Editorial Manager(tm) for The Arabian Journal for Science and Engineering B:

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1 Engineering Editorial Manager(tm) or The Arabian Journal or Science and Engineering B: Manuscript Drat Manuscript Number: AJSE-ENG-D-0-00R Title: Shear strengthening o short span reinorced concrete beams with CFRP sheets Article Type: Research Article Section/Category: Civil Engineering Keywords: Carbon Fiber reinorced Polymers; High-strength Concrete; Reinorcement; Shear strength; Strut-and-Tie Modelling. Corresponding Author: Imran A Bukhari, Ph.D Corresponding Author's Institution: First Author: Imran A Bukhari, Ph.D Order o Authors: Imran A Bukhari, Ph.D;Robert Vollum, Ph.D;Saeed Ahmad, Ph.D;Juan Sagaseta, Ph.D Abstract: This paper presents the results o a series o tests on short span reinorced concrete beams which were strengthened in shear with various arrangements o externally bonded Carbon Fibre Reinorced Polymer (CFRP) sheets. The objective o the tests was to determine the eect o changing the area and location o the CFRP sheet within the shear span. A total o iteen 0 mm x 00 mm x, mm concrete beams were tested o which our were un-strengthened control specimens. The remaining eleven beams were strengthened with varying conigurations o CFRP sheets. Parameters varied in the tests included the area o CFRP sheet, its anchorage length and the distance o the CFRP sheet rom the support. The experimental results revealed that the CFRP is more eective when it is placed close to the supports and even small areas o CFRP can give signiicant increases in shear strength. The experimental results were compared with the three dierent existing shear prediction models or estimating shear contribution o CFRP sheets. A simple strut-and-tie model (STM) is presented which gives reasonable predictions o shear strength or the beam specimens, which were strengthened with CFRP over the ull depth o the beam. The superposition method o design is replaced in EC by the variable angle truss model in which all the shear is assumed to be resisted by the truss mechanism. A simple regression equation is proposed or the calculation o eective stress in FRP to be used in EC.

2 Manuscript Shear strengthening o short span reinorced concrete beams with CFRP sheets ABSTRACT This paper presents the results o a series o tests on short span reinorced concrete beams which were strengthened in shear with various arrangements o externally bonded Carbon Fibre Reinorced Polymer (CFRP) sheets. The objective o the tests was to determine the eect o changing the area and location o the CFRP sheet within the shear span. A total o iteen 0 mm x 00 mm x, mm concrete beams were tested o which our were unstrengthened control specimens. The remaining eleven beams were strengthened with varying conigurations o CFRP sheets. Parameters varied in the tests included the area o CFRP sheet, its anchorage length and the distance o the CFRP sheet rom the support. The experimental results revealed that the CFRP is more eective when it is placed close to the supports and even small areas o CFRP can give signiicant increases in shear strength. The experimental results were compared with the three dierent existing shear prediction models or estimating shear contribution o CFRP sheets. A simple strut-and-tie model (STM) is presented which gives reasonable predictions o shear strength or the beam specimens, which were strengthened with CFRP over the ull depth o the beam. The superposition method o design is replaced in EC by the variable angle truss model in which all the shear is assumed to be resisted by the truss mechanism. A simple regression equation is proposed or the calculation o eective stress in FRP to be used in EC. Keywords: Carbon Fiber reinorced Polymers; High-strength Concrete; Reinorcement; Shear strength; Strut-and-Tie Modelling. INTRODUCTION Many existing structures designed to then current codes are unsae according to current design codes. Other concrete structures have become structurally unsound due to deterioration over time. These structures can either be rebuilt or retroitted. Strengthening is oten the most viable choice since rebuilding it usually more costly and time consuming. Structures can be strengthened with a variety o conventional techniques such as steel plate bonding, erro-cement and increasing the cross-section but experimental studies[] have shown that the use o Fibre Reinorced Polymers (FRP) has many advantages over conventional methods. CFRP composites are the most commonly used o the various types o FRP since they oer many beneits including ease o handling, light weight, durability, strength, corrosion resistance and ield-workability. The shear strength o reinorced concrete beams can be increased by externally bonding CFRP sheets to the sides o the beam cross-section. The CFRP transers loads across diagonal tension cracks in the concrete in a similar way to steel stirrups. Three dierent wrapping schemes are commonly used to strengthen reinorced concrete beams in shear with CFRP. Firstly, the CFRP is bonded to the sides o the beam, secondly, it is used to wrap the sides and bottom o the beam and thirdly, the complete section is wrapped. The irst research on shear strengthening o RC beams with composite materials was conducted by Berset in. He conducted experiments on several reinorced concrete beams strengthened with externally bonded glass FRP (GFRP) laminates and proposed a

3 simple analytical model to estimate the shear strength contribution o the GFRP composites. Ater Berset, Uji[] studied the shear behaviour o eight RC beams strengthened in shear using externally bonded Carbon Fibre Reinorced Polymers (CFRP) sheets. He ound that the application o CFRP improves the shear capacity o reinorced concrete beams. Chajes et al[] conducted experiments on T-beams strengthened in shear using dierent types o FRP abrics named aramid, E-glass, and carbon. They ound an average increase in ultimate strength o to percent. The FRP contribution was modelled in analogy with steel stirrups contribution and limiting FRP strain o 0.00 mm/mm, determined rom the tests, was assumed. The method is applied and experimentally veriied in the case o wrapped beams without stirrups. Sato et al[] also conducted research on shear strengthening using CFRP strips and continuous laminates. They described the observed ailure mode (debonding o CFRP) through a simple model to account or partial shear transer by CFRP debonding. Umezu et al[] also studied the eectiveness o totally wrapped Aramid and CFRP sheets in improving shear strength o simply supported beams. Araki et al[] conducted experiments on RC beams strengthened with various amount o totally wrapped AFRP and CFRP sheets. The conclusion drawn was that the shear capacity o RC members increased in proportion to the amount o FRP sheets. The contribution o FRP to the shear capacity was evaluated similar to calculation o stirrups. They proposed strength reduction actors o 0. and 0. or tensile strength o CFRP and AFRP sheets respectively. Norris et al[] discussed the results o a series o experimental investigations on uncracked and cracked concrete beams strengthened in shear and lexure with CFRP sheets. The experimental results show dependence o the strength, stiness and ailure modes on the ibre orientation. Malek andsaadatmanesh [] studied shear behaviour using FRP bonded plates using Compression Field Theory and truss analogy. They proposed a method or calculating the inclination angle o the shear cracks and ultimate shear capacity o RC beams externally bonded FRP plates. Malek and Saadatmanesh also presented analytical models to calculate stresses in the strengthened beam and the shear orce resisted by the composite plate. It was shown that shear ailure o the strengthened beams was controlled by either FRP racture at a stress level below its ultimate due to stress concentration or by debonding o FRP rom the concrete surace. Traintaillou [] presented a design model or computing the shear capacity o RC beams strengthened with FRP composites. He treated external FRP shear reinorcement similar to the internal reinorcement and assumed that at the ultimate limit state, the FRP develops an eective strain, ε e, which is less than the ultimate tensile strain, ε u, o FRP. Khalia et al[] presented a modiied model to calculate ε e on the basis o ew more test results. In ACI Committee 0 report, shear design guidelines or FRP construction were based on the equations proposed by Khalia et al[]. In 000, Triantaillou and Antonopoulos presented three equations or ε e which were derived rom a regression analysis o data rom seventy ive beam tests. In July 00, Technical Report on the "Design and use o externally bonded ibre reinorced polymer reinorcement (FRP EBR) or reinorced concrete structures" was published by working party o ib Task Group.. The shear prediction guidelines in the report are based on the model proposed by Triantaillou and Antonopoulos. Adhikary and Mutsuyoshi [] conducted experiments on eight concrete beams using dierent conigurations o CFRP sheets to evaluate shear strength. They ound signiicant increase in ultimate shear strength o strengthened beams. In another research, they conducted an experimental investigation or enhancing the shear capacity o reinorced concrete beams using dierent techniques. In 00, the Concrete Society published revised guidelines or strengthening beams in shear with FRP in the second edition o TR. Zhang et al[] carried out research work on shear strengthened concrete beams with CFRP and

4 observed that the ailure mechanism is dierent or CFRP strips and woven abric and concluded that strips are more eicient. It is observed rom the above review that there are ew studies on shear strengthening o RC beams. Mostly, the researchers have ocused on improvement in shear capacity by externally bonded CFRP composites using arrangements like complete wrapping, U shaped wrapping and complete side wrapping o the FRP to the beams surace. These arrangements o CFRP do not address the issue o shear enhancement by the external application o CFRP in various conigurations and anchorage lengths along the dierent areas o the shear span. In practice, mostly the beam elements are built integrally with the slab and are not o rectangular cross section as considered in most o the researches. In addition, the situations may arise when the beams are required to be strengthened in some speciic locations instead o CFRP application along the entire shear span. The eect o varying the coniguration and wrapping scheme o the CFRP has not yet thoroughly assessed. This experimental program was designed to investigate the eect o the CFRP coniguration and wrapping scheme on the shear strength o short-span reinorced concrete beams deicient in shear. The major limit o the research work is that only one test has been perormed or each strengthening scheme due to which some unexpected results may be diicult to identiy. This limitation has been observed in the already published literature on the subject thereore it is suggested to increase the database by conducting more experiments in uture.the strength o the tested beams is compared with the predictions o the models proposed by i) Khalia et al[], ii) Triantaillou and Antonopoulos[] and iii) Zhang and Hsu[]. The strength o the beams has also been assessed with a simple strut-and-tie model which was originally ormulated or the design o beams with steel shear reinorcement. The strut and tie model is shown to give good predictions o the shear strength o beams strengthened with CFRP. A simple regression equation is also proposed to be used in EC, or the calculation o eective stress in CFRP. It is shown that the variable truss angle in EC can be used or beams strengthened with CFRP. EXPERIMENTAL PROGRAMME Test Specimens: Fiteen high-strength concrete beams were tested. All the beams measured 0mm wide by 00mm deep in cross-section and, mm in length. Two mm diameter bars were used as lexural reinorcement in each beam and no internal shear reinorcement was used. Four beams were used as control specimens and eleven were strengthened using CFRP sheets. The beam details and CFRP conigurations are illustrated in Figures and respectively. CFRP sheet was applied only to the sides o the beams and no lexural strengthening was done. The strengthened beams were divided into two groups A and B, depending upon the depth o CFRP sheet. Group A was composed o six rectangular concrete beams strengthened up to the ull depth, whereas the remaining ive beams, with reduced anchorage length o CFRP sheets, were placed in Group B. The beams in Group B were strengthened over hal the beam depth to simulate the case o a T or down-stand beam where it is not possible to apply the CFRP over the ull beam depth. Material properties: The mean compressive cylinder strength o the concrete used in the beams was.mpa at days. Limestone aggregate was used with a maximum aggregate size o mm. The longitudinal reinorcement consisted o deormed bars with yield strength o MPa. The relevant material properties o the CFRP sheet are given in Table.

5 Fabrication o Beam Specimens: The beams were cast in steel orms and were cured at room temperature or days alongside 00mm long by 0mm diameter concrete cylinders. Ater grinding, the suraces o the beam were cleaned and a two part epoxy was applied in accordance with the manuacturer s recommendations. Ater curing the epoxy, the beam suraces were again ground and cleaned to remove any loose dust particles. The CFRP sheet was cut to the proper length and inused with two part epoxy beore being applied to the beam. The sheets were pressed irmly in place with a plastic roller to remove air bubbles and excess epoxy. The sheets were placed on the sides o the beam with the main ibres vertical in the conigurations shown in Figure. Test Procedure: Each beam was simply supported over a span o 00mm and tested under three point loading as shown in Figure. The ratio between the clear shear span and the eective depth (a v /d) was. The beams were loaded with hydraulic jacks at a constant rate in an internal reaction load rame. Delections were recorded at mid-span and at the supports(to observe any settlement o supports). The cracks and crack pattern were recorded at each increment in load. EXPERIMENTAL RESULTS: Cracks were marked on the beams throughout the tests to enable the cracking patterns and ailure mechanisms in the CFRP strengthened beams to be compared with the control beams. The shear strength o the beams was compared with the predictions o three dierent models available in the literature. The beams in Group A were also analysed with a strut-and-tie model (STM) developed by the Sagaseta and Vollum[], which is consistent with the recommendations or STM in EC. Experimental results are shown in Tables and. Strength: Table shows that that the CFRP sheet was eective in strengthening the beams but the contribution o the CFRP varied depending on its area and coniguration. Beams C- and C- in group A were strengthened with the same area o CFRP sheet (00 x 00mm) but the position o the sheets in the shear span was dierent. The CFRP sheet was applied adjacent to the supports in beam C, whereas it was placed 0mm rom the supports in beam C. The increase in shear strength in beam C was.kn whereas it was only.kn in beam C. Beams C and C were also strengthened with the same sized sheets o CFRP (0 x 00mm) but the distances o the sheets rom the supports were mm and mm respectively. The increase in strength in o C was.kn compared with an increase o.kn in beam C. The shear strength o C with complete side wrap was greatest at.kn whilst the increase in strength in C was only.0kn. The increase in strength was.kn in C which was strengthened with CFRP throughout its shear span over the lower hal o the beam depth within the lexural tension zone. Beams C and C were similarly strengthened over hal the beam depth with CFRP sheets measuring (00 x 0mm) placed at the centre o the shear span and adjacent to the support respectively. The increase in shear strength was.kn in beam C and.kn in beam C. Beams C0 and C were strengthened similarly with CFRP sheets measuring 0 x0mm placed at varying distances rom the support. The shear strength o both beams was increased by.kn. The increase in beams shear strength is given in Table which shows that beam C was the most eicient in terms o its combined increase in strength and cost eectiveness. Consideration o Table in conjunction with Figure shows that it is beneicial to apply CFRP sheets close to the support. Moreover, the area o CFRP sheet can be minimized with considerable increase in strength i the sheet is applied near the support. It is also shown that

6 the shear strength o the beams in Group B was reduced signiicantly compared with the beams in Group A by reducing the anchorage length o the CFRP. Ductility: Figure shows that the stiness and ultimate delection o the strengthened beams were greater stiness than in the control beams. The delection o the strengthened beams was ound to depend on the position o the CFRP sheet and its anchorage length. Increasing the distance o sheet rom the support and reducing the anchorage length decreased the delection at ailure. Zhang and Hsu[] also ound that CFRP strengthened beams give not only an increase in shear strength but also an increase in ductility. It is concluded that strengthening beams in shear with CFRP increases ductility in addition to strength. Failure Mechanism: All the control beams ailed in shear with mean shear strength o. kn. The CFRP sheets resisted the crack propagation in the shear span and changed the mode o ailure to lexure shear rather than shear ailure in the control beams. Beams C-, C- and C ailed as a result o lexure shear cracking alongwith delamination o the CFRP sheet. Beam C ailed due to de-lamination o the CFRP sheet rom the concrete surace with the concrete ailing in tension underneath the epoxy. Splitting o concrete at the top ace was also observed at ailure. The bonding between the CFRP sheet and the epoxy was good, except at ew spots where small pieces o epoxy were pulled away rom the surace o the CFRP sheet. The beam ailed due to the ormation o a lexural shear crack. Most o the beams ailed due to de-lamination o the CFRP sheet rom the concrete surace. Complete de-bonding o the CFRP sheet occurred due to diagonal cracking in one shear span o beams C and C0 whereas the CFRP sheet resisted crack propagation in the other shear span. Flexure shear ailure was observed in all the strengthened beams except beam C where only one mm wide CFRP strip was provided at each end. The crack pattern at ailure is shown or all the beams in Figure. Shear Strength Prediction Models: The nominal shear strength (V n ) o FRP strengthened concrete beams is conventionally calculated by adding the individual contributions o concrete (V c ), steel stirrups (V s ) and FRP (V ) as ollows: V n = V c + V s + V In ACI-, the design shear strength is obtained by multiplying the nominal shear strength by a strength reduction actor, Ø or which Khalia et al[] suggested a value o 0.0 or V. The contribution o the CFRP sheet to shear strength can be evaluated with the ollowing equation which is similar to that used to determine the shear contribution o steel stirrups. V E b e w d cotsin where ρ is the CFRP shear reinorcement ratio (t w /b w s ), E is the elastic modulus o CFRP, ε e is the eective tensile strain o CFRP, b w is the beam width, t is the thickness o CFRP reinorcement and w is the width, s is the spacing o CFRP which becomes equal to w or a continuous vertical CFRP reinorcement. The angle β describes the ibre orientation with respect to the longitudinal axis o the beam. d is the eective depth o CFRP reinorcement measured rom the centre o the tensile lexural reinorcement towards the lexural compressive zone in the beam. Triantaillou[], observed that the eective strain (ε e ) is a unction o the axial rigidity (ρ E ) o the externally bonded CFRP strips or sheet. Triantaillou[] determined the eective strain in the CFRP by back calculation rom experimentally derived values o V. () ()

7 An empirical relationship was developed between strain and axial rigidity by plotting eective strain versus axial rigidity or test data rom 0 beams published by various researchers. Khalia et al[] modiied Triantaillou s[] method or calculating ε e on the basis o a slightly enlarged data base o beams. The experimental data used by Khalia et al[] included two types o FRP materials (Carbon and Aramid), three dierent wrapping conigurations (sides only, U-shaped wrapping and complete wrapping), with both continuous sheets and strips o FRP. Khalia et al[] presented three equations or calculating the reduction actor (R) o which the lowest value is used to calculate the eective strain. The resulting eective strain is used in Equation () to calculate the contribution o the CFRP to the shear strength o the RC beam. Although Equation () was developed rom regression analysis o test data including both rupture and de-bonding ailure modes o CFRP, Khalia et al[] suggested using it or CFRP rupture only. R 0. E. E 0. The reduction actor or CFRP de-bonding is given by: R = 0.00( c ) / w e (t E ) 0. ε u d where w e is the eective width o the CFRP sheet which is taken as. 0.lnt E w d e e Khalia et al[] also suggested an upper limit o 0. to R to control the shear crack width and loss o aggregate interlock. In 00, Triantaillou and Antonopoulos[] presented three dierent equations using regression analysis o seventy ive experimental data, two or CFRP sheets and one or ully wrapped Aramid FRP sheets. The equation or ully wrapped CFRP sheet is given by: 0. e / 0.0 c / E u and or U-shaped or side wrapped CFRP is: min[0. e / c / E *0 ;0. c / / E ] The contribution o the CFRP sheet to the shear carrying capacity is calculated by substituting ε e rom equation () into Equation (). In 00, Zhang et.al[] presented two alternative equations or calculating the R- value. They considered the eect o concrete strength in the ollowing equation which was derived rom a regression analysis o test data: R. 0. E / c They also developed the ollowing analytical equation or calculating R rom an analysis o the bonding mechanism: R max L / e u t u () () () () () () ()

8 where L e is assumed to be mm (but urther research is needed), u is the ultimate tensile stress o CFRP and τ max is to be calculated rom the equation proposed by Hsu et.al[0] as ollows: max.*0 c.*0. where τ max is the ultimate direct shear strength in MPa. c The lowest o the values o R rom Equations () and Equation () is used to calculate the eective tensile strain in the CFRP. Zhang et al[] also recommended a maximum value o R equal to 0.. Zhang et al[] presented an equation equivalent to Equation () or calculating V. They[] took the contribution o continuous CFRP sheet to shear strength as: V w t sin b d / V e e where w e is deined in Equation (). c w s Comparison o measured and predicted shear strengths: The measured and predicted contributions o the CFRP to shear strength, V are compared in Table and Fig.. The experimental values o V were calculated by subtracting the mean shear strength o the control beams rom the shear strength o the beams with CFRP. The predicted values o V were calculated in accordance with the recommendations o Khalia et al[], Triantaillou and Antonopoulos[] and Zhang et al[]. V was calculated with Equation () with ρ = t w /(b w s ). The spacing s o the discrete strips o CFRP was taken as the clear shear span a v = mm. The eiciency o the truss action is reduced when the CFRP only extends over hal the beam depth as in some o the authors tests. Equation () is based on the truss analogy in which stirrups are assumed to extend over the ull height o the beam. The eiciency o the CFRP also decreases due to the reduction in its anchorage length when it only extends over hal the beam depth. This loss o eiciency in the CFRP was included in Equations () and () by measuring its eective depth d to the top o the CFRP. Table includes a comparison o the ratio V meas /V pred or each design method. It seems likely that the shear strength was increased in the beams in which the CFRP extended over hal the beam depth as a result o the angle o the critical shear plane being increased by the presence o the CFRP. The comparison is presented in Table or all the specimens, the specimens with CFRP over the ull beam depth and over hal the beam depth. The method o Khalia et al[] gives the most consistent predictions or V or all the authors beams and that o Triantaillou and Antonopoulos[] the least. The underestimate o V or beams C and C may be due to the early de-lamination o the CFRP sheet in beam C and de-bonding o the CFRP sheet on one o the side o beam in test C in which the shear crack crossed the CFRP sheet and propagated towards support, causing premature ailure o the beam. Equation () is based on the truss analogy and is theoretically applicable to beams in which the CFRP strips are evenly distributed within the shear span. Equation () seems less applicable or short span beams reinorced with a single CFRP strips in the shear span as in many o the tested beams. Eurocode (EC) and BS0 state that shear reinorcement is only eective in short span beams with a/d< i placed within the central three quarters o the shear span. The tests suggest that CFRP strips may be more eective, possibly due to enhancement o dowel action, in short span beams when positioned close to the support rather in the central three quarters o the shear span. Thereore, V was recalculated in terms o the total area o CFRP within the shear span as ollows: (0) ()

9 V = t w E ε e () The resulting values o V are given in Table which shows that the shear strength contribution calculated using the total area o CFRP overestimates the shear carrying capacity. Strut-and-tie model: The authors have analysed the beams in Group A, which were strengthened over their ull height, with a strut-and-tie model (STM) which was developed by Sagaseta and Vollum[] or short span beams with steel shear reinorcement. The STM model is consistent with the design recommendations in EC or strut and tie modelling. It is assumed that the shear orce is transerred to the supports via, irstly, a direct strut and, secondly, a truss system consisting o two indirect struts equilibrated by stirrups as shown in Fig.. The proportion o the shear orce taken by the direct strut () and its angle o inclination to the horizontal () are ound iteratively by solving equations () to (). Equations () and () are derived rom considerations o geometry whilst Equations () and () are derived rom consideration o horizontal equilibrium at the bottom node. n i. n n i av lb. l cot i h c. n lb lt av. nlp cot ' Ti Td / h c bcnt ' T i T Si. coti n n T d.cot. T Si n. T Si b lt Si. n '.c C l b sin c sin. b.0. cd All the terms in equations () to () are deined in Fig.. The tensile orces T i and T d in equation () and () are the horizontal components o orce in the indirect strut III and direct strut I respectively. The critical ailure mode is assumed to be crushing o the direct strut, and is implicit in equation (). The width o the direct strut was calculated in terms o the geometry o the bottom node. The eective concrete strength o the direct strut was assumed to be 0. cd where =(- ck /0) as deined in EC. The bearing stress under the plates was assumed to be uniorm and was limited to 0. cd at the bottom nodes and cd at the top nodes, as recommended in EC. The top boundary o strut III is assumed, or simplicity, to be linear so that the distance C i can be easily estimated rom horizontal equilibrium at the top node. The strut and tie model is statically determinate i the stress in the shear reinorcement is known at ailure. Sagaseta and Vollum[] ound that steel stirrups yield at ailure (T si =A sw. y ) or stirrup indices (SI) less than 0., where SI=nA sw y /(b w h c ). The STM can be i lp () () () () ()

10 applied to beams with CFRP shear reinorcement i the eective tensile stress is known in the CFRP at ailure. The CFRP sheets were assumed to be located at the centre o the shear span in the STM as shown in Fig.. The tensile orce in the CFRP was calculated as the product o the eective area o each strip (see Fig. ) and the eective tensile stress in the CFRP. CFRP was only assumed to be eective i positioned within the central three quarters o the clear shear span as stated in EC or beams with steel stirrups. This assumption was ound to be reasonable or specimens C, C and C in which the area o CFRP outside the central three quarters o the shear span was neglected. Several assumptions needed to be made regarding the geometry o the bottom node since the specimens were supported on rollers (see Fig. ). These assumptions were based on a previous analysis o a series o beams supported on rollers tested by Shin et al. [] which were reinorced with steel shear reinorcement. The beams had a v /d ratios o. and.0. Beams which ailed due to local crushing o the concrete at the support were not considered in the analysis. The bottom node was modelled assuming an equivalent bearing plate length l b,e = c.cot(see Fig. ), where is the dispersion angle measured rom roller centreline to the lexural reinorcement to the horizontal. An optimal value o. was obtained or the dispersion angle rom a back analysis o Shin s[] test results with the STM. It is suggested that is conservatively taken as 0 in practice. Shin s[] beams were reanalysed with = 0 obtaining a mean and standard deviations o P test /P calc o.0 and 0. respectively or the beams. Table shows that the strut-and-tie model described in this paper gives good predictions o the shear strength or beams in group A. The mean value o P test /P calc was 0. or the six beams analysed and the standard deviation was 0.. The worst predictions were obtained or beams C and C, which appear to have ailed prematurely due to de-bonding o the CFRP sheets without concrete ailure. Nevertheless, Table shows that the STM provided sae estimates o the ultimate strength when standard material actors o saety were applied ( c =. and =., according to ib report[]) as shown in Table. The STM predictions are relatively accurate even though the specimens had a clear shear span to eective depth ratio o which is at the upper limit o the range or which the model is applicable[]. The STM tends to give better estimates o the shear strength o the beams in series A strengthened with CFRP than the empirical design equations described in this paper. It is interesting to note that there are substantial conceptual dierences between the STM and empirical design approaches. The design ormulas, which are based on a classical truss superposition concept (V c +V ), were derived assuming a constant concrete contribution which was estimated rom the shear strength o the control beams. On the other hand, the shear component o the direct strut (V c =V) reduces with increasing stirrup index in the STM. The test data were investigated to determine which o these assumptions is most realistic. V c was estimated by subtracting the calculated value o V or each method rom the ultimate shear strength obtained in the experiments. Figure shows that the values o V c obtained rom this analysis were closer to the predictions o the STM than the constant value assumed in the remaining design methods. Even though the concrete component seemed to be overestimated in the superimposition methods, the ultimate loads predicted were similar to the STM predictions. This suggested that the reduction actor R derived in superposition methods must compensate or this overestimation o the concrete component. The existing design empirical ormulas described in this paper do not take into account the relative position o the shear reinorcement relative to the clear shear span. Although the strut-and-tie model makes allowance or changing the position o the stirrups (Si) the eect o changing this variable has a minor inluence on the predicted ultimate

11 strength o the beam. The increase in strength observed in beam C compared with C, and in lesser extend in beams C and C, due to changing the position o the CFRP closer to the support is not captured by the STM. This increase in strength could be due to enhancement o the contribution o the dowel action, which is not considered in the STM. APPLICATION OF EUROCODE The drat ENV version o EC included the Standard design method or beams in shear which was similar to Equation (). The Standard method was removed during the inal development o EC[] which now only gives the variable strut inclination method or the design o shear reinorcement in beams. It is assumed in the variable strut inclination method that the shear orce is resisted by a truss consisting o the concrete struts acting in compression and the shear reinorcement acting in tension. The angle o the concrete struts varies rom. to degrees to the longitudinal axis o the beam depending upon the applied shear orce. For members with inclined shear reinorcement, the design value o the shear orce is given by: V Rd,s = A sw (0.d) ywd (cotθ + cot β)sin β /s () where A sw is the area o steel shear reinorcement; ywd is the yield strength o the shear reinorcement; s is the spacing o the stirrups; θ is the angle in degrees o concrete strut to the longitudinal axis o the beam; β is the inclination angle o shear reinorcement. The value o cot θ is limited to < cotθ <.. EC also imposes a maximum limit on cot θ which is governed by the crushing o concrete struts. V Rd,max = 0. b w d ν cd /(cotθ + tanθ ) () where ν is a strength reduction actor or concrete cracked in shear and cd is the design value o the concrete compression orce in the direction o the longitudinal member axis. A simple regression equation is proposed or the calculation o eective stress in CFRP to be used in EC. Experimental data rom beams strengthened with CFRP, in which all the required test data was available, has been analysed to determine whether the VSI method in EC is suitable or the design o beams. All the beams were U-wrapped and details o the beams considered are given in Table. It was assumed that the external CFRP reinorcement can be treated in the same way as internal steel stirrups i the stress in the CFRP is calculated in terms o the eective strain which is lower than the ultimate value or the naked CFRP as previously discussed. Equation can be rewritten as: V Rd, = 0. ρ b w d ε e E (cotθ + cot β)sin β (0) where ρ is the CFRP reinorcement ratio which is given by ρ = t w /b w a v ; ε e is the eective tensile strain in the sheet, a v is the clear shear span and β is the angle o inclination o FRP to the longitudinal axis o the beam. The eective stress in the CFRP was calculated by back substitution into Equation 0 using the experimental values o shear strength. The reduction actor R was calculated rom the ratio o the eective stress ( e ) to the ultimate strength ( u ) o the FRP. The resulting reduction actors are plotted against axial rigidity in Figure. A power relationship was derived between the reduction actor (R EC ) and the axial rigidity (ρ E ) in a regression analysis. Figure shows that the r-squared value is relatively high indicating that a simple power expression gives a reasonable representation o the relationship between axial rigidity 0

12 and R EC. The corresponding proposed power equation or calculating the eective strain in FRP is given by: ε e = ε u {0.0(ρ E ) -0. } () The value o eective strain rom Equation () is used in Equation (0) to calculate the shear strength o the concrete beam strengthened in shear using CFRP sheets or strips. The experimental and predicted shear strengths are compared in Figure. The design datum was obtained by multiplying the eective strain given by Equation () by a reduction actor o 0. to achieve a lower bound to the test data. Figure also shows the shear strengths predicted with Equation () with V c calculated in accordance with EC using a material actor o saety o. or concrete. It is concluded that the variable truss model can be used to calculate the design shear strength o beams strengthened with CFRP. CONCLUSIONS Following conclusions have been drawn rom the research work presented in this paper:. Experimental results revealed that signiicant increase in shear strength and ductility can be achieved by proper application o CFRP sheets to shear deicient concrete beams. The presence o CFRP sheet resists the crack propagation and alters the brittle ailure mode to ductile.. For short beams, the application o CFRP sheet closer to the supports was ound beneicial as the area o CFRP sheet can be minimized with considerable increase in shear strength.. It was observed that all the strengthened beams showed relatively greater stiness than the control beams however the ultimate delection was ound higher. The delection o the strengthened beams was ound dependent upon the placement o CFRP sheet and its anchorage length, as increasing the distance o sheet rom the support and reducing the anchorage length resulted in the corresponding decrease in delection.. Comparison o experimental results with three dierent prediction models revealed that the model proposed by Khalia et al. predicted the experimental results with good accuracy and saety margin. Although the model was proposed or complete side wrap, it can also be applied eectively to dierent arrangements o CFRP sheet and anchorage lengths along the shear span o the beam.. The ultimate strength o the short span beams strengthened with CFRP sheets up to the ull depth can be well predicted using the simple strut-and-tie model suggested by the authors. The STM predictions were reasonable despite that the clear shear span to eective depth ratio was, which is near the limit o validity o the strut-and-tie model. Although the STM model allows or changing the position o the vertical reinorcement along the clear shear span, the inluence o these variations into the ultimate strength are negligible. The strut-and-tie model agreed with predictions rom empirical approaches, although the concrete contribution was not constant in the STM, as assumed in the empirical methods. This conceptual dierence between both approaches raises the question o whether the reduction actor R, which is obtained empirically assuming a classic truss concept (V c +V s ), should be applied to other methods such as STM.. The proposed equation or calculation o eective stress in CFRP can be eectively used in EC and it is shown that the variable angle truss model in EC can be used to calculate the shear strength o CFRP strengthened beams.

13 REFERENCES []. Cao, S. Y, Chen, J. F. Teng, J. G, Hao, Z. and Chen, J., Debonding in RC Beams Shear Strengthened with Complete FRP Wraps, Journal o Composites or Construction, Vol., No., October, 00, p.p. []. Adhikary, B.B. and Mutsuyoshi, H., Behavior o Concrete Beams Strengthened in Shear with Carbon-Fiber Sheets, Journal o Composites or Construction, Vol., No., June, 00,p.p. []. Berset, J., Strengthening o Reinorced Concrete Beams or Shear Using FRP Composites, MSC thesis, Department o Civil and Environmental Engineering, Massachusetts Institute o Technology, Jan.. []. Uji, K., Improving Shear Capacity o Existing Reinorced Concrete Members by Applying Carbon Fiber Sheets, Transactions o the Japan Concrete Institute, Vol.,, pp. -. []. Chajes, M. J., Januska, T.F., Mertz, D.R., Thomson, T.A., and Finch, W.W., Shear Strengthening o Reinorced Concrete Beams Using Externally Applied Composite Fabrics, ACI Structural Journal, Vol., No., May - June, pp. -0. []. Sato, Y., Ueda, T., Kakuta, Y., and Tanaka, T., Shear Reinorcing Eect o Carbon Fiber Sheet Attached to Side o Reinorced Concrete Beams, Advanced Composite Materials in Bridges and Structures, edited by El-Badry, M.M.,, pp. -. []. Umezu, K., Fujita, M., Nakai, H., and Tamaki, K., Shear Behaviour o RC Beams with Aramid Fiber Sheet, Non-Metallic (FRP) Reinorcement or Concrete Structures, Proceedings o the Third Symposium, Vol., Japan, Oct., pp. -. []. Araki, N., Matsuzaki, Y., Nakano, K., Kataoka, T., and Fukuyama, H., Shear Capacity o Retroitted RC Members with Continuous Fiber Sheets, Non-Metallic(FRP) Reinorcement or Concrete Structures, Proceedings o the Third Symposium, Vol., Japan, Oct., pp. -. []. Norris T, Saadatmanesh, H and Elsani R, Shear and lexural strengthening o R/C beams with Carbon Fiber Sheets, ASCE Journal o Structural Engineering, V., No., July,, pp. 0-. [0]. Hsu, C. T. T., Bian, H. T., and Jia, Y. X. (), Research or bond-slip using Sika s Carbodur system. Report to Sika Corporation, NJIT, Newark, N.J. []. Malek, A., and Saadatmanesh, H., Ultimate Shear Capacity o Reinorced Concrete Beams Strengthened with Web-Bonded Fiber-Reinorced Plastic, ACI Structural Journal, July- Aug., pp -. []. Triantaillou, T.C., Shear Strengthening o Reinorced Concrete Beams Using Epoxy- Bonded FRP Composites, ACI Structural Journal, Mar.-Apr., pp. 0-. []. Khalia A, Gold W, Nanni A, Abdel-Aziz MI, Contribution o externally bonded FRP to the shear capacity o RC lexural members Journal o Composites or Construction,; Vol. No.,, pp 0. []. Triantaillou, T. C., and Antonopoulos, C. P. Design o concrete lexural members strengthened in shear with FRP. Journal o Composites or Construction, Vol. No, 000, pp 0.

14 []. Technical Report on the Design and use o externally bonded ibre reinorced polymer reinorcement (FRP EBR) or reinorced concrete structures by working party o ib Task Group., July 00,pp,ISBN []. Concrete Society. Design Guidance or strengthening concrete structures using ibre composite materials, Technical Report, UK, 00. []. Zhang, Z. and Hsu, T., Shear Strengthening o Reinorced Concrete Beams Using Carbon-Fiber-Reinorced Polymer Laminates, Journal o Composites or Construction, Vol., No., April, 00.,p.p,00. []. Khalia, A. and Nanni, A., Rehabilitation o Rectangular Simply Supported RC Beams with Shear Deiciencies using CFRP Composites, Construction and Building materials, 00,,. []. Sagaseta, J. and Vollum, R., Strut-and-tie Modelling o Short Span Beams, Proceedings o the International ib Symposium 00, Tailor Made Concrete Structures: New Solutions or Our Society, May -, 00, Amsterdam. [0]. Brena, S. F., and Macri, B.M., Eect o Carbon-Fiber-Reinorced Polymer Laminate Coniguration on the Behavior o Strengthened Reinorced Concrete Beams, Journal o Composites or Construction, Vol., No., June, 00,p.p 0. []. Zhang, Z., Hsu, T. and Moren, J., Shear Strengthening o Reinorced Concrete Deep Beams using Carbon-Fiber-Reinorced Polymer Laminates, Journal o Composites or Construction, Vol., No., October, 00,p.p 0. []. Carolin, A. and Taljisten, B. Experimental Study o Strengthening or Increased Shear Bearing Capacity, Journal o Composites or Construction, Vol., No., December, 00,p.p. []. Guadagnini, M. Pilakoutas, K and Waldron, P, Shear Resistance o FRP RC Beams: Experimental Study, Journal o Composites or Construction, Vol. 0, No., December, 00,p.p. []. Shin, S.W. Lee, K.S. Moon, J.I. Ghosh S.K. Shear Strength o Reinorced High- Strength Concrete Beams with Shear Span-to-Depth Ratios between. and., ACI Structural Journal, Vol., No., January, 000, pp. -. []. Chaalal O, Nollet M.J and Perraton D, Shear Strengthening o RC Beams by externally bonded side CFRP Strips Journal o Composites or Construction,; Vol. No.,, pp. []. Bukhari I.A, Ahmad, S, Vollum R L and Sagaseta J.(00) Shear Strengthening o Reinorced Concrete Beams with CFRP, Magazine o Concrete Research, V., No., January.00, pp. -. []. BRITISH STANDARDS INSTITUTION. Eurocode -, (00) Design o Concrete Structures: General rules or buildings, BSI, London, 00.

15 Beam Re Control c (MPa). (avg) Table : Specimen Details and CFRP Properties a/d ρ l (%) b w (mm) Section Details d (mm) d s (mm) CFRP properties and wrapping schemes t (mm) E (GPa) u (MPa) β ρ (x0 - ) C ,0 0. C ,0 0. C ,0 0. C ,0 0. C ,0 0. C ,0 0. C ,0 0. C ,0 0. C ,0 0. C , C ,0 0. Beam No Table : Comparison o Experimental Results Experimental Triantaillou Khalia Zhang et V cal = STM* EC Results et al. et al al t w E ε e P u Vexp V V T V / V K V / V Z V / V V / P calc P calc / V exp / cal VEC (kn) (kn) (kn) (kn) V T (kn) V K (kn) V Z V cal (kn) P u VEC Failure mode Control Shear (avg) - Sheet C delamination Sheet C delamination Sheet C delamination Sheet C delamination C Debonding C C C Sheet delamination Sheet delamination Sheet delamination C Debonding C Debonding C Debonding Notes: STM* values obtained with a material saety actors o.0.

16 Table : Comparison o Results according to EC Section Details FRP Properties ρ Sr No Beam No ρ E V exp R EC V EC V exp / b (x0 - w d β E ) [kn] ( e / u ) [kn] V EC (mm) (mm) (GPa) (Deg) T(Sla) T(Slb) T(Sa) T(Sb) T(Sa) T(Sb) T(S-) T(S-) T(S-) K(B-CO) K(B-CO) K(C-BT) K(C-BT) K(C-BT) K(C-BT) K(A-SO-) K(A-SO-) K(A-SO-) K(A-SO-) Z(Z 0) Z(Z ) CH(RS0-) CH(RS0-) CH(RS-) CH(RS-) BC(C) BC(C) BC(C) BC(C) BC(D) AD (B-) AD (B-) AD (B-) AD (B-) AD (B-) T=Triantaillou[,]; K=Khalia et al [,], Z= Zhang et al[,] ; CH = Challal et al[]; BC= Bukhari et al[], AD = Adhikary et al[]

17 Figure : Beam Cross-section, reinorcement details and Anchorage length o CFRP () Group A () Group B

18 Figure : Beam Coniguration Details () GROUP A () GROUP B

19 Figure : Crack pattern in tested beams

20 Load (kn) Load (kn) Load (kn) Figure : Load Delection Curves 0 Mid-span delection(mm) (a) 0 Mid-span delection(mm) (b) 0 Mid-span delection(mm) (c) C C C C c C C C C

21 Load (kn) Load (kn) Figure -contd C 00 C 0 C 0 0 Mid-span delection(mm) (d) C 0 C 00 C0 0 0 Load (kn) 0 Delection (mm) (e) C 00 C Mid-span delection(mm) () 0

22 CFRP Shear Strength (kn) Figure : Prediction o shear capacity o CFRP sheets C- C- C- C- C- C- C- C- C-0 C- C- Experiment Triantaillou Khalia et al Zhang et al Figure : Strut-and-tie model or beams A

23 Vc [kn] Figure : Concrete shear component in beams in Group A Control C C C C 0 Vtest 0 STM Khalia 0 Trian Zhang SI C Vc constant Figure : Relationship between R EC and Axial Rigidity C

24 R Vexp[kN] R EC = 0.00(ρ E ) -0. r = ρ E Best Fit Line Modiied Figure : Curve between V exp and V EC (calculated) ( tests) V EC [kn] Design Datum Factored Design Datum