Response Prediction of RC Beams Externally Bondedwith Steel-Reinforced Polymers

Marisa Pecce1; Francesca Ceroni2; Andrea Prota3; and Gaetano Manfredi4

Abstract: This paper deals with an innovative technique for strengthening reinforced concrete �RC� structures using steel-reinforcedpolymer �SRP� materials. The results of an experimental campaign using RC beams strengthened in flexure with carbon fiber-reinforcedpolymer or SRP laminates are summarized, and the experimental outcomes are compared to the predictions provided by analytical modelsand code formulations in terms of flexural strength, curvature of the cross section, deflections, and crack widths. Under ultimateconditions, the ACI 440.2R-02 approach provided conservative flexural strength, and a modified expression for the bond coefficient km

was proposed. Under serviceability conditions, good agreement was obtained between experimental results and a theoretical modeldeveloped by the writers. Comparisons of code models in terms of both crack width and deflections highlighted the need for a calibrationof code formulas to account for effects due to externally bonded reinforcement.

DOI: 10.1061/�ASCE�1090-0268�2006�10:3�195�

CE Database subject headings: Concrete beams; Concrete, reinforced; Curvature; Deflection; Stiffening; Cracking; Ultimatestrength.

Introduction

Over the last decade, fiber-reinforced polymer �FRP� compositeshave emerged in construction mainly for the strengthening andrehabilitation of reinforced concrete �RC� structures �Cosenzaet al. 2001; Bakis et al. 2002�. In addition to their high mech-anical properties, these materials have other features that can beexploited, such as high durability and high resistance to aggres-sive and harsh environments, easy and rapid installation, lightweight and low impact on the original geometry of strengthenedmembers, and the possibility of targeting their density and textureto the requirements of each specific application.

Despite a wide consensus at both the academic and industriallevels that FRP composites represent a real and competitive alter-native to traditional strengthening techniques, one barrier to theirlarger diffusion in construction is their low fire resistance �Nanniet al. 2001�. This problem affects both carbon and glass laminatesand is related to the properties of the epoxy resins generally usedto impregnate the fibers. In addition, other reasons for concerninclude the linear-elastic behavior up to failure of the fibers andthe orthotropic behavior of the laminates.

1Full Professor, Engineering Dept., Univ. of Sannio, Benevento, Italy.E-mail: pecce@unisannio.it

2Assistant Professor, Engineering Dept., Univ. of Sannio, Benevento,Italy. E-mail: ceroni@unisannio.it

3Assistant Professor, Dept. of Structural Analysis and Design, Univ.of Naples Federico II, Italy. E-mail: aprota@unina.it

4Full Professor, Dept. of Structural Analysis and Design, Univ. ofNaples Federico II, Italy. E-mail: gaetano.manfredi@unina.it

Note. Discussion open until November 1, 2006. Separate discussionsmust be submitted for individual papers. To extend the closing date byone month, a written request must be filed with the ASCE ManagingEditor. The manuscript for this paper was submitted for review and pos-sible publication on November 23, 2004; approved on September 6, 2005.This paper is part of the Journal of Composites for Construction, Vol.10, No. 3, June 1, 2006. ©ASCE, ISSN 1090-0268/2006/3-195–203/

$25.00.

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The present paper deals with an innovative strengtheningsystem based on steel-reinforced polymer �SRP� compositesthat could be an alternative technique for structural applicationsthat could not be fulfilled by FRP materials. Similar to FRP, SRPcomposites are obtained by impregnating steel cords with eitheran epoxy or a cementitious matrix. The steel fibers occur in cordsidentical to those used as radial reinforcement for car tires;steel cords can vary between highly twisted cords, for optimumductility, and slightly twisted cords, which are more open toallow resin penetration �Hardwire 2002�. The steel tape has veryhigh strength and stiffness and is economical to produce, and itsdensity can be targeted to meet the requirements of reinforcement,viscosity of resin, and cosmetic applications. No special resin isrequired for wetting the steel cord reinforcement as it is for FRP,where sizing plays a critical role.

For applications where fire resistance is the parameter govern-ing the strengthening job, the use of a low-density steel tape couldovercome such a problem by installing a SRP composite impreg-nated with a cementitious matrix not sensitive to fire and hightemperatures. It is also possible to improve the bond of suchlaminates by using mechanical anchorages, which in general arenot compatible with the use of FRP. If this is done, the design ofthe anchorages could also rely on the ductility of steel fibers toredistribute high stresses at anchorage locations and prevent localfailures. In addition to fire resistance, the use of a traditionalmaterial such as a polymer-modified cementitious matrix reducesthe uncertainties and the likelihood of defects related to mixingan epoxy resin, with which typical workers in the constructionindustry are not familiar.

The use of SRP laminates in strengthening requires reassess-ment of the models at ultimate and service conditions, usually topredict the response of RC elements externally reinforced withFRP. To this end, comparisons with analytical models are per-formed to simulate the behavior of members along the entireload history �moment–curvature and load crack-width relation-ships� and confirm the validity of assumptions typically made

for RC members. This analysis is aimed at showing which main

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parameters should be recalibrated to improve the reliability ofcode formulations �Eurocode 2 1992; ACI 1995�.

Experimental Program

The experimental program was aimed at evaluating the effectof various types of external flexural reinforcements on RCbeams. A total of 10 RC shallow beams with a cross section of400�200 mm were tested. The stirrups were �8 mm steelbars spaced at 100 mm center to center. For all specimens, five�10 and two �8 steel bars were used as tensile and compressiveinternal reinforcement, respectively. All beams were tested assimply supported members over a clear span of 3.40 m andloaded to failure under a four-point configuration, with a constant-moment region of 1.0 m across the midspan. One of these beamswas not strengthened �specimen D�, while the other nine wereexternally reinforced using steel tapes �Beam Types A and B� andcarbon fiber-reinforced polymer �CFRP� laminates �Type C��Prota et al. 2004�. Type A and B beams were strengthened using3�2 and 12� cord SRP laminates, respectively. The former is amedium-density laminate, which the latter is characterized by alow density of steel fibers.

Seven beams were strengthened with steel tapes impregnatedwith epoxy resin or cementitious grout �A and B beams�; theremaining two beams �C-1 and C-2� were strengthened withCFRP laminates impregnated with epoxy resin. Two of thebeams �B-3 and B-4� were strengthened with steel tape usingcementitious grout and mechanically anchored with nail anchors.Table 1 shows the research program, summarizing for each beamthe type, matrix, bond width, bf, and number of plies of theexternally bonded reinforcement, nf.

The experimental concrete mean cube strength was 29.7 MPa.Based on experimental tests, the yield stress, ultimate stress, andultimate strain for �10 bars were 500 MPa, 600 MPa, and 0.12,respectively. The CFRP laminates had a unidirectional fiber tex-ture with a density of 300 g/m2 and an equivalent fiber thicknessof 0.167 mm �Mapei 2000�. The Young’s modulus was 230 GPa,and the ultimate tensile strain was 0.015. The experimental char-acterization of the SRP showed that the material can be consid-ered linear elastic up to failure, with no yielding of the steel; testsprovided mean ultimate tensile stress of 3,070 MPa, ultimatestrain of 0.017, and a Young’s modulus of 184 GPa. The compres-sive and splitting tensile strengths of the cementitious grout, at

Table 1. Test Matrix

BeamExternallyreinforced Matrix

bf

�mm� nf

D — — — —

A-1 Steel 3�2 E 150 1

A-2 Steel 3�2 E 300 1

A-3 Steel 3�2 E 150 2

B-1 Steel 12� E 200 1

B-2 Steel 12� C 200 1

B-3a Steel 12� C 200 1

B-4a Steel 12� C 200 2

C-1 CFRP E 300/500 2

C-2 CFRP E 300 3

Note: E�epoxy and C�cementitious.aWith nails.

28 days of curing, were equal to 41.4 and 5.2 MPa, respectively.

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Experimental-Theoretical Analysisat Ultimate Limit State

Strength and Failure Modes

The nominal flexural strength of tested beams was calculatedaccording to the recommendations of the guidelines, ACI 318 andACI 440.2R �ACI 1999, 2002�. Since the goal was to compareexperimental values, both CE �environmental-reduction factor�and � f �additional FRP strength reduction factor� were taken toequal 1. The calculations considered the above-mentionedmaterial properties.

To determine the failure mode according to the guidelines�ACI 2002�, one should check whether the effective strain ofthe external reinforcement, � fe, is no larger than the product ofthe ultimate reinforcement strain, � fu, times the bond-dependentcoefficient, km. If this condition is verified, the failure mode isconcrete crushing, and the effective strain in the composite rein-forcement is obtained from the linearity of the strain diagram. If itis not verified, the failure is due to FRP/SRP rupture, and theeffective strain is computed as

� fe = km� fu �1�

The document ACI �2002� provides two expressions forcomputing km, depending on the value of the product nf ·Ef · tf

�nf is the number of plies and Ef and tf are the Young’s modulusand nominal thickness of one ply of the external reinforcement,respectively�. For beams discussed in the present paper, thisproduct is always less than the threshold of 180 MPa, and thefollowing equation should be used:

km =1

60� fu�1 −

nEftf

360,000� � 0.90 �2�

Note that by means of km, the maximum usable strain inthe external reinforcement is reduced by ACI �2002�, and thusSRP/FRP rupture represents a conventional way to also accountfor premature failures.

For all tested beams, the ultimate neutral axis position can becomputed by a trial-and-error procedure from the equilibriumequation in which the summation of horizontal compressive�i.e., concrete and compressive steel reinforcement� and tensile�i.e., tensile steel and FRP reinforcement� forces is equal to zero.By means of the equilibrium condition, the nominal flexuralmoment Mn, strains in the concrete, steel reinforcement, and FRPcan be determined. For Beams A-2, B-4, C-1, and C-2, a failuredue to concrete crushing was predicted, while for all the other fivebeams, Eq. �1� governed and the expected failure mode involvedFRP/SRP rupture.

The results of such theoretical analysis are reported in Table 2,where a comparison with experimental outcomes is also pro-posed. Tests showed that the strength increases provided by SRPbonded with cementitious grout were smaller than those obtainedusing epoxy. CFRP was more effective than epoxy-bonded SRP interms of strength, and the epoxy resin was more effective than thecementitious grout in engaging the concrete substrate. It was alsofound that the nail anchors did not affect the performance of theSRP impregnated with cementitious grout because the lack of atransverse link in the steel tape did not allow distributing the localstress concentration at the anchor location. A detailed descriptionof experimental results can be found in Prota et al. �2004�.

As far as the failure mode is concerned, the theoretical predic-tion �concrete crushing� was not confirmed by experiments for

one beam of both Series A and B �A-2 and B-4� and for the

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two beams of Series C �Table 2�. The same amount of externalreinforcement arranged in different configurations determines thatthe ACI formulas are able to capture the failure mode of A-3 �twoplies and width equal to 37.5% that of the beam�, whereas they donot perform in the same way if the SRP is arranged in one ply, buton a width equal to 75% of that of the beam �A-2�. Since thestrain that the FRP would attain at concrete crushing by linearity�second column of Table 2� is almost equal for both �0.090 versus0.092�, the difference is due to values of km equal to 0.90 �whichwould be 1.06, but the limit controls� and 0.71 for A-2 and A-3,respectively.

For Beams B-1, B-2, and B-3, the km value would be 1.17,whereas it would be 0.95 for B-4; therefore, the limit of 0.90controls them all. This allows for a good prediction of the failuremode on B-1, B-2, and B-3 beams, while the effective strainin the SRP reinforcement is overestimated when two plies areinstalled and concrete crushing is expected �B-4�. The same hap-pens for the two CFRP-strengthened beams. Finally, for the ninestrengthened beams, the analysis according to ACI �2002� wouldprovide ultimate strains in the tensile steel reinforcement, �s,much larger than 0.005 �ranging between 0.0061 of C-2 and0.0084 of B-1� and then all largely fall into the region where thestrength reduction factor, �, is equal to 0.90. For this reason,no changes to the formulas appear necessary, considering that acorrection aiming at fitting all experimental failure modes wouldnot affect the overall safety of the strengthening design.

Regarding the nominal flexural moments, the ACI approachis conservative for both A-1 and A-2 beams and overestimatesthe strength of A-3 by 7.4% �Table 2�. With respect to Series B,it is conservative for the beam impregnated with epoxy �B-1�,whereas it overestimates the strength of those impregnatedwith cementitious grout by about 11.4% �B-2 and B-3� and 22%�B-4�; it is always conservative for the CFRP-strengthened beams�Table 2�.

The main conclusion of such comparison is that the approachof ACI �2002� overestimates by more than 10% the strength ofthe beams whose SRP reinforcement is bonded with cementitious

Table 2. Comparison between Theoretical and Experimental Predictions

Beam

Theoretical

�cu�h−c /c�−�bi km� fu � fe

Failuremode

D — — — CC

A-1 0.0119 0.0108 0.0108 SR

A-2 0.0090 0.0108 0.0090 CC

A-3 0.0092 0.0086 0.0086 SR

B-1 0.0126 0.0108 0.0108 SR

B-2 0.0126 0.0108 0.0108 SR

B-3 0.0126 0.0108 0.0108 SR

B-4 0.0095 0.0108 0.0095 CC

C-1 0.0105 0.0131 0.0105 CC

C-2 0.0080 0.0114 0.0080 CC

Note: CC=concrete crushing and SR=SRP failure.

Table 3. Theoretical Strength Using Modified km

Beam � fe

Failuremode

Mn�kNm�

B-2/B3 0.0070 SRP rupture 42.16

B-4 0.0057 SRP rupture 50.44

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grout �B-2, B-3, and B-4�. To calculate effective strains in theSRP that provide theoretical moments equal to those experimen-tally measured for the three beams, values of about 0.58 �B-2 andB-3� and 0.47 �B-4� of � fu are obtained. Based on these consid-erations, the km equation could be safely extended to externalreinforcements bonded with cementitious grout as follows:

km =1

120� fu�1 −

nfEftf

360,000� �3�

The strength prediction that would be obtained for the threebeams according to Eq. �3� are summarized in Table 3; recall thatBeams B-2 and B-3 are identical from a strength point of view, asthe presence of nails is not accounted for in the adopted formulas.Note also that the use of Eq. �3� so much reduces the effectivestrain in the SRP of the B-4 beam that the strain in its tensile steelreinforcement at ultimate is lower than 0.005 �0.0048�. Thiswould have an important repercussion from a design standpointbecause it would determine the use of a strength-reduction factorlower than 0.90.

Moment–Curvature Relationships

The behavior of tested beams was also analyzed in terms ofmoment–curvature relationships. For the control beam, theexperimental mean curvature was determined from readings oflinear variable differential transducers �LVDTs� mounted over agauge length of 350 mm across midspan at the heights of bothcompressive concrete and internal steel reinforcement �Fig. 1�a��.For the strengthened beams, the experimental mean curvature wasobtained from readings of the LVDT transducer mounted on thecompressive concrete and of strain gauges installed at midspan onthe external reinforcement �Fig. 1�b��.

ms of Strength and Failure Modes

Experimental

Fu,th

�kN�Mn

�kNm�Failuremode

Fu,exp

�kN�Mu,exp

�kNm�

43.6 26.13 Concrete crushing 49.3 29.58

85.3 51.16 SRP delamination 86.3 51.78

110.5 66.31 SRP delamination 121.1 72.66

107.8 64.69 SRP delamination 100.4 60.24

80.4 48.22 SRP delamination 88.6 53.16

80.4 48.22 SRP delamination 72.7 43.62

80.4 48.22 SRP delamination 71.5 42.90

105.7 63.44 SRP delamination 86.7 52.02

96.1 57.65 FRP delamination 96.5 57.90

121.0 72.58 FRP delamination 134.8 80.88

Fig. 1. Experimental curvature of �a� control and �b� strengthenedbeams

in Ter

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Experimental moment–curvature trends �Fig. 2� have beenanalyzed for tested beams, and it has been pointed out thatthe control beam cracked at about 5 kNm and yielded at about25 kNm, with corresponding curvatures of 1.96�10−6 and2�10−5 rad/mm, respectively. The A-1 and A-2 beams showed acracking moment of about 13.5 kNm, which was higher than thatprovided by A-3 �about 9.7 kNm�; up to the cracking moment, theA-1 and A-2 curves were very similar, even though A-2 wasslightly stiffer than A-1, which was closer to D up to its firstcracking. Then A-1 yielded at about 35.4 kNm, whereas A-2 andA-3 yielded at about 45 kNm. For these two beams, branchesbetween cracking and steel yielding and between steel yieldingand ultimate were very similar �Fig. 2�. Experimental ultimatemoment values have already been discussed for all beams in theprevious section and are summarized in Table 2.

Curves of all beams in Series B showed very similar trends upto the cracking moment of about 6 kNm and were all stiffer thanthe control beam. No matter whether the SRP tape was bondedwith epoxy or cementitious grout or nailed, Beams B-1, B-2, andB-3 showed a similar yielding moment of about 35 kNm. How-ever, B-1 and B-2 had similar branches between cracking andyielding, whereas the presence of the nails stiffened B-3, whichattained the yielding with a curvature about 20% lower than theother two beams. The higher amount of external reinforcementcaused B-4 to yield at a moment of about 43 kNm; its curvealmost overlapped that of B-2 until such beam yielded. Both

Fig. 2. Experimental moment–curvature relationships for Type Abeams

Fig. 3. Comparison between experimental and theoreticalmoment–curvature relationships for beams having almost equivalentreinforcement percentage

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CFRP-strengthened beams cracked at about 10.5 kNm and theirinitial slope was stiffer than that of D; after the cracking point, thecurves started diverging and reflected that the higher amount ofexternal reinforcement made the C-2 cross section stiffer.

Theoretical moment–curvature relationships were computedfor tested beams using the above-mentioned material properties.A typical comparison is depicted in Fig. 3 for a series of beamshaving almost equivalent external reinforcement; experimentalcurves are denoted with the symbol EX in parentheses after thecode of the relevant beam. The symbol TH is used for theoreticalcurves that were drawn considering, since the beginning, themoment of inertia of the cracked cross section and were obtainedas the sum of a continuous and a dashed line.

The continuous branch represents the moment–curvaturedetermined by stopping the analysis of the cross section whenthe strain in the external reinforcement �SRP or FRP� of eachbeam attains the value of � fe, computed according to ACI �2002��Table 2�. The dashed branch represents the portion of themoment curvature that could be attained if premature failureswere not considered, and then the ultimate composite strain wasnot reduced via the coefficient km discussed in the previoussections. Therefore, the dashed branches allow understanding ofthe reductions of strength �moment� and deformation �curvature�capacity that the cross section undergoes if premature failures�delamination� are accounted for in addition to conventionalfailure modes �concrete crushing and FRP/SRP rupture�. Asexpected, the experimental curves are in general stiffer than thetheoretical ones; this is because the experimental curves are

Table 4. Experimental Results at Service Load

BeamFserv

�kN� f

�mm�wexp

�mm� nsrm,exp

�mm�

D 27 1.8 14.40 0.120 11 100

A-1 56 1.5 23.80 0.179 11 100

A-2 72 1.7 25.89 0.165 11 100

A-3 72 1.4 29.83 0.246 11 100

B-1 53 1.7 26.75 0.250 11 95

B-2 53 1.4 28.20 0.325 12 85

B-3a 53 1.3 27.10 0.360 10 104

B-4a 69 1.3 30.28 0.264 10 100

C-1 66 1.5 26.38 0.237 10 94

C-2 80 1.7 25.60 0.182 9 106aWith nails.

Fig. 4. Experimental comparison between beams in terms of crackwidth

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mean curvatures �averaged over a length of 350 mm where ingeneral only three cracks formed�, whereas the theoretical curvesrepresent curvatures of the cracked cross section.

Experimental-Theoretical Analysisat Serviceability Limit State

Experimental Results

To summarize the experimental results and compare them to codemodels in terms of deflections, crack spacing, and width, theservice load, Fserv, is defined by dividing the theoretical ultimateload over 1.5. Table 4 reports the following data:• Service load, Fserv;• Ratio between experimental ultimate load and service load;• Experimental deflection, f , at Fserv;• Mean experimental crack width, wexp, at Fserv;• Number of cracks, n, at Fserv; and• Mean crack spacing, srm,exp, at Fserv.

Steel stirrups spaced at 100 mm influenced the developmentof cracks during the loading history, and in general no relevantdifference in crack spacing was observed between the referenceand strengthened beams. Considering the evolution of cracks fordifferent load levels until steel yielding, the crack pattern at theservice load corresponds to a stabilized cracking situation becauseno more cracks formed until the failure occurred, and crackingbecame more irregular due to local debonding at the concrete-laminate interface �Ceroni et al. 2004b�.

Crack openings, as evidenced in Fig. 4, achieved maximumreduction when carbon fibers and steel 3�2 cords were applied�Beams A2 and C2�: the reduction was greater as the width of theexternal bonded reinforcement increased �A1 and A2, C1 andC2�, while for the same width, no relevant effect was producedwhen the number of plies increased �A1 and A3�. This phenom-enon in the elastic range of steel was already evidenced by �Pecceand Ceroni 2004�.

Comparable effects were obtained for carbon �C2� and 3�2steel �A2� reinforcement with a similar equivalent reinforcementpercentage and the same width. The equivalent reinforcementpercentage is defined as eq=s+Ef /Es · f, where s and f arethe reinforcement ratios of internal and external reinforcement

Fig. 5. Ratio of experimental deflection of strengthened beam to thereference versus strengthening ratio

area over the concrete cross-sectional area �i.e., width of the cross

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section times the depth of the internal reinforcement�. Theseobservations are confirmed in Table 4, if the comparison betweendifferent beams is developed considering the ratio Fserv /wexp, dueto the variability of the service load.

When the 12� steel cords were used �B1 in Fig. 4�, values ofthe crack width were similar to the reference beam �D�, consid-ering that the ratio Fserv /wexp is almost the same and that theexternal reinforcement had no sensible effect. This is probablydue to the low density of the 12� steel cords and to the use ofcementitious grout instead of epoxy resin. In fact, due to thehigher density of the cementitious grout, the adhesive layer isthicker, giving less stiff bond relationships and a reduction ofcrack width is observed only when the number of layers of steelcords increases.

To estimate the stiffening effect of the external reinforce-ment on the unstrengthened beam, Fig. 5 shows that the ratioof experimental values of deflection, f , to the reference beamdeflection, f ref, is a function of the ratio between the axial stiffnessof the external reinforcement �EA�ext and the internal reinforce-ment �EA�int; the latter is the same for all the beams. The com-parison is reported at the service load of the reference beam andshows that by increasing the area of the external reinforcement,deflection can be reduced up to 50% for the same load due tothe tension-stiffening effect, since the inertia of the gross sectiondiffers less.

Crack Width

When external reinforcement is applied, development of crackingis modified �Sato et al. 2002; Zhang et al. 2003; Ceroni et al.2004a� because of the additional stresses transferred to the tensileconcrete by the laminate. The number of cracks and the crackspacing change, depending on the bond behavior at the concrete-laminate interface �Smith and Teng 2002a,b; Teng et al. 2001�.

Table 5. Experimental and Theoretical Crack Width at Service Load

BeamFserv

�kN�wexp

�mm�wmod

�mm��

�%�

D 27 0.120 0.11 8.3

A-1 56 0.179 0.179 −0.3

A-2 72 0.165 0.18 −9.1

A-3 72 0.246 0.21 14.6

C-1 66 0.237 0.205 13.3

C-2 80 0.182 0.166 8.8

Fig. 6. Comparison between experimental and theoretical crackwidth for unstrengthened Beam D

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Theoretical models have been developed �Ueda et al. 2002� forRC elements externally bonded with FRP, and the writers usedone model to calculate mean strain, crack width, and spacing onRC ties externally bonded with FRP laminates �Pecce and Ceroni2004�. Herein the model is extended to beams, considering thepart of the beam in tension as a tie with a section equal to theeffective area of concrete in tension surrounding the internal steelreinforcement. The approach is monodimensional and is basedon equilibrium equations for the steel bar, external reinforcement,and concrete and compatibility equations for slip between mate-rials. The experimental nonlinear constitutive relationship ofsteel, a linear constitutive relationship for CFRP and SRP basedon the experimental values of Young’s moduli, and the nonlinearlaw developed by Eligehausen et al. �1983� for the bond behaviorof steel bar in concrete are introduced in the model. For the bondbehavior of fibers externally bonded to concrete, a bilinear model�FIB 2001� is assumed, adopting the following values as the mainparameters, based on a parametric analysis �Pecce and Ceroni2004�:

�max = 3 MPa; s1 = 0.05 mm; smax = 0.1 mm

The codes provide formulations to calculate the meancrack width, wm, for RC elements in service conditions�Eurocode 2 1992; ACI 1995; FIB 2001� based on numericalparameters validated through experimental tests. Eurocode 2�1992� allows evaluating the average crack width by using thefollowing expression:

wm = �sm · srm �4�

and formulations are proposed for the mean steel strain, �sm, andthe mean crack spacing, srm, depending on the bond characteris-tics of the internal reinforcement and the loading type through

Fig. 7. Comparison between experimental and theoretical crackwidth for Beams A2 and C2

Fig. 8. Comparison between experimental and theoretical values o�b� comparison between experimental and code results

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coefficients, and on the ratio of cracking to the service bendingmoment. Therefore the mean crack spacing depends on the steelbar diameter and the geometrical percentage, , of the internalsteel reinforcement with respect to the effective concrete area intension, Act,eff, defined as the minimum value between �2.5·B ·c�and �B · �H-xc� /3�, being B, H, c, xc width, height, concrete cover,and neutral axis of the section. The parameter, , when fiberreinforcement is applied externally, could be modified by intro-ducing the contribution of external reinforcement transformedthrough the ratio of the Young’s modulus of the external to theinternal reinforcement.

The American Concrete Institute �ACI 1995� proposed anempirical formula for RC members where the computation ofcrack width does not require the evaluation of crack spacing. Theformulation of ACI �1995� depends directly on the stress in thesteel bar at the service load, and the main parameters are theeffective area of concrete in tension surrounding each steel bar,the percentage of tensile area with respect to the total area of thesection, and the concrete cover. Bond properties would be intro-duced by a bond parameter, k, experimentally calibrated andequal to 1 for ribbed steel. Since 1999 �therefore also in ACI�2002��, no formulation has been proposed by the ACI 318 codefor the evaluation of crack width, but limitations on the minimumvalue of spacing of reinforcement are provided to limit surfacecracks. Note that ACI 440.2R-02 refers to provisions of ACI318-99 for all serviceability checks, while, for the purpose ofan experimental-theoretical comparison, the provisions of ACI�1995� are used here.

In the following, experimental crack widths are comparedeither with values calculated using code formulations �ACI andEC2� or with those given by the theoretical model developedand previously introduced by the writers.

Table 5 reports the theoretical mean crack width given by themodel, wmod, and the percent difference, �, from the experimentalvalues, wexp, at the service load for the unstrengthened beam andfor those strengthened with carbon fibers and 3�2 steel cords.Beams reinforced with 12� cords are not reported because theexperimental crack widths are comparable or greater than those ofReference Beam D. The area of concrete in tension is assumedequal to the effective area Act,eff calculated according to the pro-visions of Eurocode 2 �1992� considering the experimental meancrack spacing.

Good agreement between the experimental and theoreticalvalues of crack width was observed also for the entire loadhistory for the beams strengthened with carbon fibers and steelcords using epoxy resins. As an example, Figs. 6 and 7 compare

k width: �a� comparison between experimental and model results;

f crac

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the model and experimental results for the unstrengthenedBeam D and Beams A2 and C2 with the same width �300 mm�and adhesive �epoxy� and similar equivalent reinforcementpercentage �0.74 for Beam A2 and 0.79 for Beam C2�. Theexperimental values of crack width are given by a mechanicaldeformometer and have not been registered until the service loadfor all beams.

Figs. 8�a� compare the experimental values of the crack width,wexp, at the service loads with those given by the model, whileFig. 8�b� compares the values, wcode, given by Eurocode 2 �1992�and ACI �1995� to show the reliability of different theoreticalapproaches. Fig. 8�a� confirms the effectiveness of the model. Inthe EC2 formulation the crack spacing was calculated accordingto the expression suggested by the code. The writers noticed thatby introducing the experimental crack spacing at the service load,a better agreement could be obtained �Ceroni et al. 2004b�.

ACI �1995� estimates the effective concrete area in tensionsurrounding each bar to be equal to the value of Act,eff used forformulation of Eurocode 2 �1992� divided by the number of bars.Both code formulations generally overestimate the experimentalvalues, except for two beams �B2 and B3�, which resulted in acrack width more deformable than the Reference Beam D. Thecode formulations for strengthened beams with epoxy resin showan approximation with respect to the experimental values gener-ally no higher than for the unstrengthened beam.

Fig. 9. Comparison between experimental and code values ofdeflections

Fig. 10. Comparison between experimental and code values ofdeflections for Beam A1

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Deflections

Eurocode 2 �1992� formulates the deflection by combining thedeflection calculated for the gross, f1, and the cracked section, f2,through a tension-stiffening coefficient, �, depending on loadingtype, bond properties, and ratio of cracking to service bendingmoment according to the following expression:

f = �1 − �� · f1 + � · f2 �5�

On the other hand, the ACI approach is based on a combination ofgross, Ig, and cracked, Icr, inertias using the ratio of cracking toservice bending moment, according to the following expression:

Ie = �Mcr

M�3

· Ig + �1 − �Mcr

M�3� · Icr �6�

This value of equivalent inertia is used to calculate the deflectionaccording to the load pattern. Both formulations take FRP intoaccount in the calculation of inertia of the cracked section Icr.

In both code formulations the effect of the beam weight wasadded to the applied load. Fig. 9 compares the experimentaldeflections at the service load and the values given by EC2 andACI formulations, showing that the ACI provisions underestimatethe experimental values in all cases. On the other hand, EC2mainly shows a better agreement. Note that in some cases theexperimental deflections are close to deflection f2, correspondingto the condition of cracked inertia; beams strengthened withcementitious mortar in some cases show deflections larger than f2.

Fig. 11. Comparison between experimental and code values ofdeflections for Beam C1

Fig. 12. Comparison between experimental and code values of meancurvature for Beam A1

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As an example, Figs. 10 and 11 compare the experimentaldeflection and the values given by the EC2 and ACI formulationsfor the entire load history for Beams A1 and C1, which experi-mentally showed a good tension-stiffening effect.

The combination of curvature in the hypothesis of grossand cracked inertia is also used to calculate the mean curvature,�, according to a formulation similar to the deflection of CEB�1985�

� = �1 − �� · �1 + � · �2 �7�

where the tension-stiffening coefficient � is the same used fordeflection.

Fig. 12 compares the code value of mean curvature, �code,using Eq. �7� with the experimental value, �exp, given by LVDTmeasures: the theoretical values show a good agreement with theexperimental ones.

Conclusions

The results of a theoretical-experimental analysis are presentedfor RC beams strengthened in flexure with FRP and SRP lami-nates. Regarding the ultimate behavior, the comparison allowsassessing the strength gains provided by FRP and SRP systems.For the latter, the performance of epoxy resin and cementitiousmortar are compared.

The paper confirms that the approach of ACI �2002� providesconservative strength estimates for both FRP and SRP systems, ifthe external reinforcement is bonded with epoxy. The differentbond behavior of a cementitious mortar is not predicted by thecurrent equations given by ACI �2002�; a modified expression forthe bond coefficient km has been proposed herein to extend theseequations to systems impregnated with mortar. Further tests willneed to be performed to confirm the reliability of the modifiedequation.

Regarding the behavior at service conditions, the followingconclusions are based on the experimental results:• At similar serviceability load levels, crack width becomes

smaller if the width of the laminate increases, while the num-ber of fiber layers is less important;

• Steel cords and carbon fibers, both impregnated with epoxy,gave very similar results when the reinforcement percentagewas the same;

• Low-density steel cords bonded with cementitious grout gavea low tension-stiffening effect;

• Comparisons between code formulations and experimentalvalues of crack width and deflections for beams strengthenedwith epoxy resin show a scatter generally comparable to thatobserved for unstrengthened beam. When the cementitiousmortar is used, experimental values are much larger than codevalues; and

• Beams strengthened with cementitious mortar showed a lessstiff behavior in serviceability conditions.

Acknowledgments

The writers would like to thank Hardwire LLC, PocomokeCity, Maryland; Mapei Spa, Milan, Italy; and Sika Italia, Milan,Italy, for donating the steel tapes, FRP system, and epoxy resin/

cementitious grout used to bond SRP, respectively.

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Notation

The following symbols are used in this paper:Ac � concrete area;

Act,eff � effective concrete area in tension;Afrp � area of external FRP reinforcement;

As � area of internal steel reinforcement;B � width of cross section;

bfrp � width of FRP sheet;CE � environmental reduction factor;

c � concrete cover;Ec � Young’s modulus of concrete;Ef � Young’s modulus of FRP;Es � Young’s modulus of steel bar;F � vertical applied load;

Fserv � service load;Fu,th � theoretical ultimate load;

Fu,exp � experimental ultimate load;f � deflection;

fcode � deflection calculated by codes;fexp � experimental deflection;f fu � tensile strength of FRP;f ref � deflection;f1 � deflection at condition of gross inertia;f2 � deflection at condition of cracked inertia;Ig � gross inertia;Icr � cracked inertia;H � height of cross section;km � bond-dependent coefficient;M � bending moment;

Mcr � cracking bending moment;Mn � nominal bending moment;

Mu,exp � experimental ultimate bending moment;n � number of cracks;

nf � number of FRP plies;sfrp � slip at concrete-laminate interfaces;

smax � slip at concrete-laminate interface corresponding toshear stress equal to zero;

srm � mean crack spacing;srm,exp � mean experimental crack spacing;

s1 � slip at concrete-laminate interface corresponding tomaximum shear stress;

tf � thickness of FRP sheet;wexp � experimental crack width;wm � mean crack width;

wmod � mean crack width;wcode � mean crack width;

xc � neutral axis;� fe � effective FRP strain;� fu � ultimate FRP strain;�sm � mean strain of steel bar;�2 � steel strain at cracked section;� � tension-stiffening coefficient; � ratio between experimental ultimate load over

service load; � ratio between internal reinforcement over Act,eff

s � percentage of internal reinforcement;eq � equivalent reinforcement percentage;frp � percentage of external reinforcement;

�max � maximum bond stress of FRP at concrete interface;� � steel bar diameter;� � mean curvature;

�exp � experimental curvature;

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�1 � curvature at condition of gross inertia;�2 � curvature at condition of cracked section; and� f � FRP strength reduction factor.

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