Monotonic and cyclic loading of new FRP reinforced ...

1. Introduction

The use of fiber reinforced polymer (FRP)reinforcement in new concrete construction iscurrently being explored as an innovativeconstruction material. The major driving forcebehind this effort is the superior performance ofFRPs in corrosive environments. FRPs possesshigh strength-to-weight ratio, favorable fatiguestrength, and low relaxation characteristics whencompared with steel reinforcement, offeringeconomically and structurally sound alternativein most applications. They also have high electro-magnetic transparency. An important feature forstructural applications is its high strength, whileexhibiting linearly elastic stress-straincharacteristics with virtually no ductility. Fewpilot projects have been implemented in actualpractice involving the use of FRP re-bars andgrids in concrete beams, bridge decks and slabs.The behavior of bars in tension-compressionreversals, as in the case of reinforcement inearthquake resistant elements, has not yet beenexplored. Furthermore, the inherent brittleness ofFRP reinforcement poses challenges for seismicapplications from the point of view of energy

dissipation through plastic hinges. The use ofFRP transverse reinforcement presents additionalchallenges, as shear resistance has not been wellestablished.

Nagasaka and Fukuyama (1993) carried outseveral tests on simply supported beamsreinforced with steel longitudinal bars and FRPstirrups, it was conducted that increase in stirrupratio, rw improved the stiffness reduction bycontrolling diagonal cracking increased theultimate shear capacity. The experimentalinvestigation conducted by Grira and Saatcioglu(2000) indicated that FRP grids could be used ascolumn confinement reinforcement for improvedseismic performance. Nagasaka et al. (1993) testresults showed that the ultimate shear capacity ofthe beams was determined by tensile breaking ofstirrups or crushing of diagonal compressionstruts and also the shear capacity of the beamsdepended on the amount and type of FRP used.Zhao and Maruyama (1995) during their researchfound that the longitudinal reinforcement ratio, rt,did not have a considerable influence on shearcapacity and the results were consistent withwhat might be predicted by current codes. Kawaiet al. (1991) and Nakano et al (1993) and

58 International Journal of Civil Engineerng. Vol. 6, No. 1, March 2008

Monotonic and cyclic loading of new FRP reinforced concrete cantilever beams

M.Kazem SharbatdarAsst. Prof., Dept. of Civil Engineering, Engineering Faculty, Semnan University, Semnan, Iran

Abstract : FRPs (fiber reinforced polymer) possess many favorable characteristics suitable and applicable forconstruction industry when compared with steel reinforcement. There are new ideas to use FRPs aslongitudinal or transverse reinforcement for new concrete elements particularly for bridge decks or beams.Although high tensile strength of FRP is main characteristic for applications at both areas, its weakness tobending and linear stress-strain behavior with virtually no ductility, makes it vulnerable to probablypremature failures under reversal tension-compression loading during earthquake. A pilot research projecthas been conducted to explore the characteristics of large-scale cantilever concrete beams reinforced withFRP re-bars and grids and were tested under either simulated cyclic loading or monotonically increasinglateral loading. This paper presents the test parameters and results obtained during research. The analyticalrelationships are compared with those recorded experimentally, and test results showed the diagonal cracksand either rupturing of FRP bars in tension or stability failure in compression bars at long or short shear spanbeams. The comparison of nominal moment capacities between analytical and experimental values confirmsthat plane section analysis is applicable to FRP reinforced concrete members.

Keywords: Beams, Shear and Flexural Behavior, Monotonic Loading, Fiber reinforced polymers (FRP),Longitudinal re-bars, Transverse Grids, Ductility, Plane Section Analysis

Weichen (2001) separately at their researchshowed that bending characteristics of FRPreinforced concrete beams could be predicted byusing the plane-section analysis as conventionalmethod used for steel-reinforced concretemembers so long as the yield strength ofreinforcement is replaced by a rational value forFRP strength.

2. Research Significant

Very little research has been conducted on thebehavior of FRP reinforced concrete beams tolateral load reversals, instead most of researcheson applications of FRP re-bars were at beamsloaded statically and monotonically. R.Salib et al.(2001) presented a comprehensive analyticalmodel to evaluate the strength of concrete beamsreinforced with FRP bars and the correspondingmodes of failure, including the pre-mature failureof beam due to dowel failure. Meng et al. (2001)presented a method to determine upper and lowerlimits of reinforcement ratio for CFRP reinforcedconcrete beams. The lower limit was based on theassumption of crushing concrete prior to thefailure of FRP failure but the upper limit ofreinforcement ratio is determined based on thefailure occurs in CFRP bars. Previous researchindicated that the majority of design codeprovisions for steel reinforced concrete are alsoapplicable to FRP-reinforced concrete, so long asappropriate allowable stresses are used fortension and compression capacities of FRPreinforcement. Japanese Design Guideline ofFRP Reinforced Concrete (1997), CanadianStandards Association S806-02 (2002),recommended strain compatibility analysis forthe analysis of FRP-reinforced members inflexure.

Since there was limited experimentally work onthe behavior of concrete beams reinforced withFRP bars and evaluate the tensile andcompressive strength of these FRP bars as maincharacteristic for applications of statically andreversal loading cases, a research projectincluding several phases has been conducted toexplore the characteristics of large-scale

cantilever concrete beams reinforced with FRPre-bars and grids and were tested under eithersimulated cyclic loading or monotonicallyincreasing lateral loading. And also the analyticalworks were done to find relationships in order tobe comparer with those recorded experimentally.

3. Experimental Research

3.1. Test Specimens and Setup

A total of six full-size cantilever beams,representing a portion of a continuous beambetween a fixed end and the point of inflectionwere designed, built and tested. The beams weretested in the vertical position, either undermonotonically increasing lateral loading orsimulated seismic loading consisting ofdeformation reversals. The geometry of beamspecimens is illustrated in Figure 1. Thespecimens had 305 mm wide and 405 mm deepcross-section with totally 10 bar arrangements. Atotal of 6 - 9.5 mm diameter Pultrall CFRP barswere used as top (negative) beam reinforcementand 4 same size bars were used as bottom(positive) reinforcement. These arrangementswere resulted in 0.39% and 0.26% as top andbottom reinforcement ratios, respectively. Twodifferent lengths were used; 1000 mm, and 1900or 1980 mm, corresponding to shear spans of 870mm and 1780 or 1870 mm, respectively,measured to the point of application of lateralforce. The longer shear span was intended topromote flexural behavior while the shorter spanwould promote shear failure. Four specimenswere tested under reversed cyclic loading andtwo other companion specimens were testedunder monotonic lateral loading. The actualaverage cylinder strength obtained at the time oftesting was 40 MPa. The CFRP transversereinforcement, grids, was placed either at 180mm spacing (corresponding to d/2) or 90 mmspacing (corresponding to d/4). Table 1 providesa summary of beam properties and testparameters.

The average tensile strength and modulus ofelasticity of CFRP bars were 1450 MPa and122,000 MPa, respectively. Figure 2 illustrates

59Mohammad Kazem Sharbatdar


Figure.1- Geometry of Cantilever Beams

s /2

10

00

mm

1 1 6 0 m m

s

6 3 m mD ia m e te r

H o le

52

0m

m

4 0 5 m m

S h o r t B e a m

Be am Cross-Se ction

305 m m

405

mm

s /2

1900

mm

1160mm

s

63mmDiameter

H ole

405 mm

520

mm

Long Beam

Fig.1 Geometry of Cantilever Beams

Table 1 Properties of Beams under Reversed Cyclic and Monotonic Loading

Specimen Label f 'c Reinf ρ ρ s L(MPa) Arrang. (%) (%) (mm) (mm)

(strong-side) (weak-side)CFB1 35 10-9.5 mm bar 0.39 0.26 175 1000

(AF=6-9.5 mm at top side & A'F=4-9.5 mm at bottom side of beam) (ρ=AF/bd , ρ’=A'F/bd)

CFB2 35 10-9.5 mm bar 0.39 0.26 88 1000

CFB3 35 10-9.5 mm bar 0.39 0.26 88 1000

CFB4 35 10-9.5 mm bar 0.39 0.26 175 1900

CFB5 35 10-9.5 mm bar 0.39 0.26 88 1900

CFB6 35 10-9.5 mm bar 0.39 0.26 88 1900

the tensile stress-strain relationship of bars testedat the lab; it shows linear behavior up the ruptureload. The tensile strength of these wasapproximately 4 times that of steel bars. Thetransverse reinforcement used consisted ofNEFMAC CFRP grids. The grids had arectangular configuration with 250 x 350 mmout-to-out dimensions. Two types of grids wereemployed; i) 6 x 8 mm rectangular cross-sectionforming two equal-size rectangular openings, andii) 8 x 10 mm rectangular cross-section formingtwo equal-size rectangular openings.

The beams were prepared along with attachedreinforced concrete elements, representing theframing columns. These elements were used tofix the beams to the laboratory strong floor toprovide full fixity. The instrumentation consistedof LVDTs for displacement and rotationmeasurements, and electric resistant straingauges for reinforcement strain measurements.The strain gauges were placed on longitudinaland transverse reinforcement. A 1000 kNcapacity servo controlled MTS actuator was usedto apply the lateral load directly on the beams, noaxial load was applied to the beams. A steel boxsection was attached to a steel plate by means ofdwydag pre-stressing bars and used to apply theload. The assembly was first secured near the tipof beams. The detail of test set-up, photographs,and locations of LVDTs are illustrated in Figure 3.

3.2. Observed Behavior and Test Results

Observed behavior of beams such as photographstaken during testing and also test results in terms

of hysteretic and monotonic relationships arepresented and discussed in this section. Thehysteretic behavior is presented both in terms offorce-displacement, moment-drift, moment-totalrotation relationships. Rotation readings weretaken within the potential hinge region. Thehinging region was defined as the beam segmentbetween the beam-column (footing) interface andthe section 405 mm away from the interface(equal to the longer cross-sectional dimension).The first set of readings gave total rotation ofassumed hinging region relative to the column.This set of readings consisted of rotations mostlydue to flexure and also due to anchorage slip. Therotations due to the anchorage slip weremeasured and formed the second set of readings.These readings were taken as the rotation of abeam section near the beam-column interface,relative to the column. Ideally, these readingsshould have reflected the rotation of the criticalbeam section at the interface. However, theLVDTs used required some gauge length to bepositioned on the beam. Hence, they weremounted on a section approximately 25 mmabove the interface. The difference between thetotal and anchorage slip rotations gave thosecaused by flexure.

The variations of reinforcement strains inlongitudinal and transverse reinforcement arepresented in the form of hysteretic force-strainrelationships. Each beam had four longitudinalbars instrumented with a total of 6 strain gaugesto measure the variation of strain in CFRP bars.All four corner bars were instrumented at the


0

300

600

900

1200

1500

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Strain(%)

Stress(M

Pa)

Test#1Test#3

Fig.2 Tensile Stress-Strain Relationship of Pultrall CFRP Bars

critical beam section, at the interface with theattached (column) element. Two additional straingauges were placed on one of the negativereinforcement bars in the corner to monitor thevariation of strains; one gauge was placed at 175mm away from the column and the other at 175mm inside the column. The end grids (closer tothe columns) were instrumented with straingauges, as well. Beams with d/2 grid spacing hadthe first three grids instrumented, while thosewith d/4 spacing had the first four instrumented.The amount and spacing of grid reinforcement asan important considered parameter varied in testbeams. These test parameters are expressedrelative to those required by CSA S806-02.Therefore, a summary of these requirements ispresented below. CSA S806-02 shear designrequirements are based on 45-degree trussanalogy with contributions from concrete andFRP reinforcement. Accordingly, the concreteshear resistance, Vc, without consideringreduction factors, is calculated at two different

expressions as follows:

(1)

(2)

Equation (1) is for sections with an effectivedepth greater than 300 mm and with transverseshear reinforcement less than minimum amountof shear reinforcement, bW and d Equation (2)also is for sections having either at least theminimum amount of transverse reinforcement oran effective depth not exceeding 300 mm. andare effective web width and effective depth ofsection, respectively. f Bc and EF are cylindercompressive strength of concrete and modulus ofelasticity of FRP bar in tension. Longitudinalreinforcement ratio, W, is equal to ( ).VF


dbfdbfd

V wcwcc'' 08.0)

1000130

( ��

�

dbfdbdM

VEfVdbf wcw

f

fFwccwc

'

3/1

'' 2.0035.01.0 �⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

��

db

A

w

frp

1000

mm

C ant

ileve

rBea

m

Pulley Roller

Strin

g

TemposonicLVDT(1&2) Rotation

MeasurmentLVDT's

Footing

Mecano FramingFixed to Footing

870

mm

25m

m

405

3456

MTSActuator

C

4 Dwydag Bars

Steel Plate

Steel Box

Actuator Bolts

2 Steel Angles

Fig.3 Locations of LVDT's and the Test Setup for Beams

and MF are respectively factored shear andmoment resistance calculated in accordance withultimate limit state design. Other parameters are

F,Capacity reduction factor for FRPreinforcement; AV, Area of shear reinforcementperpendicular to the axis of member withindistance s, and fFU, Ultimate strength of FRPshear reinforcement.

In all the beams tested, applied shear forces, Vrcorresponding to flexural capacities were higherthan the concrete shear resistance, Vc, therefore,shear reinforcement was required in all beams.The required area of shear reinforcement, AF, inCSA S806-02 is specified below.

(3)

Where S and fFH are spacing and maximumtensile strength of FRP transverse reinforcement,respectively. The maximum spacing of transverseshear reinforcement is limited by CSA A23.3-1994 to 0.7d or 600 mm for members subjectedto shear stresses of lower than 0.1 cf Bc, which isthe case for the tested beams. The same spacinglimit is specified as 16 times the longitudinal bardiameter, 48 times the minimum cross-sectionaldimension of FRP grid, the least dimension of thecompression member, or 300 mm for the stabilityof compression reinforcement. Furthermore, theconfinement requirements for seismic designlimit the spacing to d/4 or 150 mm, whichever issmaller. The minimum amount of shearreinforcement required is;

(4)

All long and short beams except CFB1 were ableto develop their flexural strengths. Beam CFB1was a short shear dominant beam, reinforced withgrids of totally 240 mm2 cross-section and 180-mm spacing. The spacing was less than themaximum limit of 0.7d = 255 mm for shear, buthigher than the maximum limit of d/4 = 90 mmfor confinement, though it was closer to the barstability limit of 16 times the diameter oflongitudinal bar, which came out to be 150 mm.The amount of transverse reinforcement wasapproximately 33% more than that specified byEquation (3) as required reinforcement for shear,but 22% below the minimum amount required bythe CSA S806-02, Equation (4). The beamshowed nearly elastic behavior up to about 2.2%drift ratio under reversal loading, with somestiffness degradation caused by concretecracking. However, the beam developed a widediagonal tension crack between the first and thesecond grid form the column face, when it wasloaded to 2.5% drift level in the strong direction.Widening diagonal crack completely diminishedconcrete contribution to shear, putting significantshear on the compression bars, forcing them toresist dowel forces, and developed stabilityfailure and broke, as shown in Figure 4. Thereversal of the beam had no flexural resistanceleft in the weak direction since the tensionreinforcement had all but failed during theprevious loading in the opposite direction. This is


sdfA

V FHFFF

��

FH

wcv f

sbfA

'3.0�

Diagonaltension failureDiagonaltension failureCFB1

Bar Rupturing

Fig.4 Observed Damages in Beam CFB1


-120

-90

-60

-30

0

30

60

90

120

150

-4 -3 -2 -1 0 1 2 3 4 5 6

Drift(%)

Moment, M (kN.m)

CFB1H = 1000 mmL = 870 mm

H

M = F.L

L

F

M

-160

-80

0

80

160

240

-4 -3 -2 -1 0 1 2 3 4 5 6

Drift(%)

Moment, M (kN.m)

CFB2H = 1000 mmL = 870 mm

H

M = F.L

L

F

M

Drift(%)

-160

-80

0

80

160

240

-4 -3 -2 -1 0 1 2 3 4 5

Drift(%)

Moment, M (kN.m)

CFB4H = 1900 mmL = 1780 mm

H

M = F.L

L

F

M

s = d/2=180mm

-160

-80

0

80

160

240

-4 -3 -2 -1 0 1 2 3 4 5Drift(%)

Moment, M (kN.m)

CFB5H = 1980 mmL = 1870 mm

H

M = F.L

L

F

M

s = d/4=90 mm

0

40

80

120

160

200

240

0 2 4 6 8Drift(%)

Moment, M (kN.m) CFB3H = 1000 mmL = 875 mmH

M = F.L

L

F

M

Fig.5 Hysteretic Behavior of Beam

(a) Beam CFB5 (b) Beam CFB6

Flex. failure (bars ruptured)

Flex. failure (bars ruptured)

Fig.6 Observed Damages in Beams CFB5 and CFB6

0

40

80

120

160

200

240

0 2 4 6Drift(%)

Mom

ent,M

(kN.m

)

H

M = F.L

L

F

M

CFB6H = 1980 mmL = 1870 mm

s = d/4=90 mm

evident in the hysteretic relationship shown inFigure 5. Beam CFB2 was companion to CFB1,except for the grid spacing, which was reduced to90 mm. This level of spacing is consistent withthe spacing requirement for confined concrete,specified in CSA S806 for seismic design. It alsomeets the maximum spacing requirements forshear and stability of longitudinal compressionbars. The reduction in grid spacing increased theeffectiveness of shear resistance while enhancingconcrete confinement, and developed its flexuralstrength. The hysteresis loops showed nearelastic behavior with some stiffness degradationdue to concrete cracking up to 3% drift ratios.Degradation of strength began at the first cycle of3% drift, and continued till 4% drift ratio. At thislevel of deformation, all the 4 positive barsruptured in tension causing the beam to loose itsflexural resistance in the weak direction. Thebeam was able to resist severely reduced loadingin the strong direction when pushed to 5% driftbefore the rupturing all negative bars and thenending test. Beam CFB3 was identical to beamCFB2, except it was tested under monotonicallyincreasing lateral loading. The results showedthat both Beams CFB2 and CFB3 hadapproximately the same primary (envelope)force-deformation relationship. The beamshowed increasing load resistance up to 3% drift,followed by subsequent strength decay beyondthis deformation level due to the failure of FRPbars in tension. The strength decay continuedgradually up to 6% drift ratio with a clearreduction in load resistance every time there wasbar rupture in tension.

Beam CFB4 was companion to CFB1, except forits longer length of 1900 mm with promoting theflexural behavior. The hysteretic relationshipindicates that the beam showed stable hysteresisloops up to 3.5% drift ratio, but developedsignificant strength decay after the first cycle of 4% drift ratio. The beam failed during the firstcycle at 4.5 % drift ratio due to the failure of FRPbars in tension. Beam CFB5 was identical toCFB4, except for the spacing of grids, which wasreduced to 90 mm. Hysteresis loops indicatestable behavior up to 2% drift ratio, for loading inboth directions. Figure 6 shows the beams CFB5

and CFB6 at the end of test, Beam CFB6 wasidentical to beam CFB5, except it was testedunder monotonically increasing lateral loading inthe strong direction. The results showed that bothBeams CFB5 and CFB6 had approximately thesame primary (envelope) force-deformationrelationship. The beams showed increasing loadresistance up to 4% drift, followed by subsequentstrength decay beyond this deformation level dueto the failure of FRP bars in tension. The strengthdecay continued gradually up to 6% drift ratiowith a clear reduction in load resistance everytime there was bar rupture in tension.

Strain gauge readings of beams indicated that allnegative FRP bars ruptured in tension at strains1.15% to 1.4%, but compressive barsexperienced 0.15% to 0.3% strain. FRP gridsexperienced a tensile strain of 0.3% to 0.5%.Figures 7 and 8 show the hysteretic behaviors ofstrains in bars and grids, respectively.

3.3. Effects of Test Parameters

Parameters affecting shear and also effect ofcyclic loading were as main test parameters. Thespecimens were designed with two shear spansand two spacing of transverse shearreinforcement to investigate the shear behavior ofFRP reinforced beams. While beams with shortshear span would be subjected to higher shearstresses, those with closely spaced transversegrids would have higher shear capacity. BeamsCFB1 and CFB2 had short shear spans with twodifference spacing of grid reinforcement. BeamCFB1 developed a wide diagonal tension crackdue to shear. The spacing of grid reinforcementhad been reduced by 50% in CFB2, resulted inthe doubling of the amount of shearreinforcement. The beam did not suffer fromshear failure, and behaved in the flexure modedespite its short shear span, developing 37%higher shear resistance. This is evident in Figure9 where the envelopes of hysteretic force-deformation relationships are compared.

The comparison of long beams CFB4 and CFB5with different grid spacing does not show anysignificant difference in behavior. This isexpected since these beams behaved



-90

-60

-30

0

30

60

90

120

-0.4 0.0 0.4 0.8 1.2

Strain(%)

Lateral Force, F (kN)

#46-bar sideCFB4

-90

-60

-30

0

30

60

90

120

-0.4 0.0 0.4 0.8 1.2

Strain(%)


#64-bar

CFB4

Fig.7 Bar Strain Readings in Beams

-90

-60

-30

0

30

60

90

120

0.0 0.1 0.2 0.3 0.4 0.5

Strain(%)


#17

3rd GridCFB4

-90

-60

-30

0

30

60

90

120

0.0 0.1 0.2 0.3 0.4 0.5Strain(%)


#13

2nd Grid

CFB4

Fig.8 Grid Strain Readings in Beams

-160

-80

0

80

160

240

-60 -40 -20 0 20 40 60

Lateral Displacement (mm)

CFB2CFB1


CFB2H=1000 mmS= 90 mm


-90

-60

-30

0

30

60

90

120

-80 -60 -40 -20 0 20 40 60 80


CFB5CFB4




Fig.9 Comparison of the Beams for effect of Spacing of Grids

predominantly in the flexure more because oftheir longer shear spans. Figure 10 showsenvelope curves of moment-drift relationshipsfor beams with different shear spans. Ofsignificance is the comparison of CFB1 andCFB4, both with wide grid spacing. The figureindicates that CFB1, with a short shear span wassubjected to higher shear stresses and suffered

premature shear failure, whereas CFB4, with thesame grid spacing was able to develop its flexuralstrength without shear failure. Figure 11 alsoindicates that flexural rotations measured inCFB2 were 70% and 36% higher than those ofCFB1 in the strong and weak directions,respectively. Two of the beams, CFB3 and CFB6were tested under monotonically increasing


-160

-80

0

80

160

240

-6 -4 -2 0 2 4 6

Drift (%)

CFB1CFB4

Moment, M (kN.m)



-160

-80

0

80

160

240

-6 -4 -2 0 2 4 6

Drift (%)

CFB5CFB2

Moment, M (kN.m)



Fig.10 Comparison of the Beams for effect of Shear Spans

-140

-70

0

70

140

210

-0.04 -0.02 0.00 0.02 0.04

Total Rotation(rad)

CFB2CFB1

Moment, M (kN.m)



-160

-80

0

80

160

240

-0.04 -0.02 0.00 0.02 0.04

Total Rotation(rad)

CFB5CFB4

Moment, M (kN.m)



-160

-80

0

80

160

240

-0.04 -0.02 0.00 0.02 0.04

Total Rotation(rad)

CFB1CFB4

Moment, M (kN.m)CFB1H=1000 mmS= 180 mm


-160

-80

0

80

160

240

-0.04 -0.02 0.00 0.02 0.04

Total Rotation(rad)

CFB5CFB2

Moment, M (kN.m)



Fig.11 Moment-Total Rotation Relationships of Beams

lateral loading, while all others were tested underreversed cyclic loading. Each of these two beamshad a different shear span, but the samereinforcement, including the same spacing oftransverse grids. Comparing CFB2 could see theeffect of cyclic loading and CFB3 with shortshear spans and CFB5 and CFB6 with long shearspans. The envelope curves for these four beamsare presented in Figures 12. The results indicatethat the monotonic force-deformationrelationships are similar to the envelopes ofhysteretic relationships obtained under cyclicloading, suggesting very little or no effect ofcyclic loading on beams.

4. Analytical Predictions

Analytical work has also been limited due to lackof data and proper understanding of FRPreinforced concrete behavior. Therefore,analytical research was done in this researchbased on the experimental data in order toexamine and re-assess of applicability of currentanalytical techniques intended for steelreinforced concrete structures to FRP reinforcedconcrete structures. Flexural behavior of aconcrete beam reinforced with steelreinforcement can be established by plane sectionanalysis based on some assumptions. The planesection analysis provides moment resistance of asection for a given strain profile. Different strainprofiles may be considered under increasingflexural stress conditions and the variation ofsectional moment resistance can be plotted

against sectional curvatures. The resultingdiagram provides a moment-curvaturerelationship, which exhibits all the relevantcharacteristics of a section in terms of strength,stiffness and deformability. A computer programwas used to generate analytical moment-curvature and compared with experimentalresults. An important step in conducting theanalyses was the consideration of realisticmaterial models for constituent materials. Thestress-strain relationships for unconfined andconfined concrete were adopted from earlierresearch, while the stress-strain relationship forFRP reinforcement was establishedexperimentally.

Moment-curvature relationships were computedby plane-section analysis, as described above,and were plotted for comparison withexperimentally obtained relationships.Hognestad’s concrete model (1955) was used forcover concrete and Saatcioglu and Razviconfinement model (1992) was used for coreconcrete. Concrete strength in member wasassumed to be the same as that obtained bystandard cylinder tests. Experimental curvatureswere obtained based on the LVDT readings wereinstrumented within the potential plastic hingeregion. The gauge length for LVDTs was equal to405 mm (equal to the beam dimension in thedirection of loading), which gave total rotation.Another LVDT was placed at 25 mm above thefooting to provide the rotation of the beam basesection, which caused by anchorage slip (elasticextension of FRP bars within the column). The


-160

-80

0

80

160

240

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70


CFB3CFB2

Lateral Force, F (kN)CFB2H=1000 mm, S= 90mmCyclic

CFB3H=1000 mm, S= 90 mmMonotonic

-90

-60

-30

0

30

60

90

120

-100 -80 -60 -40 -20 0 20 40 60 80 100 120


CFB6CFB5

Lateral Force, F (kN)CFB5H=1980 mm, S= 90 mmCyclic

CFB6H=1980 mm, S= 90 mmMonotonic

Fig.12 Comparison of the Beams for Effect of Cyclic Loading

difference between measured total rotation andanchorage slip gave flexural rotation within 355mm of column segment. The flexural rotationdivided by the segment length providedexperimental average curvature to be plottedagainst average moment within the 355 mmsegment for comparison with analytical moment-curvature relationship. The comparison for eachbeam is illustrated in Figures 13. The figure alsoincludes a second set of relationships forexperimental moment-curvature relationships,this time obtained from the strain gauges locatedon longitudinal FRP bars at column-footinginterface. These relationships show curvaturesand corresponding moments at exactly the beam-column interface.

The results indicate approximately linearmoment-curvature relationship for bothanalytical and experimental values because of thefailure mode of beams. All beams failed byrupturing of FRP bars in tension before crushingof concrete. Maximum compressive fiber strainrecorded was approximately 0.003, which is onlyslightly above the strain at unconfined concrete

strength. The agreement between analytical andexperimental values is reasonably good, onceagain confirming the applicability of planesection analysis to FRP reinforced concretebeams.

5. Summary And Conclusion

Experimental and analytical results of beam testsconducted in this paper present severalconclusions. Tension FRP reinforcement wouldrupture prior to significant distress in concrete atall beams except for CFB1, which was critical inshear. And also all the flexure dominant beamsdeveloped their flexural capacities computed onthe basis of plane-strain analysis. Beams withshort shear span and wide spacing of transversereinforcement developed a wide diagonal tensioncrack due to shear, resulting in diagonal tensionfailure in tensile bars, while the compression barswere subjected increased dowel action in additionto compression, and experienced stability failureand then was broke. Beams with the same gridspacing but long shear span were able to develop


0

80

160

240

0 10 20 30 40 50 60

Curvature(1/mm) x10-6

Mom

ent,

M(k

N.m

)

Beam CFB2H=1000 mmS=90 mmCyclicLoading

ModelExperimental-LVDT

------ Experimental-Strain Gauges0

80

160

240

0 20 40 60


Mom

ent,

M(k

N.m

)

Beam CFB3H=1000 mmS=90 mmMonotonicLoading


------ Experimental-Strain Gauges

Fig.13 Moment-Curvature Diagrams of Beams

0

80

160

240

0 10 20 30 40 50 60


Mom

ent,

M(k

N.m

)

Beam CFB5H=1980 mmS=90 mmCyclic Loading


------ Experimental-Strain Gauges0

80

160

240

0 10 20 30 40 50 60Curvature(1/mm) x 10-6

Mom

ent,

M(k

N.m

)

Beam CFB6H=1980 mmS=90 mmMonotonicLoading


------ Experimental-Strain Gauges

their flexural strength without shear failure,resulting in rupturing of FRP bars in tension.

The results also indicate that the force-deformation relationships obtained undermonotonically increasing lateral force are similarto the envelopes of hysteretic relationshipsobtained under reversed cyclic loading,suggesting very little or no effect of cyclicloading on beams and this implies that amonotonic curve would provide sufficientstrength envelope for hysteretic relationships ofFRP reinforced beams. The hystereticrelationship of flexure dominant FRP reinforcedbeams indicate stiffness degradation under cyclicloading, due to progressive cracking of concreteand associated softening in the member,developing approximately 3% lateral drift ratioprior to failure. This level of lateral drift may beconsidered to be sufficient for earthquakeresistant construction. Moreover the resultsindicate approximately linear moment-curvaturerelationship for both analytical and experimentalvalues because of the failure mode of beams byrupturing of FRP bars in tension before crushingof concrete. The agreement between analyticaland experimental values is reasonably good,confirming the applicability of plane sectionanalysis to FRP reinforced concrete beams.

6. Acknowledge

The author would like to acknowledge ProfessorMurat Saatcioglu (U of Ottawa) for his guidance,valuable suggestions, encouragement, andfunding and also Technical officers of theStructural Laboratory at the University of Ottawain Canada for their assistance and continuoussupport during the course of this investigation.

7. Reference

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