Shear Strength of Reinforced Concrete Columns Strengthened with Carbon Fiber Reinforced Plastic Sheet

Transcription

1 Shear Srengh of Reinforced Concree Columns Srenghened wih Carbon Fiber Reinforced Plasic Shee Lieping Ye 1 Qingrui Yue 2 Deparmen of Civil Engineering Naional Engineering Technical Tsinghua Universiy Technique Research Cener Beijing P. R. China 184 of Indusrial Building Ylp@singhua.edu.cn Beijing P. R. China 184 Shuhong Zhao 3 Quanwang Li 4 Deparmen of Civil Engineering Deparmen of Civil Engineering Tsinghua Universiy Tsinghua Universiy Beijing P. R. China 184 Beijing P. R. China 184 Absrac Seven specimens were esed o invesigae shear srengh of reinforced concree columns srenghened by wrapping carbon fiber reinforced plasic shee. All specimens were esed under laeral reversal cyclic loading and a consan axial load. The main parameers considered were RP shee amoun, shear span/deph raio and axial load raio. Many srain gauges were aached o RP shee o obain is shear conribuion. I was found ha he shear behavior of par of he srenghened column was almos he same as ha of he unsrenghened one. The parameers were found o have an influence on he shear conribuion of RP shee, which could be explained by russ-arch shear resisance mechanism. A simple superposiion mehod is suggesed o calculae he shear srengh of he srenghened column, in which a shear coefficien (ν ) is proposed o evaluae he shear conribuion of RP shee based on he es resuls. The calculaed resuls of suggesed mehod are shown o be in reasonable agreemen wih es ones. 1 Inroducion Changing of usage, upgrading of design code, increasing safey requiremen and deerioraion of srucure ofen resul in he need of srenghening or rerofiing for exising reinforced concree srucures ( srucures). Alhough many radiional mehods can be adoped, he applicaion of carbon fiber reinforced plasic shee (RP shee) impregnaed wih epoxy resin for srucures srenghening or rerofiing has received considerable aenion due o is high srengh, ligh-weigh, quick and easily handled on sie, high resisance agains corrosion and fabricaion ease. This effecive srenghening mehod of srucures, occurred abou a decade ago, has become more and more widely used in America, Canada, Japan and Europe recenly. China began he research and applicaion of RP shee for srucures srenghening in One of he major applicaions of he RP shee is for seismic srenghening of columns. Saadamanesh (1994 and 1996) found ha he srengh and duciliy of bridge concree columns could be significanly

2 increased by wrapping FRP sraps around he columns due o he confinemen of concree. The confinemen effeciveness of various parameers such as concree compressive srengh, hickness and spacing of sraps and ype of srap was sudied. Xiao (1997), Saadamanesh (1997) and Purba (1999) also sudied seismic rerofiing of columns wih prefabricaed FRP producs. The seismic performance of columns was found o be improved by increasing duciliy wih he confinemen by FRP composies or shee. As i is known ha he deficien of column for seismic performance is mainly induced by lack of shear srengh and duciliy. Alhough boh deficiencies can be improved wih wrapped FRP shee simulaneously, he shear srengh should be srong enough o avoid brile shear failure occurring before flexure failure. This is so-called srongshear-weakflexure philosophy in seismic design. Thus, he shear srengh should be evaluaed firs for seismic srenghening of columns. The shear srenghening of beams wih FRP was sudied earlier han columns. Uji (1992) sudied he shear capaciy improvemen of member by applying RP shee on he web of beam and suggesed a calculaion model for shear debonding srengh of his ype srenghening. Sao Y. (1996) found ha beams srenghened wih boom-web bonded RP shee showed effeciveness for shear srenghening compared wih ha of only web bonded. Sao K. (1996) found ha he shear conribuion of boom-web bonded RP shee wih mechanical anchorage se could be significanly increased in he coninuaion sudy. Norris (1997) sudied he effec of fiber direcion on shear srenghening. In Thanasis research (1998), he effec of RP amoun on shear srenghening of beams using web-bonded RP composie was sudied, and he effeciveness was found o be less when large amoun of RP was used. Besides, Michael (1995) and Amir M. (1998) sudied FRP composie wih differen fibers and FRP plaes o he web of beam for shear srenghening. All he sudies demonsraed he effeciveness of shear srenghening wih FRP shee or composie. Because beam srenghened wih web bonded or boom-web bonded FRP shee and composie ofen failed in debonding, hey were no suiable for column wih wrapped FRP shee. Bu he srain developmen of RP shee was found o be a key problem in deermining he shear capaciy in he beam research and he influence parameers considered were useful for he research of column. Japanese Railway Synheic Technical Research Insiue (1996) conduced a es of shear srenghening of column wih RP shee. The sudy was similar o ha described in his paper. Bu he axial load and shear span in he es are no aken as he influence parameers, and he axial load is very small compared wih ulimae axial srengh of column due o he full scale specimen adoped. To furher he undersanding of shear resisan mechanism of RP shee and he influence parameers on is srain developmen, seven ess of columns srenghened wih RP shee, including one comparison unsrenghened column, under laeral reversed cyclic loading were conduced and are described in his paper. Based on he analysis of es resuls, he shear resisan conribuion of RP shee and a simple superposiion calculaion mehod of he shear srengh for srenghened columns is suggesed. I is shown o be in reasonable agreemen beween he suggesed mehod and he es resuls of boh his paper and Japanese Railway Synheic Technical Research Insiue (1996). 2 EXPERIMENTAL RESEAH 2.1 Specimen The specimen was verical canilever column fixed a boom, as shown in figure 1. The base beam of he specimen was srong enough o provide a fixed end for he column above. The column secion was 2mm 2mm wih round corners o avoid sress concenraion of RP shee. The ransverse reinforcemen hoops were 6mm diameer wih spacing of 2mm for all specimens, which were almos equal o he minimum ransverse reinforcemen raio according he Chinese design code of concree srucure (CDCCS 1988) (ρ sv =A sv /bs=.141%). Eigh longiudinal reinforcemen bars wih diameer of 22mm were placed around he secion sides. All specimens were esed under laeral reversal cyclic loading acing a he shear span heigh a wih a push-pull jack while simulaneously subjeced o a consan axial load on he op of he column (see figure 2). The unidirecional RP shee srips were impregnaed wih polyeser resin and

3 wrapped around he column in he shear span heigh wih differen widh b and disance s o provide differen srenghening amoun. The overlap lengh of RP srip was 2mm. All specimens were designed wih srongflexure-weakshear so ha hey would fail in shear o obain shear srengh for he research purpose. The main parameers aken ino accoun in he es are as follows: (1) shear span/deph raio a/h=1.5, 2., 2.5 and 3.; where, a is shear span; h is heigh of secion. Raios a/h=1. and 3. correspond o he lower and upper limi of shear span/deph raio in he shear srengh calculaion of CDCCS (1988); (2) axial force raio n=n/f c bh; where, N is axial force; f c is prism compressive srengh of concree; b is widh of column secion. Two values of n =.15 and.34 were adoped in he specimen design (The values of parameer n in able 1 are acual values of he es). The value n=.34 approximaely correspond o he upper axial load limi in he seismic design of column of CDCCS (1988). 2A f (3) he amoun of RP shee is presened by a parameer λ = = ρ f / f, in b s f which, A = b is area of one RP shee srip; is hickness of RP shee; ρ = 2A /( b s ) is area raio of RP o concree; f is ensile srengh of RP shee; f is ensile srengh of concree, f =.395f.55 cu ; f cu is he cube compressive srengh of concree. The parameer λ provide a oal srengh raio beween RP and concree in one disance of RP srip, so ha he influences of maerial srengh raio f /f can be considered by his parameer including he area raio ρ. The value of λ was beween A f sv yv.39~1.46 in he es. The lower and upper limi value of same parameer λ sv = for ransverse b s f reinforcemen in CDCCS (1988) are.2 and 1.2, where, A sv is area of ransverse reinforcemen hoop in one disance; f yv is ensile srengh of ransversal reinforcemen; s is disance of ransverse reinforcemen hoop. The parameers for all specimens are lised in able 1. The unsrenghened specimen CS2--15 was used for comparison. The seven specimens were divided ino four groups (as shown in able 1): he influence of RP amoun could be obained in he firs group; he influence of shear span/deph raio a/h could be obained by he second, hird and fourh groups; and he influence of axial load raio could be obained beween he second and fourh groups. Two concree srenghs were used in he es and he influence was considered in parameer λ. The maerial properies of reinforcemen bars and RP shee are given in able 2, while he concree cube compressive srengh corresponding o each specimen is given in able 1. The maerial properies of RP shee were provided by he manufacure. 2.2 Measuremen and Tes Procedure Srain gauges were arranged along every RP srip in he expeced failure zone o obain he srain disribuion and developmen of RP shee (as shown in figure 2, he whie shor lines on he black RP srips). The srains of ransverse reinforcemen hoop were also measured by srain gauges. The shear force-displacemen relaion was moniored online during he es by a compuer conrol sysem. The axial load was firs applied and hen mainained consan during he es. The laeral force was applied by laeral displacemen conrolling in drif angles R= /a, here is he laeral displacemen a heigh a. The firs wo laeral reversal loading cycle were applied a he drif angles R=1/5 and 1/25, respecively. Then hree cycle loading for he following every drif angles incremen abou R=1/125 were applied unil o failure. All he columns finally failed due o he crush of concree in compressive zone under he combined acion of shear and compressive sresses, which is called shear-compression failure mode, excep ha specimen CS failed in flexure due o over shear srenghening. The specimen CS is aken as an example

4 o describe he es procedure in he following. The axial load was 186kN. No cracks were developed afer one laeral loading cycle a drif angles R=1/5. As he drif angles increased o R=1/25, flexural cracks and diagonal shear cracks were observed approximaely a he same ime. A he nex drif angle R=/125, more shear cracks were developed and he srain developmen of RP shee began o propagae more quickly due o he shear crack lengh exended across he srips. Afer hree reversal loading cycles a R=1/8, he shear cracks exending o he compression zone a he boom secion of column, some RP shee srips were found debonding from he concree surface and he ransversal reinforcemen hoop yielded. Alhough debonding occurred, he RP shee srips could coninue o susain sress increases due o he enough overlap. One of he RP shee srips in failure zone was fracured a he firs loading cycle of R=1/5. A he nex loading sep R=1/33, all RP shee srips wihin he shear span were fracured, some shear cracks widh exceeded 5mm and he concree cover peeled off, which resuled in an abrup load decreasing. When approaching failure, one of he diagonal shear cracks, called criical shear crack, became obviously wider and longer han ohers. The final shear failure was aking place along his criical shear crack. The oher columns possessed almos he same behavior as ha of specimen CS2-1-15: i.e. flexure and shear cracking, developmen of shear cracks, debonding of RP shee, fracure of RP shee and hen abrup capaciy decreasing. Figure 3 shows he crack paern near failure of hree ypical specimens. And figure 4 shows he laeral load versus drif angle hyseresis loop of hree ypical specimens. Table 3 presens he es load resuls a shear cracking, debonding and fracure of RP shee srips, and he maximum load as well as he failure mode for all specimens. The skeleon curves of laeral load versus drif angle relaionship of CS and CS are shown in figure 5, in which he curve marked wih represens ha of unsrenghened specimen CS I is eviden from figure 5 and able 3 ha he shear srengh of he srenghened columns is obviously increased. 2.3 Srain Developmen in RP Shee The shear conribuion provided by he wrapped RP shee was sudied in deail by he srain gauges placed on i. The srain disribuion and developmen of RP shee along he column heigh a he middle of secion widh are shown above abscissa in figure 6, he curve under abscissa in figure 6 is he load-srain relaion of RP shee corresponding o he black poin shown above abscissa. I was observed ha he srain of RP shee was very small before diagonal shear cracks occur and began o increase very quickly afer shear cracking. I can also be seen in figure 6(b) ha he srain of RP shee a he maximum laeral load (he circle poin) did no aain is fracure srain. 2.4 Shear Resisance of RP Shee Toal shear resisance of srenghened column can be expressed by following superposiion formula, = + (1) Toal where, is he shear resisance of par; is he shear resisance of RP shee. Assuming ha he average sress of RP shee across he criical diagonal shear crack is σ and he inclinaion angle of he criical diagonal shear crack is, as shown in figure 7, he shear resisance of RP shee can be expressed as, 2A = σ h coθ = ρ Eε bh coθ (2) s where, ε is he average srain of RP shee cross he criical shear crack, which was obained from RP shee srain gauges a or near he place where he criical shear crack passes hrough. The inclinaion angle of he criical shear crack was measured in he es.

5 Wih ε and θ obained in he es, he shear resisance of RP shee can be deermined from equaion (2). Subracing from he oal shear force Toal in equaion (1), he shear resisance provided by par of srenghened column = can be obained. In figure 5, he curves marked wih are Toal -R relaions obained by Subracing experimenal -R relaion from experimenal Toal -R relaion. I is shown ha good agreemen beween he relaions of -R and -R exiss. The maximum shear srenghs of -R and -R relaions are almos he same, while he siffness of -R relaion is a lier larger han ha of -R relaion due o he confinemen of RP shee. I mus be noiced ha reaches is maximum earlier han ha of Toal, which was clearly shown in figure 8. Based on above analysis, i is reasonable o use following superposiion formula o deermine he oal shear resisance of srenghened column a drif angle R, = + (3) Toal, R,R where,,r is he shear resisance of unsrenghened column a drif angle R;,R is he shear conribuion of RP shee a he same drif angle R. The comprehensive illusraion of equaion (3) is shown as figure 8. I could be undersood from figure 8 ha he RP shee provides more shear resisance afer decreasing over is maximum capaciy,max. This is he reason ha RP shee srain significanly increases when he par began o fail. Using equaion (2) and parameer, he shear resisance of RP shee,r corresponding o he drif angle a he maximum oal shear srengh max (see figure 8) can be wrien as,,r, R ρ Eε bh coθ = ν λ C F f bh,r = (4) where, ν is called srengh developmen coefficien of RP shee, expressed as ν Eε coθ / = f. Knowing he elasic modulus E and srengh f of RP shee, he coefficien ν depends on RP shee average srain ε and criical shear crack inclinaion angle a he oal maximum shear capaciy max. Based on he resuls of ε and obained in he es, he value of coefficien ν are shown in able 4 and figure 9 and figure 1. I is shown in figure 9 ha he coefficien ν remains consan when he parameer value of RP shee amoun changed from.39 o 1.46, so i is reasonable o consider ha he facor has less effec on he value of ν. On he oher hand, he value of ν was shown o increase wih he shear-span/deph raio a/h and decreases wih he axial load raio n=n/f c bh, as shown in figure 1. The above resuls could be explained by arch-russ shear ransfer mechanism for members (ASCE-ACI Commiee 445, 1998). The shear force resised by RP shee is mainly ransferred by russ mechanism jus like ha of ransverse reinforcemen, as shown in figure 7, bu i dose no aain is fracure srengh a he maximum shear srengh of column, while he ransverse reinforcemen is usually yield. Thus, larger shear deformaion in russ mechanism will resul in larger sress of RP shee, which induces a larger shear conribuion for RP shee. For he specimen wih larger shear-span/deph raio a/h, shear force is mainly ransferred hrough russ mechanism, which resul in a larger srain of RP shee. The axial load is mainly ransferred by arch acion and larger axial load

6 resuls in maximum shear srengh being aained in smaller russ shear deformaion, hus resul in less srain developmen for RP shee. The amoun of RP has almos no influence on he shear ransfer mechanism, so he parameer λ has less influence on he srengh developmen coefficien ν of RP shee. Based on he analysis of es resuls, an experimenal relaionship of coefficien ν wih he parameers a/h and n is given as below, ν = n +.176a h (5) / Alhough he above suggesion for coefficien ν is only based on he limied six srenghened specimens es resuls of his paper, i has a reasonable predicion of coefficien ν because he parameers were chosen a heir lower and upper limi. A beer predicion of coefficien ν could be obained if more es resuls were available. Bu few researches was conduced in he same manner as his paper. 3 CALCULATION OF SHEAR STRENGTH Alhough he shear resisance conribuion of RP shee can be obained by equaion (4) by knowing he coefficien ν ΧΦ, he shear srengh max of srenghened column is sill difficul o deermine because he shear resisance of par is in he declined par of -R relaion a he deformaion corresponding o max. To obain a simple calculaed mehod using he shear srengh,max of par, he oal shear capaciy max is rewrien as, max,max + = (5) where, represens he shear conribuion of RP shee, which is obained by subscribing he shear srengh,max of par from he shear srengh max of srenghened column, i.e. = max,max. The es resul of,max was obained from he maximum value in he curve of -R relaion, same as,max in figure 8. Defining a coefficien α = /,R, in equaion (5) can be expressed as,,r = α = α ν λ f bh = ν λ f bh (6) Where, ν is called shear srenghening coefficien of RP shee, ν=α ν. Wih he es resul of max,,max and,r deermined as saed previously, he coefficien α and he shear srenghening coefficien can be obained, as shown in able 4 and figures 11. I is shown in figure 11 ha he value of α decreases wih increase of parameer λ. The experimenal α -λ relaion based on he es resuls is given as, α = (7) λ Thus, he shear srenghening coefficien of RP shee ν can be obained as, 1.639( n +.176a / h) ν = α ν = (8) λ The comparison of es resuls and equaion (8) is shown in figure 12. I is shown ha equaion (8) has a good agreemen wih he es resuls of his paper and gives a lower bound of he es resuls of Japanese Railway

7 Synheic Technical Research Insiue (1996). To limi he value of less han 1., he value of λ mus no be less han.2 and he shear-span/deph raio a/h mus no be larger han 3. for equaion (8). Alhough srengh developmen coefficien of RP shee ν has less relaion wih he RP amoun parameer λ, he shear srenghening coefficien of RP shee decreases wih increasing λ. This means ha he larger value of λ resul in less srenghening effeciveness. Based on he above analysis, he shear srengh of concree column srenghened wih RP shee can be expressed wih he simple superposiion mehod as follows, = + (9) u The shear srengh of par can be obained direcly from he shear srengh formula of column or using he formula of design code. The shear srengh formula of column in CDCCS (1988) is expressed as follows,.2 Asv = f cbh f yv h +. 7N (1) a / h s The shear conribuion of RP shee can be deermined using equaion (6) and (8). The comparison of es resuls wih equaion (9) is shown in figure 13 and able 5. The resul of equaion (9) shows he lower c bound of es resuls, which gives enough safey for shear design. The larger value of raio u over u is c induced by he safey formula (1). The raio over in able 5 is 1.142, which is a reasonable value on he safe side. From figure 13, i should also be noiced ha he oal shear srengh was barely increased when he oal value (λ +λ sv ) greaer han 2.2, which means ha furher increasing of RP shee will provide no increasing in shear srengh for column when he value of (λ +λ sv ) exceed CONCLUSIONS (1) The shear srengh of column can be effecively increased wih he srenghening of RP shee when ransversal reinforcemen is no enough; (2) The shear resisance of RP shee becomes effecive afer occurrence of diagonal shear cracks, and he shear resisance mechanism of RP shee is almos he same as ha of reinforcemen hoop; (3) From equaion (8), he RP shee shear srenghening coefficien is increased wih shear span/deph raio and decreases wih he quaniy of RP shee and axial load raio; (4) The shear srengh of column srenghened wih RP shee can be expressed by a simple superposiion mehod, in which he shear resisance conribuion of RP shee can be deermined by he RP shee shear srenghening coefficien ν using equaion (8); (5) From he es resuls and analysis, i is known ha larger value of parameer λ resuls in less srenghening effeciveness, and here exis a maximum value of parameer λ for RP shee srenghening. When he value of (λ +λ sv ) exceed 2.2, furher increasing of RP shee will provide no increasing in shear srengh for column. (6) The suggesed shear srengh calculaion mehod for column srenghened wih RP shee has a good agreemen wih he es resuls and enough safey. APPENDIX I. NOTATION A : area of one RP srip a: shear span heigh of column b: widh of column secion b : widh of RP shee srip

8 E : modulus of RP shee f c : prism compressive srengh of concree f : ensile srengh of RP shee f cu : cube compressive srengh of concree f : ensile srengh of concree f yv : yield srengh of seel reinforcemen hoop h: deph of column secion h : effecive deph of column secion N: axial force n: axial load raio R: drif angles incremen of column specimen s: disance of reinforced hoop s : disance of RP shee srip : hickness of RP shee : shear force : shear conribuion of RP shee,r shear conribuion of RP shee a drif angle R max : maximum shear capaciy of srenghened column : shear conribuion of reinforced concree par : shear conribuion of unsrenghened column : shear conribuion provided by par of srenghened column,max : maximum shear capaciy of unsrenghened column : shear conribuion of unsrenghened column a drif angel R,R Toal,R oal shear resisance of srenghened column a drif angle R Toal : oal shear srengh of srenghened column α : shear conribuion coefficien of RP shee : average srain of RP shee cross he criical diagonal shear crack ε λ : parameer represening he raio of RP shee amoun o concree λ sv : parameer represening he raio of ransversal reinforcemen amoun o concree ν : shear srenghening coefficien of RP shee ν : srengh developmen coefficien of RP shee θ : inclined angel of criical diagonal shear crack ρ sv : area raio of ransversal reinforcemen o concree ρ : area raio of RP shee o concree : average sress of RP shee across he criical diagonal shear crack σ APPENDIX II. REFERENCES [1] Saadamanesh, H.; Ehsani, M.R. (1994). Srengh and Duciliy of Concree Columns Exernally Reinforced wih Fiber Composie Sraps. ACI Sruc. J., 91(4), [2] Saadamanesh, H., Ehsani, M.R., Jin, L. (1996). Seismic srenghening of circular bridge pier models wih fiber composies. ACI Sruc. J., 93(6), [3]Saadamanesh, H.; Ehsani, M. R.; Jin, L. (1997). Repair of earhquake-damaged columns wih FRP wraps. ACI Sruc. J., 94(2), [41]Xiao Y. (1997). Seismic Rerofi of Circular Columns Using Prefabricaed Composie Jackeing. J. of Sruc. Engrg., ASCE, 123(1),

9 [5]Purba, B. K., Mufi, A. A. (1999). Invesigaion of he behavior of circular concree columns reinforced wih carbon fiber reinforced polymer (RP) jackes. Canadian J. of Civil Engrg., 26(5), [6]Uji, K. (1992). Improving Shear Capaciy of Exising Reinforced Concree Member by Applying Carbon Fiber Shees. Trans. of Japan Concree Insiue, 14, [7] Sao, K. (1996). Shear Behaviors of Beams Srenghened wih RP Shee. Annu. Proc. of Concree Engrg., 18(2), (in Japanese) [8] Sao, Y. (1996). Sudy on Shear Resisan Mechanics of Beams Srenghened wih RP Shee. Annu. Proc. of Concree Engrg., 18(2), (in Japanese) [9] Suzuki, H. (1998). Shear Behaviors of T Secion Beams and Columns Srenghened wih RP Shee. Annu. Proc. of Concree Engrg., 2(3), (in Japanese) [1]Norris, T., Saadamanesh, H., Ehsani, M.R. (1997). Shear and Flexural Srenghening of R/C Beams wih Carbon fiber reinforced plasic shee. J. of Sruc. Engrg., ASCE, 123(7), [11]Thanasis, C. T. (1998). Shear Srenghening of Reinforced Beams Using Epoxy-Bonded FRP Composie. ACI Sruc. J. 95(2), [12]Michael, J. C. (1995). Shear Srenghening of Reinforced Concree Beams Using Exernally Applied Composie Fabrics. ACI Sruc. J. 92(3), [13]Malek, A., M.; Saadamanesh, H. (1998). Ulimae Shear Capaciy of Reinforced Concree Beams Srenghened wih Web-Bonded Fiber-Reinforced Plasic Plaes. ACI Sruc. J. 95(4), [14]Japanese Railway Synheic Technical Research Insiue (1996). Series Research Repor in he Guideline for Seismic Srenghening Design and Consrucion of Column Srenghened wih RP Shee [15]Sandard of People s Republic of China (1988). Design Code of Concree Srucure (GBJ1-89). China Archiecure & Building Press [16]ASCE-ACI Commiee 445 on Shear and orsion, (1998). Recen Approaches o Shear Design of Srucural Concree. J. of Sruc. Engrg, ASCE, 124(12), ST Figures Figure capions Figure 1 Specimen, secion and reinforcemen (Uni: mm) Figure 2 RP shee wraps, loading and srain gauges on RP shee Figure 3 Cracking paern Figure 4 Laeral load versus drif angle hyseresis Loops Figure 5 Skeleon curves of laeral load versus drif angle relaionship Figure 6 Srain disribuion and developmen of RP shee Figure 7 Shear ransfer mechanism of RP shee Figure 8 Shear resisance versus drif angle relaionships of RP and par Figure 9 ν - λ relaion Figure 1 ν - a/h relaion Figure 11 Coefficien α Figure 12 Coefficien ν Figure 13 Comparison of oal shear srengh

10 A A φ6-2 2 A-A 2 11 Figure 1 Specimen, secion and reinforcemen (Uni: mm) s a b Figure 2 RP shee wraps, loading and srain gauges on RP shee CS2--15 CS CS Figure 3 Cracking paern

11 /f bh 1.5 max =147.4k /f bh 1.5 max =177.5kN 2./f bh max =171.k R( CS R( CS R( 3 6 CS Figure 4 Laeral load versus drif angle hyseresis Loops Toal /f bh /f bh R R -1 CS CS Figure 5 Skeleon curves of laeral load versus drif angle relaionship 3 R=1/25 R=1/125 R=1/8 R=1/5( max ) -ε relaion Heigh(mm) 3 R=1/125 R=1/5( max ) -ε relaion Heigh(mm) R=1/9 R=1/ ε (1 3 µε) ε (1 3 µε) /(f bh ) /(f bh ) (a) CS (b) CS Figure 6 Srain disribuion and developmen of RP shee

12 h coθ 32 max Toal -R relaion, R h -R relaion θ s Figure 7 Shear ransfer mechanism of RP shee,max, 32 Figure 8Shear resisance versus drif ngle relaionships of RP and par ν λ=2,n=.15(+) λ=2,n=.15(-) λ Figure 9 ν - λ relaion ν n=.13 n=.16 n=.34 n=.13 n=.16 n= Figure 1 ν - a/h relaion a/h

13 α 1. Push Pull λ Figure 11 Coefficien α ν Reference 14 (n=.7, a/h=2.25) This es (n=.13, a/h=2) Eq. (8)(n=.7, a/h=2.25) Eq. (8)(n=.13, a/h=2) λ Figure 12 Coefficien ν /f bh This es This es(n=.13, a/h=2) Reference14 Eq.(9)(n=.7, a/h=2.25) Eq.(9)(n=.13, a/h=2) λ sv +λ Figure 13 Comparison of oal shear srengh

14 ST Tables No. of Columns Table 1:Specimen s parameers RP Grou f cu (MPa) a/h (b s ) CS2--15 I CS I, I CS II CS I, III F.W..16 CS III F.W..16 CS II CS I Noe, f cu : Cube srengh of concree; F.W.: Fully wrapped. s h e e n Seel bars RP Shee Table 2 Maerial Properies Yield Elasic Tensile Diameer Area Srengh (mm) (mm 2 ) f u (MPa) f y (MPa) E s (MPa) Thickness Tensile Srengh Elasic Modules (mm) f S (MPa) E S (MPa) M o d u l e s

15 No. of Columns Shear Crack load (kn) Table 3 Tes Resuls RP shee debonding load (kn) RP shee fracure load (kn) Max. load (kn) Failure mode CS Shear CS Shear CS Shear CS * Flexure CS * Shear CS Shear CS Shear Noe, *: Can observe Table 4 Shear Resisan Conribuion of RP Shee Specimen λ,r (kn) (kn) ν α CS CS CS CS CS CS Noe: + push; - pull

16 Table 5 Comparison of Calculaion and Tes Resuls Uni: kn Specimen Tes Resuls u c Calculaed Resuls c c u CS CS CS CS CS CS CS c Average of / Sandard deviaion of c / ariaion Coefficien