Aspects of Behaviour of CFRP Reinforced Concrete Beams in Bending

Construction

ARTICLE IN PRESS

www.elsevier.com/locate/conbuildmat

Construction and Building Materials xxx (2006) xxx–xxx

and Building

MATERIALS

Aspects of behaviour of CFRP reinforced concrete beams in bending

Muhammad Masood Rafi *, Ali Nadjai, Faris Ali, Didier Talamona

Fire Safety Engineering Research & Technology Centre (FireSERT), University of Ulster at Jordanstown, Shore Road, Newtownabbey BT37 0QB, UK

Received 13 February 2006; received in revised form 24 July 2006; accepted 30 August 2006

Abstract

The corrosion of steel poses a serious problem to the durability of reinforced concrete structures and fibre reinforced polymer (FRP)has emerged as a potential alternative material to the traditional steel. The results of a test series consisting of carbon FRP (CFRP) andsteel bars reinforced concrete beams are reported in this paper. The results indicated that the behaviour of CFRP and steel reinforcedbeams was similar in many aspects. Both type of beams failed in their predicted modes of failure. The strength design method underes-timated nominal moment capacity of CFRP reinforced beams. The deflection of CFRP reinforced beams was satisfactory at service loadlevel, corresponding to theoretical load capacity. The deformability factor of CFRP reinforced beams was more than 6 indicating theirductile nature of failure.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Fibre reinforced polymer; Carbon FRP; Mode of failure; Concrete beams; Reinforcement; Moment; Deflection; Deformability

1. Introduction

Reinforced concrete (RC) structures have profited fromthe unrivalled dominance of steel over all other reinforc-ing materials for more than 100 years. Superior qualitiesof steel, in terms of strength and compatibility with con-crete, make steel an effective concrete reinforcement. Steelis, however, highly susceptible to oxidation when exposedto chlorides. Although, alkaline environment of concreteprotects steel from corrosion and makes it very durableit is not always possible to provide an efficient protection.Factors such as insufficient concrete cover, poor design orworkmanship, poor concrete mix and aggressive environ-ments can break down the protection layer and may leadto corrosion of the steel rebars. These destructive environ-ments include marine surroundings, use of deicing salts onbridges and parking garages, and the use of salt contam-inated aggregates in the concrete mixture. The initial signsof distress are usually cracking and spalling of concrete,which provides access to other environmental agents like

0950-0618/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.conbuildmat.2006.08.014

* Corresponding author. Tel.: +44 28 903 68734; fax: +44 28 903 68726.E-mail address: [email protected] (M.M. Rafi).

Please cite this article in press as: Rafi MM et al., Aspects of behavioing Mater (2006), doi:10.1016/j.conbuildmat.2006.08.014

moisture to further intensify the oxidisation of steel. Ascorrosion goes on it causes a reduction in the cross-sec-tion of a steel bar, which leads to loss of bond betweenrebar and concrete. To arrest the rusting of steel remedialwork has to be carried out in order to achieve the fullpotential of the structure. This structural maintenanceincurs exorbitant costs annually. Unreliable durability ofthese structures as a result of corrosion of steel is thusa serious problem. Recent efforts and research have beenfocussed towards the introduction of innovative non-metallic materials in the construction industry. Fibre rein-forcement polymer (FRP) materials have evolved as aresult of new developments in the fields of plastics andfibre composites.

A significant amount of research work has been exe-cuted to investigate various aspects of the use of FRP barswith concrete. As a result of these efforts, the applicationsof FRP bars are becoming increasingly common as a rein-forcing material. Carbon FRP (CFRP) bars are mostlyused in prestressing applications due to their high tensilestrength, which is comparable with steel strands. Thispaper presents the results of tests carried out on concretebeams reinforced with CFRP bars. Testing of these beams

ur of CFRP reinforced concrete beams in bending, Constr Build-

mailto:[email protected]

Table 1Strength of concrete on the day of test

Beam Compressive strength (MPa)

BRS1 46.52BRS2 44.64BRC1 42.55BRC2 41.71

2 M.M. Rafi et al. / Construction and Building Materials xxx (2006) xxx–xxx

ARTICLE IN PRESS

is a part of on-going research on the behaviour of CFRPreinforced concrete beams at room and elevated tempera-tures at the University of Ulster.

In the first phase of this project a total of four specimenbeams were used. Duplicate steel and CFRP reinforcedbeams were tested at room temperature. The tests resultsof this series will serve as benchmark to study the perfor-mance of similar beams under fire conditions. Steel rein-forced beams were tested as control specimens. The studyfocused on the flexural behaviour of these beams in termsof stress–strain, load–deflection, modes of failure, load-car-rying capacity, and cracking pattern. Some of the aspectsof behaviour of these beams are discussed hereafter.Long-term behaviour and durability aspects are, however,beyond the scope of this work.

2. Experimental programme

2.1. Test specimens

The overall length of each beam was 2000 mm and thecross-section was 120 · 200 mm. Each of these beams wasreinforced with two longitudinal bars on the tension face(CFRP bars for FRP reinforced beams and steel bars forsteel reinforced beams). The beams were cast in mouldsmade of plywood stiffened with aluminium angles to main-tain the beam shape under the pressure of newly cast con-crete. A 20 mm concrete cover was used all-around thebeam. The area and nominal yield strength of the compres-sion steel and nominal concrete strength were kept con-stant for all beams in this series. Mixing of concrete wasdone in a rotating mixer. A vibrating table was used forthe compaction of concrete inside the mould. The sidesof the mould were stripped after 24 h of casting and beamswere covered with hessian. Intermittent curing (thrice a dayin summer) was carried out for 10 days and then the beamswere left air-drying in laboratory conditions until the dayof testing. Four 100 mm cubes were cast for each beam.Cubes were cured by keeping them on top of their respec-tive beam. The beams were tested as simply supportedbeams over a span of 1750 mm under a four-point static

6 mm stirrups 200

120

2 T8 bars

67

2 T10 steel / 2- 9.5 mm CFRP bars

Fig. 1. Details of a


load as shown in Fig. 1. The loads were 400 mm apart giv-ing a shear span of 675 mm.

2.2. Materials

2.2.1. ConcreteFour identical concrete mixes of 325 kg/m3 ordinary

Portland cement, 1001 kg/m3 of graded crushed stone,853 kg/m3 of sand and 216 litres/m3 of water were used.The maximum aggregate size was 10 mm. The exactamount of water varied depending on the moisture con-tents of aggregates. The slump of concrete ranged from40 to 50 mm. Cube strength after 28 days was49.23 MPa, this being the average strength of the fourcubes, one from each beam. This is equivalent to43.31 MPa cylindrical strength [1]. Table 1 shows theequivalent cylindrical strength [1] of the concrete on theday of testing. These strengths were obtained from theaverage strength of three cubes for each beam. Each beamtested is defined by letters comparing its reinforcing mate-rial and temperature conditions. The notation of beams isas: the first letter (B) stands for beam; the second letterindicates the testing temperature as R for room tempera-ture; the third letter represents the type of tension reinforc-ing bar material such as S for steel and C for CFRP bars.These notations have been consistently followed through-out the rest of the text.

2.2.2. CFRP bars

The FRP bars consisted of 9.5 mm diameter straightCFRP rods, as shown in Fig. 2. The bars were producedby an American manufacturer using the pultrusion process.

Not to Scale Dimensions in mm

400

1750

2000

5 675

100 mm c/c Typ.

P

typical beam.


Fig. 2. CFRP and tension steel bar.

M.M. Rafi et al. / Construction and Building Materials xxx (2006) xxx–xxx 3

ARTICLE IN PRESS

Continuous carbon fibres with a volume fraction of 60% byvolume were used. The nominal tensile strength and tensilemodulus of these fibres were 4.83 GPa and 234 GPa,respectively. The resin used to bond fibres was bisphenolepoxy vinyl ester. A textured surface was provided on thebar through surface treatment in order to increase the bondwith the concrete. The bar had a widely spaced spiral wind-ing imprint with textured surface in between helical rings.The surface texture was formed with the same resin withoutinvolving external fibres. Properties of CFRP bars aregiven in Table 2. The manufacturer provided results of ten-sile tests on these bars.

2.2.3. Steel bars

Tension rebars in BRS beams consisted of 10 mm diam-eter high strength deformed bars, as shown in Fig. 2. Mate-rial properties of these bars are given in Table 2. Theseproperties were determined by the tensile tests in the labo-ratory. The bars were chosen because their nominal cross-sectional area was approximately equal to the CFRP bars.It was, therefore, possible to position the steel and CFRPbars identically in the control and in the test beams. Steelreinforcing bars of the identical area of the CFRP barswere not available.

Top bars were of 8 mm diameter high strength deformedsteel for all beams. Both top and bottom steel bars werehooked at each end. The mechanical properties of top rein-forcing bars are shown in Table 2.

The reinforcement cages (Fig. 1) were tied with ironwire. Smooth 6 mm diameter closed rectangular stirrupsspaced at 100 mm centre to centre were chosen to complywith the criteria of the ultimate strength design of FRPreinforced beams given by the ACI code [2,3]. Results oftensile tests on 6 mm bars are also included in Table 2.

2.3. Instrumentation

The instrumentation was set up to measure the deflec-tion of the beam and the deformation of the reinforcing

Table 2Mechanical properties of rebars

Bar type Nominal ultimatestrengtha (MPa)

Ultimatestraina

Elastic modulus(GPa)

CFRP 1676 0.0145 135.9Steel – 10 mm 530 0.0048 201Steel – 8 mm 566 0.0049 194Steel – 6 mm 421 0.0041 200

a Parameters corresponding to 0.2% offset yield stress for steel bars.


bar. Strain gauges were used to measure deformation andto monitor bond of tension bars. The deflection at midspanwas recorded using linear variable differential transducers(LVDTs). These LVDTs were placed on both sides of thebeam at the centre. Horizontal LVDTs were used at theend of the BRC beams additionally to measure the slip ofthe CFRP bars. Computer aided data acquisition systemswere used to record continuously, load, deflection, slipand strain. Thus this data could be obtained easily at anytime during each test.

2.4. Test procedure

The specimens were placed on half-round supports,which were spaced at a distance equal to the test span ofthe beam. Loading was applied in small increments,through 38 mm diameter rollers, by means of a 200 kNhydraulic jack. Steel plates 25 mm wide and 5 mm thickwere placed under each roller on the top of the beam inorder to avoid local crushing. Each load increment was2.5 kN for BRS and 5 kN for BRC beams and was mea-sured with a 200 kN load cell. All beams were tested to fail-ure. The beams were 2–3 months old at the time of testing.Immediately after the load increment, cracks were identi-fied using a magnifying glass and marked. The ends ofthe cracks were labelled with the corresponding load step.Three minutes were allowed for the completion of the pro-cess before the next increment of load was applied. Themonitoring of cracks continued over the entire loadingspectrum.

The operator manually controlled load, which was dis-played on the monitor screen, and made the necessaryadjustments to keep load as constant as possible. For alltests the load was removed after the applied load droppedsubstantially below the ultimate load. A complete test tookapproximately 1 h.

3. Analysis of test results

3.1. Cracking behaviour

Concrete is a weak material in tension and cracks whensubjected to high local tensile stresses. Its low tensile capac-ity can be attributed to the high stress concentration underload [4]. Flexural cracking in beams is not only unavoid-able but is necessary to allow tension reinforcement to playits part. The formation and propagation of cracks dependon the tensile strength of the concrete. When the principaltensile stress in concrete exceeds its tensile strength, cracks



ARTICLE IN PRESS

form perpendicular to the direction of this stress. A sectionof least resistance may develop microscopic cracks as aresult of very high stresses, while the other parts may stillbe subjected to low stresses. This section is likely to bethe one with many aggregate-paste interfaces [5]. A numberof factors may affect the spacing and width of cracks. How-ever, investigators have not completely agreed on the fun-damental factors of crack formation [5]. Extensivecracking generally takes place in flexural members likebeams and causes a change in the behaviour of thesemembers.

3.1.1. Cracking in BRC beams

Typical cracking behaviour of BRC beams is shown inFigs. 3a and b. Cracking started in the constant momentregion with the cracks originating from bottom fibres, asthe principal stresses were the greatest at these extremefibres. These cracks were mainly vertical flexural cracks,which were perpendicular to the beam longitudinal axissince the shear stresses were absent in this zone. These ini-tial cracks traversed quite deeply into the compressionzone. The height of initial cracks was between 35 and129 mm. This shows that immediately after cracking theneutral axis shifted quite deeply into the compression zone.Cracks outside this central zone originated as vertical flex-ural cracks at a relatively lower load level, as shear stresseswere initially small. However, as the load increased shearstresses became high and the principal stresses were gener-ated at approximately 45�. These stresses transformed theinitial flexural cracks into inclined diagonal tension cracksat higher load levels. With increasing load these inclinedcracks propagated towards the load points on top of the

Fig. 3. Cracking pa


beam. The crack spacing also decreased rapidly with theincreasing load. However, the spacing of cracks remainedapproximately constant after an applied load of 30 kN.As the cracking initiates on the tension side of a beam,stresses are transferred to the reinforcement, thus relievingthe concrete, at and adjacent to these cracks. After exten-sive cracking has taken place, the uncracked concretebetween consecutive cracks becomes small and subject toa very high longitudinal stress gradient. These highlystressed uncracked segments of concrete require higheraverage tensile stresses to induce further cracking at thisstage, as the new cracks may be forced to pass throughthe cement paste and aggregates instead of developingalong paths of least strength [5]. The strain in the FRP barsat this stage reached an average value of 0.0034. Beyondthis load level only existing cracks grew in length withthe increase in load with almost no change in number ofcracks. Some tertiary as well as shear cracks also developednear the ultimate capacity of the beam. Tertiary cracksformed at the level of tension reinforcement.

3.1.2. Cracking in BRS beamsThe cracking pattern of BRS1 and BRS2 is shown in

Figs. 3c and d. Similar to BRC beams cracking in BRSbeams also started with vertical flexural cracks in the con-stant moment region. However, for BRS beams very fewcracks outside the pure bending zone turned into inclinedcracks and most of these were relatively vertical as shownin Figs. 3c and d. These beams showed a classic reinforcedconcrete crack pattern involving fewer and larger cracks.The spacing of cracks, however, decreased as the loadincreased. The crack formation became stabilized once

ttern of beams.



ARTICLE IN PRESS

again after a load of 30 kN. The average strain in steel barsat this load level was recorded as 0.0024. Few tertiarycracks also formed around reinforcement at higher loadlevels.

3.1.3. Comparison between BRC and BRS beamsThe number of cracks and the average crack spacing at

failure for all beams is shown in Table 3. Spacing was mea-sured with a steel rule to the nearest 1 mm. It can be seenthat both BRC and BRS type of beams developed almostsame number of cracks at failure with similar average spac-ing. The width of cracks in BRC beams was considerablynarrow. This shows a good mechanical bond betweenCFRP bars and surrounding concrete.

No horizontal crack at the reinforcement level wasobserved in any of the tested beams. When the load wasremoved the cracks on BRC beams were observed to close.This is due to the fact that FRP bars exhibit linearly elasticbehaviour up to failure. Since BRC beams failed by thecrushing of concrete, CFRP bars recovered most of theirdeformation after the load was removed. On the contrary,no change in the crack width was observed in BRS beamsafter removal of the load as steel bars were in their irrevers-ible strain-hardening zone once they yielded.

3.2. Modes of failure

The design of both BRS and BRC beams was based onACI Code [2,3]. BRC beams were designed over-reinforcedusing reinforcement ratio (q) (Eq. (1)) greater than the bal-anced reinforcement ratio (qb). The balanced reinforce-ment ratio corresponds to the condition when the strainin the extreme concrete fibres in compression reaches toits ultimate value of ec = 0.003 [2,3] at the same time whenthe strain on the tension steel reaches to yield strain. Bal-anced reinforcement ratio can be calculated using Eq. (2).BRS beams were under-reinforced beams with reinforce-ment ratio less than balanced reinforcement ratio.

qs ¼As

bd

qf ¼Af

bd

ð1Þ

qsb ¼ 0:85b1

fc

fy

� 600

600þ fy

qfb ¼ 0:85b1

fc

ffu

� Efec

Efec þ ffu

ð2Þ

where qs is the actual reinforcement ratio of steel, qf the ac-tual reinforcement ratio of FRP, qsb the balanced steel

Table 3Number of cracks and average crack spacing

Beam Number of cracks Spacing of cracks (mm)

BRS1 13 96.00BRS2 12 100.00BRC1 18 77.00BRC2 15 99.00


reinforcement ratio, qfb the balanced FRP reinforcementratio, As the area of steel bars, Af the area of FRP bars,fc the ultimate concrete strength (MPa), b the width ofthe section, d the effective depth of the section, fy the yieldstrength of steel (MPa), ffu the ultimate tensile strength ofFRP (MPa), ec the maximum concrete strain at extremecompression fibres, Ef the modulus of elasticity of FRPbars (MPa), and b1 ¼ 0:85� 0:05fc�28

7P 0:65.

For design guidelines in Europe, Pilakoutas et al. [6]proposed a minimum amount of FRP reinforcement toachieve the failure of a section through concrete crushing.The minimum reinforcement can be calculated from Eq.(3). ec in Eq. (3) is taken as 0.0035 [6]

qmin ¼0:81ðfc þ 8Þec

ffuffu

Efþ ec

� � ð3Þ

Balanced and actual reinforcement ratios for both types ofbeams are given in Table 4. The last column of Table 4 alsogives the minimum reinforcement ratio (qmin) according toEq. (3) for BRC beams. It is evident that BRC beams ful-filled the requirements of over-reinforced section describedby both ACI Code [3] and Eq. (3).

From Table 4 a compression failure of BRC beams anda tension failure of BRS beams can be anticipated. Table 5presents the observed modes of failure of all beams. Thebehaviour of both BRS beams was similar, they both failedby the crushing of concrete after the tension reinforcementyielded and the BRC beams failed in compression asexpected. In beam BRC1 the diagonal tension crack causedfailure. Formation of diagonal tension cracks takes place inbeams in a region where large compression stresses exist ina direction perpendicular to the maximum tensile stresses[5]. This diagonal tension crack in BRC1 originated as avertical crack at a distance of approximately 120 mm fromthe support. The crack, however, gradually bent overtowards the point of load application as it propagatedupward and became almost horizontal before reachingthe load point. The beam, nevertheless, kept on taking loadas this diagonal tension crack propagated and opened up.Finally, the concrete above this crack crushed adjacent tothe load point in the shear span as shown in Fig. 3a.BRC2 beam failed by the crushing of concrete betweenpoint loads as shown in Fig. 3b.

Table 5 shows cracking loads of beams where it can beseen that the cracking loads for all four beams are veryclose to each other despite the two differing reinforcingmaterials. Discussion on this aspect is covered in Section3.3. The ultimate load carried by the beam is also shownin Table 5 and it can be noticed that BRC beams carriedmore than twice the load on BRS beams. This was due

Table 4Balanced, actual and minimum reinforcement ratio

Beam type qb Actual q qmin (Eq. (3))

BRS beam 0.0277 0.0077 –BRC beam 0.0032 0.0070 0.0055


Table 5Load, deflection and modes of failure

Beam Pcr (kN) Pu (kN) D at Pyielda (mm) D at Pu (mm) D at P35% (mm) Modes of failure

BRS1 7.8 41.9 6.92 29.16 1.75 Steel yieldingBRS2 7.5 40.1 7.50 27.78 1.74 Steel yieldingBRC1 7.1 88.9 11.14 35.26 8.60 Shear compressionBRC2 7.1 86.5 10.96 35.50 8.37 Compression

a Deflection in BRC beams corresponding to yielding of steel bars in BRS beams.


ARTICLE IN PRESS

to strength of CFRP, which was much higher than yieldstrength of steel bars (Table 2). Failure modes of beamsare presented in Fig. 3.

3.3. Cracking and ultimate moment

ACI code [2] expresses flexural strength of concrete interms of modulus of rupture [Eq. (4)], which is the maxi-mum tensile stress of concrete in bending [4]. Eurocode 2,part1-1 [7] suggests the use of a mean value of axial tensilestrength of concrete, which is given by Eq. (5). To calculatecracking moment Eq. (6) can then be used

fr ¼ 0:62ffiffiffiffifc

pð4Þ

fct ¼ 0:30� f ð2=3Þc ð5Þ

M crACI¼ frIg

yb

M crEurocode¼ fctIg

yb

ð6Þ

where fr is the modulus of rupture (MPa), fct the mean axialtensile strength of concrete (MPa), Mcr the cracking mo-ment, Ig the gross moment of inertia about centroidal axisof concrete section without reinforcement, and yb is the dis-tance from centroidal axis of concrete section to the ex-treme tension fibers, neglecting reinforcement.

The nominal moment capacity of under-reinforced steelRC section can be determined using Eq. (7). This equationis common to both ACI code [2] and Eurocode 2 [7] in theabsence of safety factors and could be arrived at using con-ditions of compatibility of strain and equilibrium of forces.For FRP reinforced beams failing in compression, Eq. (8)taken from ACI code [3] can be used.

Mns ¼ Asfy d � Asfy

1:7f cb

� �ð7Þ

Mnf ¼ Afff d 1� 0:59Afff

fcbd

� �ð8Þ

Table 6Cracking moment and moment capacity

Beam (Mcr)Exp.(kN m) Theoretical Mcr (kN m)

ACI Code Eurocode

BRS1 2.63 3.38 3.10BRS2 2.53 3.31 3.02BRC1 2.40 3.24 2.93BRC2 2.40 3.20 2.89


where Mns is the nominal moment capacity of steel rein-forced section and Mnf is the nominal moment capacityof FRP reinforced section

ff ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðEfecÞ2

4þ 0:85b1fc

qf

Efec

s� 0:5Efec

0@

1A

6 ffu ðFrom ACI ½3�Þ ð9Þ

It can be expected from Eq. (6) that the cracking momentand hence cracking load is independent of the tension rein-forcing material type. Masmoudi et al. [8] have also shownthat theoretical Mcr is nearly unaffected by the second mo-ment of area of the reinforcement. Table 6 presents theoret-ical and experimental cracking moment and nominalmoment capacities of all four beams. It is evident thatthe tensile strength of the concrete in bending is overesti-mated by the value of modulus of rupture, as also foundby Benmokrane et al. [9]. The theoretical Mcr values basedon direct tensile strength of concrete adopted by Eurocode2 [7] are quite close to the experimental values of crackingmoment. This is because the tensile strength of concrete inbending determined from a modulus of rupture test tendsto be higher than tensile strength from a direct tension test[10]. The slight difference between experimental and theo-retical Mcr values may partly be due to the variation ofstrength of concrete in larger structural element and smal-ler test specimens (cubes/cylinders).

It can be observed from the last column of Table 6 thatEq. (7) predicted the nominal moment reasonably well forsteel reinforced beams. However, Eq. (8) underestimatedthe nominal capacity of FRP beams to about 33%. Sinceboth BRC beams were over-reinforced, maximum momentcapacity depended on the maximum concrete strain at fail-ure. It thus seems likely that as a result of the confinementprovided especially by the stirrups the actual strain in con-crete exceeded maximum concrete strain of 0.003 assumedby ACI code [3]. This has been pointed out also by Nanni[11] and Benmokrane et al.[12].

(Mn)Exp. (kN m) (Mn)Th. (kN m) ðMnÞTh:

ðMnÞExp:

14.14 13.29 0.9413.53 13.36 0.9930.00 20.04 0.6729.19 19.91 0.68



ARTICLE IN PRESS

3.4. Load–deflection history

One of the important factors that affect the serviceabilityof a RC flexural member is its deflection. Deflection is afunction of load, span length, second moment of areaand modulus of elasticity of material. The stiffness of amember is largely dependant on both the second momentof area and the modulus of elasticity. Table 5 presents acomparison of deflection at different stages of loading ofbeams. Service load is considered as 35% of the ultimateload [13].

Fig. 4 shows the experimental load–deflection histories.The initial linear part of the graphs has a very steep slope,which corresponds to the uncracked condition of thesebeams. In this region the deflection is proportional to theapplied load and the entire concrete section is consideredeffective in resisting the loads. As can be seen fromFig. 4, the behaviour of both types of beams is similarbefore cracking when the beams are stiff. The end pointof this linear part is an indication of the initiation of crack-ing in the beam.

The next segment that immediately follows this linearpart provides information about the bond quality and ten-sion stiffening effects due to crack spacing. The slope of thispart is smaller than the slope of the initial linear segment.This shows that the rate of deflection per unit load is higherafter the beam has cracked, which is an indication of thereduction in the stiffness of the cracked beam. Stiffness hereis defined as load per unit deflection. It can be seen, how-ever, from the widening of the gap between BRS andBRC curves in Fig. 4 that the rate of reduction in the stiff-ness of BRC beams became higher with the increase inload. Average difference in the stiffness of both types ofbeams at the yielding of steel bars was about 38%. Thiscan be attributed to the low elastic modulus of CFRPbar, which is 32% less than a steel bar. The reduced stiffnessof FRP reinforced beams after cracking has also beenreported by various other researchers [9,11,14–18].

The last part of the curve is an indication of possiblefailure mechanism of the structure. As shown in Fig. 4,both BRS beams showed a very ductile behaviour and bothbeams failed at nearly the same load after undergoing con-

0102030405060708090

100

0 5 10 15 20 25 30 35 40 45 50Deflection (mm)

Lo

ad (

kN)

BRC1

BRC2BRS1

BRS2

Fig. 4. Load–deflection history.


siderable deformation with very small increase in the loadonce steel yielded. The ultimate load of BRS beams wasaround 53% lower than BRC beams while the deflectionof BRC beams at ultimate state was 25% greater thanBRS beams on the average, as can be seen in Table 5.The ultimate load here is considered as the maximum loadcarried by the beam. At failure, the deflection of BRCbeams was on the average 7% less than BRS1 beam, as evi-dent in Fig. 4. This shows that up to the yielding of steelbars BRC beams deflected more than BRS beams due tofactors related to the low elastic modulus of CFRP bars.However, after yielding BRS beams exhibited a much fas-ter rate of deflection than BRC beams with a negligiblechange in load. Span to deflection ratio at failure for allthe beams is shown in Table 7. It can be seen in Fig. 4 thatsome variations existed in the deflection at failure for eachtype of beam due to the variations in the maximum con-crete strain. Substantial deflection recovery was observedin BRC beams after the load was taken of. This shows thatCFRP bars remained within the elastic range at failurestage as shown in Fig. 4.

It can also be seen from Fig. 4 that load-carryingcapacity of both BRC beams dropped gradually aftercrushing of concrete. This shows that despite beingover-reinforced FRP reinforced beams can have a ductilefailure mode as well as a kind of energy dissipation mech-anism. Sudden drop in loads near the failure as visible inload–deflection curves of BRC beams was due to theopening of cracks.

If the deflection of beams at service load, which is givenin Table 5, is compared with the deflection limit of span/360 set by ACI code [2], it appears that both BRC beamsdeflected more than the allowable limit. This aspect, how-ever, does not necessarily need to control the entire designwork in every situation. The structural designers encounterexcessive deflection issues very often associated with steelreinforced beams. They are, therefore, not only aware ofthe nature of this issue but are well equipped with practicalsolutions if they face constraints on the design. For exam-ple, if the situation allows an initial camber in the beam canbe provided to reduce the amount of final deflection afterthe application of full service load. The design of beamswith FRP bars might make these types of solutions a reg-ular part of the design in most of the cases. However, con-sidering the benefits offered by FRP bars this should not betoo much of a worrying factor. Nevertheless, it emphasisesthe importance of a reliable method of predicting theoret-ical deflection of FRP reinforced beams.

Table 7Span to deflection ratio at failure

Beam Span/deflection

BRS1 37BRS2 44.5BRC1 39BRC2 40


Table 8Ductility index and deformability factor

Beam le Ratio of le Deformabilityfactor (Eq. (11))

BRS1 8.28 3.80 13.84BRS2 7.26 3.33 10.10BRC1 3.01 1.38 28.36BRC2 2.18 1.00 30.53


ARTICLE IN PRESS

Another aspect of this issue is that the limiting deflectionof span/360 during the test reached at the applied load of19.5 and 20.2 MPa, respectively, for BRC1 and BRC2, ascan be seen in Fig. 4. These values are 33% and 34% of the-oretical ultimate load (Table 6) and correspond to serviceload stage. Unless a different approach of designing FRPreinforced concrete beams is required by code, servicedeflection of BRC beams corresponding to theoretical loadcapacity is satisfactory.

3.5. Ductility and deformability

Ductility of a structure can be defined as its ability toabsorb energy without critical failure. Ductility generallyrefers to the amount of inelastic deformation which a mate-rial or structure experiences before complete failure. Thisdeformation can be measured in terms of displacement,strain or curvature. Ductile behaviour allows a structureto undergo large plastic deformations with little decreasein strength and hence avoids brittle failure.

Conventional steel reinforced beams have a distinct elas-tic and inelastic phase of deformation before and afteryielding of steel. Hence for these structures, ductility canbe defined quantitatively as the ratio of the total deforma-tion at failure divided by the deformation at the elasticlimit.

The behaviour of FRP reinforced structures is linear upto failure. The energy released at failure for these beams islinear as well [19] as shown in Fig. 4. Grace et al. [20] havesuggested a ductility classification of beams based on theratio of inelastic energy to the total energy. They termedthis ratio as energy ratio.

Naaman and Joeong [21] proposed following equationto compute the ductility index le for beams reinforced withFRP bars.

le ¼1

2

ET

EEl

þ 1

� �ð10Þ

P1

P2

S1

S2

Loa

d

Deflection

Ela

stic

Ene

rgy,

EE

l

Inelastic Energy S

Pu

( )2

21211

P

SPPSPS

−+=

Fig. 5. Ductility index [21].


where ET is the total energy, which is area under load–deflection curve and EEl is the elastic energy, which is areaof the triangle formed at the failure load by a line whoseslope is S (Fig. 5).

Ductility indices for all beams are shown in Table 8. Thefailure load has been considered as the load at failure ofeach of these beams. As can be expected, it can be seenfrom the column of ‘Ratio of le’ that BRS beams werearound 4 times more ductile than BRC beams.

However, there is an agreement between many research-ers that FRP reinforced beams should be compared on thebasis of their deformability with steel reinforced beamsrather than ductility. Jaeger et al. [22] presented the con-cept of deformability factor and strength factor. Theyfound that the product of these two factors remainsapproximately between 6 and 7 for steel reinforced beamsirrespective of the reinforcement ratio. They termed thisproduct overall factor and proposed a value not less than6 for all type of reinforcement.

Newhook et al. [23] proposed a method of calculatingdeformability factor as given by Eq. (11)

Deformability Factor

¼Moment at Ultimate State�Curvature at Ultimate State

Moment at Service State�Curvature at Service Stateð11Þ

Newhook et al. [23] proposed 0.0020 as maximum strain inFRP reinforcement at service state and 0.0012 for steel. Ta-ble 8 shows deformability factors for all beams accordingto Eq. (11). Curvature at ultimate state in the above equa-tion was calculated using a concrete strain of 0.0035 andactual reinforcement strain recorded during the test. Ulti-mate moment is taken as the maximum recorded unfac-tored moment resisted by the beam. It can be seen thatthe deformability factors for all beams are greater than 6.These beams can, therefore, be considered safe from bothstrength and deformability aspects.

4. Conclusions

The results of experimental testing on CFRP and steelreinforced beams were presented. The behaviour of bothtypes of beams was found similar in many respects. Theimportant features of the comparison of behaviourbetween BRC and BRS types of beams are listed asfollows:



ARTICLE IN PRESS

1. The cracking behaviour and pattern of both steel andCFRP reinforced beams was similar. Both types ofbeams developed nearly equal numbers of cracks withan equal average crack spacing at failure.

2. BRS beams failed by steel yielding and BRC typebeams failed by concrete crushing as per their design.

3. The cracking load for all beams was nearly the same.4. The maximum concrete strain in compression at fail-

ure exceeded 0.003 in BRC beams.5. The ACI code equation underestimated the ultimate

capacity of BRC beams.6. BRC beams deflected more than the BRS type beams

after cracking. However, after yielding of steel therate of deflection in BRS beams was more thanBRC beams.

7. The service deflection of span/360 of BRC beams cor-responding to theoretical ultimate load, as deter-mined by code equations, was satisfactory.

8. The issue of deflection of FRP reinforced beams canalso be addressed by practical solutions of controllingdeflection at service state such as by providing an ini-tial camber in the beam.

9. BRC beams failed in ductile fashion. However, theywere less ductile than BRS beams.

10. The deformability factor of BRC beams was greaterthan 6.

11. More tests are, however, needed to investigate theinfluence of other parameters such as concretestrength on the behaviour of CFRP bars reinforcedstructures.

Acknowledgements

The authors wish to acknowledge the support providedfor this research by the School of Built Environment,University of Ulster; Dr. Alan Leacock, Lecturer, Schoolof Electrical and Mechanical Engineering for tensile test-ing of steel bars and all the laboratory technical staffmembers.

References

[1] Neville MA. Properties of concrete. England: Longman Scientific &Technical; 1981. p. 529–565.

[2] American Concrete Institute. Building code requirements for struc-tural concrete, ACI 318-95, Detroit (MI); 1995.

[3] American Concrete Institute. Guide for the design and constructionof concrete reinforced with FRP Bars, ACI 440.1R-01, Detroit (MI);2001.

[4] Hassoun MN. Design of reinforced concrete structures. USA: PWSpublishers; 1985. p. 14–182.


[5] Broms B, Raab A. The fundamental concept of the crackingphenomenon in reinforced concrete beams. Final Progress Report –Phase I, Cornell University; 1961.

[6] Pilakoutas K, Neocleous K, Guadagnini M. Design philosophy issuesof fiber reinforced polymer reinforced concrete structures. ASCE JCompos Constr 2002;6(3):154–61.

[7] Eurocode 2. Design of concrete structures, Part1-1: general rules andrules for buildings, Brussels; 1992.

[8] Masmoudi R, Benmokrane R, Chaallal O. Cracking behaviour ofconcrete beams reinforced with fiber reinforced plastic rebars. Can JCivil Eng 1996;23:1172–9.

[9] Benmokrane B, Chaallal O, Masmoudi R. Flexural response ofconcrete beams reinforced with FRP reinforcing bars. ACI Struct J1996;91(2):46–55.

[10] Mirza SA, Hatzinikdas M, Macgregor JG. Statistical descriptions ofstrength in concrete. J Struct Div Proc ASCE 1979;ST6:1021–37.

[11] Nanni A. Flexural behaviour and design of RC members using FRPreinforcement. ASCE J Struct Eng 1993;119(11):3345–59.

[12] Benmokrane B, Masmoudi R. FRP C-bar as reinforcing rod forconcrete structures. In: El-Badry MM, editor. Proceedings of 2ndinternational conference on advanced composite materials in bridgesand structures, Montreal, Que.; 1996. p. 181–8.

[13] Al-Salloum AY, Alsayed HS, Almusallam HT, Amjad AM. Somedesign considerations for concrete beams reinforced by GFRP bars.In: Saadatmanesh H, Ehsani RM, editors. Proceedings of firstinternational conference on composites in infrastructure, Tucson(AZ); 1996. p. 318–31.

[14] Faza SS, GangaRao HVS. Pre- and post-cracking deflection behav-iour of concrete beams reinforced with fibre-reinforced plastic rebars.In: Neale KW, Labossiere P, editors. Proceedings of 1st internationalconference on advanced composite materials in bridges and structures(ACMBS 1), CSCE, Sherbrooke, Que.; 1992. p. 151–60.

[15] Saadatmanesh H, Ehsani MR. Fiber composite bar for reinforcedconcrete construction. J Compos Mater 1991;25:188–203.

[16] Nawy EG, Neuwerth GE. Fiberglass reinforced concrete slabs andbeams. J Struct Div 1977;103(ST2):421–40.

[17] Theriault M, Benmokrane B. Effects of FRP reinforcement ratio andconcrete strength on flexural behavior of concrete beams. J ComposConstruct 1998;2(1):7–16.

[18] Toutanji H, Deng Y. Deflection and crack-width prediction ofconcrete beams reinforced with glass FRP rods. Constr Build Mater2003;17:69–74.

[19] Alsyed HS, Alhozaimy MA. Ductility of concrete beams reinforcedwith FRP bars and steel fibers. J Compos Mater 1999;33(19):1792–806.

[20] Grace FN, Soliman KA, Abdel-Sayed G, Saleh RK. Behaviour andductility of simple and continuous FRP reinforced beams. ASCE JCompos Constr 1998;2(4):186–94.

[21] Naaman AE, Joeng SM. Structural ductility of concrete beamsprestressed with FRP tendons. In: Taerwe L, editor. Proceedings of2nd International RILEM symposium (FRPRCS-2), non-metallic(FRP) reinforcement for concrete structures, RILEM. London: E &FN Spon; 1995. p. 379–86.

[22] Jaeger GL, Mufti AA, Tadros G. The concept of the overallperformance factor in rectangular-section reinforced concrete beams.In: Proceedings of the third international symposium on non-metallic(FRP) reinforcement for concrete structures, vol. 2, Sapporo, Japan;1997. p. 551–8.

[23] Newhook J, Ghali A, Tadros G. Cracking and deformability ofconcrete flexural sections with fiber reinforced polymer. ASCE JStruct Eng 2001;128(9):1195–201.


Aspects of Behaviour of CFRP Reinforced Concrete Beams in Bending

Documents

Transcript of Aspects of Behaviour of CFRP Reinforced Concrete Beams in Bending