SHEAR STRENGTHENING OF RC BEAMS WITH NSM CFRP LAMINATES: EXPERIMENTAL RESEARCH AND ANALYTICAL FORMULATION. S. J. E. Dias 1 and J. A. O.

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1 SHEAR STRENGTHENING OF RC BEAMS WITH NSM CFRP LAMINATES: EXPERIMENTAL RESEARCH AND ANALYTICAL FORMULATION S. J. E. Dia 1 and J. A. O. Barro 2 1 Aitant Pro., ISISE, Dep. o Civil Eng., Univ. o Minho, Azurém, Guimarãe, Portugal 2 Full Pro., ISISE, Dep. o Civil Eng., Univ. o Minho, Azurém, Guimarãe, Portugal ABSTRACT The eectivene o the NSM technique with CFRP laminate or the hear trengthening o RC beam with a certain percentage o teel tirrup wa aeed by an extenive experimental reearch. In thi context, the inluence o the ollowing parameter wa invetigated: concrete trength; percentage o exiting teel tirrup; percentage and inclination o the CFRP laminate; exitence o crack when the RC beam are hear trengthened with NSM CFRP laminate. The reult how that the higher i the concrete trength cla the larger i the eectivene o the NSM technique. The eectivene o the CFRP laminate wa higher in the beam with the lower percentage o teel tirrup. Inclined laminate were more eective than vertical laminate and the hear reitance o the beam ha increaed with the percentage o laminate. Pre-cracked RC beam hear trengthened with NSM CFRP laminate have preented a load carrying capacity imilar to that o the homologou beam that were uncracked when trengthened. Taking the reult obtained in the experimental reearch, an lytical ormulation to predict the contribution o the poible ditinct NSM hear trengthening coniguration or the hear reitance o RC beam wa developed. Thi lytical ormulation i preented and it predictive perormance i aeed. KEYWORDS: CFRP laminate, NSM technique, Shear trengthening, RC beam, Experimental reult, Analytical ormulation 1. INTRODUCTION Uing advanced compoite material like carbon iber reinorced polymer (CFRP), competitive tructural trengthening olution can be developed due to the high trength-to-weight ratio, high durability (non corrodible), electromagnetic neutrality, eae o handling, rapid execution with low labor, and practically unlimited availability in ize, geometry and dimenion o thee material [1-3]. In conequence, the trengthening technique baed on the ue o CFRP compoite material have been intenively invetigated and applied in cae where they contitute olution that compete with the traditional trengthening technique applied in reinorced concrete (RC) tructure. 1

2 A RC beam need to be hear trengthened when i deiciently reinorced in hear, become ubjected to higher load, or when it hear capacity all below it lexural capacity ater have been ubmitted to a lexural trengthening intervention. The hear ailure mode o a RC element hould be avoided ince it i brittle and unpredictable. Near urace mounted (NSM) with CFRP laminate i a technique that can be ued or the hear trengthening o RC beam [4-6]. Thi technique involve the intallation o narrow trip o CFRP laminate, o rectangular cro ection, into thin lit open on the concrete cover o the lateral ace o the beam. The laminate are poitioned orthogonally to the beam axi, or a orthogonal a poible to the predicted direction o the hear ailure crack, or to the already exiting hear crack. Experimental reearch ha demontrated that the NSM technique provide higher trengthening eectivene than the Externally Bonded Reinorcing (EBR) technique with CFRP [4, 7]. Thi act i derived rom the larger ratio between the CFRP-concrete bond perimeter and the cro ectional area o the CFRP element in cae o NSM, and i alo caued by the coninement provided by the urrounding concrete to the CFRP laminate [7, 8]. A urther advantage o the NSM technique i it ability to igniicantly reduce the probability o harm reulting rom act o vandalim, mechanical damage and aging eect. When NSM i ued, the appearance o a tructural trengthened element i practically unaected by the trengthening intervention. To appraie the perormance o the application o NSM CFRP laminate or the hear trengthening o RC beam having a certain percentage o exiting teel tirrup, an extenive experimental reearch wa carried out. Four erie o tet with T cro ection RC beam were executed with the purpoe o evaluating the inluence o the ollowing parameter on the eectivene o the NSM hear trengthening technique: concrete trength, percentage o exiting teel tirrup, percentage and orientation o the CFRP laminate. The trengthening intervention oten involve concrete element already cracked. To evaluate the inluence, on the trengthening eectivene, o already exiting crack when a beam i hear trengthened with NSM CFRP laminate, ome o the RC beam were pre-cracked prior to their trengthening. A detailed decription o the carried out experimental reearch, and a dicuion o the obtained reult are done in the preent paper. Conidering the reult obtained in the experimental reearch, an lytical ormulation to predict the contribution o the NSM CFRP laminate or the hear capacity o a RC beam wa developed. The lytical ormulation i decribed and it predictive perormance i aeed in thi paper. 2. EXPERIMENTAL PROGRAM 2.1. Tet erie The experimental program i compoed o our erie o RC beam (erie A, B, C and D). Fig. 1 repreent the T cro ection geometry and reinorcement detailment or each erie, a well a the longitudinal geometry, loading coniguration and upport condition. The general inormation o the teted erie o beam i repreented in Table 1. 2

3 The adopted reinorcement ytem were deigned to aure hear ailure mode or all the teted beam. To avoid hear ailure in the L r beam pan (Fig. 1), in thi pan wa applied teel tirrup o 6 mm diameter paced at 75 mm (φ6@75mm) in erie A, B and C, and teel tirrup o 8 mm diameter paced at 80 mm (φ8@80mm) in erie D. For each erie, the dierence between the teted beam are retricted to the hear reinorcement ytem applied in the L i beam pan. A chematically repreented in Fig. 1, the laminate were ditributed along the AB line, where A repreent the beam upport at it tet ide and B i obtained auming load degradation at 45º. A general lyi o the data o Table 1 how that the teted beam had percentage o longitudinal tenile teel bar (ρ l ) around 3% and had percentage o teel tirrup (ρ w ) ranging between 0.10% and 0.17%. In term o concrete, three type were baically ued: concrete o low trength ( = 18.6 MPa, where i the average concrete compreive trength at the age o the beam tet), concrete o medium trength ( = 31.1/39.7 MPa) and concrete o high trength ( = 59.4 MPa). Three orientation o the laminate with repect to the beam axi were teted, Fig. 1, (θ = 90º - vertical laminate; θ = 45º - laminate at 45º; θ = 60º - laminate at 60º), and the level o the CFRP percentage (ρ ) lyzed ranged between 0.06% and 0.19%. The monitored beam pan (L i ) wa 2.5 time the eective depth o the beam (L i /d=2.5) or erie A, B and C and 3.3 time the eective depth o the beam (L i /d=3.3) or erie D. In erie A ( = 31.1 MPa) a particular emphai wa given to the inluence o the percentage (ρ ) and orientation o the laminate (θ ) on the hear trengthening o RC beam that have a certain percentage o teel tirrup. In act, exiting RC beam requiring hear trengthening intervention oten have a certain percentage o teel tirrup. Three inclination o laminate were teted (45º, 60º and 90º) and, or each inclination, three level o the CFRP percentage (ρ = 0.06%; ρ = 0.09% to 0.10%; ρ = 0.13% to 0.16%) were applied in RC beam with a percentage o teel tirrup o 0.10% (ρ w = 0.10%). The highet percentage o laminate wa deigned to provide a maximum load imilar to the one o the RC reerence beam (without CFRP) reinorced with the highet reinorcement ratio o teel tirrup (ρ w = 0.24%). For thi purpoe a CFRP laminate i aumed a working like a teel tirrup, but intead o conidering the yield tre o the material, a tre in the laminate correponding to a train o 0.5% wa adopted. Thi train limit i a compromie between the maximum value recommended by ACI [1] or the EBR (0.4%), and the 0.59% value obtained in pullout bending tet with NSM trengthening technique uing CFRP laminate [9]. For the lowet and intermediate percentage o laminate, the pacing o laminate or each θ (90º, 60º and 45º) wa obtained with the purpoe o providing imilar contribution or the hear reitance. Serie B ( = 39.7 MPa) had the intent o expanding the range o the CFRP percentage teted in erie A (ρ = 0.07% to 0.08%; ρ = 0.11% to 0.13%; ρ = 0.16% to 0.19%) and to evaluate the eect o the percentage o teel tirrup (ρ w ) in the eectivene o the NSM technique with CFRP laminate. For thi purpoe, everal CFRP coniguration were applied in RC beam with dierent ρ w : 0.10% and 0.17%. For thi erie o beam, and uing the criterion above 3

4 mentioned or erie A, the highet percentage o laminate wa deigned to provide a maximum load imilar to the one o the RC reerence beam (without CFRP) reinorced with the highet reinorcement ratio o teel tirrup (ρ w = 0.28%). For the lowet and intermediate percentage o laminate, the pacing o laminate or each θ (90º, 60º and 45º) wa obtained with the purpoe o providing imilar contribution or the hear reitance. Serie C wa carried out to appraie the poibility o the application o NSM CFRP laminate or the hear trengthening o low trength concrete beam having a certain percentage o exiting teel tirrup. The average concrete compreive trength at the age o the beam tet wa 18.6 MPa. Some o the CFRP coniguration adopted in the beam o erie B were alo applied in beam o erie C (the only dierence between the beam o erie B and C wa the concrete trength). In act, in erie C ive NSM hear trengthening coniguration (three CFRP orientation and two level o CFRP percentage) were applied in RC beam with a teel tirrup percentage (ρ w ) o 0.10% and 0.17%. The eectivene o NSM technique with CFRP laminate or the hear trengthening o high-trength concrete beam with a certain percentage o exiting teel tirrup wa aeed in the tet o the beam o erie D. Some o the CFRP coniguration adopted in the beam o erie B and C were alo applied in beam o erie D (beam with ρ w =0.10% and ρ w =0.16%) that had an average concrete compreive trength o 59.4 MPa at the age o the beam tet. To evaluate the inluence, on the trengthening eectivene, o already exiting crack when a beam i hear trengthened with NSM CFRP laminate, in erie D ome o the RC beam were pre-cracked prior to their trengthening. The CFRP hear trengthening arrangement adopted in thi experimental reearch are indicated in Table 2. A an example, in Fig. 2 are repreented three CFRP coniguration (beam 2S-10LV-B, 2S-10LI45-B and 2S-9LI60-B) adopted in the beam o erie B with ρ w = 0.10% (2S-R-B i the reerence beam without CFRP). In each erie, and or each percentage o teel tirrup, one beam without CFRP wa teted (ee Table 2). CFK 150/2000 S&P laminate were ued in the preent experimental reearch. In erie A the laminate had a croection o mm 2, while in the other erie the laminate had a cro-ection o mm 2. For each erie o the teted beam, the average value o the young modulu, E, and the train at ailure, ε u, o the adopted laminate are indicated in Table 3. Uing a diamond cutter, lit o about 4-5 mm width and mm depth were opened on the concrete cover (o about 22 mm thickne) o the lateral ace o the beam web, according to the pre-deined arrangement or the laminate (the laminate were not anchored to the beam lange; they were retricted to the beam web). The MBrace Rein 220 [10] epoxy adheive wa ued to bond the laminate to the concrete. 4

5 The three point beam bending tet (Fig. 1) were carried out uing a ervo cloed-loop control equipment, taking the ignal read in the diplacement tranducer (LVDT), placed at the loaded ection, to control the tet at a delection rate o 0.01 mm/econd Analyi o the experimental reult General behavior o a RC beam hear trengthening with NSM CFRP laminate Fig. 3 how the typical relationhip between the applied load and the delection o the loaded ection, F-u, or a RC beam hear trengthened with NSM CFRP laminate and or the correponding reerence beam. Up to the ormation o the hear crack in the reerence beam both beam have quite imilar F-u relationhip. At thi delection limit the reerence beam preented an appreciate decreae in the tine, which did not occur in the trengthened beam. In thi beam a igniicant decreae in the tine only occur or a load level much higher than the one correponding to the hear crack ormation in the reerence beam. Thi reveal that the CFRP laminate bridging the urace o the hear crack oer reitance, mainly to crack opening, reulting a maller degradation o the hear tre traner between the ace o the crack due to aggregate interlock eect. Thereore, or delection above the delection correponding to the ormation o the hear crack in the reerence beam, the tine o the trengthened beam i much higher than the tine o the reerence beam. Thu, the CFRP hear trengthening coniguration provided an increae in term o tine and in term o maximum load (F max ). The crack opening reiting mechanim provided by the laminate bridging the hear crack alo contribute to increae the load at which tirrup enter in their platic phae. In general the value o the delection at the loaded ection in correpondence to F max o the trengthened beam ( u CFRP F max ) were higher re F max than thoe occurred in the correponding reerence beam ( u ) The eect o pre-crack Fig. 4 how the F-u relationhip or the NSM beam with ρ w = 0.10%, where the only dierence between them i retricted to the preence, or not, o pre-crack when the trengthening intervention i applied (the F-u o the reerence beam 3S-R-D i alo included in Fig. 4). The main dierence between the behavior o trengthened beam with or without pre-crack reide in an expected lo o initial tine in the pre-cracked pecimen (up to the maximum load applied in the pre-cracking tet that wa about 240 kn). In the beam with pre-crack the mobilization o the CFRP laminate tarted jut ater the opening proce o the pre-crack, while the mobilization o the CFRP laminate in the non pre-cracked beam only occurred when the hear crack ha ormed. However, the pre-cracking did not aect the eicacy o the NSM hear trengthening technique in term o load carrying capacity and ultimate delection. 5

6 Failure mode o the NSM hear trengthened beam with CFRP laminate The global lyi o the ailure mode o the teted beam with CFRP laminate indicate that the eicacy o NSM technique or the hear trengthening o RC beam increae with the concrete trength. Three type o ailure mode have eentially occurred in the trengthened beam. In the irt, which occurred eentially in the beam o erie A, B and C, the laminate ailed by concrete racture, having the concrete become adhered to the detached laminate (ee Fig. 5a). In the beam with the highet percentage o CFRP the critical ailure mode i governed by a group eect o the laminate that conit on the premature detachment o a concrete layer that include the laminate (ee Fig. 5b and 5c). Thi evidence indicate that the eicacy o NSM hear trengthening i limited by laminate pacing, a a recent lytical model ha alo conirmed [11]. The econd ailure mode i characterized by the liding o CFRP laminate (interace between the CFRP and the adheive) croing the hear ailure crack. Thi ailure mode wa oberved in ome beam o erie D (ee Fig. 5d). In thi erie alo occurred the third ailure mode: the rupture o the CFRP (ee Fig. 5e). The higher concrete trength cla o the beam o erie D can jutiy thee two lat type o ailure mode, ince concrete wa not o prone to racture during the debond proce o the laminate bridging the hear ailure crack Contribution o the CFRP or the hear reitance o the beam (V ) and evaluation o the eective train o the CFRP (ε e ) The inluence on the eectivene o the NSM hear trengthening technique with CFRP laminate o parameter like concrete trength cla, percentage o exiting teel tirrup, percentage and orientation o the laminate will be aeed in term o the contribution o the laminate or the hear reitance o the beam (V ). The eective train in the laminate (ε e ), which correpond to the level o mobilization o the CFRP when the trengthened RC beam reache it hear capacity, wa alo regitered and wa ued a an indicator o the NSM trengthening eectivene. The hear reitance o a trengthened beam (V t ) wa obtained conidering the value o F max (all o the teted beam ailed by hear) and taking into account the orce equilibrium equation: V t = 0.6 F max or the beam o erie A, B and C; V t = 0.5 F max or the beam o erie D. For each o the 49 hear trengthened beam teted in the preent experimental reearch, Table 3 preent the value o F max and V t. The hear capacity contributed by the CFRP (V ) wa obtained by ubtracting the hear reitance o the reerence beam (V re. ) rom the hear reitance o the trengthened beam (V t ): V t = V re. + V (1) In thi approach it i aumed that the teel tirrup give the ame contribution in the trengthened and in the correponding reerence beam. Thi aumption did not occur in ome o the teted beam, ince when thee 6

7 trengthened beam were compared to the correponding reerence beam it wa oberved a dierent level o mobilization o the teel tirrup. Fig. 6 preent two trengthened beam o erie A (2S-5LI45-A and 2S-8LI45-A) where the contribution o teel tirrup or the hear reitance o the beam wa le than the one occurred in the reerence beam (2S-R-A). In the reerence beam 2S-R-A two teel tirrup (tirrup 1, cloet to the upport, and tirrup 2 cloet to the loaded ection - ee Fig. 6) croed the hear ailure crack in the web o the beam, and both contributed or the hear orce traner between the ace o thi crack. In beam 2S-5LI45-A and 2S-8LI45-A the diagonal hear ailure crack wa only croed by one teel tirrup (tirrup 1 in Fig. 6) in the web o the beam. In beam 2S-5LI45-A the tirrup 2 wa intercepted ater the above mentioned crack ha progreed through the tranition zone between the web and the lange (Fig. 6). Thereore, it i reaonable to aume that the level o mobilization o the tirrup 2 when 2S- 5LI45-A beam ha reached it maximum capacity wa lower than the level o mobilization o the tirrup 2 on the reerence beam at it ailure. In thi repect, the beam 2S-8LI45-A had a behavior imilar to the beam 2S-5LI45-A. However, in thi beam the ditance between the ection when the hear crack intercepted the web/lange tranition zone and the tirrup 2 wa higher than in the cae o beam 2S-5LI45-A. Conidering thee evidence it i reaonable to admit that the contribution o the tirrup 2 in the beam 2S-8LI45-A or the reitance to the hear ailure crack wa marginal. The occurrence jut decribed in the beam 2S-5LI45-A wa alo oberved in the beam 2S-3LV-A, 2S-5LV-A, 2S-8LV-A, 2S-5LI60-A, 2S- 7LI60-A, 2S-7LV-B, 2S-10LV-B, 2S-7LV-C, 3S-10LV-D, 3S-5LI45-D, 3S-9LI45-D, 3S-5LI60-D, 3S-8LI60-D and 3S-5LI45F2-D. The occurrence decribed in the beam 2S-8LI45-A wa alo oberved in the beam 2S-3LI45-A and 3S- 6LV-D. In order to take into account the dierent level o mobilization o the teel tirrup in the trengthened and in the correponding reerence beam it wa aumed or the cae o beam 2S-5LI45-A that the tirrup 2 ha contributed 50% o it ull capacity (yielded). For the cae o the beam 2S-8LI45-A it wa aumed that the tirrup 2 did not contribute or the reitance o the hear ailure crack. The 50% o the ull contribution o a teel tirrup or the hear reitance i obtained by the ollowing equation: V = 0.5 A (2) w ym where Aw i the cro ectional area o the two arm o a teel tirrup, and ym i the average value o it tre at yield initiation. Table 3 preent the value o the contribution o the CFRP laminate or the hear reitance o the teted beam, V, conidering the equation (1), which i deignated a cenario A, and the value o V auming the inerior contribution o teel tirrup in ome trengthened beam, in agreement with the trategy decribed previouly, that correpond to the cenario deignated by B. The orce reulting rom the tenile tre in the CFRP laminate croing the hear ailure crack ( F ) i deined a, 7

8 F = n A (3) v e where e i the eective tre in the laminate and i obtained multiplying the elatic modulu o the CFRP, E, by the eective train, ε e. In equation (3) A v i the cro ectional area o a CFRP tirrup that i ormed by two lateral laminate: A = 2 a b (4) v where a and b are the dimenion o the laminate cro ection. The number o laminate croed by the hear ailure crack (n ) i obtained by the equation (5) where h w i the web depth o the beam (equal to the length o vertical laminate), α i the orientation o the hear ailure crack, the beam axi, and i the pacing o laminate (ee Fig. 7). The vertical projection o the orce n θ i the inclination o the CFRP laminate with repect to ( cot g α + cot g θ ) hw = (5) F i the contribution o the CFRP to the hear reitance o the beam (V ): V = F in θ (6) Conidering the equation (3) to (6), the value o V can be obtained rom: And, conequently: ( cot g α + cot g θ ) inθ A v V = hw ε e E (7) ( ) cot g α + cot g θ inθ A v ε e = V h w E (8) Adopting the value o V aociated to the above mentioned cenario B and conidering or the inclination o the hear ailure crack an angle o 45º ( α =45º), it wa obtained, or each NSM beam, the value o the eective train o the CFRP (ε e ) indicated in the lat column o the Table Inluence o the concrete trength on the NSM trengthening eectivene According to Table 4, ive arrangement (olution 1 to 5) o NSM CFRP laminate were ued in RC beam that were manuactured with dierent concrete compreive trength ( ) at the age o beam tet: 39.7 MPa (erie B), 18.6 MPa (erie C), and 59.4 MPa (erie D). Four o thee coniguration (olution 2 to 5) were applied in RC beam with a percentage o teel tirrup (ρ w ) o 0.10% (erie B, C and D) and in RC beam with ρ w = 0.16% (erie D) or ρ w = 0.17% (erie B and C). For thee beam the value o the hear capacity contributed by the CFRP (V ) according to the 8

9 cenario B are repreented graphically in Fig. 8, being viible the increae o the NSM eectivene with the increae o the concrete trength. According to the value o Fig. 8, the average value o the V or NSM arrangement adopted in beam o erie B ( = 39.7 MPa), C ( = 18.6 MPa) and D ( = 59.4 MPa) wa 54.2 kn, 35.4 kn and 97.0 kn, repectively. Thereore, the average value o V obtained in erie D and B wa, repectively, 1.5 and 2.7 time the average value o V o erie C. Fig. 8 alo how the tendency line or the diagram V v deined conidering the average value o V above mentioned or the three erie o beam. The average value o the CFRP eective train (ε e obtained rom equation (8), ee Table 3) or the trengthening coniguration o the Table 4 wa 5.6, 3.6 and 9.8, repectively, or erie B, C and D. The reult howed that the hear trengthening eectivene o the NSM technique increae with the concrete trength o the beam to trengthen. Thi tendency i revealed on the load carrying capacity o the beam and on the eective train in the CFRP laminate. However, rom the obtained reult it can be concluded that the NSM technique i till eective or the hear trengthening o RC beam o an average concrete compreive trength o 18.6 MPa at the age o the beam tet, which can be conidered a the lowet concrete trength cla or tructural purpoe Inluence o the percentage o teel tirrup on the NSM trengthening eectivene To etimate the inluence o the percentage o exiting teel tirrup in the eectivene o the NSM hear trengthening technique uing CFRP laminate, iteen arrangement o NSM CFRP laminate (ee Table 5) were applied in RC beam with ρ w = 0.10% (erie B, C and D) and in beam with ρ w = 0.16% (erie D) or ρ w = 0.17% (erie B and C). For thee beam the value o the hear capacity contributed by the CFRP (V ) according to the cenario B are repreented graphically in Fig. 9, being viible that the amount o exiting teel tirrup play a very important role on the eectivene o the NSM hear trengthening technique with CFRP laminate. In act, the eectivene o the CFRP wa higher in the beam with the lower percentage o teel tirrup lyed (ρ w = 0.10%), regardle the concrete trength cla o the teted beam. However, the level o the inluence o the percentage o exiting teel tirrup eem to be a larger a maller i the concrete trength. In Fig. 9 the parameter R repreent, or each type o concrete, the ratio between the average value o V obtained in the beam with the highet percentage o tirrup and the average value o V obtained in the beam with the lowet percentage o tirrup (the value regarding the olution 1 and 7 were excluded or thi lyi). The value o R or the beam o erie B, C and D wa, repectively, 0.82, 0.75 and 0.92, which conirm the aorementioned tendency between exiting teel tirrup and concrete trength. In addition to the three point or the three type o concrete teted it wa introduced the trend line or the variation o the parameter R with. 9

10 The average value o the CFRP eective train (ε e - ee Table 3) or the trengthening coniguration o Table 5 correponding to the RC beam with ρ w = 0.10% wa 5.9, 4.1 and 10.6, repectively, or erie B, C and D. The average value o ε e or the trengthening coniguration o Table 5 correponding to the RC beam with ρ w = 0.16% (erie D) and ρ w = 0.17% (erie B and C) wa 4.9, 3.1 and 9.7, repectively, or erie B, C and D. Thee number conirm the decreae o ε e with the increae o the percentage o exiting teel tirrup o the beam to trengthen Inluence o percentage and orientation o the CFRP laminate on the NSM trengthening eectivene According to Fig. 10a), in general or each erie o teted beam an increae o the percentage o CFRP led to an increae o the beam hear reitance. However, it wa veriied (Fig. 10b) a tendency to the decreae o the level o the eectivene o the CFRP with the increae o the percentage o the CFRP. In all the teted erie o beam it wa veriied that, regardle the percentage o CFRP, the percentage o teel tirrup, and the concrete compreive trength, inclined laminate were more eective than vertical laminate in term o increaing the tine, the maximum load, the deormation at ailure, and the level o mobilization o the CFRP at ailure o the beam. Thi i jutiied by the orientation o the hear ailure crack that had a tendency to be almot orthogonal to the inclined laminate (Fig. 11). Furthermore, or vertical laminate the total reiting bond length o the CFRP i lower than that o wa oberved or the cae o inclined laminate. The relationhip between the eective train ε e (Table 3) and the tine o the CFRP (E ρ ) with repect to the concrete reitance (in term o ) i preented in Fig. 12, where it i poible to ee the better perormance o the inclined laminate. The eective train o the CFRP laminate decreae with the increae o the value o E ρ ( ) 2 3. Thi tendency wa more pronounced or the cae o inclined laminate. 3. ANALYTICAL FORMULATION 3.1. Strategy or the development o the lytical ormulation The contribution o the NSM CFRP laminate or the hear capacity o a RC beam, identiied by V, can be obtained uing the equation (7). Thi equation i imilar to that or teel hear reinorcement, but intead o the train at yield initiation o the teel tirrup, the concept o eective train in the laminate (ε e ) i adopted. Baed on the data derived rom the experimental program decribed in thi paper, the equation in order to obtain the value o the parameter ε e or the poible ditinct NSM hear trengthening coniguration wa aeed by adopting the ollowing trategy: 10

11 i) or each inclination o the CFRP (θ ) that wa invetigated in the experimental program (45º, 60º and 90º) it wa 2 3 deined the equation that relate ε e with the parameter ( ρ E ρ ) ( ) E +. Thu, according the experimental reult, our parameter with high inluence on the behavior o a RC beam hear trengthening with NSM CFRP laminate were conidered in thi lytical ormulation: the percentage (ρ ) and the orientation (θ ) o the CFRP laminate; the concrete trength in term o the average value o the concrete compreive trength in cylinder ( ); and the percentage o teel tirrup (ρ w ). Each o thee equation correpond to the bet it o the value o ε e obtained uing equation (8), conidering the experimental reult o V and 45º or the orientation o the hear 2 3 ailure crack (α). In the parameter ( ρ E ρ ) ( ) w w E + it wa adopted 200 GPa or the elaticity modulu o the teel tirrup (E ). ii) baed on the three equation determined in the tep i), it wa deined an equation that allow obtaining ε e rom the 2 3 parameter ( ρ E ρ ) ( ) E + and the CFRP orientation (θ ). w iii) conidering the equation deined in the tep ii) and uing equation (7) it wa poible to calculate the value o the contribution V or each o the teted beam in the experimental program decribed in thi paper. The comparion between experimental and lytical value o V wa done, and a aety actor wa deined in order to aure that the lytical ormulation provide aety prediction or 95% o the teted beam. A ae prediction mean that the ratio between the experimental and the lytical value o the contribution o NSM CFRP laminate or the hear reitance o a RC beam i higher than Development o the lytical ormulation 2 3 Fig. 13 how the relationhip between ε e and ( ρ E ρ ) ( ) E + parameter or the cae o laminate at 45º, 60º and 90º, when 90% o the beam teted in the experimental program that wa decribed in the irt part o thi paper wa conidered. In act, the ollowing RC beam were not conidered in thi lyi: 5S-5LI45F-D beam or the cae o θ = 45º; 5S-8LI60-D beam or the cae o θ = 60º; 2S-3LV-A, 2S-4LV-B and 4S-7LV-C beam or the cae o θ = 90º. For thee beam the obtained value o ε e (ee Table 3) were much higher (in two beam) or much lower (in three beam) than the value o ε e determined in the remaining teted beam. In Fig. 13 the line that bet it the ε e veru 2 3 ( ρ E ρ ) ( ) E + experimental reult or each inclination o the CFRP i alo repreented. Thee line are w deined rom the ollowing equation: or the laminate at 45º (Fig. 13a) w 11

12 or the laminate at 60º (Fig. 13b) or the laminate at 90º (vertical laminate) (Fig. 13c) In equation (9), (10) and (11) ε ε ε e e e [( E ρ + E ρ ) ( )] = (9) w [( E ρ + E ρ ) ( )] = (10) w [( E ρ + E ρ ) ( )] = (11) w E and E are in GPa and i in MPa. Furthermore, ρ and ρ w are introduced like a ratio and not in percentage (value obtained with the equation in the ootnote o Table 1 but eliminating the term 100). Fig. 13d) preent, or the above mentioned three inclination o the CFRP, the relationhip between ε e and 2 3 ( ρ E ρ ) ( ) E + parameter according to the equation (9), (10) and (11). The minimum value o the w 2 3 ( ρ E ρ ) ( ) E + parameter or the teted beam wa 0.022, and or the laminate at 45º, 60º and w 90º, repectively, while the maximum value wa 0.083, and or the laminate at 45º, 60º and 90º, repectively. Fig. 13d) alo repreent equation (9), (10) and (11) or a higher range o value o the 2 3 ( ρ E ρ ) ( ) E + parameter, namely 0.01 to 0.1. Furthermore, the maximum value o ε e i limited to the w ultimate train o the CFRP (ε u ) obtained rom uniaxial tenile tet (the horizontal line in Figure 13d) repreent the average value o ε u o the CFRP laminate ued in the experimental program). Equation (9) to (11) have the ollowing general ormat: ε e C2 [( E ρ + E ρ ) ( )] = C (12) where C 1 and C 2 can be obtained a a unction o the CFRP orientation (θ ). In act, conidering the value o C 1 and C 2 o the equation (9), (10) and (11), repectively, or the cae o θ equal to 45º, 60º and 90º, it i poible to deine equation (13) and (14) or the parameter C 1 and C 2, repectively, both a unction o the θ, and with R 2 =1: w C θ + 2 = θ e (13) C θ 2 = θ e (14) Conidering the equation (12), (13) and (14), the lytical ormulation that determine the value o the ε e parameter rom the relevant data o the RC beam to be trengthened and the governing characteritic o the NSM CFRP laminate i: 12

13 ε e = e θ θ 2 3 [( E ρ + E ρ ) ( )] w θ θ e (15) 3.3. Validation o the lytical ormulation By uing equation (15), the lytical value o the CFRP eective train ( ε beam conidered in the etablihment o the lytical ormulation. Introducing the e ) were determined or all the teted ε e value in equation (7), the contribution o NSM hear trengthening coniguration or the hear reitance o the RC beam ( V ) wa calculated. By conidering the lytical ( V ) and the experimental reult ( V ), the k = exp exp V V ratio wa determined and i repreented in Fig. 14a). For thi lyi, it wa conidered the value o cenario B decribed in the ection o thi paper. exp V aociated to the Table 6 compare V and V exp value or each o the 44 RC beam hear trengthened with NSM CFRP laminate conidered in the development o the preent lytical ormulation. The value o V were obtained by conidering the average value o the material propertie. Conidering thi act, in the lyi o the k = V exp V ratio, a k 1.0 i ynonymou o aety condition. For the Table 6, the average value or the k parameter ( k med 1.01 and the correponding tandard deviation value wa The value o the k med parameter i, in act, quite cloe to the unity, evidencing that in average term the lytical model predict with high accuracy the experimental reult. However, in individual term, ome beam preented a k value ar below the unity (ee Fig. 14a), uch i the cae o 2S-6LI60-B (k =0.73), 2S-9LI60-B (k =0.74) and 4S-7LV-B (k = 0.71) beam. The ailure mode oberved in thee three beam can jutiy their relatively low experimental value o V. In act, when 2S-6LI60-B and 4S-7LV-B beam reached it maximum load capacity, there were laminate already diabled and thereore were not part o the reitance mechanim to the hear ailure crack. Thi act conditioned the perormance o the hear trengthening olution with NSM CFRP laminate. The maximum load o the beam 2S- 9LI60-B wa achieved immediately beore the debonding o a laminate with a reduced bond length. Although thi beam ha hown certain ductility, it load carrying capacity ha not increaed ater the above mentioned debonding o the CFRP. Since Equation (15) doe not attend to all eect that inluence the eectivene o the CFRP laminate, an uncertainty actor, deignated γ, i propoed (Equation (16)), having been determined in order to accomplih that 95% o the lyzed RC beam have a k value equal or greater to the unity. Following thi criterion a value o 1.3 wa obtained or the γ. 13 ) wa

14 ε e = e θ θ ( θ θ 2 ) e + [( E ρ + E ρw) ( )] γ 2 (16) For each o the above mentioned 44 RC beam hear trengthened with NSM CFRP laminate, Table 6 preent the value o the eective train o the CFRP ( ε ) obtained with equation (16) and the aociated lytical value o V e ( V ) obtained with equation (7). Conidering thee value o exp exp V and the value o V, Table 6 alo preent the value o the parameter k = V V (ee Fig. 14b). Fig. 15 compare the experimental and the lytical value o exp V ( V and V, repectively) or the beam conidered in the development o the lytical ormulation. According to thi igure, 95% o the above mentioned beam are in the aety zone (at the let ide o diagonal line). Furthermore, the average value o the k parameter conidering the aety actor γ equal to 1.3 wa 1.31 and the correponding tandard deviation value wa CONCLUSIONS In the preent paper the eectivene o the NSM hear trengthening technique with CFRP laminate applied or RC beam with a certain percentage o teel tirrup wa aeed by an extenive experimental reearch. In thi context, the inluence o the ollowing parameter wa appraied: concrete trength; percentage o exiting teel tirrup; percentage and inclination o the CFRP laminate; exitence o crack when the RC beam are hear trengthened with NSM CFRP laminate. Baed on the data derived rom the above mentioned experimental reearch, an lytical ormulation or the prediction o the NSM hear trengthening contribution wa developed. From the obtained experimental reult it can be concluded that the NSM hear trengthening technique with CFRP laminate i an eective technique or the hear trengthening o RC beam that contain a certain percentage o teel tirrup. The CFRP hear trengthening coniguration provided an increae not only in term o maximum load, but alo in term o load carrying capacity ater hear crack ormation. In general, the value o the delection at the loaded ection in correpondence to F max o the trengthened beam were higher than thoe occurred in the correponding reerence beam. Regardle o the percentage o CFRP, percentage o exiting teel tirrup and concrete trength, it wa veriied that inclined laminate are more eective than vertical laminate. An increae o the percentage o CFRP led to an increae o the beam hear reitance. The increae o the percentage o exiting teel tirrup ha a detrimental eect on the NSM hear trengthening eectivene. The main dierence o the behavior o NSM CFRP beam with and without pre-crack reide in an expected lo o initial tine in the pre-cracked beam. In thee beam the mobilization o the CFRP laminate tarted jut ater the 14

15 opening proce o the pre-crack, while the mobilization o the CFRP laminate in the non pre-cracked beam only occurred when the hear crack ha ormed. However, the pre-cracking did not aect the eicacy o the NSM hear trengthening technique in term o load carrying capacity and ultimate delection. The contribution o the NSM CFRP laminate or the beam hear reitance i limited by the concrete tenile trength. In act, thi technique i more eective when applied to RC beam o high-trength concrete, not only in term o increaing the load carrying capacity o the beam, but alo in auring higher mobilization o the tenile propertie o the CFRP. However, rom the obtained reult it can be concluded that the NSM hear trengthening technique with CFRP laminate i till eective in RC beam made by the lowet tructural concrete trength cla ( ck 12MPa). Baed on the inding o the experimental program (reult o the tet o 44 RC beam hear trengthened with NSM CFRP laminate), it wa deined an equation to obtain the value o eective train (ε e ). Thi equation i dependent o the CFRP orientation ( 2 3 θ ) and the parameter ( ρ E ρ ) ( ) E + that include the percentage o CFRP ( ρ ), the percentage o teel tirrup ( ρ w ) and the concrete compreive trength ( ). The lytical ( V ) exp and the experimental ( V ) reult o the CFRP hear contribution are compared conidering the ratio k (k = w V exp V ). In order to aure a aety condition (k 1) or 95% o the lyzed beam it wa introduced a aety actor equal 1.3. ACKNOWLEDGEMENTS The author wih to acknowledge the upport provided by the Empreiteiro Caai, Degua, S&P and Secil (Unibetão, Braga). The tudy reported in thi paper i part o the reearch project PTDC/ECM/114511/2009, upported by the Portuguee Foundation or Science and Technology (FCT). REFERENCES [1] ACI Committee 440, Guide or the deign and contruction o externally bonded FRP ytem or trengthening concrete tructure, American Concrete Intitute, 118 pp. (2002). [2] ib - Bulletin 14, Externally bonded FRP reinorcement or RC tructure, Technical report by Tak Group 9.3 FRP (Fiber Reinorced Polymer) reinorcement or concrete tructure, Féderation Internationale du Béton - ib, July, 130 pp. (2001). [3] Baki, C.E., Bank, L.C., Brown, V.L., Coenza, E., Davalo, J.F., Leko, J.J., Machida, A., Rikalla, S.H. and Triantaillou, T.C., Fiber-reinorced polymer compoite or contruction tate-o-the-art review, Journal o Compoite or Contruction, 6(2), (2002). 15

16 [4] Barro, J.A.O. and Dia, S.J.E., Near urace mounted CFRP laminate or hear trengthening o concrete beam, Journal Cement and Concrete Compoite, 28(3), (2006). [5] Kotynia, R., Shear trengthening o RC beam with NSM CFRP laminate, 8 th International Sympoium on Fiber Reinorced Polymer Reinorcement or Concrete Structure (FRPRCS-8), Patra, Greece, July (2007). [6] El-Hacha, R. and Wagner, M., Shear Strengthening o Reinorced Concrete Beam uing Near-Surace Mounted CFRP Strip, 9 th International Sympoium on Fiber Reinorced Polymer Reinorcement or Concrete Structure (FRPRCS-9), Sydney, Autralia, July, 10 pp. (2009). [7] El-Hacha, R. and Rikalla, S.H., Near-urace-mounted iber-reinorced polymer reinorcement or lexural trengthening o concrete tructure, ACI Structural Journal, 101(5), (2004). [8] Cota, I.G. and Barro, J.A.O., Aement o the bond behavior o NSM FRP material by pullout tet, Firt Middle Eat Conerence on Smart Monitoring, Aement and Rehabilitation o Civil Structure, Dubai, 8-10 February (2011). [9] Sena-Cruz, J.M. and Barro, J.A.O., Bond between near-urace mounted CFRP laminate trip and concrete in tructural trengthening, Journal o Compoite or Contruction, 8(6), (2004). [10] Degua Contruction Chemical Portugal, Technical Report MBrace Rein 220, May (2003). [11] Bianco, V., Barro, J.A.O., Monti, G., New approach or modeling the contribution o NSM FRP trip or hear trengthening o RC beam, ASCE Compoite or Contruction Journal, 14(1), 36-48, (2010). 16

17 TABLES AND FIGURES Lit o Table: Table 1 - General inormation about the erie o the teted RC beam Table 2 - CFRP hear trengthening coniguration o the teted beam in erie A, B, C and D Table 3 - Experimental reult o the 49 beam hear trengthened with NSM CFRP laminate Table 4 - CFRP coniguration applied in RC beam with three type o concrete Table 5 - CFRP coniguration applied in RC beam with two level o the percentage o teel tirrup Table 6 - Comparion between the experimental and lytical value Lit o Figure: Fig. 1 - General inormation about the teted RC beam (dimenion in mm) Fig. 2 - Beam o erie B with ρ w = 0.10%: the reerence beam without CFRP (beam 2S-R-B) and the beam hear trengthened with the highet percentage o CFRP (dimenion in mm) Fig. 3 - Behavior o RC beam hear trengthened with NSM CFRP laminate (comparion with the behavior o the correponding reerence RC beam) Fig. 4 - Pre-cracking eect in term o the orce v delection at the loaded-ection Fig. 5 - Failure mode o the RC beam hear trengthened with NSM CFRP laminate Fig. 6 - Mobilization o teel tirrup croing the hear ailure crack: a) 2S-R-A reerence beam, b) 2S-5LI45-A and 2S-8LI45-A trengthened beam Fig. 7 - Data or the lytical deinition o the eective train o the CFRP Fig. 8 - Inluence o the concrete trength in the eectivene o the NSM hear trengthening technique uing CFRP laminate Fig. 9 - Inluence o the percentage o exiting teel tirrup in the eectivene o the NSM hear trengthening technique uing CFRP laminate Fig Inluence o the percentage o the CFRP in the eectivene o the NSM hear trengthening technique uing CFRP laminate Fig RC beam hear trengthened with: a) vertical and b) inclined laminate Fig Inluence o the orientation o the CFRP in the eectivene o the NSM hear trengthening technique uing CFRP laminate 17

18 2 3 Fig Eective train o the CFRP (ε e ) v ( E ρ + E ρ ) ( ) w Fig Value o the k parameter or all the lyzed hear trengthened RC beam: a) with γ = 1.0; b) with γ = 1.3 Fig Comparion between the experimental and lytical value o the CFRP contribution or the hear reitance (V ) 18

19 Table 1 - General inormation about the erie o the teted RC beam. ρ Serie θ [%] (2) [º] 0.06 A (ρ l = 2.9 %) (1) ρ w [%] (3) [MPa] 0.10 (φ6@300) (4) B (φ6@300) (ρ l = 2.8 %) (φ6@180) C (φ6@300) (ρ l = 2.8 %) (φ6@180) D (φ6@300) (ρ l = 3.1 %) (φ6@200) (1) The percentage o the longitudinal tenile reinorcement wa obtained rom ρ l = ( Al ( bw d )) 100 where A l i the cro ectional area o the longitudinal tenile teel reinorcement (ee Fig. 1), b w = 180 mm i the width o the beam web and d i the ditance rom extreme compreion iber to the centroid o tenile reinorcement. (2) The CFRP percentage wa obtained rom ρ = ( 2 a b ) ( bw inθ ) 100 where a and b are the dimenion o the laminate cro ection. (3) The percentage o the vertical teel tirrup wa obtained rom ρw = ( Aw ( bw w) ) 100 where A w i the cro ectional o the arm o a teel tirrup, and w i the pacing o the tirrup. (4) φ6@300 mean teel tirrup o 6 mm diameter paced at 300 mm in the hear pan L i. L i /d 19

20 Table 2 - CFRP hear trengthening coniguration o the teted beam in erie A, B, C and D. Deignation o the beam (ρ w = 0.10%) {2S-R-A}* Serie A Number o laminate ( mm 2 ) θ [º] [mm] 2S-3LV-A S-5LV-A S-8LV-A S-3LI45-A S-5LI45-A S-8LI45-A S-3LI60-A S-5LI60-A S-7LI60-A Serie B Deignation o the beam Number o laminate θ ρ (ρ w = 0.10%) (ρ w = 0.17%) ( mm 2 ) [º] [mm] [%] {2S-R-B}* {4S-R-B}* 2S-4LV-B 4S-4LV-B ** 4S-4LVa-B ** S-7LV-B 4S-7LV-B S-10LV-B (1) S-4LI45-B 4S-4LI45-B S-7LI45-B 4S-7LI45-B S-10LI45-B S-4LI60-B 4S-4LI60-B S-6LI60-B 4S-6LI60-B S-9LI60-B Serie C Deignation o the beam Number o laminate ( mm 2 ) θ [º] [mm] (ρ w = 0.10%) {2S-R-C}* (ρ w = 0.17%) {4S-R-C}* 2S-7LV-C 4S-7LV-C S-4LI45-C 4S-4LI45-C S-7LI45-C 4S-7LI45-C S-4LI60-C 4S-4LI60-C S-6LI60-C 4S-6LI60-C (2) Serie D Deignation o the beam Number o laminate ( mm 2 ) θ [º] [mm] (ρ w = 0.10%) {3S-R-D}* (ρ w = 0.16%) {5S-R-D}* 3S-6LV-D S-10LV-D S-5LI45-D 5S-5LI45-D 3S-5LI45F1-D*** 5S-5LI45F-D (3) S-5LI45F2-D*** - 3S-9LI45-D 5S-9LI45-D S-5LI60-D 5S-5LI60-D S-5LI60F-D 60 3S-8LI60-D 5S-8LI60-D (1) In the deignation 2S-10LV-B (ee Fig. 2), 2S mean two teel tirrup in the hear pan L i, 10LV mean ten vertical laminate in each ace o the hear pan L i, B mean erie B. (2) In the deignation 4S-6LI60-C, 4S mean our teel tirrup in the hear pan L i, 6LI60 mean ix laminate at 60º in each ace o the hear pan L i, C mean erie C. (3) In the deignation 5S-5LI45F-D, 5S mean ive tirrup in the hear pan L i, 5LI45 mean ive laminate at 45º in each ace o the hear pan L i, F mean that the beam wa pre-cracked, D mean erie D. * Reerence beam without CFRP. ** The ame CFRP coniguration wa applied in two beam (the dierence wa the poition o the laminate in the hear pan L i ). *** The ame CFRP coniguration wa applied in two pre-cracked beam with ρ w = 0.10%. ρ [%] ρ [%] ρ [%] 20

21 Serie A Serie B Serie C Serie D Beam Table 3 - Experimental reult o the 49 beam hear trengthened with NSM CFRP laminate. [MPa] ρ [%] E [GPa] ε u [ ] θ [º] ρ w [%] ρ l [%] L i /d [mm] a b [mm 2 ] F max [kn] V t [kn] V [kn] (1) V [kn] (2) 2S-3LV-A S-5LV-A S-8LV-A S-3LI45-A S-5LI45-A S-8LI45-A S-3LI60-A S-5LI60-A S-7LI60-A S-4LV-B S-7LV-B S-10LV-B S-4LI45-B S-7LI45-B S-10LI45-B S-4LI60-B S-6LI60-B S-9LI60-B S-4LV-B S-4LVa-B S-7LV-B S-4LI45-B S-7LI45-B S-4LI60-B S-6LI60-B S-7LV-C S-4LI45-C S-7LI45-C S-4LI60-C S-6LI60-C S-7LV-C S-4LI45-C S-7LI45-C S-4LI60-C S-6LI60-C S-6LV-D S-10LV-D S-5LI45-D S-9LI45-D S-5LI60-D S-8LI60-D S-5LI45F1-D S-5LI45F2-D S-5LI45-D S-9LI45-D S-5LI60-D S-8LI60-D S-5LI45F-D S-5LI60F-D (1) Value obtained conidering the cenario A. (2) Value obtained conidering the cenario B. ε e [ ] 21

22 Table 4 - CFRP coniguration applied in RC beam with three type o concrete. Beam CFRP ρ w ρ θ coniguration [%] [%] [º] [mm] Serie B Serie C Serie D ( = 39.7 MPa) ( = 18.6 MPa) ( = 59.4 MPa) Solution S-7LV-B 2S-7LV-C 3S-10LV-D Solution 2a S-4LI45-B 2S-4LI45-C 3S-5LI45-D Solution 2b S-4LI45-B 4S-4LI45-C 5S-5LI45-D Solution 3a S-4LI60-B 2S-4LI60-C 3S-5LI60-D Solution 3b S-4LI60-B 4S-4LI60-C 5S-5LI60-D Solution 4a S-7LI45-B 2S-7LI45-C 3S-9LI45-D Solution 4b S-7LI45-B 4S-7LI45-C 5S-9LI45-D Solution 5a S-6LI60-B 2S-6LI60-C 3S-8LI60-D Solution 5b S-6LI60-B 4S-6LI60-C 5S-8LI60-D Table 5 - CFRP coniguration applied in RC beam with two level o the percentage o teel tirrup. CFRP coniguration ρ [%] θ [º] [mm] Beam Serie ρ w = 0.10% ρ w = 0.16%-0.17% (1) Solution B 2S-4LV-B 4S-4LV-B Solution B 2S-7LV-B 4S-7LV-B Solution B 2S-4LI45-B 4S-4LI45-B Solution B 2S-7LI45-B 4S-7LI45-B Solution B 2S-4LI60-B 4S-4LI60-B Solution B 2S-6LI60-B 4S-6LI60-B Solution C 2S-7LV-C 4S-7LV-C Solution C 2S-4LI45-C 4S-4LI45-C Solution C 2S-7LI45-C 4S-7LI45-C Solution C 2S-4LI60-C 4S-4LI60-C Solution C 2S-6LI60-C 4S-6LI60-C Solution D 3S-5LI45-D 5S-5LI45-D Solution D 3S-9LI45-D 5S-9LI45-D Solution D 3S-5LI60-D 5S-5LI60-D Solution D 3S-8LI60-D 5S-8LI60-D (1) ρw = 0.16% or the beam o erie D and ρw = 0.17% or the beam o erie B and C. 22

23 Beam exp V [kn] Table 6 Comparion between the experimental and lytical value. ε e (1) [ ] γ = 1.0 (uing equation (15)) γ = 1.3 (uing equation (16)) ε e [ ] [ ] 2S-5LV-A S-8LV-A S-3LI45-A S-5LI45-A S-8LI45-A S-3LI60-A S-5LI60-A S-7LI60-A S-7LV-B S-10LV-B S-4LI45-B S-7LI45-B S-10LI45-B S-4LI60-B S-6LI60-B S-9LI60-B S-4LV-B S-4LVa-B S-7LV-B S-4LI45-B S-7LI45-B S-4LI60-B S-6LI60-B S-7LV-C S-4LI45-C S-7LI45-C S-4LI60-C S-6LI60-C S-4LI45-C S-7LI45-C S-4LI60-C S-6LI60-C S-6LV-D S-10LV-D S-5LI45-D S-9LI45-D S-5LI45F1-D S-5LI45F2-D S-5LI60-D S-8LI60-D S-5LI45-D S-9LI45-D S-5LI60-D S-5LI60F-D V [kn] (1) Eective train o the CFRP obtained with Eq. (8) conidering exp V and α = 45º. k ε e V [kn] k 23

24 Steel tirrup F 45º B A θ NSM CFRP laminate L i Serie A, B and C: L i = 900 mm Serie D: L i = 1200 m L r Serie A, B and C: L r = 1350 mm Serie D: L r = 1200 m Serie A Serie B and C Serie D //300 in Li //75 in L r //300 in L i or 6//180 in L i 180 6//75 in L r //300 in L i or 6//200 in L i 180 8//80 in L r Fig. 1 - General inormation about the teted RC beam (dimenion in mm). 24

25 2S-R-B F x300 F 18x S-10LV-B 40 9x S-10LI45-B 3x300 18x F 55 7x x300 F 18x S-9LI60-B 54 8x x300 18x Fig. 2 - Beam o erie B with ρ w = 0.10%: the reerence beam without CFRP (beam 2S-R-B) and the beam hear trengthened with the highet percentage o CFRP (dimenion in mm). 25

26 Phae II CFRP u Fmax Force (kn) Formationo the hear crack in the reerence beam without CFRP Force (kn) re u Fmax re F max CFRP F max Reerence beam Shear trengthened beam with CFRP Phae I Delection at loaded-ection (mm) Delection at loaded-ection (mm) Fig. 3 - Behavior o RC beam hear trengthened with NSM CFRP laminate (comparion with the behavior o the correponding reerence RC beam) Pre-cracking eect In thi beam the hear ailure crack wa croed with a number o laminate higher than wa coccurred in the beam 3S-5LI45F2-D Force (kn) Homologou beam with and without pre-crack preented imilar behavior 3S-R-D 3S-5LI45-D 3S-5LI45F1-D 3S-5LI45F2-D Delection at loaded-ection (mm) Fig. 4 - Pre-cracking eect in term o the orce v delection at the loaded-ection. 26

27 Concrete racture a) Beam 2S-4LI45-B (concrete racture) b) Beam 2S-10LI45-B (concrete racture) c) Beam 2S-7LI45-C (concrete racture) Sliding o the CFRP CFRP rupture d) Beam 3S-6LV-D (liding o the CFRP) e) Beam 3S-5LI60-D (CFRP rupture) Fig. 5 - Failure mode o the RC beam hear trengthened with NSM CFRP laminate. 2S-R-A 2S-5LI45-A 2S-8LI45-A Stirrup 1 Stirrup 2 Stirrup 1 Stirrup 2 Stirrup 1 Stirrup 2 a) b) Fig. 6 - Mobilization o teel tirrup croing the hear ailure crack: a) 2S-R-A reerence beam, b) 2S-5LI45-A and 2S-8LI45-A trengthened beam. 27

28 Shear crack CFRP laminate CFRP laminate h w CFRP laminate α θ h w (cotg α + cotg θ ) Fig. 7 - Data or the lytical deinition o the eective train o the CFRP V (kn) Sol. 1 Sol. 2a Sol. 2b Sol. 3a Sol. 3b Sol. 4a Sol. 4b Sol. 5a Sol. 5b Série B Série C Série D Serie (MPa) B 39.7 C 18.6 D kn ( 2.7 the value o the erie C) V (kn) kn ( 1.5 the value o the erie C) kn (MPa) Fig. 8 - Inluence o the concrete trength in the eectivene o the NSM hear trengthening technique uing CFRP laminate. 28

29 140.0 Série B ( = 39.7 MPa) Série C ( = 18.6 MPa) Série D ( = 59.4 MPa) V (kn) Sol. 1 Sol. 2 Sol. 3 Sol. 4 Sol. 5 Sol. 6 Sol. 7 Sol. 8 Sol. 9 Sol. 10 Percentage o tirrup = 0.10% Percentage o tirrup = 0.16%-0.17% Sol. 11 Sol. 12 Sol. 13 Sol. 14 Sol (Serie C) 0.82 (Serie B) 0.92 (Serie D) R (MPa) Fig. 9 - Inluence o the percentage o exiting teel tirrup in the eectivene o the NSM hear trengthening technique uing CFRP laminate. V (kn) Serie A ( = 31.1 MPa) Serie B ( = 39.7 MPa) Serie C ( = 18.6 MPa) Serie D ( = 59.4 MPa) ρ (%) ε e ( ) Serie A Serie B Serie C Serie D Serie A Serie B Serie C Serie D a) b) Fig Inluence o the percentage o the CFRP in the eectivene o the NSM hear trengthening technique uing CFRP laminate. ρ (%) 29

30 CFRP trengthening coniguration with vertical laminate (ρ = 0.08%) CFRP trengthening coniguration with inclined laminate (ρ = 0.08%) a) b) Fig RC beam hear trengthened with: a) vertical and b) inclined laminate. ε e ( ) Vertical laminate Laminate at 45º Laminate at 60º Vertical laminate Laminate at 45º Laminate at 60º E ρ /( ) 2/3 Fig Inluence o the orientation o the CFRP in the eectivene o the NSM hear trengthening technique uing CFRP laminate. 30