EXPERIMENTAL AND ANALYTICAL STUDIES OF STRENGTHENING USING DRILLED-IN BONDED SHEAR REINFORCEMENT

Transcription

1 Accepté pour publication dan: STRUCTURAL FAULTS & REPAIR-014, 15th International Conference, 9th 10th July 014, Edinburgh, Scotland, ISBN No: X. Paper number: 1145 EXPERIMENTAL AND ANALYTICAL STUDIES OF STRENGTHENING USING DRILLED-IN BONDED SHEAR REINFORCEMENT Mathieu Fiet & Prof. Joée Batien Univerité Laval Dept. of Civil Engineering 1065 Avenue de la Médecine Québec, Qc, Canada Prof. Deni Mitchell McGill Univerity Dept. of Civil Engineering 817 Sherbrooke Street Wet Montréal, QC, Canada KEYWORDS: Shear, Bridge, Strengthening, Evaluation, Repair. ABSTRACT In order to tudy mean of improving the behaviour of thick lab without hear reinforcement a erie of large-cale beam repreenting thick lab wa contructed and teted. Companion pecimen were trengthened uing drilled-in reinforcing bar to tudy the effectivene of thi repair technique. The behaviour of thee beam, before and after trengthening, i compared. An additional experimental program uing pull-out pecimen enabled a tudy of the bond characteritic of drilled-in reinforcement having different embedment length. An analytical model to predict the bond-tre veru lip relationhip enabled the development of a method for predicting the influence of the added hear reinforcement in improving the hear trength. Thee prediction are compared with the experimental reult and provide a practical mean of aeing the influence of pot-intalled hear reinforcement. INTRODUCTION On September 30 th, 006, the Concorde overpa (Laval, Qc, Canada) collaped, killing five people and injuring ix other. Even though the original deign repected tandard at the time, a hear failure in the cantilever region of the upporting concrete thick lab led to the collape (Johnon et al, 007). The hear failure mode of untrengthened thick lab i very brittle and provide no warning ign of the approaching collape. For the Concorde overpa collape, invetigation have hown that concrete degradation with time reulted in the propagation of inclined cracking, followed by a hear failure. That event raied quetion concerning the afety of many aging concrete thick lab bridge without hear reinforcement. Moreover, the invetigation ha howed that the minimum amount of hear reinforcement recommended by the current Canadian tandard (CAN-CSA, 006) would have prevented the Concorde overpa collape (Johnon et al, 007; Mitchell et al, 011). Thu, method to introduce, at leat, the minimum amount of hear reinforcement into thick concrete lab have gain wide interet. In order to tudy the behaviour of thick lab without hear reinforcement, a erie of large-cale beam repreenting thick lab were contructed and teted (Provencher 011; Cuon 01; Fiet et al, 01). Companion pecimen were trengthened uing drilled-in reinforcing bonded bar to tudy the effectivene of thi repair technique. The intallation of bonded bar i illutrated in Fig. 1. Thi involve drilling hole in the concrete element from the top urface, down to the flexural reinforcement (Fig. 1a). The hole need to be cleaned with high preure air and water (Fig. 1b), and filled with the epoxy adheive (figure 1c). Thereafter, teel reinforcing bar are inerted into the hole (Fig. 1d). In comparion with other trengthening method ued on narrow beam (De Lorenzi and Nanni, 001; Adhikary and Mutoyohi, 006; Barro and Dia, 006; Fernández and al, 010), the propoed method ha the advantage of being effective on wide thick lab.

2 Detail of the beam that repreent portion of thick lab along with the trengthening detail are ummarized in Table 1 and Fig.. The beam have a 4 m free pan, a width, b, of 610 mm and a depth, h, of 750 mm. Slab B3 and B4 were trengthened with bonded drilled-in hear reinforcement. For comparion purpoe, lab S1 contain conventional tirrup intalled before concrete cating. Reinforcing bar ued for the hear reinforcement were 15M, (diameter of 15.9 mm). Reult howed that the heartrengthened lab uing bonded reinforcement can exhibit failure load 46% higher compared with companion untrengthened lab. However, the predicted hear trength uing deign proviion of current tandard and auming that the drilled-in reinforcement wa fully effective wa 9% higher than the experimental reult. Thi obervation can be attributed to the diagonal hear crack location. Figure 3 how the cracking pattern of trengthened lab B after failure. The embedded length L b of the hear reinforcement (dahed line) i determined by the main hear crack location, influencing the maximum tenile tree developed in the hear reinforcement. It i apparent that ome of the bonded reinforcing bar were not fully anchored and therefore unable to develop their full yield trength f yv a aumed by current tandard for conventional tirrup. Fig. 1: Intallation procedure of bonded hear reinforcement Fig. Cro ection of lab pecimen (unit: mm) Table 1 Detail of teted lab pecimen Slab Number of h d flex v v / dv A v f yv f c E c teted lab (mm) (mm) (%) (mm) (mm²) (MPa) (MPa) (MPa) B B S Objective The main objective of the reearch program i to develop an approach for predicting the increae in hear trength of trengthened thick lab. Firt, thi paper preent an invetigation of the behaviour of epoxy bonded hear reinforcement uing pull-out tet, aociated analytical modelling and finite element (FE) model. The pull-out tet have been performed to determine the bond-lip behaviour of the bonded reinforcing bar. Secondly, on the bai on thi bond-lip behaviour, finite element modelling ha been developed with VecTor (Wong and Vecchio, 00) to examine the behaviour of trengthened lab and it bonded hear reinforcement.

3 Fig. 3: Failure of lab with bonded hear reinforcement Fig. 4: Behaviour of bonded hear reinforcement at crack location Force Stre Slip Bond tre Reinforcement with anchorage Bonded reinforcement Fig. 5: Force, tre, lip and bond ditribution along anchored and bonded reinforcing bar BEHAVIOUR OF BONDED REINFORCING BARS The behaviour of bonded reinforcing bar at a crack interface can be viewed a two pull-out tet, one on each ide of the crack (Fig. 3 and 4). The maximum teel tre σ developed at the crack i function of the crack width, bond propertie and the bar embedded length. Fig. 5 preent the difference in behaviour between bonded hear reinforcement and conventional tirrup. For tirrup, the extremitie of the reinforcing bar are well anchored and hence can develop their yield reitance. At the extremitie of the teel element, the diplacement L =0 and the teel tre σ L >0. Thi i imilar to the behaviour of a rebar between two crack (Lee et al., 010). For reinforcement bonded with the help of an adheive, the axial tre ha to be tranferred from the teel to the urrounding concrete. Thu, at the rebar free extremity, σ L =0 and L >0. It can alo be oberved in Fig. 5 that the bond tre ditribution i not contant along the rebar. The bond tre i function of the lip between the rebar and urrounding concrete which i function of the train and the tree developed in the two material. Knowing the tre, train and bond ditribution, Equation 1 decribe the relationhip for the lippage (Baláz, 1993; Lee et al., 010). d 4(1 n) 0 (1) dx Edb Where, n i the elatic modulu ratio of teel to concrete (E /E c ), ρ i the reinforcement ratio (A /A c ), and τ() i the local bond-lip behaviour at the interface.

4 Model for local bond tre relationhip The VecTor oftware i capable of predicting the repone of concrete element (Ghorbani-Renani et al., 009; Vecchio 004) and wa choen to model lab trengthened with bonded reinforcing bar. Thi oftware ue two dimenional finite element to model concrete tructure, including a rotating meared crack aumption, baed on the Modified Compreion Field Theory (MCFT) (Vecchio and Collin, 1986) and Diturbed Stre Field Model (DSFM) (Vecchio, 000). Becaue current Canadian tandard are baed on MCFT, VecTor i a ueful tool to undertake a tudy of the behaviour of trengthened lab and to ultimately ugget a more adapted deign method for future implement in Canadian tandard. In addition, VecTor ha the ability to define local bond-lip behaviour of the bar-concrete interface, according to pre-defined model (Eligehanon et al, 1983; Harajli et Mukaddam, 1988) or by defining an alternative model. Comparion with experimental pull-out tet Pull-out tet with embedded length between 13 mm and 500 mm were carried out to determine the bond tre lip behaviour of the epoxy adheive ued a the bonding agent at the rebar-concrete interface. The concrete mix and teel reinforcing bar ued were the ame a thoe in the teted lab. Figure 6 preent the experimental bond-lip relationhip of the epoxy adheive. For comparion purpoe, predefined VecTor local bond-lip model (Eligehanon, Harajli) and the fib model code 010 bond lip model (fib, 013) for the concrete-teel interface are alo hown in Fig. 6. The pull out tet wa performed on a 15M rebar with a 30mm embedded length. The concrete compreive trength of thi tet wa 46 MPa. The reulting maximum bond trength wa MPa at a lip of 0.77 mm. The pot-peak fracture energy determined between the lip at τ max and the maximal diplacement wa 169 N-m. It can be een that the pre-defined model for the concrete-teel interface do not adequately predict the bond behaviour of the concrete-epoxy-adheive-teel interface. The bond-lip behaviour of the adheive i tiffer than the pre-defined model. Moreover, the maximum bond tre of the epoxy adheive i not well modelled. The experimental bond trength i about MPa at 0.77 mm wherea the prediction uing the Eligehauen model i about MPa at 1.4 mm. Likewie, the pot peak behaviour of both pre-defined model how a higher lip and reidual friction bond tre compared to experimental reult. Thu, predefined bond-tre relationhip in VecTor are not uitable to model the local behaviour of the teted adheive for the concrete-epoxy-teel interface. Propoed local bond-lip model In order to increae the accuracy of the bond-lip behaviour conidered in the FE model and future deign calculation, a trilinear bond relationhip i uggeted (Fig. 7 and Equation to 4). The firt linear branch of the bond-lip relationhip decribe the acending behaviour and the parameter were choen to bet repreent the average pre-peak tiffne. The econd linear egment decribe the contant peak behaviour and the third linear egment i defined in order to repect the fracture energy of the tet. 1 1 () max 1 1 (3) 1 max max f f 3 (4) Beide the trilinear model, another bond model which howed alo a good fit with the experimental behaviour wa introduced to olve the governing Equation 1. Thi uggeted exponential model (Equa-

5 tion 5 and 6) i baed on the work of Coenza et al (1997). The parameter r and K mut be calibrated according to experimental reult. Figure 8 and Table preent in more detail the exponential and the trilinear bond-lip model for the epoxy adheive that wa ued. r max 1 e K max f e f (6) (5) Fig. 6: Bond-lip behaviour of epoxy adheive and comparion with predefined model Fig. 7: Specific triliner bond-lip relationhip in VecTor Fig. 8: Bond-lip uggeted model and comparion with experimental pull-out tet Table : Parameter for trilinear and exponential bond-lip model 1 max f 1 3 r K (MPa) (MPa) (MPa) (mm) (mm) (mm) (mm) (mm) Trilinear Exponential DESCRIPTION OF FE MODEL FOR SLABS A tudy of bonded hear trengthened lab, including the trilinear bond-lip model, wa performed with VecTor. Slab were modelled with D membrane element. The longitudinal reinforcing bar and hear reinforcement were modelled with dicrete tru element. Conventional tirrup were modeled conidering perfect bond between the tru element and the urrounding concrete wherea contact element were ued between the teel and concrete element for the epoxy bonded reinforcement. Baic program option were elected for the material propertie. The teel behaviour i modelled with a trilinear tre-train relationhip. The concrete compreion behaviour i model according to the model uggeted by Hohikuma et al. (1997) and take into account lateral confinement and compreion oftening. In tenion, the behaviour i linear up to the tenile trength and the pot-peak behaviour i repreented with a linear law driven by the cracking energy G f. The tenion tiffening effect i alo included according to the model of Lee & al. (010). Thi model take into account the tenion tiffening after the yielding of the teel reinforcement. All relevant equation and complete reference can be found in the VecTor reference manual (Wong and Vecchio, 00).

6 RESULTS AND DISCUSSION Experimental cracking pattern and FE prediction Several analye have been performed according to the variou reinforcement layout preented in Table 1. Figure 9 and 10 how the experimental cracking pattern of lab B3 and B4 and the aociated FE prediction. For comparion purpoe, the reult for lab S1 containing conventional tirrup are alo preented. In a meared crack model, each element (integration point) reaching the concrete tenile trength will exhibit a crack. However the one with wider opening (main crack) are illutrated in bold in Fig. 10. Figure 9 and 10 how good correlation between the FE model prediction and the experimental cracking pattern. Fig. 9: Experimental cracking, lab with tirrup (S1) and epoxy bonded reinforcement (B3-B4) Fig. 10: FE cracking prediction, lab with tirrup (S1) and epoxy bonded reinforcement (B3-B4) Experimental hear carrying capacity and comparion to CSA code and FE model Table 3 how a ummary of experimental and numerical reult a well a prediction uing the Canadian code approach. It can be een that uing the code equation and auming that the epoxy bonded hear reinforcement act a conventional tirrup reult in unconervative prediction. However, by taking into account the bond behaviour, the predicted hear trength by the FE model are cloe to the experimental reult. VecTor predict almot the ame hear capacity for lab B3 a the experiment. Likewie, with an average experimental and a FE prediction hear capacity of and repectively, the FE model etimate the hear capacity of lab B4 within 5%. For all hear trengthened lab with epoxy bonded reinforcement, the average of the predicted hear capacitie divided by the experimental capacitie wa and the coefficient of variation wa The hear trength provided by the hear reinforcement (V) i determined knowing the reinforcing bar area and the teel tre at the main hear crack. The concrete contribution to hear trength Vc i the difference between the total hear trength and the teel trength contribution. By comparing the tandard VS-CSA and the FE VS-FE prediction, it can be oberved that VS-CSA i overetimated by the current tandard for the trengthened lab auming fully bonded reinforcement. For lab B3 with hear reinforcement pacing of 470 mm, VS-FE i below the fully bonded prediction by 5.4%. The concrete contribution VC-FE predicted by FE model i alo 51.% below the concrete contribution etimated by the current tandard VC-CSA for thi lab. With a cloer pacing of hear reinforcement of 370 mm in lab B4, the trength prediction (tandard veru FE) are cloer. The tandard overetimate the teel (VS-CSA/VS-FE) and concrete contribution (VC-CSA/VCFE) of lab B4 by about 5.7% and 8.% repectively. Indeed, with cloer hear reinforcement pacing, the likelihood for a main hear crack to intercept a reinforcing bar in it central portion i increaed. Thu, more bar are able to develop their yield trength and VS i cloer to the tandard prediction auming fully bonded reinforcement. In the cae of tirrup, the reinforcement i well anchored and i able to develop it full yield trength which may not be the cae for hort embedded length of epoxy

7 bonded reinforcement. The embedment length for the lab B3 bar are preented in Table 4 and the bar tree extracted from either the experiment or the FE reult. Knowing the rebar numbering previouly preented in Fig. 9, it can be oberved that the axial teel tre predicted by VecTor for the horter embedded length bonded reinforcing bar (bar R3) i below the teel yield trength of 480 MPa. Slab B3 B4 Slab B3 Table 3: Comparion between experimental, Canadian tandard and VecTor reult Tet Vexp VCSA VS CSA VC CSA VFE VS FE VC FE number [kn] [kn] [kn] [kn] [kn] [kn] [kn] Table 4: Embedded length of epoxy bonded hear reinforcement of lab B3 Experimental VecTor Rebar Embedded Max Steel Embedded Steel number length Stre* length Stre Tet number 1 Max Steel Stre* (mm) (MPa) (mm) (MPa) (MPa) R R R R *Maximum teel tre according to the maltab model and the exponential bond behaviour, for the experimental embedded length. EFFECT OF BOND AND SLIP ON SHEAR RESISTANCE Model decription In order to tudy the effect of bond on hear reitance mechanim and the ditribution of tree and lip along a bar, a reference tool wa developed. Thi tool numerically olve the governing bond Equation 1 with the help of matlab. Unlike VecTor, thi matlab tool enable the lip, bond tre and teel tre ditribution along a bonded rebar to be determined for different local bond-lip relationhip. For thi particular tudy, the exponential (Equation 5 and 6) local bond-lip relationhip i ued. Becaue the matlab model can make ue of a much refined meh (5000 linear element intead of few element in the VecTor meh model), the prediction of tree and lip along the bar i more precie. Moreover, the exponential bond-lip relationhip ued i better correlated to the experimental bond-lip relationhip than the trilinear model ued in VecTor (FE). Thu, the predicted behaviour i expected to be cloer to the experimental behaviour. Therefore, thi matlab bond model i ued a a reference model for bondlip behaviour along an epoxy bonded reinforcing bar. Embedded length and maximum axial teel tre Table 4 preent the embedded length and the maximum axial tre in the bar according to the matlab bond model. The determined maximum axial tre i limited by the bond along the rebar and the ultimate teel trength (f uv =690 MPa). It can be oberved that, for long embedded length, the maximal axial tre i limited by the teel trength f uv. However, for the epoxy bonded hear reinforcement numbered R3, the embedded length i too hort to develop the yield trength and the maximum teel axial tre i therefore limited by bond. According to the VecTor model (FE), the lab B3 failure mode reult from the yielding of hear reinforcement R while the axial tre in hear reinforcement R3 i lower than the maximum value of 34

8 MPa. Thi reult can be explained by the crack width and the aggregate interlock mechanim. At teel yielding, the crack width increae rapidly and the hear trength provided by aggregate interlock (v c ) decreae (Equation 7). Thu, the maximum hear carrying capacity can be reached before the maximum teel tre can be developed in all the epoxy bonded hear reinforcement intercepting the main hear crack. Axial teel tre at failure Figure 11 preent the loading prediction by the matlab model of a bonded rebar (15M) according to two different embedded length of 40 and 130 mm. In a concrete element ubjected to hear and aociate diagonal crack, the lip of rebar i related to the crack width in the vertical direction. Referring to Fig. 3 and 9 where bar with variou embedded length cro main diagonal crack, figure 11 preent the axial tre-lip behaviour aociated to two rebar with different embedded length. Figure 11 how that, for the horter embedded length, the maximum teel tre reached at 1 mm lip i under the ultimate trength of 690 MPa. For the longer embedded length, yield trength (480 MPa) and ultimate teel trength are reached at about 0.16 mm and 1.5 mm, repectively. The combined maximum hear capacity provided by the bonded hear reinforcement i reached at an intermediate lip of 1.05 mm. Alo, Fig. 11 how that, when yielding of the 130 mm embedded length bar i reached, the teel tre in the other rebar i 31 MPa. It may be underlined that thi value i imilar to the teel tree determined by Vec- Tor for bar R3 in lab 3 (horter embedded length of 36 and 46 mm) of 44. MPa and MPa. Fig. 11: Steel tre function of applied lip for hort and long embedded length Fig. 1: Slip along full anchored bar or bonded bar, applied tre 480 MPa v c fc 4w 0.31 a 16 w 1 (8) Effect of anchorage on aggregate interlock Fig. 1 how the lip ditribution along a fully anchored bar (tirrup) and an epoxy bonded bar. The model aume no diplacement and no teel tre at the rebar extremity a tated previouly in Fig. 5. The reult howed in Fig. 1 concern a 15M rebar pull out tet with an equivalent loading of 480 MPa (correponding to yielding) with an embedded length of 100 mm. A expected, for the ame applied tre, the lip of the bonded bar i larger than the fully anchored one. Since for hear crack, the crack width partly depend on the hear reinforcement lip, it i alo expected that the crack width of epoxy bonded hear trengthened lab will be larger than crack developed in lab with fully anchored bar (tirrup). The crack width can alo be expreed a the product of crack pacing and the train (Equation 8). Thu, for the ame bar tenile train, the crack pacing hould be larger for bonded reinforcement. Thi i ob- g (7)

9 erved through the cracking pattern of Fig. 9 and 10. Slab S1 reinforced with tirrup have experienced more hear crack than lab B3 or B4 trengthened with epoxy bonded hear reinforcement. By knowing that the aggregate interlock capability decreae with wider crack, the concrete contribution V C hould be affected in a imilar way. That may explain why the concrete contribution preented in Table 3 are lower than the CAN-CSA tandard prediction auming fully bonded reinforcement. Thu, it i alo expected that the proviion of current tandard will reult in an overetimation of V C when epoxy bonded hear reinforcement i ued a a trengthening technique. CONCLUSION AND FUTURE WORK The main goal of thi reearch i to develop model capable of predicting the increae in hear trength of thick lab trengthened with epoxy bonded hear reinforcement. Pot-intalled hear reinforcing bar were inerted in drilled-in hole and bonded to the concrete with an epoxy adheive. Thi paper preent the influence of the anchorage condition on the efficiency of thi hear trengthening technique. For conventional tirrup, well anchored condition exit and, at location where a crack intercept the tirrup, the tirrup are able to develop their full yield trength. For epoxy bonded hear reinforcement, the diagonal main hear crack define the embedment length of the rebar. Therefore, the tre carried by thee rebar can be limited by the bond trength. Pull-out tet have been carried out to determine the local bond-lip relationhip of concrete-epoxy adheive-teel interface. Thi behaviour ha been introduced in the FE oftware VecTor to model hear trengthened lab with epoxy bonded reinforcement. It appeared that VecTor pre-defined bond-lip model for the concrete-teel interface were not able to reproduce the epoxy adheive behaviour. Thu, two propoed model were judged adequate to reproduce the adheive behaviour. A imple trilinear relationhip wa ued for the FE model of lab and a more precie exponential relationhip wa ued to compare the lip, bond tre and axial teel tre ditribution along the bonded rebar. After the FE analyi of lab with epoxy bonded rebar and analyi of the bond-lip propertie, the following concluion can be drawn: - With an adequate bond model, a good correlation between numerical and experimental reult can be obtained; - The current CAN-CSA tandard, auming fully bonded reinforcement, overetimate both the teel contribution V S and the concrete contribution V C component of the hear capacity; - With maller hear reinforcement pacing, the main hear crack intercept more bar in their mid-height region enabling them to develop their yield trength. Therefore the V S contribution to hear capacity i cloer to tandard prediction auming fully bonded reinforcement; - The maximum axial rebar capacity i driven by bond propertie for hort embedded length and limited by the teel trength for long embedded length and hence the maximum capacity of each epoxy bonded reinforcing bar i not necearily reached at lab failure; - The lip of hear reinforcement at a crack location i larger for epoxy bonded bar than for well anchored tirrup. Thu for uch larger crack width, the aggregate interlock capability i reduced. Even if the experimental program ha demontrated the efficiency of pot-intalled hear reinforcement bonded to the concrete tructure, the tirrup deign procedure in the current tandard hould not be ued for drilled-in bonded hear reinforcement. The next tep of thi reearch program will be to develop

10 a deign method for the thi hear trengthening technique taking into account the effect of bond-lip behaviour on the V S and V C hear capacity component. ACKNOWLEDGMENT The Reearch reported in thi paper wa made poible by the funding from the Natural Science and Engineering Reearch Council of Canada (NSERC) and the Fond de Recherche du Québec Nature et Technologie (FRQNT). The author wih alo to acknowledge the work of Philippe Provencher, Benoit Cuon and Felix-Antoine Villemure who performed the experimental lab tet and the pull-out tet during their mater project. SYMBOLES a g b d d b d v f c f yv h n v θ v c w A v Aggregate ize Slab width Effective flexural depth Reinforcing bar diameter Effective hear depth, taken a the greater of 0.9d and 0.7h Cylinder concrete compreive trength Yield trength of hear reinforcement Slab height Ratio of elatic modulu (E /E c ) Slip, relative diplacement between concrete and teel interface Spacing of hear reinforcement Crack pacing inclined at principal tenile tre angle Shear tre in concrete Crack width Area of all hear reinforcement within a ditance v E c E F c F G f L b V c V 1 ρ ρ flex σ c σ τ τ f τ max Elatic modulu of concrete (initial tangent tiffne) Elatic modulu of teel Force in concrete Force in teel Cracking energy Embedded length Shear carrying capacity provide by concrete Shear carrying capacity provide by hear reinforcement Principal tenile train Reinforcement ratio (A /A c ) Reinforcement ratio of flexural reinforcement (A /(d b) ) Axial tre in concrete Axial tre in teel Bond tre Reidual bond trength (friction) Maximum bond trength REFERENCES Adhikary, B.B. and Mutuyohi, H. (006), Shear trengthening of reinforced concrete beam uing variou technique, Contruction and Building Material, Elevier, No. 0, Baláz, G. L. (1993), Cracking Analye Baed on Slip and Bond Stre, ACI Material Journal, Vol. 90, No. 4, Barro, J.A.O. and Dia, S.J.E. (006), Near urface mounted CFRP laminate for hear trengthening of concrete beam, Cement & Concrete Compoite, Elevier, No. 8, CAN-CSA, Canadian Standard Aociation (006), Canadian Highway Bridge Deign Code CAN- CSA S6-06, 768 p. Coenza, E., Manfredi, G., and Realfonzo, R. (1997). Behavior and modeling of bond of FRP rebar to concrete. J. Compo. for Contr., ASCE, Vol. 1 No., Cuon, B. (01), Renforcement de dalle épaie en ciaillement, (Mater Thei in French) Civil Engineering department, Univerité Laval, Québec, Canada, 119p.

11 De Lorenzi, L. and Nanni, A. (001), Shear Strengthening of Reinforced Concrete Beam with Near- Surface Mounted Fiber-Reinforced Polymer Rod, ACI Structural Journal, Vol. 98, No. 1, pp Eligehauen, R., Popov, E. and Bertero, V. (1983), Local Bond Stre-Slip relationhip of Deformed Bar under Generalized Excitation, Report No. UCB/EERC-83/3, Earthquake Engineering Center, Univerity of California, Berkeley. Fernández-Ruiz, M., Muttoni, A. and Kunz, J. (010), Strengthening of Flat Slab Againt Punching Shear Uing Pot-Intalled Shear Reinforcement, ACI Structural Journal, Vol. 107, No. 4, fib International Federation for Structural Concrete (013), Model Code for Concrete Structure p. Fiet, M., Batien, J. and Mitchell, D. (01), Pot-Intalled Shear Reinforcement for Concrete Thick Slab, The 9th fib International Ph.D. Sympoium in Civil Engineering, Karlruhe, Germany Ghorbani-Renani, I., Veley, N., Tremblay, R., Palermo, D., Maicotte, B. and Léger, P. (009), Modeling and teting Influence of Scaling Effect on Inelatic Repone of Shear Wall, ACI Structural Journal, Vol. 106, No. 3, Harajli, M.H. and Mukaddam, M.A. (1988), Slip of Steel Bar in Concrete Joint under Cyclic Loading, Journal of Structural Engineering, ASCE, Vol. 114, No. 9, Hohikuma, J., Kawahima, K., Nagaya, K. and Taylor, A.W. (1997), "Stre-Strain Model for Confined Reinforced Concrete in Bridge Pier", Journal of Structural Engineering, ASCE, Vol. 13, No. 5, Johnon, P. M., Couture, A., and Nicolet, R. (007), Commiion of inquiry into the collape of a portion of the de la Concorde overpa, Library and National Archive of Quebec. p. Lee, S.C., Cho, J.Y. and Vecchio, F.J. (011), Model for pot-yield tenion tiffening and rebar rupture in concrete member, Engineering Structure, Elevier, Vol. 33, Mitchell, D., Marchand, J., Croteau, P. and Cook, W. D. (011), Concorde Overpa Collape: Structural Apect, Journal of Performance of Contructed Facilitie, ASCE, Vol. 5, No. 6, Provencher, P. (011), Renforcement de dalle épaie en ciaillement, (Mater Thei in French) Civil Engineering department, Univerité Laval, Québec, Canada, 14p. Vecchio, F.J. (000), Diturbed Stre Field Model for Reinforced Concrete: Formulation, Journal of Structural Engineering, ASCE, Vol. 16, No.9, Vecchio, F.J. (004), Experimental and Analytical Reexamination of Claic Concrete Beam Tet, Journal of Structural Engineering, ASCE, Vol. 130, No. 3, Vecchio, F.J. and Collin, M.P. (1986), The Modified Compreion Field Theory for Reinforced Concrete Element Subjected to Shear, ACI Journal, Vol. 83, No., Wong, P. S. and Vecchio, F. J.(00) VecTor and FormWork Uer Manual, { vector}, 13p