 2 Kiem diifng do chinh xac ciing thilc theo ham luong cot docp
cd khuynh hddng cho ket qud t d t hon vdi cdc dam cd ham Idpng cdt doc cao (p > 2%), trong khi do, vdi cac dam co ham lupng cdt dpc cdng thap (p £ 2%), gid trj dif dodn qud thien ve an toan. Bdy la van d l rat dang quan tam, vi cac dam trong thdc t l thddng c6 ham IdOng cdt dpc p s 2%.
Tfnh chfnh xac cda cac cfing thdc con duoc kiem chdng dinh lupng thfing qua vigc so sanh d o vdng d d dodn 5^^.^^,^ vdi dd vdng thdc nghigm d ^ ^ ^ trong trang thdi sir dung dda trgn k i t qua t h i nghigm ciia 77 dam ([2], [4], [18], [19]) (Hinh 2) Trong dfi. dd vdng gid^ han sd d y n g 6^^_p dUOC xdc dinh bdng 17240 vdi L la n h l p t f n h t o a n c u a d a m . Cdc dam dCingdl kiem chdng co cddng d p chju nen cua be tfing fc t d 23.6 d i n 79MPa, ham lupng cot dpc p t d 0.43%
den 3.35% vd m d dun dan hoi ciia thanh FRP, E (td40 den 135.9GPa). Cdc dam ddoc t h i nghigm theo so dd udn 3 hodc 4 diem. Cac dam bi phd
hoai t h e o cac k i l u udn - ^on -at ket hO[X Su da dang va m i l n gid t n <^rc 73t tUOng doi rdng ciia cdc t h d n g sd vifa d l cap nhdm d d m bao cho vigc kiem chdng 6uac khdch quan va t d dd co t h e dua ra cdc k i t ludn chfnh xdc ve kha nang dng d u n g cua cac cdng thdc da cd. K i t qua cho thay, cdc cdng thdc ciia Benmokrane [10] va Al- Sunna [4] cho k i t qud chgnh Idch n h i l u nhat so vdi thifc nghiem va d d phan tdn ciia k i t qui tuang ddi ldn. Gia trj trung binh Iwlean cua ti so 6 ^ / 5 ^ ^ ^ va hg sd bien thign tuong img COV ciia 2 cdn^%hdc nay lan Idcrt la Mean =1.97, COV =0.3 va Mean =1.89, COV =0,32.
Cdc cdng thdc cda Al-Sayed [11], ciia Fanre [15], ISIS Canada [17] cung cho gia tri lech khd n h l l u so vdi thdc nghigm va d d n g thdi do phan tdn ciia k i t qud ciJng khd Idn. Cdng thdc Al-Sayed cho gid tri IWean =1.76 va COV =035.
Cflng thdc cua Farve cung cho Mean =1.77, tuy nhien, vdi he sd bien thign n h d hon, COV =0.33.
Cdng thdc ciia ISIS cho gia trj Mean =1.74 vd COV =0.35. Cac cdng thdc cdn lai cho k i t qud gan vdi thdc nghigm htJn, t r o n g do, cdng thdc d o Rati [6] de xuat cho ket qua t d t nhat vdi do phan tan thap nhat. Gid tri Mean vd COV theo cdng thdc cda Rafi la 1.39 va 0.27.
N h d vay, cac cfing thdc da cd, mac du cho k i t qud d d dodn thien v l an toan nhdng cd sd chenh Igch Idn so vdi ket q u i thUC nghigm.
Vdi cac dam cd ham lupng cdt doc < 2%, cdc cflng thdc deu cho ket qua qua thap so vdi thdc nghiem. Ngoai ra, nghign cdu [18] cho thay, le thdc nghiem Idn hdn so vdi cflng thdc Bischoff (cfing thdc chfnh xdc nhat trong nhdm cfing t h d c t i n h theo dp cong trung binh) lgn den 1.35 lan trong giai dpan sd d u n g va su chgnh lech nay t l le thuan vdi sif gia tang ham Iddng cdt doc trong dam. Ngodi ra, cac cdng thdc deu cho k i t qud chinh xac vdi thdc nghiem trong glai doan trddc khi ndt, tuy nhidn, t r o n g giai doan sau khi vet ndt xudt hign, sif khde bigt giOa gid trj ly t h u y l t va thdc nghiem cdng Idn khi tdi trpng cang tang Cd nghia rang tdc d d chuyen ddi t i l t dign t d trang thai nguyen sang trang thdi ndt t i n h theo cac cdng thdc nhanh hon so vdi thdc te. Hien t d p n g nay ed t h e d o hieu dng
"tension stiffening" chda ddoc ddnh gid mdt each chinh xac trong cdng thdc ciia Bischoffva ea t r o n g cae edng thdc khac va dac bigt vdi cdc dam ed ham Idong cdt doe n h d h o n 2%.
4.DeXUATC0NGTHaCM0lVAKI^M CHONG 4 . 1 . De xuat cdng thdc mdi Cac tdc gia d l xuat cfing thdc mdi bSng cdch xdt lai dnh hudng eda ham luong cdt doc den gid trj mfi-men qudn tinh t i l t dien dac blfit trong giai doan sau khi ndt va higu chinh tdc dp chuyen ddi t i l t dien tCr trang thai n g u y i n sang trang thai ndt t h d n g qua vigc d i l u chinh sd m u ' m " c d a t i sd ( M ^ M , ) trong cdng thdc cua BIschoff (2007). \figc d l l u chinh sd m u " m " ndy ddpc thdc hien dua tren ket qua t h i nghiem cda 77 d a m cda cdc nghien c d u tnjoc ,. ciia chi'nh
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tdc gid. Cdng thdc thdc d l xudt cd dang n h d
| ^ ^ . . ^ k ^ n f A f d ^ ( - k ^ )
k = V 2 p f n f + ( p f n f ^ - p f n f Trong d d :
M^ : m d men do tdi tde dung sinh ra;
I : md men quan tfnh t i l t dign nguygn;
1^^ : md men quan tinh t i l t dign nift [13];
k' . h e s d [ 1 3 ] ;
p, ; ham Idong cdt doc, p, =A, / (bd);
n, : t l s d , = E,/E^;
b, d : b l rdng va ehieu cao Idm viec dam;
E, : mfi dun dan hoi cdt FRP;
E^ : mfi dun dan hfii bg tdng, = 4750(f')0.5
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Hg sfi thyc nghiem " m " ddpc xdc djnh dda
^i^ trgn d d ligu thUc nghiem bSng phddng phdp ,^i hdi qui phi t u y i n n h d sau:
'^''- m = 1 . 2 S - 1 0 . p . ^ . | - :**•• E, E^ v d i p E , < 2 (4a)
; " J v d i p E , a 2 (4b)
^ ^ 0 0 vdng ddm bg tdng ddOc xde djnh:
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Trong dd:
E : md dun dan hdi cdt thep, =200 GPa;
a ' : khoang each t d g d i tda den diem dat Idc.
4^2. K i l m chdng cdng thdc d l xudt Tfnh chfnh xdc cua cdng thdc de xuat dddc kiem chdng tren 77 mau dam thdc nghigm tuong t d nhd Muc 3 va ddpc so sanh vdi 2 cdng thdc chinh xac nhdt trong cac cdng thdc da cd Dd la cfing thdc ciia Rafi va Nadjai dai dien eho phuong phdp dfi cdng trung binh va Bischoif dai dign cho cdng thdc d p cong trung binh, Ngoai ra, cdng thdc d l xuat cdn ddpc so sdnh vdi cdng thdc trong [13j. D d chfnh xdc cua cdng thdc ddoc danh gia dda tren gia tri t r u n g binh (Mean), va he sd bien thien (COV). K i t qud kiem chdng (Hinh 3) cho thay, cdng thdc d l xudt cho ketqua gdn vdi k i t qud thdc nghiem h o n s o v d i cdng thirc ciia cac tdc gia khac. Dieu nay t h i hign qua gid trj trung binh (Mean) va hg sd b i l n thien (COV) tdOng dng ciia tl sd d ^ „ , p , ^ / 5„r-,e,B t d c d n g thdc d l xudt la 1.15 va 0.25.'
5. KfTLUAN
Td cdc k i t qud nghign cdu, cdc k i t ludn dupe rut ra nhu sau.
- Cfing thdc d l xuat d u d o a n dp vdng chinh xae cho cd dim bg tdng cdt FRP lan cdt thep.
Gia tri trung binh (Mean) va hg sd bien thidn (COV) tdong ifng cda t l sd do vflng d d doan vd dd vdng thdc nghigm trong giai doan sd dung
^iBv r«j^^Kiv,BCB*''^^"9 *'^'^'^'^^'"^^*'^ 1.15va o!26*
- Cae edng thdc da ed eho k i t qua an toan, tuy nhlen, trong trddng hdp dam ed ham Iddng cdt dpc < 2%, cdc cdng thdc eho k i t qud qua nhd so vdi thuc nghiem vd cd sU phdn tdn Idn.
- Trong so cdc cdng thdc da cd, cde eflng thdc cda Safi va Nadjai, va cua BIschoff cho ket qua sdt vdi thdc nghiem nhat. Gid t n Mean va COV theo cflng thdc ciDa Rafi va Nadjai Id 1.39 vd 0 27; cCia BIschoff Id 1.58 vd 0.31.
-Tinh chinh xac va dn dinh cua cfing thdc d l xuat trgn m i l n khao sat tdong ddi rdng cho thay cdng thdc de xuat cd dd tin cdy cao; vi vdy, cd the sd dung d l d d dodn chfnh xac do vflng ciia dam be tdng cdt FRP,
6 . L O I C A M O N
N g h i e n c d u n d y d U o c t a i t r o b d i T r u d n g D H B a c h K h o a T R H d C h l M i n h t r o n g d l t a i m a s d T - i a X D - 2 0 1 5 - 4 8 .
T A I L i l u THAM KHiiO
[1] Branson (1965) Design procedures for computing deflection5.ACIJoumalPKiceedings,65, pp. 7 3 0 - 7 3 5 .
12) Yost J. fi.. Gross, S R, and Dinehart, D. W. (2003).
Effective moment of inertia for glass fiber reinfiirced concrete beaiiis,AaStructuialJoumal. 100(6), pp, 732-738,
13] Bischoff, P H. 2005. Reevaluation of deflection piedicfion fi)r concrete beams reinforced w i t h steel and fiber reinforced polymer bars. Journal of Stnictural Engineenng-ASCE, 131(5), pp. 752-767
[4] Al-Sunna, R,A.S. (2006). Deflection behai/iour of FRP reinforced concrete flexural members. PhD thesis, Univeisity of Sheffield.
[5] Bischofl^, P, H , and Scanlon, A. (2007). Effective moment of ineftia lot calculating deflections of concrete members containing steel lemforcement and fiber-reinforced polymer reirforcementACIStfucturalJoumal, 104(1), pp. 68-75.
[6] Rafi, M. M , and Nadjai, A (2009), Evaluation of ACl 440 deflection model for fiber reinforced concrete beams and suggested modification ACl Stmcluial Ioumal, 106(6), pp. 762- 771.
[7] Bischo^, P H (2007), 'Rational Model for Calculating Defledion of Reinforced Concrete Beams and Slatis', Canadian Journal of Civil Engineering, 34{8),pp 992-1002.
[8] Federation Internationale du 8^ton (fib), Model Code 2010 - Final draft, Vol 1, federation Internationale du beton.
Bulletin 65, Lausanne, Switzerland, 2012, Vol. 2,3S0p.
[9] European Committee fiir Standardization (CEM. (2004).
Design of concrete structures Partl-l:Generalrulesandrulesfor buildings Eurocode 2, Brussels, Belgium.
[10] Benmokiane, B, Chaallal 0, Masmoudi R. (1996) Flexural response of conciete beams reinforced with FRP reinfiiiciiigbars ACIStnictJ93(l),pp 4 6 - 5 5 .
[11] Al-Sayed, S.H, AI-Sa!loum, U.. Almusallam, TH.
(2000). Performance of glass fiber reinfiirced plastic bars as a reinforcing material for concrete stmctures. Composites Part B, 31,pp. 555-567
[12)Tautan|i,H A . a n d S a a f i , M (2000). Flexural behaviour of concrete beams reinforced with Glass Fiber - Reinforced Polymer (GFRP) bars, ACl Structural Joumal, 100(6), pp, 712-719.
[13] ACl Commitlee440,l R (2006). Guide forthe design and construction of concrete remfiirced w i t h FRP Bare, Farmington Hills, Mtch,pp 1-44.
[14] Faza, S.S, and Gangafiao, H,V.S, (1992), Pre- and Post-Cracking Deflection Behavior of Concrete Beams fleinforced w i t h Fiber-Reinfijrced Plastic Rebars, Proceedings of the First International Conference on Advance Composite Matenals in Bndges and Stmctures (ACMBS-I), Canadian Sodety of Civil Engineers, Sherbrooke, Cananda, pp. 129-137,
[IS] Favre, R„ and Cliarif, H , (1994). Basic Model and Simplified Calculations of Deformations According to theCEB-FIP Model Code 1990, ACl Structural journal, 91 (2), pp. 169-177,
[16] Hall, T„ and Ghali. A. (2000). Long-term deflection prediction of concrete membeis reinforced with glass fibre reinfiiiced polymer bars. Canadian Journal of Civil Engineering, 27, pp. 8 9 0 - 8 9 8 .
[17] ISIS M03-01. Reinforcing Concrete Structures w i t h Fiber Reinforced Polymers. Canadian Network of Centers of Excellence on Intelligent Sensing for Innovative Structures (ISIS Canada), UniversityofWinnipeg, Manitoba, Canada, 2001,81p [18] Nguyen Minh Long, Vo Le Ngocfiien, Pham Hong Son, Hofiiic Duy (2014) M nang khang mit uon ciia dSm b§ tfing cot pol)imersflithuytinh.TapchiXaydulig,3,pp 103-108.
[19] Barns, C , Torres, L,Turan, A., Baena, M , and Catalan, A (2009). An experimentstudy of the flexural behaviourof GFRP RC beams and comparison w i t h prediction models. Composite Structures, 91,pp. 286-295.
