INVESTIGATING THE EFFECT OF FRP CONFIGURATION ON THE ULTIMATE TORSIONAL CAPACITY OF FRP STRENGHTNED REINFORCED CONCRETE BEAMS

Transcription

1 INVESTIGTING THE EFFECT OF FRP CONFIGURTION ON THE ULTIMTE TORSIONL CPCITY OF FRP STRENGHTNED REINFORCED CONCRETE BEMS M. meli 1 * and H.R. Rnagh 2 1 Cenre r Buil Inrarucure Reearch, Faculy Engineering, Univeriy Technlgy Sydney, uralia 2 Deparmen Civil Engineering, Univeriy Queenland, uralia KEYWORDS: Reinrced Cncree, Trin, Beam, FRP, Srenghening. 1 INTRODUCTION In recen year, many udie n lexural and hear renghening reinrced cncree member have been carried u uing exernally bnded ibre reinrced plymer (FRP) [1-3]. Reearch n rinal renghening, hwever, ha n been a ppular and ur underanding i behaviur i very limied a a reul. M he udie n rinal renghening have been experimenal [4-9]. Fr example, Ghbarah (2001) perrmed me rinal e n reinrced cncree beam ha were renghened wih CFRP (carbn ibre reinrced plymer) and GFRP (gla ibre reinrced plymer) in dieren cnigurain. Hi reul hwed ha he renghening increaed he rengh a well a he duciliy level he beam. meli e al. (2004) preened he reul an experimenal prgram n FRP renghened beam ubjeced rin uing CFRP and GFRP wrap. nalyical reearch n rinal renghening i even mre limied cmparing he experimenal reearch. FIB (2001) preened an analyical mehd evaluae he cnribuin FRP wrapped RC beam under rin. Thi cnribuin r ully wrapped beam i preened a: b e E Tu, 2bh c (1) where i he angle rin crack meaured rm he member lngiudinal axi, e i he eecive rain in he ibre ( be bained uing he recmmendain FIB, 2001), b and h are he cr ecinal dimenin he beam, b i widh FRP, E i he mdulu elaiciy FRP, and i he pacing he FRP rip. Eq. (1) i derived baed n enile rce carried by FRP hee n each ide a cr-ecin renghened beam. The her analyical mehd knwn he auhr r he evaluain FRP cnribuin in he ulimae rinal capaciy he renghened RC beam i he ne preened by Nainal Reearch Cuncil (2004) [11]. The exprein r he FRP cnribuin in hi mehd i imilar Eq. (1) when e E replace e ; ha i he eecive FRP rengh ( be calculaed uing he recmmendain reerence [11]). Uer he w abve-menined analyical mehd have ar aumed ha he cnribuin cncree and eel reinrcemen in he ulimae rque FRP renghened beam can be calculaed baed n mdel applicable unrenghened reinrced cncree beam. Thi aumpin may be inaccurae. Cnidering ha in a renghened beam, FRP, cncree and reinrcemen d inerac in repne he lad, he diribuin ree amng hee elemen and wihin he bdy cncree may n be imilar he unrenghened RC beam. In hi paper, an analyical mehd r evaluaing he rinal capaciy renghened RC beam uing verical and hriznal FRP rip i preened. The new analyical mehd i baed n equilibrium and cmpaibiliy cndiin beween cncree, eel, and FRP hrughu he lading regime rm which he ulimae rque FRP renghened beam can be calculaed. The mehd i an exenin he analyical mehd preened in reerence [12] and i claimed be a reanable ep ahead in he develpmen analyical mehd applicable rinally renghened beam.

2 2 THE PROPOSED METHOD mng he analyical udie available r predicing he repne reinrced cncree beam under rin, Cmprein Field Thery (CFT) [13] i knwn a he mdel which be decribe he ineracin dieren cmpnen eel and cncree hrughu he lading regime up unil ailure. The mdel evaluae he ulimae rinal rengh RC beam. Bh equilibrium and cmpaibiliy cndiin are incrpraed in he Cmprein Field Thery. CFT aume ha cncree carrie n enin aer cracking and he inclinain angle he diagnal cmpreive re i he ame a he inclinain angle he principal cmpreive rain. CFT deine he relainhip beween hear rain, l, and he rain in lngiudinal bar ( l ) and irrup ( ) and he maximum diagnal cmpreive rain in cncree ( ), a (Figure 1): d 2( d l ) l (2) an and l 2 d ( ) an (3) Figure 1. Mhr circle rain The abve prvide a mean relae he angle crack,, (meaured rm he hriznal beam axi) and he rain geher a: 2 l d an (4) d Figure 2 hw a reinrced cncree beam, which i wrapped wih FRP verical rip widh a a pacing v and wih FRP hriznal rip widh b h a a pacing h (Figure 2). The eel irrup are aumed be paced a alng he beam. Cnidering ha he hriznal and verical FRP rip bnded n he urace he beam ac a an exernal reinrcemen and reaing hee imilarly he inernal lngiudinal eel bar and eel irrup repecively, he llwing analyical develpmen can be derived. The exernal rque T i reied by he angenial cmpnen he diagnal cmprein which prduce a hear lw, q, arund he perimeer wihin he hickne d. The diagnal cmprein in he cncree ru prduce a hriznal cmpnen which mu be equilibraed by he al enin rce in he lngiudinal eel, alng he lngiudinal direcin he beam,, given by: h h N b v, and in FRP layu p T p N h h q (5) an 2 an

3 where p i he perimeer hear lw pah, direcin (hriznally), erm and and h i he area he FRP rip layu alng he beam h i he re a FRP, and i he area encled by he hear lw. The p can be aken a: a 2 h ph (6) p p 4a h where h i he area encled by he cenreline ranvere hp eel bar (irrup) and p h i he uer perimeer he cncree cr-ecin paing hrugh he cenre irrup. The diagnal cmpreive rain in cncree ru i maximum a he urace,, and decreae linearly zer a a deph d. The variain he diagnal cncree ree in he cncree alng he hickne d can be impliied a a unirm re 1 c d acing ver a deph 1 d a. The equilibrium a crner elemen hw ha he rce in he irrup i: d (7) v v T q an an (8) 2 v where v and v are he area he verical FRP rip, and v i he re a FRP. Figure 2. FRP renghened reinrced cncree beam The hear lw q caued by diagnal ree acing a an inclinain angle can be expreed by: q c a in c (9) 1 Replacing hear lw rm Eq. (9) in Eq. (8) give 1 c v v v a in c an (10) Frm Eq. (5) and (9), hen:

4 N 1 h c p h a in c an (11) dding Eq. (10) and Eq. (11) give N 1 h h c p 1 c v v v a (12) pplying he relainhip beween he curvaure he cncree ru and he angle wi geher wih imple mahemaical manipulain, he ae he rain in irrup,, and in he lngiudinal bar, l, can be expreed a: and 1 1 c h 1 v v ph 2 v d (13) c h l 1 1 p 2 p 1 h h h d N (14) The ulimae rque T, may be calculaed by: N h h v v T 2 (15) p v I huld be ned ha in he abve exprein, he value v and h may be replaced by v E v h E h v h (16a) (16b) In he abve, E v and E h are he mdulu elaiciy he verical and hriznal FRP rip repecively, and v and h are he rain a verical and hriznal FRP rip repecively. The relainhip beween v and h, and can be bained cnidering a linear rain relain a: cc d v (17a) d cc d h l (18b) d where cc i he cncree cver and d i he deph neural axi. The prcedure r calculaing he ulimae rinal rengh he FRP renghened beam, T, in he abve-menined analyical mehd invlve ieraing n and calculaing he required d

5 parameer while imulaneuly aiying he equilibrium and cmpaibiliy cndiin. The prcedure cninue unil eiher d r v r h reach heir deined ulimae value r T ar reduce. In he reul ha will be preened in he nex ecin, he rain limi in cncree i aumed be , and he maximum rain FRP i aken a e a preened by FIB (2001). Teed Beam Cr- Secin, mmxmm Table 1. Characeriic he eed beam Lengh, mm c, MPa C1 a 150x G1 a 150x C2 a 150x G2 a 150x Diameer irrup and Rebar **, mm 6.35, 11.3 & , 11.3 & , 11.3 & , 11.3 & 16 y and * yl, MPa Sirrup pacing, mm 435, , , , L5 b 150x , , L6 b 150x , , DR c 250x & , CFS d 150x , 6 502, GFS d 150x , 6 502, CFE d 150x , 6 502, GFE d 150x , 6 502, S4 e 279x , , L4 e 279x , , B0L4/90S4 e 279x , , ( a ) [4],( b ) [8], ( c ) [7], ( d ) [6], ( e ) [5]. ** One rebar lcaed a each crner. *** y i he irrup yield re and yl i he lngiudinal eel bar yield re. 3 PREDICTIONS OF THE PROPOSED METHOD GINST TESTS RESULTS In hi ecin he abiliy he preened mehd evaluae he ulimae rinal rengh FRP renghened RC beam i inveigaed. Beam chen r hi udy are he appeared in he publihed paper and cmpaible wih he analyical mehd in erm he arrangemen reinrcemen and renghening cheme [4-9]. The phyical prperie he eed beam are hwn in Table 1. Deail renghening cheme, value he ulimae rque bained rm he e and he crrepnding rque prediced by he new mehd and by FIB mehd are hwn in Figure 3 and Table 2. i een, he predicin he FIB S mehd in m cae (wih he exempin pecimen C1) are airly le han he experimenal reul. The average he rque rai FIB analyical mehd he experimenal reul, T FIB / T E, r renghened beam wih verical ully wrapped cheme and he wih verical rip are and repecively. Fr beam renghened wih hriznal FRP rip, like beam 0L4, FIB mehd i n applicable a i de n prvide an analyical predicin r hi renghening cnigurain. Due hi prblem, in beam B0L4/90S4 wih ne layer lngiudinal layu GFRP alng he enire beam, and ne layer verical rip, he cnribuin he lngiudinal layu FRP ued r renghening cann be aken in accun by FIB mehd in evaluaing he ulimae rque. The ulimae rque in Table 2 prediced by he new analyical mehd preened in hi paper have a gd agreemen wih he e reul verall cmpared wih he FIB mehd ha he average rque rai, T NM / T E, r he beam renghened wih verical ully wrapped FRP i Thi average rai r beam renghened wih FRP rip i and hw a beer agreemen

6 wih he experimenal reul. In paricular, he reul he new mehd r renghened beam wih lngiudinal FRP laying, beam 0L4 and B0L4/90S4, hw ha he new mdel i capable predicing he ulimae rque reanably. The gverning ailure mde prediced by he mehd wa FRP rupure. Thi wa und agree wih he experimenal bervain. (a) verical wrapping arund he whle cr-ecin and alng he enire lengh, beam C1, G1, DR, CFE, GFE (b) verical wrapping arund he whle cr-ecin in rip, beam C2, G2, L6, CFS, 90S4 (c) lngiudinal layu wrapping alng he enire lengh, beam 0L4 (d) lngiudinal layu wrapping alng he enire lengh and verical wrapping arund he whle cr-ecin in rip, beam B0L4/90S4 Figure 3. Schemaic renghening cheme he eed beam in Table 2 4 COMPRING THE ULTIMTE TORQUES OF LONGITUDINL ND VERTICL LYING In hi ecin, he reul a numerical udy n he eec lngiudinal and verical FRP laying n he ulimae rque uing he new analyical mehd develped in hi paper i preened. in he publihed lieraure he number e perrmed n beam renghened wih lngiudinal layu FRP have been very ew in cmparin he renghening wih verical FRP wrap, he numerical udy prped here can imprve underanding he dieren cheme menined abve. In he numerical udy a beam wih cr ecinal dimenin 200mmx200mm and wih a lengh 2000mm under pure rin i cnidered. The arrangemen reinrcemen r hi beam are ur 16mm diameer lngiudinal eel bar (ne a each crner) and 8mm diameer eel bar r irrup placed a 100mm alng he lengh he beam. The mdulu elaiciy eel bar i 200GPa and he yield re lngiudinal bar and irrup i aken a 500 MPa. The cmpreive rengh cncree r he beam i 30MPa. Three renghening cheme are aumed: cheme 1- verical FRP rip 100mm paced a 100mm (Figure 3a); cheme 2- lngiudinal FRP laying alng he enire lengh he beam (Figure 3b); and cheme 3- cmbinain cheme 1 and cheme 2 (Figure 3c). The hickne and mdulu elaiciy he FRP ibre are 0.165mm and 240GPa repecively (MBrace C130). Three dieren number layer; ne layer, w layer, r hree layer; are aumed be applied r all renghening cheme. The reul he ulimae rque r he abve-menined cae udie are hwn in Table 3. i een, verall, he eec lngiudinal renghening cheme increae he ulimae rinal capaciy i lwer han he verical cheme ha he percenage increae in he ulimae rque r beam VS1, VS2, and VS3 (beam wih verical renghening cheme) are mre han 10% cmpared he crrepnding beam LS1, LS2, LS3 repecively. expeced uing cmbinain verical and lngiudinal renghening cheme (cheme 3) reul in larger ulimae rque in cmparin individual renghening cheme (cheme 1 r cheme 2). Hwever, a he number FRP layer increae, he rend grwh in he percenage increae in he ulimae rque decreae. Table 2. nalyical predicin again e reul in erm he ulimae rque Srenghening cheme Thickne and mdulu Ulimae rque, kn.m Rai rque

7 Beam a C1 G1 C2 G2 L6 DR CFS GFS CFE GFE 90S4 0L4 B0L4/ 90S4 Verical ully wrapped CFRP alng he enire beam, ne layer Verical ully wrapped GFRP alng he enire beam, ne layer Verical CFRP rip 100mm paced a 200mm, ne layer Verical GFRP rip 100mm paced a 200mm, ne layer Verical CFRP rip 60mm paced a 150mm, ne layer Verical CFRP ully wrapped alng he enire beam, ne layer Verical CFRP rip 100mm paced a 100mm, ne layer Verical GFRP rip 100mm paced a 100mm, ne layer Verical ully wrapped CFRP alng he enire beam, ne layer Verical ully wrapped GFRP alng he enire beam, ne layer Verical GFRP rip 114.3mm paced a 114.3mm, ne layer Lngiudinal layu GFRP alng he enire beam, ne layer lngiudinal layu GFRP alng he enire beam, and Verical rip 114.3mm paced a 114.3mm, ne layer elaiciy he ibre 240,000MPa 73,000MPa 240,000MPa 73,000MPa 0.111mm, 235,000MPa 240,000MPa 243,789MPa 72,723MPa 243,789MPa 72,723MPa 72,000MPa 72,000MPa 72,000MPa New Mehd, T NM FIB Mehd, T FIB Experime nal reul, T FIB / T E T NM / T E T E N/ b 29 N/ c ve. (including verical ully wrapped beam) ve. (including verical rip wrapped beam) a The beam are he ame a he preened in Table 1 FIB mehd cann evaluae he ulimae rinal capaciy hriznal FRP rip Thi calculain i baed n he capaciy verical FRP rip Table 3. Reul he numerical udy uing he new analyical mehd prped in hi paper Cae udy Srenghening cheme Ulimae rque, kn.m % increae a

8 R b N/ VS1 Verical FRP rip 100mm paced a 100mm, ne layer VS2 Verical FRP rip 100mm paced a 100mm, w layer VS3 Verical FRP rip 100mm paced a 100mm, hree layer LS1 Lngiudinal layu FRP alng he enire beam, ne layer Lngiudinal layu FRP alng LS2 he enire beam, w layer Lngiudinal layu FRP alng LS3 he enire beam, hree layer Verical FRP rip 100mm VS1/LS paced a 100mm, ne layer and 52 Lngiudinal layu FRP alng he enire beam, ne layer Verical FRP rip 100mm VS2/LS paced a 100mm, ne layer and 76 Lngiudinal layu FRP alng he enire beam, w layer Verical FRP rip 100mm VS3/LS paced a 100mm, ne layer and Lngiudinal layu FRP alng 95 he enire beam, hree layer a Cmpared he beam wihu renghening (beam R) b Beam wihu renghening 5 CONCLUSION n analyical mehd wa preened in hi paper evaluae he ulimae rque reinrced cncree beam renghened exernally wih verical and/r lngiudinal FRP wrap. Equilibrium and cmpaibiliy cndiin r all elemen invlved including cncree, reinrcemen and FRP were cnidered in he new analyical mehd. The ulimae rque prediced by he mehd were in gd agreemen wih he experimen. The average rque rai hwed ha he prped mehd i cnervaive r ully wrapped beam, while lighly uncnervaive r rip wrapping. The mehd wa und be mre accurae han he FIB mehd verall. The reul he numerical udy prped in he paper hwed ha, verall, he eec lngiudinal renghening cheme in increaing he ulimae rinal capaciy wa lwer han he verical cheme. Mrever, i wa und ha in he cmbined renghening cheme (lngiudinal plu verical rip), a he number FRP layer applied increae, he rend grwh in he percenage increae he ulimae rque decreae. REFERENCES [1] Khalia., Gld W.J., Nanni., ziz MI. (1998). Cnribuin exernally bnded FRP hear capaciy lexural member., SCE Jurnal Cmpie r Cnrucin, 2(4), [2] Malek M., Saadamaneh, H. (1998). Ulimae hear capaciy reinrced cncree beam renghened wih web-bnded iber-reinrced plaic plae, CI Srucural Jurnal, 95(4): [3] Trianaillu, T.C. (1998). Shear renghening reinrced cncree beam uing epxybnded FRP cmpie., CI Srucural Jurnal, 95(2), [4] Ghbarah,. (2001). FRP cmpie in civil engineering. Prc., FRP Cmpie in Civil Engineering, CICE2001, Hng Kng, I, Balkema Publiher, Lndn. [5] Panchacharam, S., and Belarbi,. (2002). Trin behaviur reinrced cncree beam renghened wih FRP cmpie. Prc., Fir FIB Cngre n Cncree Srucure in he 21 Cenury, Oaka, Japan, 10 page (Publihed in CD-ROM). [6] meli, M., Rnagh, H.R., and Dux, P.F. (2004). Experimenal inveigain n FRP renghening beam in rin, Prc., 2 nd Inernainal Cnerence n FRP cmpie in Civil Engineering, December 2004, delaide, uralia, Balkema Publiher, Lndn.

9 [7] Rnagh, H.R. and Dux, P.F. (2003). Full-Scale rin eing cncree beam renghened wih CFRP. Prc., The ir inernainal cnerence n he perrmance cnrucin maerial in he New Millennium, Cair, [8] Zhang, J.W., Lu, Z.T., and Zhu, H. Experimenal udy n he behaviur RC rinal member exernally bnded wih CFRP. Prc., FRP Cmpie in Civil Engineering, CICE2001, Hng Kng, Balkema Publiher, Lndn. [9] Hii,.K.Y., and l-mahaidi, R. (2006). n experimenal and numerical inveigain n rinal renghening lid and bx-ecin RC beam uing CFRP laminae, Jurnal Cmpie Srucure, 75, [10] FIB (CEB-FIP) (2001). Exernally bnded FRP reinrcemen r RC rucure, Technical Repr, Bullein N. 14, Spring-Digial-Druck, Sugar. [11] Nainal Reearch Cuncil. (2004). Guide r he deign and cnrucin exernally bnded FRP yem r renghening exiing rucure, CNR-DT 200, Rme. [12] meli, M., and Rnagh, H.R. (2006). n nalyical Mehd r Evaluaing he Ulimae Trque FRP Srenghened Reinrced Cncree Beam, Submied he SCE Jurnal Cmpie r Cnrucin. [13] Cllin, M. P., and Michell, D. (1980). Shear and rin deign prereed and nnprereed cncree beam. PCI Jurnal, 25(4),