Flexural Strength of RC Beams Strengthened with Prestressed CFRP Sheets Part II

Transcription

1 Flexural Strength o RC Beams Strengthened with Prestressed CFRP Sheets Part II by Piyong Yu, Pedro Frano Silva, and Antonio Nanni Biography: Piyong Yu is a strutural Engineer with Matrix Engineering Corporation, Chiago, IL. His researh interests deal with the use o FRP or the strutural rehabilitation o buildings and bridges. ACI member Pedro F. Silva is an Assoiate Proessor o Civil and Environmental Engineering at the George Washington University, DC. He is a member o ACI Committees 0 and 1. His researh interests inlude the development o innovative perormane-based proedures or the design and retroit o strutures, and use o FRP or the strutural rehabilitation o strutures Antonio Nanni, Fellow ACI, is Proessor and Chair in the Department o Civil, Arhitetural and Environmental Engineering at the University o Miami and Proessor o Strutural Engineering at the University o Naples Federio II. He is hair o ACI Committee and member o ACI Committees 0,, and. His researh interests inlude onstrution materials, their strutural perormane and ield appliation

2 ABSTRACT A prototype mehanial devie was developed under this researh program or prestressing arbon iber reinored polymer (CFRP) sheets. This devie oers signiiant eatures suh as: the CFRP sheets are anhored diretly to the devie itsel, the prestress ores are applied manually by a torque wrenh without the need or power operated hydrauli jaks, and the transer operation is aomplished at slow strain rate. To investigate the easibility o using this devie or strengthening o reinored onrete (RC) beams, seven beams were strengthened with prestressed CFRP sheets at dierent prestressing levels. In an aompanying paper, the main eatures and the appliation proedures or this mehanial devie along with levels o prestressing losses beore and ater transer are disussed. In this paper, theoretial and experimental results related to prestressing levels that an lead to debonding o the sheets immediately ater transer and during lexural testing are disussed in detail together with the investigation on the inrease in the lexural apaity that results rom prestressing and anhoring the CFRP sheets at the beam ends with U-wraps. Keywords: debonding; iber reinored polymer; lexure; premature; prestressing; RC beams; strengthening

3 INTRODUCTION FRP omposites have been extensively used to inrease the lexural apaity o RC beams. In the last deade, researhers have also onsidered the prospets o prestressing FRP sheets and laminates as a means or inreasing the lexural apaity and servieability o RC beams (Triantillou et al., 1; Char et al., 1; Izumo et al., 1; Quantrill and Hollaway, 1; EI-Haha et al., 001). Researh results have shown that, depending on the level o prestressing, the immediate beneits o prestressing FRP omposites are that the raking and yielding moment apaity and servieability o these beams an be improved, and, depending on the level o prestressing, the beam ailure mode an hange rom onrete rushing to FRP rupture (Wight et al., 001). Researh has also shown that when the beams are strengthened with prestressed FRP omposites the propensity or premature ailure inreases due to higher shear stress onentrations in the adhesive layer and at the uto points. These premature ailure modes an be either by onrete over separation or interaial FRP debonding. Test results have shown that some o these premature ailures may be delayed or avoided by anhoring the prestressed FRP omposites lose to the ut o points. Validated by other researhers, analyses show that when onrete rushing is the predominant ailure mode o the beams strengthened with prestressed FRP omposites, an inrease in the prestressing level auses also an inrease in the lexural apaity. When the FRP omposite is not prestressed and the ailure mode is haraterized by FRP rupture, experimental and analytial results both validate that prestressing the FRP sheets does not lead to an inrease in the lexural apaity but only an inrease in servieability (Char et al., 1; Garden et al., 1).

4 Some drawbaks assoiated with the devies urrently ound in the literature are that the mehanial system must be anhored to the beam surae using high apaity bolts, the transer operation is aomplished under high strain rates, and these mehanial systems must be power operated (Triantillou et al., 1; Char et al., 1; Quantrill and Hollaway, 1; EI-Haha et al., 001). In order to improve on these devies, a simple yet untional mehanial devie was developed in this program to prestress CFRP sheets (Yu et al., 00). Attrative eatures o this devie are that the prestressing was ahieved manually without the need or hydrauli jaks and transer was aomplished under slow strain rates. In order to investigate the easibility o using this devie or strengthening appliations, seven RC beams were strengthened with prestressed CFRP sheets at dierent prestressing levels. Test results show that the devie was eiient in prestressing the CFRP sheets to at least 0% o the ultimate strength, and in all beams prestressing losses ater transer amounted to less than % o the initial prestress. Dierent than the expeted ailure mode, the strengthened beam with a non-prestressed CFRP sheet ailed due to FRP rupture. In two o the prestressed beams, U- wraps were also installed at the end o the CFRP sheets to delay or avoid delamination o the CFRP sheets and the ailure mode o these beams was also by FRP rupture. In all the other prestressed beams without end anhors ailure was by onrete over separation and below the ultimate apaity o the beams anhored with the U-wraps. Conrete over separation, FRP end debonding, intermediate raks indued debonding or midspan debonding are reported as the major premature ailure modes o strengthened RC beams using FRP sheets (Teng et al., 00; Thomsen et al., 00). Shear apaity based models, onrete tooth models, and interaial stress based models have been developed to predit the premature ailure o RC beams strengthened with FRP omposites (Smith and Teng, 001). For

5 RC beams strengthened with prestressed FRP omposites, high stress onentrations at the uto points greatly inreases the propensity or end debonding and onrete over separation (Quantrill and Hollaway, 1; Teng et al., 00). In many o the stress based models proposed in the literature, the ailure riterion is based on the tensile strength o onrete and the lassial -D plane stress. Sine urrent models do not address the ontribution o prestress to the premature ailure mode, in this researh program, the ailure model proposed by Tumialan et al. (1) was modiied to inlude the inluene o prestressing on the ailure riterion. In this paper, the behavior o RC beams strengthened with prestressed and non-prestressed CFRP sheets are ompared against an unstrengthened beam. Flexural analysis o RC beams strengthened with prestressed CFRP sheets is also disussed in greater detail in this paper. Both moment-urvature and diret methods o analyses were employed in the analyses and were subsequently validated and ompared against the experimental results. Validated by other researhers, the main result rom this researh indiate that prestressing o the CFRP sheets inreases the lexural apaity with a derease in the dutility apaity o RC beams. Experimental results also suggest that a higher tensile strength o onrete at onrete over separation exeeded those values stipulated in the Amerian Conrete Institute (ACI) design speiiations (00). In a irst aompanying paper the main omponents and installation proedures or the mehanial devie are desribed in great detail and this paper mainly disusses the experimental and analytial results rom the lexure program. RESEARCH SIGNIFICANCE In this researh program, a mehanial devie was developed or manually prestressing CFRP sheets and strengthening o RC beams. This program investigated the ollowing: i) losses o prestress, ii) level o prestressing that would lead to debonding o the sheets during transer,

6 iii) premature and lexural ailure during the bending tests, and iv) inreases in the lexural apaity resulting rom prestressing and anhoring the CFRP sheets. A omprehensive theoretial analysis is also presented to show the inluene o prestressing on the ailure mode o RC beams. EXPERIMENTAL PROGRAM Test Matrix In order to investigate the easibility o using the prototype mehanial devie or prestressing CFRP sheets (Yu et al., 00), a total o eight RC beams were tested in this program. As shown in Figure 1a the beams were 0 mm ( in.) wide by mm ( in.) deep and were strengthened to the prestressing levels listed in Table 1. Beam A was the unstrengthened ontrol speimen and was used to establish a perormane baseline or the strengthened beams. Beam B was the strengthened ontrol speimen and was used to establish a perormane baseline but, in this ase, or the prestressed beams. Beams C, D and E were all prestressed to 1% o the ultimate strength o the CFRP sheets, but in beam E end anhors in the orm o U-wraps were also installed. Beams F and G were prestressed to 0% o the ultimate strength o the CFRP sheets but, as in beam E, in beam G end anhors were also installed. Finally, beam H was prestressed to 0%. Development o the test matrix in terms o the beam ross setion dimensions and reinorement ratios were obtained based on a detailed theoretial analysis with the main objetive to best quantiy the eets o prestressing the external CFRP sheets. Steel Reinorement Details These beams were built using two D1 (#) bars on the tension side leading to a reinorement ratio, ρ s, o 0.%, and two D (#) bars on the ompression side. In its unstrengthened ondition the balaned steel reinorement ratio was nearly.%, indiating that

7 the lexural apaity or Beam A was mainly ontrolled by yielding o the longitudinal reinorement and ailure by onrete rushing. As depited in Table 1, this ailure mode was also substantiated by the experimental results. CFRP Composite Reinorement Details The CFRP sheets used were 0.1 mm (0.00 in.) thik and 0 mm ( in.) wide leading to a total reinorement area o. mm (0.0 in. ). In all the strengthened beams, the sheets were then bonded to the RC beams using a mm (1/ in.) adhesive thikness, whih was ontrolled with glass beads. For the strengthened beams, the CFRP sheets reinorement ratio, ρ, was 0.0%. Using an ultimate onrete strain o 0.00, the FRP balaned reinorement ratio was nearly 0.0%, indiating the ailure mode was mainly ontrolled by onrete rushing well beore FRP rupture. This was the target design or this researh, beause analysis learly show that, apart rom premature ailure modes, when ailure o the non-prestressed beams is by onrete rushing inrease in the prestress level provides or an inrease in the lexural apaity and, beyond a ertain level o prestress level, the ailure mode an be altered to ailure by FRP rupture. These observations will be urther substantiated in a later setion when presenting the results derived rom the analytial work. As depited in Table 1, the observed ailure o Beam B was by FRP rupture, whih ontradits the expeted ailure mode. Under higher ultimate onrete strain onditions, suh as 0.00, the FRP balaned reinorement ratio is in the order o 0.0%, indiating that, in this ase, the ailure mode was mainly ontrolled by the properties o CFRP sheets. As suh, it is reommended that uture researh should address other levels o FRP reinorement ratio that an learly substantiate the inluene that prestressing the CFRP sheets have on the ailure mode. Material Properties

8 Material properties are shown in Table, where the haraterization o the arbon ibers, primer, putty and saturant were provided by the manuaturers. Six ylindrial onrete speimens measuring approximately 0 mm ( in.) diameter by 00 mm ( in.) deep were ast and tested aording to ASTM C at a loading rate o. kn/se (00 lb/se). The average onrete ompression strength was. MPa (,00 psi) with a standard deviation o.1 MPa (00 psi). Five tensile strength tests or the D1 (# ) bars were onduted aording to ASTM A0, with an average yield and ultimate strength o MPa (. ksi) and 1 MPa (. ksi), respetively. For both strength levels the standard deviation was nearly. MPa (. ksi). Speimen Preparation Prior to strengthening, the surae o the RC beams was roughened until the aggregates were exposed, ollowed by vauum leaning to remove the dust and any loose partiles. First a thin layer o primer was applied to the prepared surae o the RC beams by using a palette knie, whih was ollowed by a layer o putty. Sine Beam B was not prestressed, the CFRP sheet was bonded ater the irst layer o saturant was applied. For the prestressed beams, two other layers o adhesive were used to bond the prestressed CFRP sheets to the RC beams. Prestressing o the CFRP Sheets For the prestressed beams, the CFRP sheets were irst prepared by impregnating the ibers with a saturant on a lat surae. The sheets were then prestressed using the mehanial devie developed in this researh program (Yu et al., 00). Ater the CFRP sheets were prestressed, the next step onsisted o bonding the prestressed CFRP sheets to the RC beams. Figure shows the mehanial devie with the prestressed CFRP sheet already bonded to the RC beam. Ater bonding, the prestressing devie stayed in plae or at least 0 hours in order to allow the adhesive to properly ure.

9 Ater this stage, the transer proess was arried out by slowly releasing the prestressing in the CFRP sheets. In these types o appliations the transer operation is typially aomplished under high strain rates. This issue was mitigated by this devie, beause, transer o the prestressing ores was arried out under slow strain rates. Ater the transer proess was ompleted, the prestressed sheets were ut, and the mehanial devie was removed and leaned or urther appliations. Further details pertaining to this devie an be ound in the irst aompanying paper (Yu et al., 00). Flexural Testing Setup The beams were tested in a our-point loading with a entral onstant moment region o mm ( in.) and a span length o.1 mm ( in.). The overall test setup is depited in Figure 1b. One hydrauli jak was used or loading o the beams at mid-span and heavy duty steel rollers were used at the loading and supporting points to provide bearing and ritionless rotational supports. The mid-span deletion was measured by two string transduers and the external load and mid-span deletions were reorded with a data aquisition system. INTERFACIAL SHEAR STRESSES AFTER TRANSFER Works by Triantaillou and Deskovi () and Karam (1) have been used extensively to trae the development o interaial shear stresses in RC beams strengthened with prestressed FRP sheets. Upon releasing the prestressing ore, transer o stresses rom the prestressed CFRP sheets to the RC beams leads to shear stresses in the adhesive layer with higher stresses developing at both ends o the CFRP sheets. For low levels o prestressing, these materials stay within the elasti range. Based on the assumption that shear is the governing mode o deormation in the adhesive layer, Karam (1) proposed the ollowing expression to desribe the distribution o the interaial shear stresses, τ p,x, as a untion o the initial prestressing ore in the CFRP sheets beore transer, and along the length, l, o the CFRP sheet

10 τ ε E A p e px, = sinh( wx) τ max E osh( wl) taw A (1 + n Aβ ) G a Eq. 1 1 Where the variables w and β are Gw a (1 + n Aβ ) 1 h w =, and tae β = A + I Eq. a T As shown in Figure a, x is taken rom the enter o the beam, and l is hal the length o the CFRP sheet. In these equations, the unraked transormed setion moment o inertia, I T, was used in the analysis at transer. As the prestressing ore inreases, higher interaial shear stresses develop with a limiting value orresponding to τ max. Reently, a ew loal bond stressslip models have been developed to estimate τ max (Wu et al., 00; Lu et al., 00). Aording to these models, the bond stress-slip relationship inludes one asending branh and one desending branh. Lu et al. (00) have proposed the ollowing expression to ompute the maximum bond shear strength, τ max, as a untion o the tensile strength o onrete τ max w. b = 1. = 1. = w w = b b t t t Eq Where b and w were equal to eah other. As suh, substituting or the tensile strength o onrete, t, in Eq., one obtains the maximum bond shear strength, τ max. Another bond stressslip model was proposed by Saadatmanesh and Malek (1), in whih they used a dierent / relation or τ max given by 0. ( ) (MPa) [0.1 ( ) / (ksi)]. However, in this researh program, the more reent work by Lu et al. (00) was adopted beause it led to results that best orrelate to the experiments and was developed based on the geometri relations between the CFRP sheets, the onrete surae, and the tensile strength o the onrete. The value or τ max

11 was subsequently used in this setion to best quantiy the prestressing level or debonding o the CFRP sheets at transer. One the interaial shear stresses omputed in terms o Eq. 1 reahes the maximum bond shear strength, τ max, regions o plasti behavior develop at the edges o the CFRP sheets. These regions are governed by the bond stress-slip nonlinear relationships between the adhesive layer and the onrete substrate, and in the work by Triantaillou and Deskovi () the interaial shear stress distribution dereases linearly rom τ max aording to x l o τ p( x> lo) = τmax + 1 Eq. lo l As shown in Figure a l o is the loation when the interaial shear stress reahes τ max. At debonding, the elasti range dereases rom l to l o, and within l-l o the interaial shear stress distribution dereases approximately linearly rom the peak stress, τ max, to zero at the edges o the CFRP sheet. Triantaillou and Deskovi () developed design harts that were used to approximate l o at onset o debonding. Using the orresponding material and geometri properties o the RC beams used in this experimental program l o was approximated at 0. l rom these harts. It is important to emphasize that or dierent material properties and length o the CFRP sheets this ratio is dierent. In RC beams, sine the tensile strength o onrete is signiiantly lower than the adhesive layer strength, the nonlinear region is dominated by the onrete substrate material properties and ailure o the system is governed by the tensile strength o onrete. In the researh program onduted by Tumialan et al. (1), they used a value or the tensile strength o onrete equal 0 to 0. (MPa) [. (psi)]. Based on this tensile strength and using Eq. one obtains that 1 τ max is 0. (MPa) [. (psi)]. Other values used in the work by Ziraba et al. (1) and

12 Triantaillou and Deskovi () are presented in Table. In this researh program, these three values were used as limiting values to estimate the value at whih debonding o the CFRP sheets was likely to our. Analysis orresponding to the level o prestressing neessary to impose debonding o the CFRP sheets in RC beams and the work onduted to establish the prestressing levels shown in Table 1 is disussed next. Using the ross setion dimensions and the test setup shown in Figure 1, the material properties presented in Table, and with an adhesive layer thikness, t a, equal to mm (1/ in.) plots or the interaial shear stress along the length o the CFRP sheets and as a untion o the initial prestressing ore, P o, were developed and are shown in Figure b. As shown in this igure, it is lear that or the % and 1% prestressing levels the ull length o the CFRP sheet is still within the elasti range. Then, as the prestressing level inreases to 0% and % regions o nonlinear behavior develops; but, delamination o the CFRP sheets has not yet initiated. Based on this igure, interaial debonding will our when the prestressing ore at transer is approximately 0% o the ultimate strength o the CFRP sheet as τ max is reahed when x equals to l o. It is lear that in the analytial studies depited in Figure b the value or τ max was 1 established at 1.0 (MPa) [1.0 (psi)]; however, or other levels o τ max debonding will ertainly our at a dierent prestressing level. As the thikness o the adhesive layer, t a, is likely to vary within the development length, parametri studies were onduted to quantiy the eets o t a on the interaial shear stress at the debonding and as a untion o the prestressing. In these studies three dierent values or t a were onsidered, namely: 1.,.0, and. mm (0.0, 0.1, and 0.1in.). Next, the value o the interaial shear stress at the end o the elasti region (or x=l o ) was obtained by substituting x to l o in Eq. 1. Results rom these parametri studies are depited in Figure. This igure shows that 1

13 or a given prestressing level, the interaial shear stresses are higher or those onditions with thinner adhesives. Also plotted in this igure are the three values presented in Table. This suggests that debonding o the CFRP sheets will our at a lower prestressing level or thinner adhesive layers and lower τ max ; however, results are predominantly more sensitive to variations in the maximum bond shear strength. Furthermore, reognizing that the intersetion o these urves depits the limits at whih debonding is likely to our, the prestressing levels were seleted or the beams shown in Table 1. THEORETICAL FLEXURAL ANALYSIS Theoretial analyses were undertaken to investigate the perormane o the prestressed beams rom the transer stage up to ultimate, and to evaluate premature ailure modes during transer and lexural testing. As shown in Figure, the RC beams strengthened with the prestressed CFRP sheets were evaluated at dierent limit levels. Strains at Transer and Deompression The irst stage that may be onsidered in prestressed onrete members is the release o the T initial prestress (see Figure a). During transer, the strain levels in the onrete top ibers, ε t,, T and bottom, ε b,, ibers are Top Fibers: ε, Bottom Fibers: ε, 1 y = n ε A + bh Z T p b t e t 1 y = n ε A + + bh Z T p b b e b Eq. In the expressions presented herein, ompression and tension strains or stresses are deined as positive and negative, respetively. To develop deompression in the bottom ibers an external moment, M D, must be applied to the setion resulting in the ollowing inremental strains in the top, ε, and bottom, ε, ibers D t D b 1

14 M D D T b t, b EZ t Zt = ε EZ T D b, b M Z D M D T ε =+ =+ ε ; εb = = ε, b EZ b Eq. Combining these inremental strains with the initial prestressing strains the overall strain D D levels at deompression in the onrete top, ε t,, and bottom, ε b,, ibers are (see Figure b) Top Fibers: ε, = ε, + ε = ε, + ε, Z D T D T T b t t t t b Zt Bottom Fibers: ε D, = ε T D, + ε = 0 b b b Eq. Deinition o the strain distribution at deompression was an eiient intermediate step beause it provided or ease in establishing inremental strain distributions at other load levels, predominantly at ultimate. Failure Governed by Conrete Crushing When ailure o a RC beam is initiated by onrete rushing, the ultimate lexural apaity o the beams was (see Figure ) β1 β1 β1 M N = A s s d + Eε ea h + A s s d where the total strain in the FRP, ε e, at ultimate was Eq. p D U ε = ε + ε + ε Eq. e e 1 In Eq., the strains in the CFRP sheets were omputed using the linear variations o strain depited in Figure, with ε p e D D p 1 b = κε u; ε y = ε b = n A ε e + bh Zb ε U h = ε u 1 Eq. 1

15 The stresses in the CFRP sheets were subsequently obtained by multiplying ε e by E, Similarly, U the strains in the tension, ε s, and ompression, ε U s, steel at ultimate were U U Tension steel: ε s = εu d φ Eq. U U Compression steel: ε s = εu d φ The stresses in the reinoring steel were then obtained rom these strain values and by onsidering strain hardening beyond yielding. In Eq. the urvature at ultimate was given by the relation ε U u φ = Eq. 1 In the previous equations, at ultimate was initially alulated by assuming that s = s = y and ε e = ε u. Then aording to priniples well established in the literature, the proess onsisted o iteratively seleting and updating the strains though strain ompatibility in the steel and FRP reinorement until internal ore equilibrium was attained in the setion. Failure Governed by FRP Rupture At this limit state level the strain inrease rom deompression (see Figure b) is U u p D ( ε ε ) ε = ε + Eq. 1 e The neutral axis depth was then omputed through an iteration proess proposed by Miller and Nanni (1). Aording to this proedure, when ailure o the member is initiated by FRP rupture and onrete rushing does not govern this ailure mode the ollowing parameters were adopted to desribe the onrete ompression stress blok: (see Figure ) (Miller and Nanni, 1 1) β = 1 1 [ ε ε ) tan ( ε ε )] ( ( ε ε )ln(1 + ε ε ) Eq. 1 1

16 0. ln(1 + ε γ = β ε ε ε = E ε ) Eq. 1 Eq In these expressions ε is a strain ator given by Eq. 1, and ε is the strain in the onrete in the extreme ibers within the ompression zone at ailure o the CFRP sheets. These expressions are evaluated iteratively where initially ε is equal to ε u. Then at subsequent iterations the value or ε is updated until internal ore equilibrium is ahieved. The lexural apaity o the strengthened beams is alulated with Eq., by using β 1 and γ based on Eqs. 1 1, 1, respetively, and with ε e equal to ε u. These equations were then implemented in a program to develop the moment-urvature plots shown in Figure a. In ombination with this strain level the urvature at rupture o the CFRP sheets is ε U φ = Eq. 1 Design o the beam ross setion dimensions and reinorement ratios were urther substantiated by this analysis with the main objetive o best quantiying the eets that prestressing the external CFRP sheets have on the lexural perormane o RC beams. Figure a shows that or the strengthened beam B and the beams prestressed with 1% o the ultimate strength (i.e. beams C, D, and E) ailure was likely to be by onrete rushing. Under higher levels o prestressing, beams F and G were likely to ail by FRP rupture. In addition, barring premature ailures, prestressed beams up to 0% were likely to ahieve higher levels o apaity. Above this prestress level, the beams will only experiene a derease in the ultimate urvature apaity and no inrease in the lexural apaity. Analysis onsidering higher levels o reinorement ratios or the CFRP sheets was also onsidered and results are presented in Figure b. Reerring to this igure it is lear that or a 1

17 reinorement ratio o 0.0% and a prestressing level o % ailure is simultaneously by onrete rushing and FRP rupture. These analyses learly show that, unless other modes o ailure suh as FRP delamination or onrete over separation dominates the ailure mode, under inreasing levels o prestressing the ailure mode o ompression ontrolled setions hanges rom onrete rushing to FRP rupture (Wight et al., 001). However, as the reinorement ratio inreases, ailure o the beams is likely to be governed by onrete rushing under any level o prestressing. As suh, the reinorement ratio or the CFRP sheets used in this researh program was set at 0.0% as a means to iner the inluene and inrease in lexural apaity o the prestressing level on the ailure mode o the RC beams. Premature Failure Conrete Cover Separation Theoretial models to estimate premature ailures inluding onrete over separation and FRP end debonding, have been developed based on an evaluation o the peak shear, normal (peeling), and longitudinal stresses at the uto point o FRP sheets together with a ailure riterion or onrete (Smith and Teng 001). One these stresses at the uto point are determined, the prinipal tensile stresses, σ p,x, are easily omputed by employing a D Mohr irle o analysis or σ σ + σ σ σ = + + τ xx, yx, xx, yx, px, 0, x t Eq Where τ o,x, σ y,x, and σ x,x are the shear, normal and longitudinal stresses, varying along the length o the beam, respetively. The subsript x in these variables suggests that stresses vary along the length o the beam and, as suh, the prinipal tensile stresses were evaluated at eah load level and along the length o the beam as a untion o x. Conrete over separation is then assumed to initiate when the prinipal tensile stresses exeed t. Expressions to evaluate these shear, normal 1

18 1 1 and longitudinal stresses o RC beams strengthened with FRP sheets have been previously derived (Malek et al., 1; Tumialan et al., 1). Tumialan et al., (1) used one onrete over separation model based on the stress solution proposed rom Roberts (1). In their models, Roberts (1) used a staged analysis approah and another model adopted a diret deormation ompatibility equation (Smith and Teng 001), whih was suessully used by Malek et al. (1). These analyses were based on a series o assumptions, inluding linear elasti and isotropi behavior o the FRP, adhesive, onrete and steel, and omplete omposite ation with no slip between the sheets and onrete (Malek et al., 1; Smith and Teng 001). Sine these models did not aount or the prestressing in FRP sheets, the expressions used by Malek et al. (1) and Tumialan et al. (1) were modiied in this researh program to inlude: i) the inluene o the prestressing on these stresses, and ii) variations in the moment o inertia I x and neutral axis depth x along the length o the beam given by 1 with τ G t ( ) a 0, x = Vx + Mx h x n + τ p, x E t ta Ix Eq. 1 1 and σ σ E a t = τ E t a yx, ox, p xx, x e x 1 ( ) ( h ) x x Eq. 0 = M ε E A h Eq. 1 I In Eqs. 1 to 1, the subsript x denotes these quantities were evaluated along the length o the beam, and the shear stress inrease due to the prestressing was also inluded in the analysis. In these expressions the variation in the neutral axis, x, along the length o the beam was obtained diretly rom the moment urvature analysis and the setion moment inertia, I x, was 1

19 I x M x = Eq. E φ x Conrete over delamination was evaluated by using Eq. 1 in onjuntion with the moment urvature analysis results presented in Figure a and the stress values omputed by Eqs. 1 to 1. Figure a presents the results or the beams stressed to 1% at transer and ultimate. At any o these stage levels the maximum prinipal tensile stresses our near the end o the CFRP, and the hanges in slope at the ultimate stage level are due to variations in the beam stiness due to onrete raking and yielding o the tension steel. Similar results were derived or the other beams. Based on the results presented in Figure a, results or Figure b were obtained at inreasing levels o the applied load and at loations o maximum prinipal tensile stress level. Based on these analyses, the beams tested under this researh program were likely to ail by premature onrete over separation or FRP debonding or the normalized prinipal tensile stresses values depited in Table. In Figure b the alulated values or the normalized prinipal tensile stresses at whih beams C, D, F and H developed the premature ailure during the experimental program are shown in light gray. These results are disussed next. It is also important to note that or beams E and G the CFRP sheets were anhored with U-wraps and, as a result, no onrete over separation was expeted or these beams. These results were orroborated by the experimental results. Reerring to Figure b and based on the experimental results it was possible to establish limiting values or the tensile strength o onrete Theoretial Deormation Calulations The theoretial mid-span deletion was alulated by implementing the two-omponent beam element (Clough et. al., 1). In this model, the bilinear moment-urvature relationships are ahieved by deining two beam elements onneted in parallel suh that one element represents the post-yield stiness (see Figure b) while the other the elasti-peretly plasti 1

20 relationship (see Figure ). These two elements, when in parallel, an easily desribe the bilinear moment-urvature relationships o RC members shown in Figure a. Due to the symmetri response o the beams investigated in this researh only hal o the beam is modeled with elements limited by nodes 1 and, and and, (see Figure d). Aording to this two-omponent beam element, the omplete nonlinear stiness matrix or Element 1, E 1, is EI E1 = a (1+ r) a(1 + r) (1+ r) ra a(1 r) a ( r) a(1 r) ra (1+ r) a(1 + r) (1+ r) ra ra ra ra ra Eq. For Element, E, the nonlinear stiness matrix is E rei = b 1 b 1 b b b b b 1 b 1 b b b b b Eq. Ater inal assembly o the global stiness matrix and through stati ondensation o the vertial deletion at node the relation to alulate the deletion at mid-span is ( a + a r + 1 a b + b ) a ΔVi Δ Di = i Eq. 1 ri EIY In Eq., EI Y is the seant yield stiness obtained rom the moment urvature analyses, and r i is the instantaneous stiness ratio r i ΔM i i = ; EI / Δφ Y EI Y = M φ Y Y Eq In Eq., ΔM i and Δφ i are the inremental moment and urvature within the onstant moment region, and M Y and φ Y are the irst yield moment and urvature also within the onstant moment region. The expression given by Eq. was then ompared against the experimental 0

21 results onduted in the researh by Wight et al. (001) and results are shown in Figure. This igure indiates that the theoretial results mathed well with the experimental results based on the researh by Wight et. al. (001). This model was urther explored in this researh program to develop the load deormation response or the tested beams. EXPERIMENTAL RESULTS AND DISCUSSION In this researh program, eight RC beams were tested aording to the setup shown in Figure 1b. Key experimental results obtained during prestressing and transer are reported in an aompanying paper, and key experimental results obtained during the lexural program are presented next. The reorded and theoretial load versus mid-span deletion are shown in Figure a, and the theoretial versus the experimental loads reorded at ailure and yielding are shown in Figure b. Beam A: As expeted, beam A ailed by onrete rushing ater yielding o the tensile reinorement. Reported in Table the yield and ultimate loads or this beam were. kn (1.1 kips) and.1 kn (1.0 kips), at a orresponding mid-span deletion o. mm (0. in.) and. mm (. in.), respetively. These values indiate that the displaement dutility apaity, μ Δ, o this beam was nearly. omputed based on Δu.. μ Δ = = SI US =. (Beam A) Δ. 0. y Eq where Δ y and Δ u are the irst yield and ultimate deletion at mid-span, respetively. In Figure a, the deletion o beam A was trunated at 0. mm (1.0 in.) or better illustration o the test results or the strengthened beams. Beam B: Compared to beam A, the addition o the non-prestressed sheet to beam B inreased the yield and ultimate load to 1.0 kn (1. kips) and. kn (1. kips) with no signiiant hanges in the initial bending stiness, but a substantial inrease in the post-yield 1

22 stiness. This led to an inrease in the yield deletion to.1 mm (0. in.), and a derease in the ultimate deletion to. mm (0. in.), orresponding to a displaement dutility apaity o.. Figure b indiates that the apaity o beam B was nearly the same as the theoretial apaity. However, ontrary to theoretial preditions, beam B did not ail by onrete rushing but instead by FRP rupture. Beam B ailed due to rupture o the CFRP sheet within the onstant moment region and minor rushing o the over onrete was observed near the point o load appliation, as shown in Figure. Furthermore, reorded strain readings did not exeed 1.%, whih are onsistent with the strains expeted rom the theoretial analysis, but signiiantly lower than the ultimate strain o 1.%. However, as depited in Figure, it is lear that the CFRP sheet ratured within the projetion o one o the raks, suggesting that the sheet ratured due to the stress onentrations that developed as the rak widened. Ye et al., (00) have proposed an equation to estimate the strains in the FRP ater the initiation and development o lexural raks and beore debonding ours within a lexural dominated region. They have proposed the ollowing equation to alulate the FRP strain at debonding ε = ξ b IC w t E L t d (SI) ε = ξ b IC w t E L t d (US) Eq. Based on Eq. 0, it is likely that the strains in the CFRP sheets in the viinity o the lexural raks was 1.% whih exeeded the ultimate strain o the sheets. Beams C, D, and F: Prestressed beams C, D, and F ailed due to onrete over separation starting rom one o the uto points, as shown in Figures 1 and 1. In addition, as depited in Figure, these beams ailed at a signiiantly lower load than the estimated theoretial load. Using the normalized prinipal tensile stress analysis disussed in Figure b, onrete over separation was the likely ailure mode or these beams. Based on this analysis and the loads

23 ahieved during lexural testing, it is reommended that or studies onerning onrete over separation a range o 1.00 to 1. (MPa) [1.0 to 1.0 (psi)] should be used or the tensile strength o prestressed beams Beams E, and G: Prestressed beams E and G, ailed due to FRP rupture near the U-wraps and at a higher load level than beams C, D, and F, as shown in Figure b. Upon sudden energy released debonding was observed along the entire length o the CFRP sheets as shown in Figures 1 and 1b. Similar to other researh programs (Lu et al., 00) the addition o the U-wraps learly avoided the premature onrete over separation and inreased the lexural apaity o these prestressed beams. Beause ailure was dominated by FRP rupture, summary o test results presented in Table shows that the ultimate apaity o these prestressed beams were nearly the same as the beam with a non-prestressed sheet. As suh, in uture researh projets it is reommended to modiy the design o the beams suh that ailure o the non-prestressed beam is learly dominated by onrete rushing. Furthermore, ompared with beam B, the addition o the prestressed sheet to beams E and G inreased the yield and ultimate loads, respetively, to.0 and.0 kn (1. and 1.0 kips) and. and 1. kn (0. and. kips). However, in these two beams the displaement dutility apaity was. and., respetively, whih is not signiiantly lower than in beam B. Beam H: During transer, only beam H, whih was prestressed to 0% o the ultimate strength, ailed due to debonding o the CFRP sheet near the uto points, as shown in Figure 1. It is lear that ailure ourred away rom the onrete-adhesive interae, as evidened by the onrete remaining in the CFRP sheets. This is a strong indiation that the tensile strength o the onrete and not the adhesive was reahed under this level o prestressing. Aording to the

24 ailure modes reported in Table 1 and values rom Table, it is reasonable to iner that the tensile strength o onrete was within 1.00 (MPa) [1.0 (psi)] and 1.0 (MPa) [1.0 (psi)], whih are signiiantly higher than the value 0. (MPa) [. (psi)] speiied by ACI (00). CONCLUSIONS This researh program investigated the easibility o prestressing CFRP sheets using an innovative mehanial devie that was developed under this researh program. Signiiant eatures o this devie are that the prestressing ore was applied manually by a torque wrenh without the need or power operated hydrauli jaks, and the transer operation was aomplished at slow strain rates. Observations were reorded during the experimental program regarding the level o prestressing that would lead to debonding o the sheets immediately ater transer and during lexural testing. Similarly, the inrease in the lexural apaity that would result rom prestressing the CFRP sheets and providing U-wraps at the ends o the prestressed CFRP sheets was studied. The ollowing onlusions were reahed: 1. Corroborated by experimental evidene, analytial studies onsidering ater transer and during lexural testing suggest that values o the tensile strength o onrete are likely to be 1 higher than suggested by ACI. Researh results indiate that values in the order o (MPa) [1.0 (psi)] to 1.0 (MPa) [1.0 (psi)] an be attained or the tensile strength 1 o onrete.

25 In all the beams studied in this researh program, as well as those reviewed in the literature, there was no indiation o interaial debonding within regions o lexure-dominated response. As suh, in RC beams prestressed with CFRP sheets, the predominant premature ailure mode is by onrete over separation unless the CFRP sheets are eetively anhored with U-wraps or an equivalent system. For those beams prestressed with CFRP sheets and anhored at the end with U-wraps, onrete over separation was averted irrespetive o the initial prestressing ore present in the CFRP sheets, and the predited theoretial apaity was ahieved.. Compared with the unretroitted ontrol beam, the addition o prestressed and nonprestressed sheets inreased the raking load by nearly three to six times, respetively, and the yield and ultimate loads by nearly %. Meanwhile, the displaement dutility apaity o the system was redued by nearly ive times. This is in line with other researh results, whih indiate that prestressing FRP sheets an eetively inrease raking moment and lexural apaity o RC beams with a toll on dutility. ACKNOWLEDGMENT The inanial support o NSF via the Industry/University Cooperative Researh Center titled Repair o Buildings and Bridges with Composites is grateully aknowledged.

26 A A A s A s ΔD i E E NOTATIONS =gross ross-setional area o RC beams =ross-setional area o CFRP sheets =ross-setional area o the steel reinorement in tension =ross-setional area o the steel reinorement in tension = inremental mid-span deletion =modulus o elastiity o onrete =modulus o elastiity o CFRP sheets EI =seant yield stiness omputed by Eq. Y E s G a M A =modulus o elastiity o steel =shear modulus o adhesive =moment in ontrol beam A M =moment at deompression D Δ M i = inremental moment M =nominal moment apaity N M =moment at ultimate U M x =varying moment along the length o the beam P =point load applied on RC beams as shown in Figure 1 P 0 =initial prestress ore in the CFRP sheet at transer or: P = ε E A p o e V x ΔV i =varying shear ore along the length o the beam =inremental applied shear ore Z =unraked setion modulus with respet to the bottom ibers or: I Z = T b b y b I Z =unraked setion modulus with respet to the top ibers or: Z = T t a =distane rom the supports to the points loads b =hal the distane between the point loads t y t

27 b =width o RC beams b w =squared root term in Eq. x d d y =varying depth o the neutral axis along the length o the beam =depth o the neutral axis at ultimate =distane rom extreme ompressive iber to enter o tension reinorement =distane rom extreme ompressive iber to enter o ompression reinorement =ompressive strength o onrete =yielding strength o steel reinorement =tensile strength o CFRP sheet u s =stress in the tension reinorement =stress in the ompression reinorement s t h =tensile strength apaity o the onrete substrate =depth o the beam l l o =distane rom the enter o the beam to the end o CFRP sheet =distane rom the enter o the beam to the end o elasti range o the FRP sheet n E =ratio o the elasti modulus o CFRP over onrete or: n = E r =post yield stiness ratio omputed by Eq. t a t =thikness o adhesive =thikness o CFRP sheet w =alulation oeiient omputed in terms o Eq. w =width o the CFRP sheet 1 x y b y t =distane rom midspan o the beam =distane rom bottom beam ibers to neutral axis or the unraked setion =distane rom top beam ibers to neutral axis or the unraked setion

28 Δ y Δ u =yield deletion =ultimate deletion Δ φ i =inremental urvature U φ φ x =ultimate urvature =varying urvature along the length o the beam 1 α A =ratio o the area o CFRP over the onrete or: α = bh β β 1 ε =onstant or given geometri properties o RC beams =stress ator, shall be taken rom 0. and drop to 0. as in ACI 1-0 when onrete rushing is the main ailure mode. Otherwise, it is deined by Eq. 1. =strain o onrete o the extreme iber at the ompressive zone ε =strain ator ε =ultimate strain o onrete u ε ; ε =strain at top and bottom ibers, respetively, ater deompression D D t, b, ε ; ε =strain at top and bottom ibers, respetively, ater transer T T t, b, p ε =eetive strain o CFRP sheets beore transer e U ε ; ε =strain in the tension and ompression reinorement, respetively, at ultimate s U s D U ε ; ε ; ε =strain in CFRP sheets at nominal, deompression and ultimate e D D ε ; ε =strain at top and bottom ibers, respetively, due to M D t b ε u =ultimate strain o CFRP sheets γ =onstant omputed by Eq. 1 ξ = ator onsidering the anhorage o the FRP sheet: ξ=1. or sheets with end anhorages and ξ=1.0 with no end anhorages κ =initial prestress level (% u ) μ Δ =displaement dutility apaity given by Eq.

29 σ =varying longitudinal stresses along the length o the beam x, x σ =varying normal stresses along the length o the beam yx, τ px, =varying shear stress due to prestress along the length o the beam τ max =maximum shear stress or CFRP bonded joints beore debonding τ = varying shear stresses due to prestress and lexural ations ox, 1

30 REFERENCES Amerian Conrete Institute, ACI 1 Committee (00), Building Codes Requirements or Strutural Conrete (ACI 1-0) and Commentary (ACI 1R-0), Amerian onrete institute, Farmington Hills, MI. Char, M.S., Saadatmanesh, H., and Ehsani, M.R. (1), Conrete Girders Externally Prestressed with Composite Plates, PCI Journal, Vol., No., pp. 0-1, May-June Clough, R.W., Benuska, K.L., and Wilson, E.L. (1), Inelasti Earthquake Response o Tall Buildings, Proeedings, Third World Conerene on Earthquake Engineering, New Zealand National Committee on Earthquake Engineering, Vol., 1, pp. -. EI-Haha, R., Wight, R.G., and Green, M.F. (001), Prestressed iber-reinored polymer laminates or strengthening strutures, Progress in Strutural Engineering and Materials, Vol., No., pp. 1- Garden, H.N., Hollaway, L.C., and Thorne, A.M. (1), The Strengthening and Deormation Behavior o Reinored Conrete Beams Upgraded using Prestressed Composite Plates, Materials and Strutures, May, Vol. 1, pp. - Izumo, K., Saeki, N., Asamizu, T., and Shimura, K. (1), Strengthening Reinored Conrete Beams by Using Prestressed Fiber Sheets, Non-Metalli (FRP) Reinorement or Conrete Strutures, Vol. 1, pp. - Lu, X.Z, Teng, J.G., Ye, L.P., Jiang, J.J. (00), Bond-slip Models or FRP Sheets/Plates Bonded to Conrete, Engineering Strutures, Vol., pp. 0- Karam, G.N. (1), Optimal Design or Prestressing with FRP Sheets in Strutural Members, Advaned Composite Materials in Bridge and Strutures, Canadian Soiety or Civil Engineer, ed. K.W. Neale and P.Labossiere, pp. - 0

31 Miller, B., and Nanni, A. (1), Bond Between CFRP Sheets and Conrete, Materials and Constrution: Exploring the Connetion, Proeedings o the Fith Materials Congress, L. C. Bank, ed., ASCE, Cininnati, Ohio, May 1, pp. 0-. Quantrill, R.J., and Hollaway, L.C. (1), The Flexural Rehabilitation o Reinored Conrete Beams by the Use o Prestressed Advaned Composite Plates, Composite Siene and Tehnology, Vol., pp. 1-1 Roberts, T.M. (1), Approximate Analysis o Shear and Normal Stress Conentrations in the Adhesive Layer o Plated RC Beams, The Strutural Engineer, Vol., No.1, Jun, pp. - Saadatmannesh, H, and Malek, A.M. (1), Design Guidelines or Flexural Strengthening o RC Beams with FRP plates, Journal o Composites or Constrution, Vol., No., pp. 1-1 Smith, S.T., and Teng, J.G. (001), Interaial Stresses in Plated Beams, Engineering Strutures, Vol., pp. -1 Smith, S.T., and Teng, J.G. (00), FRP-strengthened RC beams. II: Assessment o Debonding Strength Models, Engineering Strutures, Vol., pp. -1 Teng, J.G., Chen, J.F., Smith, S.T., and Lan, L. (00), FRP-strengthened RC strutures, Wiley, New York Thomsen H., Spaone, E., Limkatanyu, S., and Camata, G. (00), Failure Mode Analysis o Reinored Conrete Beams Strengthened in Flexure with Externally Bonded Fiberreinored Polymers, Journal o Composite or Constrution, Vol., No., pp.1-1 1

32 Triantaillou, T.C., and Deskovi, N. (), Innovative Prestressing with FRP Sheets: Mehanis o Short-term Behavior, Journal o Engineering Mehanis, Vol., No., pp.1- Triantaillou, T.C., Deskovi, N., and Deuring M. (1), Strengthening o Conrete Strutures with Prestressed Fiber Reinored Plasti Sheets, ACI Strutural Journal, Vol., No., pp.- Tumialan, J.G., Belarbi, A., Nanni. A. (1), Reinored Conrete Beams Strengthened with CFRP Composites: Failure Due to Conrete Cover Delamination, Report, Center or Inrastruture Engineering Studies, University o Missouri-Rolla, Rolla, MO Varastehpou, H., and Hamelin, P. (1), Strengthening o Conrete Beams using Fiber- Reinored Plastis, Materials and Strutures, Vol. 0, Apr, pp. -1. Wight, R. G., Green, M. F., and Erki, M-A. (001), Prestressed FRP Sheets or Poststrengthening Reinored Conrete Beams, Journal o Composite or Constrution, Vol., No., Nov. 001, pp. 1-0 Wu, Z., Yuan, H., and Niu, H. (00), Stress Transer and Frature Propagation in Dierent Kinds o Adhesive Joints, Journal o Engineering Mehanis, Vol. 1, No., May, pp. -. Ye, L.P., Lu, X.Z., and Chen, J.F. (00), Design Proposals or the Debonding Strengths o FRP Strengthened RC Beams in the Chinese Design Code, Proeeding o International Symposium on Bond Behavior o FRP in Strutures (BBFS 00), De.-, Hong Kong, China, pp. - Yu, P., Silva, P.F., and Nanni, A. (00), Desription o a Mehanial Devie or Prestressing o CFRP Sheets Part I, ACI Strutural Journal, Aepted, May 00.

33 Ziraba, Y.N., Baluh, M.H., Basunbul, I.A., Azad, A.K., Al-sulaimani, G.J., and Shari, A.M. (1), Combined Experimental-numerial Approah to Charaterization o Steel-glue- onrete interae, Materials and Strutures, Vol., April, pp. 1-

34 LIST OF TABLES Table 1. Test Matrix Table. Material Properties Table. Relation between t and σ max Table. Theoretial Results Evaluation o Cover Conrete Separation Table. Experimental Results LIST OF FIGURES Figure 1. Four-Point Bending Test Setup Figure. RC Beam Plus Mehanial Devie Beore Transer Figure. Interaial Shear Stress Distribution Figure. Interae Shear Stress Value at Limit o Elasti Region (i.e. x = l ) Figure. Three-Phase Prestressing Analyses Figure. Theoretial Flexural Analyses Figure. Evaluation o Conrete Cover Delamination Figure : Nonlinear Model or Deormation Calulations Figure. Load versus Deletion (Wight et. al., 001) Figure. Theoretial versus Experimental Results Figure. Failure Mode o Beam B Figure 1. Failure Mode o Beams Prestressed to 1% Figure 1. Failure Mode o Beams Prestressed to 0% Figure 1. Failure o Beam H Prestressed to 0%

35 Table 1. Test Matrix Beam Prestress/Tensile End Failure Mode ID Strength (%) Anhors Expeted Observed A Mode I Mode I B 0 -- Modes II or Mode IV IIIb C 1 -- Modes II or Mode IIIb IIIb D 1 -- Modes II or Mode IIIb IIIb E 1 U-Wraps Mode II Mode IV F 0 -- Mode IIIa or Mode IIIb IV G 0 U-Wraps Mode IV Mode IV H 0 -- Mode IIIa or Mode IIIa IV Failure Mode I: Conrete rushing beyond steel yielding Failure Mode II: Conrete rushing beore FRP rupture Failure Mode III: Premature FRP debonding a: during transer b: during lexure testing Failure Mode IV: FRP rupture beore onrete rushing

36 Table. Material Properties Tensile strength MPa (ksi) Ultimate strain (%) Elasti modulus GPa (ksi) Compressive strength MPa (ksi) Conrete (.) Steel bars (.) -- 1 (,00) -- CFRP sheet * 0 (0) 1. (,000) -- Saturant (.0).0 1. (0) -- * A = 0.1 mm (0.00 in.) thik x 0 mm ( in.) wide =. mm (0.0 in. ).

37 Table. Relation between Conrete tensile Strength, t, and Maximum Shear Stress at Failure, τ max Reerene t MPa (ksi) * τ max MPa (ksi) * Tumialan et al. (1) 0. (.) 0. (.) Ziraba et al., (1) 0. (.) 1.0 (1.0) Triantaillou and Deskovi () 1. (1.) 1. (1.) * Values shown were normalized in terms o

38 Beam ID Table. Theoretial Results Evaluation o Cover Conrete Separation Normalized Prinipal Tensile Stresses ater Transer * ( in ( in psi) Normalized Prinipal Tensile Stresses near Ultimate * ( in ( in psi) Derived rom Test Results * ( in MPa) MPa) MPa) ( in psi) B C and D F H * Values shown were normalized in terms o using =.MPa (,00 psi)

39 Beam ID A B C D E F G Table. Experimental Results First Crak First Yield Ultimate Δ r P r Δ P mm. kn r / y P y Δ P mm. kn y / u P u mm. kn P (in) (kips) r,a P (in) (kips) y,a (in) (kips) (0.01) (1.0) (0.) (1.1) (.) 1.0) (0.0) (.) (0.) (1.) (0.) (1.) (0.) (.) (0.) (1.) (0.) (1.0) (0.0) (.1) (0.) (1.0) (0.) (1.1) (0.1) (.1) (0.) (1.) (0.) (0.) (0.0) (.0) (0.) (1.) (0.) (1.) (0.0) (.0) (0.) (1.0) (0.) (.) Δ u / Δ y P u / P u,a H

40 mm (1in.) -D (#) D 1mm (in.) 0mm (in.) wide CFRP sheet 0mm (in.) b (a) Cross setion h mm (in.) -D1 (#) Laboratory Strong Floor 1mm (in.) Equal Spaes o mm (in.) a b P Jak w/ Load Cell P P Steel Loading Beam RC Beam Strain CFRP Sheet Transduer.1m (in.).m (in.) (b) Test setup Figure 1. Four-Point Bending Test Setup 1mm (in.) 0

41 WT setion CFRP sheet RC beam Cut here Figure. RC Beam Plus Mehanial Devie Beore Transer 1

42 P C L P a RC Beam h CFRP Sheet 1 Interae Shear Stress (MPa) Elasti Range along l o x l τ max l o l-l o Interaial Shear Stress Distribution along l Region o Plasti Behavior along l-l o (a) Shematis o Stress Distribution Distane x (in.) % Prestress % Prestress 0 % prestress 1% Prestress % Prestress x<l o (l-l o ) Shear Stress (psi) Distane rom enter o CFRP sheets, x (mm) (b) Stress Distribution Analysis Results Figure. Interaial Shear Stress Distribution 0

43 Interae Shear Stress (MPa) 1 t a = 1. mm (1/1in.) t a =.0 mm (1/in.) t a =. mm (/1in.) Beams C, D & E Beams F & G Beam H Shear Stress (psi) Initial Prestress Level (% u ) Figure. Interae Shear Stress Value at Limit o Elasti Region (i.e. x = l ) 0

44 p ε t y t ε T s T ε,t NA 1 M D M U ε T s T ε s p ε A T ε,t + = p ε b y b (a) Strains at transer NA T φ T ε,b D ε t D Δφ + D ε b y t y b p ε e T φ T ε s T ε,b ε D s D φ = D ε s D ε (b) Strains at deompression γ ε U φ β 1 D,b D ε,t ε = 0 s s p D ε e ε U ε E ε () Strain and stress distribution at ultimate Figure. Three-Phase Prestressing Analyses e

45 Moment (kn-m) Normalized Flexural Capaity (Mu/MA) Curvature (1/in.) Balaned Failure FRP Rupture Conrete Crushing Beam H Beam A - ontrol Beam B - 0% Beams C, D and E - 1% Beam w/ 0% prestress Beams F and G - 0% Beam H - 0% Curvature (1/m) EI Y rei Y Beam A (a) Moment Curvature Analyses ρ = 0.1% ρ = 0.% ρ = 0.0% Conrete Crushing Balaned Failure Initial Prestress Level (% u) (b) Ultimate Capaity FRP Rupture Figure. Theoretial Flexural Analyses 0 Moment (kips-in.)

46 Normalized Priniple Tensile Stresses (σ p / ) [MPa] Distane rom Center o Beam (in.) Indiates Loation o Cover Delamination at Ultimate Indiates Loation o Cover Delamination at Prestress Transer Unraked Setion Craked Setion σ p Stress Distribution at Transer Beam Centerline Loation or Point Load σ p Stress Distribution at Ultimate Limit or Yielding o Tension Steel Distane rom Center o Beam (mm) (a) Stress Distribution along Beam Length and at two Dierent Load Levels (σ p / ) [psi] Beams C, D, F & H 0 Point Load P (kn) Beam B Beam H 1 Load P (kips) 0 Beam E Beam G Normalized Priniple Tensile Stresses (b) Conrete Cover Delamination Figure. Evaluation o Conrete Cover Delamination 0

47 M U M Y M U- M Y M Y EI y rei o rei y (1-r)EI y 1 φ Y (a)nonlinear Element φ U P 1 φ Y φ U (b) Elasti Component P φ Y φ U () Nonlinear Component Note: Beause o symmetry only hal o the beam was modeled a b a L=.m (in.) 1 Denotes node number 1 Denotes element number (d) Analtyial Model Figure : Nonlinear Model or Deormation Calulations

48 Point Load (kn) Deletion (in.) Beam Cwith CFRP Prestressed to % Beam D with CFRP Prestressed to % Beam A Beam B Load (kips) Theoretial Beam A by Wight et. al. (001) Beam B by Wight et. al. (001) Beam C & D by Wight et. al. (001) Mid-Span Deletion (mm) Figure. Load versus Deletion (Wight et al., 001) 0 0

49 Point Load (kn) Deletion (in.) Beam F Beam G Beam C Beam D Beam E Beam B Beam A Theoretial Beam A Beam B Beam C Beam D Beam E Beam F Beam G Mid-Span Deletion (mm) (a) Load vs. Deletion Load (kips) Point Load (kn) Beam B Beam E Beam C Beam D Initial Prestress Level (% u) Beam G Beam F Beam A Experimental - Ultimate Experimental - Ultimate Experimental - Yield Analysis - Ultimate Analysis - Yield (b) Results at Yield and Ultimate Stages Load (kips) Figure. Theoretial versus Experimental Results

50 Figure. Failure Mode o Beam B 0

51 (a) Beam C (b) Beam D () Beam E Figure 1. Failure Mode o Beams Prestressed to 1% 1

52 (a) Beam F (b) Beam G Figure 1. Failure Mode o Beams Prestressed to 0% Beam side Figure 1. Failure o Beam H prestressed to 0%