flexural cracks in fiber-reinforced concrete beams with
TRANSCRIPT
Title no. 107-S31
Flexural Cracks in Fiber-Reinforced Concrete Beams with Fiber-Reinforced Polymer Reinforcing Bars by Won K. Lee, Daniel C. Jansen, Kenneth B. Berlin, and Ian E. Cohen
Fiber-reinforced polymer (FRP) reinforcing bars have aTtracted considerable 0llellli0l1 for applications where corrosion of steel reinforcement is problemaric. Due 10 rhe generally low elastic modulus and poor bond clwracreristics of FRP as coil/pared 10
steel reinforcing bars, the use of FRP results in IGI:i?er crack widlhs under senJice loads. Fiber-reinforced concrete (FRe) is proposed for use with FRP to reduce crack widths. The work presenred herein includes the resulrs from J6 beams tesred under ./imr-poinr belUiing with either Grade 420 (Grade 60) steel or FRP reinforcing bars, and either plain concrete or FRe. A modified Gergely-Lutz model was applied ro the measured crack widths to calculate bond coefficielJls thar were used to quantify the effixtiveness of FRC in reducing crack widths. In Ihe heal1L~ with steel reinforcing bars, rhe FRC was found 10 have litlle inlluence on crack widths. i/1 rhe beams with FRP reinforcing bars, the FRC was found to significantly reduce maximum crack widths.
Keywords: composites; crack widths; fiber'reinforced concrete; fiberreinforced polymer; reinforced concrete.
INTRODUCTION The corrosion of steel reinforcement is one of the most
common causes of deterioration in reinforced concrete structures. Steel reinforcement embedded in concrete is ordinarily protected from corrosion by a passive oxide layer that forms on the sudace of the reinforcement in the high pH environment provided by the cement paste. Corrosion can occur in the presence of moisture and oxygen, however, if the'protective oxide layer is broken down. Corrosion is often initiated by chloride ions, which can penetrate the concrete to the level of the reinforcement and can lead to a breakdown of the protective oxide layer when the chloride ion concentration is sufficiently high. Structures susceptible to chlorideinduced corrosion include those exposed to deicing salts (for example, highway bridges and parking structures) and those exposed to seawater (marine structures). Current methods of combating corrosion in reinforced concrete include protecting the reinforcing bar itself (for example, epoxy coatings and galvanized or stainless steel) or decreasing the permeability of concrete to prevent the ingress of chloride ions (through the use of silica fume, fly ash, and other pozzolans). The use of these methods, however, is inhibited by such factors as cost and questions of long-term effectiveness.
Recently, advanced composite materials have been applied to mitigate the problem of corrosion in reinforced concrete. One form of composite being studied is the composite reinforcing bar for use in place of traditional steel reinforcing bars.. A number of recent studies has been perfonnedusing these composite bars as flexural reinforcement in reinforced concrete. 1.7 These composites, known commonly as fiber-reinforced polymers (FRPs), have high tensile strengths in comparison to steel and, more. importantly, are resistant to corrosion. Additional benefits to the FRP bars are
ACI Structural Journal/May-June 2010
their electromagnetic and radio transparency and their low weight compared to steel. However, FRP bars also have some characteristics that make them disadvantageous compared to steel. Most types of FRP have a low elastic modulus and uTe[mively poor bond to concrete as compared to steel bars. A direct result of these characteristics is larger crack widths and larger dellections under service loads as compared to beams reinforced similarly with steel. In addition, FRPs display linear elastic behavior in tension until failure and exhibit no yielding, making it difficult to design members to fail in a ductile fashion. Finally, concerns exist regarding the long-term durability of FRP bars (with respect to chemical, temperature, and other effects).8
To mitigate the problem of excessive crack widthS arising from the use of FRP bars as llexural reinforcement, fiberreinforced concrete (FRC) is proposed in place of plain concrete in I~RP-reinforced beams. The addition offibers has been shown to improve crack resistance in concreteY, I 0 The purpose of this study is to determine whether the use of FRC can improve the cracking response (as measured by maximum crack widths and number of cracks) of beams reinforced with FRP bars. In this study, plain and FRC beams with two types of FRP reinforcing bar and varying reinforcement ratios were tested under a four-point bending load, and the cracking response was measured in the constant-moment region of the beams. The cracking responses of the specimens were studied to quantify any improvements that came about as a result of the fiber reinforcement.
RESEARCH SIGNIFICANCE The corrosion of reinforcing steel leads to the deterioration
of many reinforced concrete structures. The use of composite materials such as FRPs can prevent corrosion deterioration, but their use can lead to excessive cracking due to their typically low elastic moduli and poor bond characteristics. The application of FRC to beams reinforced with FRP reinforcing bars is being investigated to determine the possible improvements to maximum crack widths. This is one of a limited number of experimental investigations that consider the use of a fiber-reinforced, cement-based matrix with FRP reinforcing bars. The research provides quantitative data on the crack width responses for plain and polypropylene FRC beams with both GFRP and CFRP reinforcing bars.
Act Structural Journal, V. 107. No.3. May-June 2010. MS No. S·20011-4JO.R2 received May 25. 2009, and reviewed under Institute publication
policies. Copyright © 2OlO, Americ<JJl Concrete Institute. All rights reserved, including Ule making of copies unless pennission is obtained from the copyright proprietors., Pertinent discussion inciudinE author's closure, if any, wiJ) be published in the March·Apri) 20)) ACI Structural Journal if the discussion is received by November I, 2010.
Title no. 107-S31
Flexural Cracks in Fiber-Reinforced Concrete Beams withFiber-Reinforced Polymer Reinforcing Barsby Won K. Lee, Daniel C. Jansen, Kenneth B. Berlin, and Ian E. Cohen
Fiber-reinforced polymer (FRP) reinforcing bars have aTtractedconsiderable 0llellli0l1 for applications where corrosion of steelreinforcement is problemaric. Due 10 rhe generally low elasticmodulus and poor bond clwracreristics of FRP as coil/pared 10
steel reinforcing bars, the use of FRP results in IGI:i?er crack widlhsunder senJice loads. Fiber-reinforced concrete (FRe) is proposedfor use with FRP to reduce crack widths. The work presenredherein includes the resulrs from J6 beams tesred under ./imr-poinrbelUiing with either Grade 420 (Grade 60) steel or FRP reinforcingbars, and either plain concrete or FRe. A modified Gergely-Lutzmodel was applied ro the measured crack widths to calculate bondcoefficielJls thar were used to quantify the effixtiveness of FRC inreducing crack widths. In Ihe heal1L~ with steel reinforcing bars, rheFRC was found 10 have litlle inlluence on crack widths. i/1 rhebeams with FRP reinforcing bars, the FRC was found to significantlyreduce maximum crack widths.
Keywords: composites; crack widths; fiber'reinforced concrete; fiberreinforced polymer; reinforced concrete.
INTRODUCTIONThe corrosion of steel reinforcement is one of the most
common causes of deterioration in reinforced concretestructures. Steel reinforcement embedded in concrete isordinarily protected from corrosion by a passive oxide layerthat forms on the sudace of the reinforcement in the high pHenvironment provided by the cement paste. Corrosion canoccur in the presence of moisture and oxygen, however, ifthe'protective oxide layer is broken down. Corrosion is ofteninitiated by chloride ions, which can penetrate the concreteto the level of the reinforcement and can lead to a breakdownof the protective oxide layer when the chloride ion concentrationis sufficiently high. Structures susceptible to chlorideinduced corrosion include those exposed to deicing salts (forexample, highway bridges and parking structures) and thoseexposed to seawater (marine structures). Current methods ofcombating corrosion in reinforced concrete include protectingthe reinforcing bar itself (for example, epoxy coatingsand galvanized or stainless steel) or decreasing the permeabilityof concrete to prevent the ingress of chloride ions (through theuse of silica fume, fly ash, and other pozzolans). The use of thesemethods, however, is inhibited by such factors as cost andquestions of long-term effectiveness.
Recently, advanced composite materials have beenapplied to mitigate the problem of corrosion in reinforcedconcrete. One form of composite being studied is thecomposite reinforcing bar for use in place of traditional steelreinforcing bars.. A number of recent studies has beenperfonnedusing these composite bars as flexural reinforcementin reinforced concrete. 1.7 These composites, known commonlyas fiber-reinforced polymers (FRPs), have high tensilestrengths in comparison to steel and, more. importantly, areresistant to corrosion. Additional benefits to the FRP bars are
ACI Structural Journal/May-June 2010
their electromagnetic and radio transparency and their lowweight compared to steel. However, FRP bars also havesome characteristics that make them disadvantageouscompared to steel. Most types of FRP have a low elasticmodulus and uTe[mively poor bond to concrete as comparedto steel bars. A direct result of these characteristics is largercrack widths and larger dellections under service loads ascompared to beams reinforced similarly with steel. In addition,FRPs display linear elastic behavior in tension until failureand exhibit no yielding, making it difficult to designmembers to fail in a ductile fashion. Finally, concerns existregarding the long-term durability of FRP bars (with respectto chemical, temperature, and other effects).8
To mitigate the problem of excessive crack widthS arisingfrom the use of FRP bars as llexural reinforcement, fiberreinforced concrete (FRC) is proposed in place of plainconcrete in I~RP-reinforced beams. The addition offibers hasbeen shown to improve crack resistance in concreteY, I 0 Thepurpose of this study is to determine whether the use of FRCcan improve the cracking response (as measured bymaximum crack widths and number of cracks) of beamsreinforced with FRP bars. In this study, plain and FRCbeams with two types of FRP reinforcing bar and varyingreinforcement ratios were tested under a four-point bendingload, and the cracking response was measured in theconstant-moment region of the beams. The cracking responsesof the specimens were studied to quantify any improvementsthat came about as a result of the fiber reinforcement.
RESEARCH SIGNIFICANCEThe corrosion of reinforcing steel leads to the deterioration
of many reinforced concrete structures. The use ofcomposite materials such as FRPs can prevent corrosiondeterioration, but their use can lead to excessive crackingdue to their typically low elastic moduli and poor bondcharacteristics. The application of FRC to beams reinforcedwith FRP reinforcing bars is being investigated to determinethe possible improvements to maximum crack widths. Thisis one of a limited number of experimental investigationsthat consider the use of a fiber-reinforced, cement-basedmatrix with FRP reinforcing bars. The research providesquantitative data on the crack width responses for plainand polypropylene FRC beams with both GFRP andCFRP reinforcing bars.
Act Structural Journal, V. 107. No.3. May-June 2010.MS No. S·20011-4JO.R2 received May 25. 2009, and reviewed under Institute publication
policies. Copyright © 2OlO, Americ<JJl Concrete Institute. All rights reserved, including Ulemaking of copies unless pennission is obtained from the copyright proprietors., Pertinentdiscussion inciudinE author's closure, if any, wiJ) be published in the March·Apri) 20))ACI Structural Journal if the discussion is received by November I, 2010.
.J ,
AC/ nj,""ber Won K. uc Is a SI7licfural Englnur 01 ForeIVElseS<:t!7 enSine",. Sail Francisco, ,·pI. 7ft! re(:elved his 8S in dvi/ enginurins and hi~ MS in Tfruclura) engiiJer;ring /rtJm Tu/u Univerl/!); Medford. MA. and hu MS in lTlLChanicaJ engl' ulng and PhD In slytlC/ural ftnglneering Jrom SwnJord Unlverslry, Sranford, CA. His research interests include high·pr:r[omumce tnatdrial/{, sustaiJ1able bUilding materials and design, finite element analysLr, anll seismic hehflvioy ofreinforced concrete Slnictures.
ACI member Daniel C. Janlen is an ASAOtiaJe Prufe.ryor OJ Ihft California Polylechnic Srale Univer.rily, San Lui. OM,po, CA He is a member ofAC/ CtJmmluees 363. HighSrreJlglh Cvncrete: 55.5, Concrete wllh Recycled MaJerial.r; and Jolnl AC/-ASCE Commiuee 446, Fmcrure Mechanics ofConae/e. l1is research lIT/ere.,., Include hlghsirength concrete, high·performance materials, fracture IJnd MltWxe ofconcrele. and recycled materlal.v.
Kenneth fl. ncrJin is Ilw ceo ar Bling(acfOy, LLC, and I, pur,wing his MBA Jlom Ihe UCLA Anderson Schoof of Milnagemem, Los Ant<eles, CA. He received hL, BS in civil englneerlnlt from 7\415 Univer"ity and his MS in "truefural engineering from rhe Universify of Texm 111 Aus11n, AlWin, TX.
tan E. Cohen is 11f1 Altomey Itt New York City spedulizln? in parenr lilit<rJ/ion. fie received hi" as In civil engitICering and MS In slrucrural engineering from Tufr., Universify and his.lf) jiomllo,'lon College Law School, Bosrol1',MA.
Fig. 1·~Reil7.forcing bars (top to bottom: steel, CFR?, and FRP).
~~,:~){ DI:~o~:) H 12Smm
(:Sill.)
Pig. 2-~jJecimen geometry and loading conditions.
EXPERIMEN'rAlINVESTIGATION Materials
Reinforcing bars-Two types of FRP reinforcing bars are used in this investigation: glassFRP (GFRP) bars and carbon FRP (CFRP) bars. The GFRP bars are formed using the pultrusion method, and contain E-glass fibers in a vinylester resin 11latrix. the GFRP bars have a helically-wound fiber on the .outside of the bar to produce surface deformations and t\l'e cOiltt';d with a coarse silica sand to improve its bond to
c.oncrule. tbe CFR.P bat;s are also formed using the pultlUsion method, and contain carbon fibers in a thermosetting resin matJ'ix.. the CFRP bars have no surface coatings or deformations, the tensile str 5s-strain behavior of the FRP bars, typical of O1osttypes of FRP bars, is linear elastic until failure. with no ductility or yielding. The control beams contain conventional Grade 420 (Grade 60) Sle I reinforcing Qfl{s. The ste I. GFRP, fUld CFRP reinforcing bars u ed in the study can be seen in Fig,. 1 nnd the me hanica! properties of lhe FR P ban;' are provided in Table 1, Although there apJ)ea,r
,Table 1-:-Mechani~,alpropertiesof reinforcing.bar,s .. 'Bar size, '(Nominal Elastic
,<>.
Yield Tensib metric diameter, modulus, strength, strengT,h.
Bar type (U.S.) mm(ill.) GPa (ksi) MPa (ksi) MPa (ksi)
GFRP q,6 (No.2) 6.4 (0.25) 37.8 (5490) NA 507 (74) I GFRP <p1O (No.3) 9.5 (0.375) 43.3 (6280) NA 769 (l J2)
GFRP .p13 (No.4) 12.7 (0.50) 45.6 (6610) NA 690 (100)
CFRP q,6 (No.2) 6,4 (0.25) 1378 (20,000) NA 2068 (300)
CPRP <p10 (No.3) 95 (0.375) 132.3 (19,200) NA 2068 (300)
CPRP q,13 (No.4) 12.7 (0.50) 132.3 (19,200) NA 2068 (300)
NotSteel <pJO (No.3) 6.4 (0.25) 200.0 (29,000) 361 (52.4) measured
NotSteel q,13 (No.4) 95 (0.375) 200,0 (29,000) 448 (65.0)
measured
'Data provided by manufaclurer Note: NA is nol applicable.
to be surface deformations on the CFRP bar in Fig. I, the apparent deformations are simply variations in color; the bar itself was quite smooth.
Concrete-Normal-stJength concrete was used in this investigation. The concrete contained Type II portland cement and a Grade 100 ground, granulated blast-furnace slag at a 50% replacement of cement by weight. The maximum nominal size of the coarse aggregate was 9.5 mm (3/8 in.). The concrete had a water-cementitious material ratio (wlcm) of 0.46. The ratio of cementslag:fine aggregate: coarse aggregate:water was 1:1:3.77:3.75:0.91. Air entrainment was provided to produce a concrete that would be representative of a mixture design used in a cold weather environment. where corrosion often occurs due to deicing salt exposure. An air-entraining admixture was used at a dosage of 82 mL/lOO kg (1.3 oz/lOO lb) of cementitious material for the plain concrete. The air content for plain concrete as measured using the pressure method was 7%. The target 28-day compressive strength of the concrete was 35 MPa (5 ksi).
The FRC used in this investigation contained crimped, polypropylene fibers at a fiber volu)11e fraction of I%. The polypropylene fibers had a tensile strength of 540 MPa (78 ksi) and an elastic modulus of 9.5 GPa (1378 ksi). The fiber~ were 40 mm (1.56 in.) inlength with an aspect ratio oJ 90. The FRC had the same m.ixture proporti9ns as the plain concryte, with the exception that a Type F, high-range water-reducing admixture was usedto provid~ adequate workability given the presence of the fibers. A high-range water-reducing admixtllre was used ata dosage of 240 mUIOO kg (3.7 oz/IOO Ib) ()f cementiti.ous materia~. An air-entraining admixture was used at the same proportiqns as the plain concrete mixture, with a resulting air contentQf approximat,ely 10%.
Specimens The reinforced concrete beam specimens were rectangular
in cross section, with a width of 125 mm (5 in.) and a height of 250 mill (lOin.).. Each reinforced beam specimen contained tWO, reinforcing bars placed in a single layer at a depth of 200 mm (8 in.). Specimen geometry and reinforcement layout details can be seen ilrFig. 2, The reinforcing bar types tested'were GFRP, CFR1\and Grade 420 (Gra'de60) steel using bar'sizes ofeither~6(No, 2),<1>10 (No.3); or <1>13 (No.4). t\iotalof16 beams weretested and arelisted,inTable,2with their. respective reinforcement ratios. The beams with;:<1>6
ACI ,Stn:Jctural J6urnal/May~June'20~1O 322
.J ,
AC/ nj''mber Won K. uc Is a SI7licfural Englnur 01 ForeIVElseS<:t!7 enSine",. SailFrancisco, ,·pI. 7ft! re(:elved his 8S in dvi/ enginurins and hi~ MS in Tfruclura)engiiJer;ring frtJm Tufu Univerl/!); Medford. MA. and hu MS in lTlLChanicaJ engl, ulngand PhD In slytlC/ural "nglneering Jrom SwnJord Unlverslry, Sranford, CA. Hisresearch interests include high·pr:r[omumce material/{. sustaiJ1able bUilding materialsand design, finite element analysLr, anll seismic hehflvioy ofreinforced concrete Slnictures.
ACI member Daniel C. Janlen is an ANAOtiaJe Prufe.fyor OJ th" California PolylechnicSrale Univer.rity, San Lui. OM,po, CA He is a member ofAC/ CtJmmluees 363. HighSrreJ1gth Cvncrete: 55.5, Concrete wllh Recycled MaJerial.r; and Jolnl AC/-ASCECommiuee 446, Fmcrure MechaJ1ics ofConae/e. l1is research lIT/ere.,., Include hlghsirength concrete, high·performance materials. fracture IJnd MltWxe ofconcrele. andrecycled materlal.v.
Kenneth fl. ncrJin is Ilw ceo ar Bling(actoy, LLC, and I, pur,wing his MBA Jlom IheUCLA Anderson Schoof of Milnagemem, Los Ant<eles, CA. H" received hL, BS in civilenglneerlnlt from 7\415 Univer"ity and his MS in "tructural "ngincer/ng from rheUniversity of Texm 01 AlIstln, AlWin, TX.
tan E. Cohen is ilf! Altomey Itt New York City spedalizln? in parenr lilit<rJ/ion. fierecelv,,<f hi" as In civil engiMering and MS In slrucrural engineering from Tufr.,Universify and his.lf) jiorn /lo,'lon Colfeg" Law School, Bosrol1',MA.
Fig. 1·~Reil7.forcing bars (top to bottom: steel, CFR?,and FRP).
~~,:~){ DI:~o~:)H12Smm
(:Sill.)
Pig. 2-~jJecimen geometry and loading conditions.
EXPERIMEN'rAlINVESTIGATIONMaterials
Reinforcing bars-Two types of FRP reinforcing bars areused in this investigation: glassFRP (GFRP) bars and carbonFRP (CFRP) bars. The GFRP bars are formed using thepultrusion method, and contain E-glass fibers in a vinylesterresin 11lutrix. the GFRP bars have a helically-wound fiber onthe .outside of the bar to produce surface deformations andt\l'e cOiltt';d with a coarse silica sand to improve its bond to
c.oncrule. tbe CFR.P bat;s are also formed using the pultlUsionmethod, and contain carbon fibers in a thermosetting resinmatJ'ix.. the CFRP bars have no surface coatings ordeformations, the tensile str 5s-strain behavior of the FRPbars, typical of O1osttypes of FRP bars, is linear elastic untilfailure. with no ductility or yielding. The control beamscontain conventional Grade 420 (Grade 60) Sle I reinforcingQfl{s. The ste I. GFRP, fUld CFRP reinforcing bars u ed in thestudy can be seen in Fig,. 1 nnd the me hanica! properties oflhe FR P ban;' are provided in Table 1, Although there apJ)ea,r
322
,Table 1-:-Mechani~,alpropertiesof reinforcing.bar,s.. 'Bar size, '(Nominal Elastic
,<>.
Yield Tensibmetric diameter, modulus, strength, strengT,h.
Bar type (U.S.) mm(ill.) GPa (ksi) MPa (ksi) MPa (ksi)
GFRP q,6 (No.2) 6.4 (0.25) 37.8 (5490) I NA 507 (74)
GFRP <p1O (No.3) 9.5 (0.375) 43.3 (6280) NA 769 (l J2)
GFRP .p13 (No.4) 12.7 (0.50) 45.6 (6610) NA 690 (100)-
CFRP q,6 (No.2) 6,4 (0.25) 1378 (20,000) NA 2068 (300)-
CPRP <p10 (No.3) 95 (0.375) 132.3 (19,200) NA 2068 (300)-
CPRP q,13 (No.4) 12.7 (0.50) 132.3 (19,200) NA 2068 (300)-
Steel <pJO (No.3) 6.4 (0.25) 200.0 (29,000) 361 (52.4) Notmeasured
Steel q,13 (No.4) 95 (0.375) 200,0 (29,000) 448 (65.0) Notmeasured
'Data provided by manufaclurerNote: NA is nol applicable.
to be surface deformations on the CFRP bar in Fig. I, theapparent deformations are simply variations in color; the baritself was quite smooth.
Concrete-Normal-stJength concrete was used in thisinvestigation. The concrete contained Type II portlandcement and a Grade 100 ground, granulated blast-furnaceslag at a 50% replacement of cement by weight. Themaximum nominal size of the coarse aggregate was 9.5 mm(3/8 in.). The concrete had a water-cementitious materialratio (wlcm) of 0.46. The ratio of cementslag:fine aggregate:coarse aggregate:water was 1:1:3.77:3.75:0.91. Airentrainment was provided to produce a concrete that wouldbe representative of a mixture design used in a cold weatherenvironment. where corrosion often occurs due to deicingsalt exposure. An air-entraining admixture was used at adosage of 82 mL/lOO kg (1.3 oz/lOO lb) of cementitiousmaterial for the plain concrete. The air content for plainconcrete as measured using the pressure method was 7%.The target 28-day compressive strength of the concrete was35 MPa (5 ksi).
The FRC used in this investigation contained crimped,polypropylene fibers at a fiber volu)11e fraction of I%. Thepolypropylene fibers had a tensile strength of 540 MPa (78 ksi)and an elastic modulus of 9.5 GPa (1378 ksi). The fiber~ were40 mm (1.56 in.) inlength with an aspect ratio oJ 90. TheFRC had the same m.ixture proporti9ns as the plain concryte,with the exception that a Type F, high-range water-reducingadmixture was usedto provid~ adequate workability given thepresence of the fibers. A high-range water-reducing admixtllrewas used ata dosage of 240 mUIOO kg (3.7 oz/IOO Ib) ()fcementiti.ous materia~. An air-entraining admixture was usedat the same proportiqns as the plain concrete mixtrne, with aresulting air contentQf approximat,ely 10%.
SpecimensThe reinforced concrete beam specimens were rectangular
in cross section, with a width of 125 mm (5 in.) and a heightof 250 mill (lOin.).. Each reinforced beam specimencontained tWO, reinforcing bars placed in a single layer at adepth of 200 mm (8 in.). Specimen geometry and reinforcementlayout details can be seen ilrFig. 2, The reinforcing bar typestested'were GFRP, CFR1\and Grade 420 (Grade 60) steelusing bar'sizes ofeither~6(No, 2),<1>10 (No.3); or <1>13 (No.4).t\iotalof16 beams weretested and arelisted,inTable,2withtheir. respective reinforcement ratios. The beams witht'<I>6
ACI ,Stn:Jctural J6urnal/May~June'20~1O
------
Table 2 - Test specimens
I R mforcing Specirn.:n bar lypo!:
IG2~O GFRP i! G3NO GFRP I
G4NO GFRP, G2PI I GFRP
G3Pl GFRP
G4Pl GFRP
C2NO CFRP
C3NO CPRI'
C4NO CFRP
C2PI CFRP
C3PI C1:1~P
C4P1 CPRI'
S3NO Steel
S4NO Steel
531'1 Steel
541'1 Steel
"., .; '., C· :.: ',,:,
Bar iu. Concre.le COl11plloion c)'lindcr Modulu' of fU)IUre. Reinforcing ratj(j' IBalan~ed rei1lforclng m~lIic (U.S.) type ;;trcnglh, MPn (P,i) MPn (psi p, %
~ (No.2) Plain 43 (6180) 5.6 (810) 0.25Cc $10(No.3) Plain 39 (5120) 6,1 (890) 0.55
$13(No.4) Plain W (5720) 5,4 (780) 0,98i <1>6 (No.2) FRC 31 (4490) 52 (750) 0.25I ~IO (No.3) FRC 33(4810) 5.2 (750) 0.55
$13 (No.4) FRC 30 (4300) 5.0 (720) 0.98
$6 (No.2) Plain 39 (5720) 5.5 (790) 0.25
¢10 (No.3) Plain 43 (6170) 55 (790) 0.55
¢13 (No.4) Plain 42 (6040) ).7 (820) 098
$6 (No.2) FRC 35 (5010) 5.2 (750) 0.25
~10 (No.3) FRC 31 (4490) 5.2 (750) 0.55
¢13 (No.4) FRC 33 (4760) 5.0 (720) 0.98 -
¢IO (No.3) Plain 38 (5560) 5.6(810) 0.55I ¢ 13 (No.4) Plain 51 (7460) 6.7 (970) 0.98
,pO (No.3) FRC 29 (4260) 78 (690) 0.55I 4)13 (No.4) FRC 36 (5220) 49 (710) 0.98
·Compuled using experimel1lally measured values where available.
(No.2) and ~ 10 (No.3) bars were under-reinforced beams, while the beams with ~13 (No, 4) beams were over-reinforced.
The beams were cast using a standard laboratory drum mixer. Two reinforced concrete beams, nine 100 x 200 mm (4 x 8 in.) compression cylinders, and three 100 x 100 x 355 mm (4 x 4 x 14 in.) modulus of rupture prisms were cast at the same time. The cylinders were used to measure compressive strength and static modulus of elasticity. Each reinforced beam was filJed in three layers, and consolidation was performed with tbe use of an internal vibrator. All specimens were cured at room temperature (16 to noc [60,8 to 80,6°PJ) for 24 hours. After 24 hours, the specimens were removed from their forms, The reinforced beams were wrapped in wet burlap, covered in plastic, and allowed to cure for 14 days at room temperature, After 14 days, the plastic and wet burlap were removed and the reinforced beams were allowed to cure in the ambient environment until testing. Specimens were tested at an age between 27 and 31 days. Six of the compression cylinders were placed in a 100% relative humidity environment at 23°C (73.4°F) after demolding for curing until testing at an age of 28 days as per ASTM C39 standards. The remaining three cylinders (referred to as companion cylinders) and the three modulus of rupture prisms were kept with the reinforced concrete beam specimens after demolding to cure under the same conditions. These specimens were tested at the same time as the reinforced concrete beam's to better represent the actual mechanical properties of the concrete in the beam,
Testing configuration The beams were simply supported and subjected to a four
point bending load, as shown in Fig. 2. The beams contained no compression reinforcement and no internal shear reinforcement. The beams were tested in a screw-driven testing machine with a 1.33 MN (300 kip) load capacity. A reinforced beam specimen in the testing machine is shown 'in Fig. 3. The shear reinforcement consisted of externally applied steel stirrups. Ten external, 19 mm (3/4 in.) d.iameter stirrups were applied at a spacing ofroughly 50 mm (2 in.) on the two outer spans to prevent shear failure. The stirrups were attached and tightened prior to testing. External stirrups
ACIStructural Journal/May-June 2010
Fig. 3-Phdtograph o!,beam being tested.
ratIo Pb' 0/0.
0.96·
0,48
0.61
0.78
I 0,43
I 0.51
0,43
I 0,48
0.4:';
039--_.----- 0.39
0.39
3.60
4.23
2.99
3.45
were used rather than internal stirrups because of the fact that they could be reused for each beam specimen, thus conserving materials and time far bending the reinforcing bars. Although the confining effect of the external stirrups was not as great as that of internal stirrups, it was not expected to significantly influence the testing results. Loading was applied in a quasi-static manner, with a constant testing machine crosshead displacement rate of 0.5 mm/minute (0.02 in.lminute), For a full description of the testing procedures, refer to Lee. 11
Digital image analysis for crack width measurement A digital image analysis system was used to measure the
formation and growth of cracks in a specimen during testing. The digital image analysis system is a nondestructive method of data acquisition that does not require the direct attachment of any instrumentation to the specimen. Digital image analysis is essentially used as a method of measuring relative displacements across the surface of a specimen. The system requires the capture ofhigh-resolution digital images of the face of a specimen throughout the testing.
The principle upon which the digital image analysis is based is' the matching of image subsets between two different images, as showncinFig.'4. The first i.mage,·ar the
32:3
I'.. :
. iJ' : t j
- ,,'.; C· :.: ',,:,'., , -
I R mforcing Bar iu. Concre.le COl11plloion c)'lindcr Modulu' of fU)IUre. Reinforcing ratj(j' IBalan~ed rei1lforclngSpecirn.:n bar lypo!: m~lIic (U.S.) type ;;trcnglh, MPn (P,i) MPn (psi p, % rauo Pb' 0/0.
G2~O I GFRP i ~ (No.2) Plain 43 (6180) 5.6 (810) Cc 0.25 0.96·!I -
G3NO GFRP $10(No.3) Plain 39 (5120) 6,1 (890) 0.55 0,48
G4NO , GFRP $13(No.4) Plain W (5720) i 5,4 (780) 0,98 0.61
G2PI I GFRP <1>6 (No.2) FRC 31 (4490) I 52 (750) 0.25 0.78
G3Pl GFRP ~IO (No.3) FRC 33(4810) 5.2 (750) 0.55 I 0,43
G4Pl GFRP $13 (No.4) FRC 30 (4300) 5.0 (720) 0.98 I 0.51
C2NO CFRP $6 (No.2) Plain 39 (5720) 5.5 (790) 0.25
I
0,43
C3NO CPRI' ¢10 (No.3) Plain 43 (6170) 55 (790) 0.55 0,48
C4NO CFRP ¢13 (No.4) Plain 42 (6040) ).7 (820) 098 0.4:';
C2PI CFRP $6 (No.2) FRC 35 (5010) 5.2 (750) 0.25 039--------_.------
C3PI C1:1~P $10 (No.3) FRC 31 (4490) 5.2 (750) 0.55 0.39
C4P1 CPRI' ¢13 (No.4) FRC 33 (4760) 5.0 (720) 0.98 0.39-
IS3NO Steel $10 (No.3) Plain 38 (5560) 5.6(810) 0.55 3.60
S4NO Steel $ 13 (No.4) Plain 51 (7460) 6.7 (970) 0.98 4.23
531'1 Steel ,pO (No.3) FRC 29 (4260) I 78 (690) 0.55 2.99
S4PI Steel 4)13 (No.4) FRC 36 (5220) 49 (710) 0.98 3.45
Table 2 Test specimens
·Compuled using experimel1lally measured values where available.
(No.2) and ~10 (No.3) bars were under-reinforced beams,while the beams with ~13 (No, 4) beams were over-reinforced.
The beams were cast using a standard laboratory drummixer. Two reinforced concrete beams, nine 100 x 200 mm(4 x 8 in.) compression cylinders, and three 100 x 100 x 355 mm(4 x 4 x 14 in.) modulus of rupture prisms were cast at thesame time. The cylinders were used to measure compressivestrength and static modulus of elasticity. Each reinforcedbeam was filJed in three layers, and consolidation wasperformed with tbe use of an internal vibrator. All specimenswere cured at room temperature (16 to noc [60,8 to 80,6°PJ)for 24 hours. After 24 hours, the specimens were removedfrom their forms, The reinforced beams were wrapped in wetburlap, covered in plastic, and allowed to cure for 14 days atroom temperature, After 14 days, the plastic and wet burlapwere removed and the reinforced beams were allowed tocure in the ambient environment until testing. Specimenswere tested at an age between 27 and 31 days. Six of thecompression cylinders were placed in a 100% relativehumidity environment at 23°C (73.4°F) after demolding forcuring until testing at an age of 28 days as per ASTM C39standards. The remaining three cylinders (referred to ascompanion cylinders) and the three modulus of ruptureprisms were kept with the reinforced concrete beam specimensafter demolding to cure under the same conditions. Thesespecimens were tested at the same time as the reinforcedconcrete beam's to better represent the actual mechanicalproperties of the concrete in the beam,
Testing configurationThe beams were simply supported and subjected to a four
point bending load, as shown in Fig. 2. The beams containedno compression reinforcement and no internal shearreinforcement. The beams were tested in a screw-driventesting machine with a 1.33 MN (300 kip) load capacity. Areinforced beam specimen in the testing machine is shown 'inFig. 3. The shear reinforcement consisted of externallyapplied steel stirrups. Ten external, 19 mm (3/4 in.) d.iameterstirrups were applied at a spacing ofroughly 50 mm (2 in.)on the two outer spans to prevent shear failure. The stirrupswere attached and tightened prior to testing. External stirrups
ACIStructural Journal/May-June 2010
Fig. 3-Phdtograph o!,beam being tested.
were used rather than internal stirrups because of the fact thatthey could be reused for each beam specimen, thusconserving materials and time far bending the reinforcingbars. Although the confining effect of the external stirrupswas not as great as that of internal stirrups, it was notexpected to significantly influence the testing results.Loading was applied in a quasi-static manner, with aconstant testing machine crosshead displacement rate of0.5 mm/minute (0.02 in.lminute), For a full description ofthe testing procedures, refer to Lee. 11
Digital image analysis for crack width measurementA digital image analysis system was used to measure the
formation and growth of cracks in a specimen during testing.The digital image analysis system is a nondestructivemethod of data acquisition that does not require the directattachment of any instrumentation to the specimen. Digitalimage analysis is essentially used as a method of measuringrelative displacements across the surface of a specimen. Thesystem requires the capture ofhigh-resolution digital imagesof the face of a specimen throughout the testing.
The principle upon which the digital image analysis isbased is' the matching of image subsets between twodifferent images, as showncinFig.'4. The first i.mage,·ar the
32:3
I'..
. iJ':tj
Reference Image Targcllmage
Fig. 4-fmage subset matching for digital image analysis.
Fig. 5-Example contour plOI of horizontaL displacements from processed digifal image (corresponds to Fig. 13 for Specimen G4NO).
Crllck Width (in)
o 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 8 . ., 70
J Ii' • I I • , I
7 . '" ... ~ _ : _ ~ ~ 60
1 - ~ .- - ~ -1'· •. ~ \" ~ -- - ~ - ., - - ". - • - - r - . - , .~. . 50
:. ... -"O¢'~r:-<> ..... : .. l : ~ J <: : .. 40 ...; o-o-t.:....dl,Ql . ~. ;.
<>=• . _ Cf'7"rfD'. --L...--..._~.I..-....-.-.." 30 8~Ci'7 -- ..:. .. " : ... ~-o . G2NO • Crack 1 o
~ '. . .:... _ ; .. I -0' G2NO . Crack 2 .. 20
... . ....;.. _. __ ._~ .... I --G2PI-Crackl --\0 : : 1 -+-G21'1 .. Crack 2
o I---.;.--~'--~'-'::==::::===~====~ .. 0
o 0.2 0.4 0.6 0.8 1.2
Crllck Width (mm)
Fig. 6--Momem versus ,crack widths in rjX5 (No.2) GFRPreinjlln'eCl beams.
reference image, is of the undeformed specimen (that is, prior to the appUcation of any load). The second image, or tlle target image, is of the deformed specimen at some point during loading. The digital image analysis system detennines the chtl1lge in location of a small, square subset region of the image, or sub·image, between the reference image and the target image. This change in location is given in terms of relative horizontal and verti.cal displacements. For any given sub-image'on me reference image, the target image is scanned until that same sub-image is located. Once the new location ofille slIb-ihlage is foqnd, the vector d.isplacement (m; It) iSdetetntined. Matching of image subsets is then pel'formed'i'lt a regularly spaced grid of uodes (each node being at Ihe:centerof a cSLlb~lma.gej across the entire image. The speclme.usutfacestb'Cbe pholographedare sprayed with a speckle pat.tern or\!ai:imi.. had . of paint. (as shown in Fig. 4) to provide distinct patterns that are distinguishable for matClting by Ute digital irilug analysis software.
The processing of the vector clisplacements for any given target image can provide sul'face displacement maps and allows for the measurement of cracks throughout the entire face of the specimen. In this research, a high resolution camera was used to capture images of one face of the beam in the constant-moment region at regularly spaced time intervals. Each image was then processed to produce contour plots of vertical and horizontal displacements, as well as measurements of crack widths at multiple heights in the cross section for all cracks. An example contour plot of horizontal surface displacements from a processed image is shown in Fig. 5. Three cracks are visible in the contour plot, and their widths can be measured to a high precision. Based on previous experience, the system has been shown to have an average resolution slightly better than 0.008 mm (0.0003 in.). Furtl1er details on the digital image analysis system and processing of images to determine crack widths can be found in Lee ll or Jansen et al. 12 .
EXPERIMENTAL RESULTS AND DISCUSSION The beam testing results with regard to failure modes,
load-deflection response, and moment-curvature response are not presented in this paper, as the primary focus is on the cracking behavior. Full details of the beam testing results can be found in Lee. 11 The modulus of rupture and companion cylinder compressive strength values are given in Table 2. The compressive strength of the FRC was found, on average, to be approximately 23% lower than the plain concrete. The lower compressive strength is likely due to the increased air content of the FRC concrete mixtures.
To compare the cracking behavior between the beam specimens, plots are made of the moment versus the crack width. The crack widths are measured within the constantmoment region of the beam. The digital image analysis system allowed for the measurement of the crack widths at any height of interest in the specimen. The crack widths are taken at the height of the reinforcing bars, and all individual cracks are shown in the plots.
Crack widths in GFRP-reinforced beams For beams reinforced with GFRP bars, the polypropylene
fibers improved the cracking behavior of the beams with respect to the size of crack widths that were observed. Shown in Fig. 6 is the moment versus crack width plot comparing the two specimens reinforced with <1>6 (No.2) GFRP bars (G2NO and G2Pl). The number of cracks present in both beams is the same, as two cracks had fanned in both specimens; however, the widths of the cracks in the beam with FRC are significantly smaller than in the beam wit~out fiber reinforcement. Comparing the two beams at a moment of 5 kN-m (44 kip-in.), the maximum crack width in Specimen G2NO is approximately 0.75 mm (0.030 in.), whereas the maximum crack width in Specimen G2Pl is only 0.30 mm (0.012 in.).
For Specimens G4NO and G4PI (<1>13 [No.4] GFRP bars), which were over-reinforced beams, the fiber reinforcement greatly improves the cracking response that was observed, as shown in Fig. 7. In Specimen G4NO, only three cracks formed, all within a short time span of each other. As loading continued, these three cracks continued to grow.without the formation of additional cracks. In contrast, Specimen G4Pl saw the fonnation ·of several additional intermediate cracks followingtbe formation ofthe first cracks. The fonnation of neW1cracks was made'~possible by the presence of the fibers. The ability of the fibers to carry tensile stress aUhe locations
ACJ5Structu ral' JournaI/May.,June,·2010 324
EXPERIMENTAL RESULTS AND DISCUSSIONThe beam testing results with regard to failure modes,
load-deflection response, and moment-curvature responseare not presented in this paper, as the primary focus is on thecracking behavior. Full details of the beam testing results canbe found in Lee. 11 The modulus of rupture and companioncylinder compressive strength values are given in Table 2.The compressive strength of the FRC was found, on average,to be approximately 23% lower than the plain concrete. Thelower compressive strength is likely due to the increased aircontent of the FRC concrete mixtures.
To compare the cracking behavior between the beamspecimens, plots are made of the moment versus the crackwidth. The crack widths are measured within the constantmoment region of the beam. The digital image analysissystem allowed for the measurement of the crack widths atany height of interest in the specimen. The crack widths aretaken at the height of the reinforcing bars, and all individualcracks are shown in the plots.
ACJ5Structu ral' JournaI/May.,June,·2010
The processing of the vector clisplacements for any giventarget image can provide sul'face displacement maps andallows for the measurement of cracks throughout the entireface of the specimen. In this research, a high resolutioncamera was used to capture images of one face of the beamin the constant-moment region at regularly spaced timeintervals. Each image was then processed to producecontour plots of vertical and horizontal displacements, as wellas measurements of crack widths at multiple heights in thecross section for all cracks. An example contour plot ofhorizontal surface displacements from a processed image isshown in Fig. 5. Three cracks are visible in the contour plot,and their widths can be measured to a high precision. Basedon previous experience, the system has been shown to havean average resolution slightly better than 0.008 mm (0.0003 in.).Furtl1er details on the digital image analysis system andprocessing of images to determine crack widths can be foundin Lee ll or Jansen et al. 12 .
Crack widths in GFRP-reinforced beamsFor beams reinforced with GFRP bars, the polypropylene
fibers improved the cracking behavior of the beams withrespect to the size of crack widths that were observed. Shownin Fig. 6 is the moment versus crack width plot comparingthe two specimens reinforced with <1>6 (No.2) GFRP bars(G2NO and G2Pl). The number of cracks present in bothbeams is the same, as two cracks had fanned in both specimens;however, the widths of the cracks in the beam with FRC aresignificantly smaller than in the beam wit~out fiber reinforcement. Comparing the two beams at a moment of 5 kN-m(44 kip-in.), the maximum crack width in Specimen G2NO isapproximately 0.75 mm (0.030 in.), whereas the maximumcrack width in Specimen G2Pl is only 0.30 mm (0.012 in.).
For Specimens G4NO and G4PI (<1>13 [No.4] GFRP bars),which were over-reinforced beams, the fiber reinforcementgreatly improves the cracking response that was observed, asshown in Fig. 7. In Specimen G4NO, only three cracksformed, all within a short time span of each other. As loadingcontinued, these three cracks continued to grow.without theformation of additional cracks. In contrast, Specimen G4Plsaw the fonnation ·of several additional intermediate cracksfollowingtbe formation ofthe first cracks. The fonnation ofneW1cracks was made'~possible by the presence of the fibers.The ability of the fibers to carry tensile stress atthe locations
...=<>8o~
. 50
.. 40
Targcllmage
Crllck Width (mm)
Crllck Width (in)
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04., 70
Reference Image
o8 .
7 . '"
J Ii, •I I • , I
...~ _ : _ ~ ~ 60
1 - ~ .- - ~ -1'· •. ~ \" ~ -- - ~ - ., - - ". - • - - r - . --, .~.
:. ... -"O¢'~r:-<> ..... : ..l : ~ J <: :; o-o-t.:....dl,Ql . ~. • ;.. _ Cf'7"rfD'. --L...--..._~.I..-....-.-.." 30~Ci'7-- ..:. .. " : ... ~-o . G2NO • Crack 1
'. . .:... _ ; .. I -0' G2NO . Crack 2 .. 20
... . ....;.. _. __ ._~ .... I --G2PI-Crackl --\0: : 1 -+-G21'1 .. Crack 2
o I---.;.--~'--~'-'::==::::===~====~ .. 0
o 0.2 0.4 0.6 0.8 1.2
reference image, is of the undeformed specimen (that is,prior to the appUcation of any load). The second image, ortlle target image, is of the deformed specimen at some pointduring loading. The digital image analysis system detenninesthe chtl1lge in location of a small, square subset region of theimage, or sub·image, between the reference image and thetarget image. This change in location is given in terms ofrelative horizontal and verti.cal displacements. For any givensub-image'on me reference image, the target image isscanned until that same sub-image is located. Once the newlocation ofille slIb-ihlage is foqnd, the vector d.isplacement(m; It) isdetetntined. Matching of image subsets is thenpel'formed'i'lt a regularly spaced grid of uodes (each nodebeing at Ihe:centerof a cSLlb~lma.gej across the entire image.The speclme.usutfacestb'Cbe pholographedare sprayed witha speckle pat.tern or\!ai:imi.. had . of paint. (as shown inFig. 4) to provide distinct patterns that are distinguishablefor matClting by Ute digital irilug analysis software.
Fig. 4-fmage subset matching for digital image analysis.
Fig. 6--Momem versus ,crack widths in rjX5 (No.2) GFRPreinjlln'eCl beams.
324
Fig. 5-Example contour plOI of horizontaL displacementsfrom processed digifal image (corresponds to Fig. 13 forSpecimen G4NO).
-}
Crack Widtb (in) o 0.005 0.0 I 0.015 0.Q2 0.025 0.Q3
150
125
.:100 ~ ;:75 .. e
.. ::;q
50
25
a 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Crllck Width (mm)
Fig. 7-Moment versus crack widths in <pl3 (No.4) CFRp· reinforced beams.
of the cracks prevented the localization of the cracking to a degree, which allowed for the formation of successive, inlermediate cracks in the specimen. This effect was pronounced in the two over-reinforced specimens, as the number of cracks observed in Specimen G4Pl was double the number observed in Specimen G4NO. The final crack patterns for Specimens G4NO and G4P I are shown in Fig. 8.
Crack widths in CFRP-reinforced beams As with the GFRP-reinforced specimens, the presence of
the polypropylene fibers significantly improved the cracking behavior of the CFRP-reinforced specimens. The same trends are seen as in the GFRP-reinforced specimens, where the beams with lower reinforcement ratios saw reductions in crack widths but not the number of cracks, whereas the over-reinforced beams saw reductions in crack widths and an increase in the number of cracks that formed. Shown in Fig. 9 is the moment versus crack width plot for Specimens C2NO and C2PI (4)6 [No. 2J CFRP bars). The difference in the maximum crack width observed between the two beams is substantial. At a moment of 10 kN-m (89 k-in.), the maximum crack width seen in Specimen C2NO is approximately 1.1 mm (0.043 in.), whereas the maximum crack width seen in Specimen C2P] is only 0.6 mm (0.024 in.).
The beams that experience the greatest benefit to the cracking response with the addition of fiber reinforcement are the two specimens with 4>13 (No.4) CFRP reinforcing bars (Specimens C4NO and C4PI). Like the two overreinforced beams with GFRP bars, the number of cracks increased with the presence of fibers. It was the crack widths, however, that were most affected by the presence of the fibers. The crack widths in Specimen C4NO were considerably higher than in Specimen C4PI. The moment versus crack width plot for these two beams was shown in Fig. 10. At a moment of 15 kN-m (133 k-in.), there was a large difference in the maximum crack width observed in the two beams. The maximum crack width in Specimen C4NO was approximately 1.0 mm (0.039 in.), in comparison with a maximum crack width in Specimen C4PI of approximately 0.3 mm (0.012 in.). The final crack patterns for Specimens C4NO and C4PI are shown in Fig. 11. The reduction in crack widths with the presence of the polypropylene fibers for beams with both types of FRP bars is similar to what has been found in another study.13
AGI Structural Journal/May~June 2010
~i """:"' .- :I~:
.' JJ ','.... - , ,..••..I• -, .,.... 'T-'
I
(hI
Fig. 8--Final crack patterns for beams: (a) Specimen G4NO; and (b) Speci/l/en G4P j.
Cmck Width (in) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
24 -.----..,..---..,.----..,..---..,.----,,, . 200 , 20 "1-·
, , -- 150B 16 -----. -~ -------~ :9
:,pocO ~ ~~ ~r..rlUJ'1' -'-'-:..:..:..::. -- - -'.. 100 1i5 -a . C2NO • Crack I 8e .,
-0 • C2NO - Crack 2 ~~ 8 --C2PI . Crack I -- 50 --C2PI - Crack 3
--C21' I . Crack 2
o-1-----..----,...----..----,...----1- 0
0.0 0.4 0.8 1.2 1.6 2.0
CrHck Width (mm)
Fig. 9-Momen.t versus crack widths in. ¢6 (No.2) CFRp· reinforced beams.
Cnlck Width (In)
0.00 0.02 0.04 0.06 0.08 0.10 40 -,-----,----,---_---,-----,---r-o---,.- 350
35 - , , . - 300 , , ,
•• l _ •• .i __ . __ .J•• _.__ .:.. _1 1 • __30 . _. ,: : :1-0 .C4NO - Cr~ck I .. 250 :? IB 't.~ 25 .. - - ... -- -- " -- -- -, -::>' C4NO - Crack 2 _ 200 6 -lI . C4NO - Crack 3 .. CC 20·· I --C4PI . Crack 1 .. 150 E '1
.,E 15- ::--C4PI . Crack 2 -- ~ ~ -C4PI . Crack 3 . - 100
10· --C4PI . Crack 4
" - _. " - - • - - .• _. - - - -I __ - ~ _ .• : _ ~ -:- - • •• 50 I
, '.1 I
o +-----;.---;'---;---;..---;...--.;---1- 0
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8
Crack Width (rom) I ;I
Fig. lO-Moment versus crack widths in ¢13 (No.4) CFRPreinforced beams.
Crack widths in steel-reinforced beams The presence of fiber reinforcement does not significantly
affect the cracking response of beams reinforced with steel bars. The number and width of cracks observed in specimens with steel bars does not vary between beams with plain concrete and those with FRC. The plots of moment versus crack width for Specimens S3NO and S3PI can be seen in Fig. 12. While it appears that there are two cracks in Specimen S3S 1 and only one crack in Specimen S3NO, a second crack had in fact· formed in Specimen S3NO but was outside the
325
-}
,I
't.
"I
'.1I
I;I
I'1::
,- 300
. 200
0,10
(hI
~i """:"'
•
.- :I~:
.' JJ','. ..I... - , ,..•• I
-, .,.... 'T-'
,,,"1-·
,, -- 150-~ -------~ :9
:,pocO ~ ~
~r..rlUJ'1' -'-'-:..:..:..::. -- - -'.. 100 1i-a . C2NO • Crack I 8.,-0 • C2NO - Crack 2 ~
--C2PI . Crack I -- 50--e2pl - Crack 3
--C21' I . Crack 2
Cnlck Width (In)
0.04 0.06 0.080.02
,,, , ,•• l _.' .i __ . __ .J•• _.__ .:.. _1 1 • __
: : :1-0 .C4NO - Cr~ck I .. 250 :?- - ... -- -- " -- -- -, -::>' C4NO - Crack 2 _ 200 ~
-lI . C4NO - Crack 3 .. C--C4PI . Crack 1 .. 150 E--C4PI . Crack 2 -- ~
-C4PI . Crack 3 . - 100--C4PI . Crack 4
- .- " - - • - - .• _. - - - -I __ - ~ _ .• : _ ~ -:- - ~ ". 50,
o +-----;.---;'---;---;..---;...--.;---1- 0
0.0 0.4 0.8 1.2 1.6 2,0 2.4 2.8
10·
35 -
0.0040 -,-----,----,---_---,-----,---r-o---,.- 350
20
Crack Width (rom)
Cmck Width (in)0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
24 -.----..,..---..,.----..,..---..,.----,
o-1-----..----,...----..----,...----1- 0
0.0 0.4 0,8 1.2 1.6 2.0
CrHck Width (mm)
Fig. 8--Final crack patterns for beams: (a) Specimen G4NO;and (b) Speci/l/en G4P j.
325
30 . _.
B~ 25 ,.-
C 20 ..
E., 15-~
B 16 -----.
~5e~ 8
Crack widths in steel-reinforced beamsThe presence of fiber reinforcement does not significantly
affect the cracking response of beams reinforced with steelbars. The number and width of cracks observed in specimenswith steel bars does not vary between beams with plainconcrete and those with FRC. The plots of moment versuscrack width for Specimens S3NO and S3Pl can be seen inFig. 12. While it appears that there are two cracks in SpecimenS3S 1 and only one crack in Specimen S3NO, a second crackhad in fact' formed in Specimen S3NO but was outside the
Fig. lO-Moment versus crack widths in ¢13 (No.4) CFRPreinforced beams.
Fig. 9-Momen.t versus crack widths in. ¢6 (No.2) CFRp·reinforced beams.
0.Q3
150
125
100 .:~
75 ;:..e
.. q
50 ::;
25
a0.7 0.80.1 0.2 0.3 0.4 0.5 0.6
Crllck Width (mm)
AGI Structural Journal/May~June 2010
of the cracks prevented the localization of the cracking to adegree, which allowed for the formation of successive,inlermediate cracks in the specimen. This effect waspronounced in the two over-reinforced specimens, as thenumber of cracks observed in Specimen G4Pl was doublethe number observed in Specimen G4NO. The final crackpatterns for Specimens G4NO and G4P I are shown in Fig. 8.
Crack Widtb (In)o 0.005 0.0 I 0.015 0.Q2 0.025
Fig. 7-Moment versus crack widths in <pl3 (No.4) CFRp·reinforced beams.
Crack widths in CFRP-reinforced beamsAs with the GFRP-reinforced specimens, the presence of
the polypropylene fibers significantly improved the crackingbehavior of the CFRP-reinforced specimens. The sametrends are seen as in the GFRP-reinforced specimens, wherethe beams with lower reinforcement ratios saw reductionsin crack widths but not the number of cracks, whereas theover-reinforced beams saw reductions in crack widths and anincrease in the number of cracks that formed. Shown in Fig. 9is the moment versus crack width plot for Specimens C2NOand C2PI (4)6 [No. 2J CFRP bars). The difference in themaximum crack width observed between the two beams issubstantial. At a moment of 10 kN-m (89 k-in.), themaximum crack width seen in Specimen C2NO is approximately1.1 mm (0.043 in.), whereas the maximum crack width seenin Specimen C2P] is only 0.6 mm (0.024 in.).
The beams that experience the greatest benefit to thecracking response with the addition of fiber reinforcementare the two specimens with 4>13 (No.4) CFRP reinforcingbars (Specimens C4NO and C4Pl). Like the two overreinforced beams with GFRP bars, the number of cracksincreased with the presence of fibers. It was the crack widths,however, that were most affected by the presence of thefibers. The crack widths in Specimen C4NO were considerablyhigher than in Specimen C4PI. The moment versus crackwidth plot for these two beams was shown in Fig. 10. At amoment of 15 kN-m (133 k-in.), there was a large differencein the maximum crack width observed in the two beams. Themaximum crack width in Specimen C4NO was approximately1.0 mm (0.039 in.), in comparison with a maximum crackwidth in Specimen C4Pl of approximately 0.3 mm (0.012 in.).The final crack patterns for Specimens C4NO and C4Pl areshown in Fig. 11. The reduction in crack widths with thepresence of the polypropylene fibers for beams with bothtypes of FRP bars is similar to what has been found inanother study.13
19
Fig. Ii-Final crack pallernsfor beams': (a) Specimen C4NO; and (h) Specimen C4P J.
Crack Width (In) <l.00 0.02 0.04 0.06 0.08 0.10 0.12
14 .r---------------.----,-- 120
.. .. Cl:IJQ.aoof:P~ D9: 0\ r:P D-~@ ': - 100
12
• _ .1. .•• 1. __ !_.J 10· - 80 :§'
g 8· ~ - - ~ - . - ~ C60 ...~ 6 Ei8 0o .... 40 ~
~. 4 .;- -. - --S31'1 - Crack I
-S3?1 - Crack 2 _:- 20 2'" -a .S3NO - Crack I
o 1----I----:---.-4f-----.1----.1---+ 0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crllck Width (mm)
Fig. J2--Moment versus crack widths in rjJlO (No.3) steel,.eil~fi),.ced beams.
range of tJ1e viewing area of the digital image a.nalysis (that is, it was not within the afea of the beam captured by the digital photograph) and could therefore not be measured. The fibers had no effect on the crack widths while the steel remained elastic, which was the region of importance in design considerations. Whereas the crack widths slightly decreased with tJ1e use of fibers after the steel began to yield, the aClllal width of the cracks after that point became less important. The yielding of steel in a reinforced concrete SITUctllTal element' corresponds to t.he overload of that member, and serviceability considerations lose importance as compared 10 safety consiclerat'ions. Similar behavior is seen in Specimens S4NO and S4Pl.
The fact L1ulL the fibers do not significantly affect the cracking response of the specimens is likely due to the high elastic modulus <U1d better bond chafHcteristics of the steel reinforcing bars, in ndditiol) to tJle low modulus of the fibers in comparison to the reinforcing bars. A higher volume fraction of fibers 01' tJle use of stiffer fibers (for example, steel fibers) mIll' have led to a mOre pronounced effect on the cracking response of the, steel-reinforced beams.
CRACK WIDTH MODELlNG Use ofmQdlfledoGergely-Lutz equation
ACl Commluee 440,hus 1l10duJedthe Gergely-Lutz equation for predicting nick widths tot use witb, FRP-reinforced ooncret membeJ:S. 14 The original Ge'1,~ly-Lutz equation was au empirical qua.tioll tlll1t,,;,:asdeveloped based on data from numerous. ste.e.l.reinforeed concrete specimens}S The suggesl d·· 'mQdlficaoons are based on lb or tical and
326
experimental studies performed by several researchers J6
on FRP-reinforced concrete members and are implemented to incorporate the effects of the differing bond and mechanical properties ofFRP reinforcement compared to steel reinforcement. Other recent research has led to further proposed modifications of the ACI 440 equation20; however, only the current ACI 440 equation is considered herein.
The Gergely-Lutz equation for FRP-reinforced members is modified from the original equation by a corrective coefficient that accounts for the differences in bond characteristics between steel reinforcement and FRP reinforcement. This modified Gergely-Lutz equation is shown in Eq. (1)
w = 2.2 ykbfj·VdeA}' nun, MPa (I)Ef
Plots of the moment versus the crack width are created for all reinforced concrete beam specimens tested. To calculate the crack width from the applied moment using the GergelyLutz equation, it is necessary to express the stress in the reinforcement in terms of the moment. This relationship is shown in Eq. (2), and follows from a cracked section analysis.
(2)
As the stress can now be represented as a function of the moment, the modified Gergely-Lutz equation can now be used to plot the moment versus the crack width. The substitution of Eq. (2) into Eq. (1) yields the modified Gergely-Lutz equation expressed as a function of the applied moment, which can be seen in Eq. (3)
d-y·22= _. . __er k M3l f(iAAw Y b ;,jUel'1,. (3)Ee fer
Calculating crack width at height of reinforcement The crack widths at the height of the reinforcing bars on
the face of the specimen are determined from the digital image analysis. The Gergely-Lutz equation is used for calculating the maximum crack width at the extreme tensile face of the specimen. To use the Gergely-Lutz equation for comparison with the data, the equation is used with the value of y set equal to I. The value of y is equal to the ratio of the distance from the neutral axis to the tensile face of the specimen (where the crack width is to be ca.lculated) and the distance from the neutral axis to the centroid of the tensile reinforcement. Therefore, if the crack widths vary linearly tbroughout the beightof the cross section, the crack width at tbe height of the reinforcing bars can be calculated using a y value of 1.
The use of the Gergely-Lutz equation for calculating the crack width at the height of the reinforcing bars is dependent on the assumption that the crack widths vary linearly with height. This. assumption is found to be valid based on the results from the digital image analysis. The digital image analysis allows for' the measurement of'crack widths at multiple heights in the specimen and, therefore, the vari'ation of crack width with height can be easily seen. In all cases, the crack widrhsare indeed t0und to vary linearly with height. Figure 13 shows thevariati0i1 of crack width with height f0f Specimen G4NO for the image shown in Fig. 5.
iACliStructural'journal/May~June 2010
(I)
(3)
(2)
22 d-y·= _. . __er k M3l f(iAAw Y b ;,jUe/'1,.
Ee fer
w = 2.2 ykbfj·VdeA}' nun, MPaEf
iACliStructural'journal/May~June 2010
experimental studies performed by several researchers J6- 19
on FRP-reinforced concrete members and are implementedto incorporate the effects of the differing bond and mechanicalproperties ofFRP reinforcement compared to steel reinforcement.Other recent research has led to further proposed modifications ofthe ACI 440 equation20; however, only the current ACI 440equation is considered herein.
The Gergely-Lutz equation for FRP-reinforced membersis modified from the original equation by a corrective coefficient that accounts for the differences in bond characteristicsbetween steel reinforcement and FRP reinforcement. Thismodified Gergely-Lutz equation is shown in Eq. (1)
As the stress can now be represented as a function of themoment, the modified Gergely-Lutz equation can now beused to plot the moment versus the crack width. Thesubstitution of Eq. (2) into Eq. (1) yields the modifiedGergely-Lutz equation expressed as a function of the appliedmoment, which can be seen in Eq. (3)
Plots of the moment versus the crack width are created forall reinforced concrete beam specimens tested. To calculatethe crack width from the applied moment using the GergelyLutz equation, it is necessary to express the stress in thereinforcement in terms of the moment. This relationship isshown in Eq. (2), and follows from a cracked section analysis.
Calculating crack width at height of reinforcementThe crack widths at the height of the reinforcing bars on
the face of the specimen are determined from the digitalimage analysis. The Gergely-Lutz equation is used forcalculating the maximum crack width at the extreme tensileface of the specimen. To use the Gergely-Lutz equation forcomparison with the data, the equation is used with the valueof y set equal to I. The value of y is equal to the ratio of thedistance from the neutral axis to the tensile face of thespecimen (where the crack width is to be ca.lculated) and thedistance from the neutral axis to the centroid of the tensilereinforcement. Therefore, if the crack widths vary linearlytbroughout the beightof the cross section, the crack width attbe height of the reinforcing bars can be calculated using a yvalue of 1.
The use of the Gergely-Lutz equation for calculating thecrack width at the height of the reinforcing bars is dependenton the assumption that the crack widths vary linearly withheight. This. assumption is found to be valid based on theresults from the digital image analysis. The digital imageanalysis allows for' the measurement of'crack widths atmultiple heights in the specimen and, therefore, the vari'ationof crack width with height can be easily seen. In all cases, thecrack widrhsare indeed t0und to vary linearly with height.Figure 13 shows thevariati0i1 of crack width with height f0fSpecimen G4NO for the image shown in Fig. 5.
0.12
-- 120
- 100
- 80 :§'~
60 C...Ei0
40 ~
_:- 20
0
3.02.5
0.10
.;- -. - --S31'1 - Crack I
-S3?1 - Crack 2-a .S3NO - Crack I
~ - - ~ - . -
1.0 1.5 2.0
Crllck Width (mm)
Crack Width (In)0.04 0.06 0.08
0.5
0.02
.. .. Cl:IJQ.aoof:P~ D9:0\ r:P D-~@ ':
• _ .1. .•• 1. __ !_.
o 1----I----:---.-4f-----.1----.1---+
0.0
<l.00
14 .r---------------.----,12
2'"
J 10·
g 8·
~ 68o....~. 4
Fig. J2--Moment versus crack widths in rjJlO (No.3) steel,.eil~fi),.ced beams.
Fig. Ii-Final crack pallernsfor beams': (a) Specimen C4NO;and (h) Specimen C4P J.
CRACK WIDTH MODELlNGUse ofmQdlfledoGergely-Lutz equation
ACl Commluee 440,hus 1l10duJedthe Gergely-Lutz equationfor predicting nick widths tot use witb, FRP-reinforcedooncret membeJ:S. 14 The original Ge'1,~ly-Lutz equationwas au empirical qua.tioll tlll1t,,;,:asdeveloped based on datafrom numerous. ste.e.l.reinforeed concrete specimens}S Thesuggesl d·· 'mQdlficaoons are based on lb or tical and
range of tJ1e viewing area of the digital image a.nalysis (thatis, it was not within the afea of the beam captured by thedigital photograph) and could therefore not be measured.The fibers had no effect on the crack widths while the steelremained elastic, which was the region of importance indesign considerations. Whereas the crack widths slightlydecreased with tJ1e use of fibers after the steel began to yield,the aClllal width of the cracks after that point became lessimportant. The yielding of steel in a reinforced concrete slTUctllTalelement' corresponds to t.he overload of that member, andserviceability considerations lose importance as compared10 safety consiclerat'ions. Similar behavior is seen inSpecimens S4NO and S4Pl.
The fact L1ulL the fibers do not significantly affect thecracking response of the specimens is likely due to the highelastic modulus <U1d better bond chafHcteristics of the steelreinforcing bars, in ndditiol) to tJle low modulus of the fibersin comparison to the reinforcing bars. A higher volume fractionof fibers 01' tJle use of stiffer fibers (for example, steel fibers)mIll' have led to a mOre pronounced effect on the crackingresponse of the,steel-reinforced beams.
326
7
*
Table 3-Calculated bond coefficients� Crllck Width (in)
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 250 r---~---""""'--'--""""'----~-----,
Rei.nforcUlg Reinforcing Plain bar IYP<: barsiu concrete FRC kb.FRc'kto.f'lnir.
3 1.02 LOI 0.99 Steel
4 0.73 0.61 084
2 1.57 0.67 0.42
GFRP 3 1.97 0.84 0.43
4 1.04 0.57 , 0.55
2 1.74 0.92 0.53
CFRP 3 1.55 0.95 0.61
4 2.98 0.76 0.26
At the time when this image was taken, it can be seen lllat two fairly large cracks have formed in the specimen. The behavior seen is typical of the behavior seen in all of the specimens. The crack widths vary linearly regardless of the load or the number of cracks present. This observation allows for the Gergely-Lutz equation with a y value of 1 to be used to calculate the crack widths at the height of the reinforcement.
The modified Gergely-Lutz equation was compared with the experimentally observed crack width behavior in the beams. The observed behavior, however, was fundamentally different than what was predicted by the Gergely-Lutz equation. The Gergely-Lutz equation for predicting crack widths is a linear equation (with a slope depending on the material and section properties) that passes through the origin. The observed response, however, was that the plot of moment (which is related to the stress in the reinforcement) versus the crack width wi)] not, jf extrapolated backwards, pass through the origin. Intuitively, the plot would not be expected to pass through zero, as a crack does not form immediately with application of moment (neglecting preexisting microcracks), and will only form when the tensile strength of the concrete has been reached. This behavior was observed in all specimens tested, with all plots intercepting the ordinate at a point that was not the origin.
To account for the differences seen in the cracking behavior between specimens and with respect to the Gergely-Lutz equation, a linear regression was performed on the data with the line forced through the experimentally measured cracking moment of the beam. It was at the cracking moment where the crack first formed and began to increase in width with increasing moment. A modification to the Gergely-Lutz equation was used to allow the equation for maximum crack width to pass through a point on the y-axis equal to the cracking moment, rather than forcing it to pass through the origin. The modification to the Gergely-Lutz equation is given in Eq. (4)
d-W = 2.2. ~yk (M - M )Vd A M M (4)
E ler b er e r > cr e
Linear regressions are then performed for all specimens with the lines forced through the y-axis at a moment equal to the cracking moment. For example, the moment versus maximum crack width and the best-fit linear regressions for Specimens C4NO and C4Pl are shown in Fig. 14.
ACIStructural JournaI/May-June\201 0
t I I I
200 ... -- .....;.... --.---~ ------I~~:I~~=_~8~~;~~;1--, : • 1._ .... '-. - - -- - - - , .. 6!150 . ,
i··5
'a; 100 .. -----~\_-- ·4 :=
.. 3
50 .
o-!-----,----,----"'-.,.;a...----,-----i. 0
0.0� 0.2 0.4 0.6 0.8 1.0� Cruck Width (mlU)�
Fig. 13-Crack width versus height (Specimen G4NO).
C.'l\ck WidUl (in)
o 0.0 I 0.02 0.03 0.04 0.05 0.06 0.07� 40 r--~-----.,.--,...---,----r--l350
...- Specimen C4P I35 .. 300 -0- Specimen C4NO
30 ... R2 = 0.9985 .. 2508'� --.5I 25 I
~~ 200 '--' '-' ..... ..... 20� c::c::� <l.l<l.l 150 8�8 15 ' > 0�0 : R" = 0.9949 ~ ~ ,� 100
\0
.. 50
o -1----;----;---1---+---+--,----1- 0
o 0.25 0.5 0.75 I 1.25 1.5 l.75
Crack Width (mm)
Fig. 14-Moment versus maximum crack width for ¢J3 (No.4) CFRP-reinforced beams.
Corrective bond coefficients The slope of the best-fit linear regressions are used to
back-calculate the corrective bond coefficient kb using Eq. (4). The bond coefficients are calculated for all specimens tested, and a summary of the results is given in Table 3. It should be noted that the following comments are based on the results from the testing of a single beam in each case. Further experimental studies should be conducted to generate additional data and thus allow for more conclusive results.
For a given reinforcing bar type, no clear correlation between the bond coefficient and the bar size/reinforcement : f,ratio was observed, in the sense that the bond coefficients do not monotonically increase or decrease with increasing bar size/reinforcement ratio. The value of the bond coefficient for FRC beams, however, was consistently smaller than the value for plain concrete beams. While it was difticult to make any strong conclusions regarding the effect of bar size/ ., ,reinforcement ratio on the hondcoefficient, it was clear that the addition of polypropylene fibers to the concrete consistently leads to reduced values when FRP reinforcing bars are used. ': ,
327" 'I
I
*
Crllck Width (in)
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040250 r---~---""""'--'--""""'----~-----,
··5
·4
.. 3
.... '-. - - -- - - - , .. 6
.. -----~\_--
• 1._.,
t I I I
... -- .. --; .... --.---~ ------I~~:I~~=_~8~~;~~;1--, :7
200
50 .
!150
i'a; 100:=
Rei.nforcUlg Reinforcing Plainbar IYP<: barsiu concrete FRC kb.FRc'kto.f'lnir.
3 1.02 LOI 0.99Steel
4 0.73 0.61 084
2 1.57 0.67 0.42
GFRP 3 1.97 0.84 0.43
4 1.04 0.57 , 0.55
2 1.74 0.92 0.53
CFRP 3 1.55 0.95 0.61
4 2.98 0.76 0.26
Table 3-Calculated bond coefficients
Fig. 13-Crack width versus height (Specimen G4NO).
.,,
':,
: f,
0.06 0.07
350
C.'l\ck WidUl (in)
0.0 I 0.02 0.03 0.04 0.05o40 r--~-----.,.--,...---,----r--l
35 ...- Specimen C4P I.. 300
30 ... R2 = 0.9985-0- Specimen C4NO
8' .. 250 ---I 25 .5~
I
200 ~'--'
'-' .......... 20 c::c:: <l.l<l.l 150 88 15 ' > 00 : R" = 0.9949 ~:;
\0, 100
.. 50
o -1----;----;---1---+---+--,----1- 0
o 0.25 0.5 0.75 I 1.25 1.5 l.75
Crack Width (mm)
o-!-----,----,----"'-.,.;a...----,-----i. 0
0.0 0.2 0.4 0.6 0.8 1.0Cruck Width (mlU)
Fig. 14-Moment versus maximum crack width for ¢J3(No.4) CFRP-reinforced beams.
Corrective bond coefficientsThe slope of the best-fit linear regressions are used to
back-calculate the corrective bond coefficient kb using Eq. (4).The bond coefficients are calculated for all specimens tested,and a summary of the results is given in Table 3. It should benoted that the following comments are based on the resultsfrom the testing of a single beam in each case. Furtherexperimental studies should be conducted to generateadditional data and thus allow for more conclusive results.
For a given reinforcing bar type, no clear correlationbetween the bond coefficient and the bar size/reinforcementratio was observed, in the sense that the bond coefficients donot monotonically increase or decrease with increasing barsize/reinforcement ratio. The value of the bond coefficientfor FRC beams, however, was consistently smaller than thevalue for plain concrete beams. While it was difticult tomake any strong conclusions regarding the effect of bar size/reinforcement ratio on the hondcoefficient, it was clear thatthe addition of polypropylene fibers to the concreteconsistently leads to reduced values when FRP reinforcingbars are used.
d--W = 2.2. ~yk (M - M )Vd A M M (4)
Ee
ler b er e r > cr
At the time when this image was taken, it can be seen lllattwo fairly large cracks have formed in the specimen. Thebehavior seen is typical of the behavior seen in all of thespecimens. The crack widths vary linearly regardless of theload or the number of cracks present. This observationallows for the Gergely-Lutz equation with a y value of 1to be used to calculate the crack widths at the height ofthe reinforcement.
The modified Gergely-Lutz equation was compared withthe experimentally observed crack width behavior in thebeams. The observed behavior, however, was fundamentallydifferent than what was predicted by the Gergely-Lutz equation.The Gergely-Lutz equation for predicting crack widths is alinear equation (with a slope depending on the material andsection properties) that passes through the origin. Theobserved response, however, was that the plot of moment(which is related to the stress in the reinforcement) versus thecrack width wi)] not, jf extrapolated backwards, pass throughthe origin. Intuitively, the plot would not be expected to passthrough zero, as a crack does not form immediately withapplication of moment (neglecting preexisting microcracks),and will only form when the tensile strength of the concretehas been reached. This behavior was observed in all specimenstested, with all plots intercepting the ordinate at a point thatwas not the origin.
To account for the differences seen in the cracking behaviorbetween specimens and with respect to the Gergely-Lutzequation, a linear regression was performed on the data withthe line forced through the experimentally measuredcracking moment of the beam. It was at the cracking momentwhere the crack first formed and began to increase in widthwith increasing moment. A modification to the Gergely-Lutzequation was used to allow the equation for maximum crackwidth to pass through a point on the y-axis equal to thecracking moment, rather than forcing it to pass through theorigin. The modification to the Gergely-Lutz equation isgiven in Eq. (4)
Linear regressions are then performed for all specimenswith the lines forced through the y-axis at a moment equal tothe cracking moment. For example, the moment versusmaximum crack width and the best-fit linear regressions forSpecimens C4NO and C4Pl are shown in Fig. 14.
ACIStructural JournaI/May-June\201 0 327" I'I
The bond coefficients found for steel bars with J?J~in
concrete were close to.l" as expected, because the original Gergely-Lutz equation was based on the use of steel-reinforced conCrete. A reduction in the bond coefficient from a value of I would, in the context of the Gergely-Lutz equation, mean improved bond characteristics of the reinforcing bar in comparison to steel. In a more general sense, however, it would mean that there would be a decrease seen in the maximum crack widths observed. The use offiber reinforcement has been shown to improve the bond characteristics of reinforcing bars to concrete. 21 -23 Therefore, the decrease in the bond coefficient signifies both improved bond between concrete and reinforcing bar, as well as an overall reduction in crack widths due to bridging effects of the fibers.
'l'here was little reduction in the value of the corrective bond coefficient with the use of PRC in the steel-reinforced specimens, as the value of kb was reduced by only 1% for the beam with <t> J0 (No.3) bars and by approximately 16% for the beam with <t> 13 (No.4) bars. This was not a large reduction, and was consistent with the observed cracking response, as the crack widlhs were seen to be nominally unaffected by the presence of the polypropylene fibers.
The bond coefficients found for the three GPRP beams were larger than 1, meaning that the GPRP bars had bond characteristics worse than that of steel, despite the fact that thc bars had Jugs and a coarse sand-epoxy coating meant to improve the bond characteristics. The bond coefficient values are shown in Table 3. Research has shown that the bond between PRP bars and concrete is highly dependent on and can be *~~atJy ir.nproved ?y the ~ug geom:try an.d .resin propertles 2 .~. Studies on various GFRP bars 1rom different manufacturers have shown bond coefficients ranging from 0.71 (0 1.83, meaning that the bars can have bond characteristics superior to or inferior to steel. 14 The bond coefficient for the GFRP-reinforced beams with FRC were reduced by approximately 57% for the (1)6 (No.2) and (plO (No.3) beams and by approximately 45% for the (Id 3 (No.4) beam as compared lO their counterpart beams with plain concrete. The significant decrease in the maximum crack widths observed is a result of this considerable decrease in the bond coefficient.
The bond coefficients for the CFRP-reinforced beams with plain concrete were also greuter than I. The bond coefficients are presented in Table 3. The values are much higher than those found for the beams with steel reinforcemenl, which indicates a significant reduction in the bond quality of the CFRP reinforcing bars. The CFRP bars used in this study were very smooth, with no physical deformations or coatings to improve its bond to concrete. The high value of the bond coetJicient that was found was not unexpected.
Like Ule GFRP-reinforced specimens, [he addition of polypropylene fibers to the concrete leads to a large reduction in the bond coe1Ticient. The bond coefficient is reduced by approximately 47, 39, and 74% for the beams with 416 (No.2), (ldO(No. 3), and ~l3 (No.4) bars, respectively. The reduction il1 maximum crack widths observed is the most pronounced in 1110 specimens with the CPRP bars, which are smooth and have no deformations. The presence of fibers has a greater effect on reducing crack widths when used with reinforcing barswit11 pm)!'· bond chm·acteristics.
CONCLUSIONS The ct'aoJ6ng 'behavior of pillin lUl,djJolypropyleile PRC
beams witheithel' steel,'GPRP, orGFRP reinfbi'cingbars was measured llsij.1g a digit/it imaging system. Thef01lowing
conclusions can be drawn from the results of the experimental investigation;
J. The addition of polypropylene fibers to the concrete improves the cracking behavior (reduced crack widths and spacing) of beams reinforced with PRP bars, with more improvement seen in beams with CFRP reinforcing bars than in beams with GFRP reinforcing bars.
2. The addition of polypropylene fibers to the concrete does not significantly improve the preyield cracking behavior of beams reinforced with steel bars.
3. A modification to the Gergely-Lutz equation given by ACI Committee 440 for predicting crack widths in PRPreinforced beams is implemented and was used to calculate bond coefficients for FRP-reinforced beams with plain concrete and PRe. The bond coefficients were used as a proxy to quantify the improvements to the crack width response of the beams, where reduced bond coefficients signified reductions in maximum crack width. The use of PRC was found to reduce the bond coefficient on the order of 45 to 55% for the GPRP-reinforced beams, 45 to 75% for the CFRP-reinforced beams, and 1 to 15% for the steelreinforced beams. Based on the data found in this set of tests, no clear correlution between bond coefficient and bar size/ reinforcement ratio was found.
ACKNOWLEDGMENTS The authors wish to thank Hughes Brothers, Inc., Blue Circle Cement,
W.R. Grace, and Wakefield Materials for providing the FRP reinforcing bars. cement and slag, admixtures and fiber reinforcement, and aggregates, respectively. The authors would also like to thank 1. Kelble for his assistance with the experimental testing.
NOTATION .II,.� concrete area surrounding one tension bm' equal to total effective
tension area of concrete surrounding reinforcement and having same centroid, divided by number of bars
d depth to centroid of tension reinforcement de thickness of concrete cover measured from tension face to center
of bar closest to that face E elastic modulus of concretee Ef� etastic modulus of FRP reinforcement .Ii stress in FRP reinforcement ler moment of inertia of cracked section kb corrective bond coefficient M applied moment Mer cracking moment IV crack width Yer depth to centroid of cracked section £f strain in FRP reinforcement y ratio of distance from tension face to neutrat axis to distance from
centroid of reinforcement to neutral axis
REFERENCES I. Nanni, A., "Flexural Behavior and Design of RC Members Using FRP
Reinforcement," Journal of Siructural Engineering, V. I t9, No. II, 1993, pp, 3344-3359.
2. Nanni, A.,"North American Design Guidelines for Concrete Reinforcement and Strengthening Using FRP: Principles, Applications and Unresolved lssues," Construction aJ1(1 Building Materials, V. 17, No. 6-7, 2003, pp. 439-446.
3. Benmokrane, B.; Chaallal, 0.; and Masmoudi, R., "Flexural Response of Concrete Beams Reinforced with FRP Reinforcing Bm'S," ACI Structural Journal, V. 93, No. I, Jan.-Feb: 1996, pp. 46-55.
4. Masmoudi, R.; Benmok:rane, R; and Chaallal, 0., "Cracking Behaviour of Concrete Beams Reinforced with FRP Rebars," Canadian Journal of Civil Engineering, V. 23, No.6, 1996, pp. 1172-1179.
5. Masmoudi, R.; Theriault, M.; and Benmokrane. B., "Flexural Behavior ofConcrete Beams Reinfprced with Defonned Fiber Reinforced Plastic Reinforcing Rpds," ACISlructural Journal, V. 95, No.6, Nov.-Dec. 1998, pp. 665-676.
5. Tomanji, H. A., and Saafi, M .. "Flexural Behavior of Concrete Beams Reinforced with Glass Fiber:Reinforced Potymer (GFRP) Bars," ACI
;p,.r;.;.a~;trLICtLjral Journal/May-June 201 0 328
The bond coefficients found for steel bars with J?J~in
concrete were close to.l" as expected, because the originalGergely-Lutz equation was based on the use of steel-reinforcedconcrete. A reduction in the bond coefficient from a value ofI would, in the context of the Gergely-Lutz equation, meanimproved bond characteristics of the reinforcing bar incomparison to steel. In a more general sense, however, itwould mean that there would be a decrease seen in themaximum crack widths observed. The use offiber reinforcement has been shown to improve the bond characteristics ofreinforcing bars to concrete. 21 -23 Therefore, the decrease inthe bond coefficient signifies both improved bond betweenconcrete and reinforcing bar, as well as an overall reductionin crack widths due to bridging effects of the fibers.
'l'here was little reduction in the value of the correctivebond coefficient with the use of PRC in the steel-reinforcedspecimens, as the value of kb was reduced by only 1% for thebeam with <t> J0 (No.3) bars and by approximately 16% forthe beam with <t> 13 (No.4) bars. This was not a large reduction,and was consistent with the observed cracking response, asthe crack widths were seen to be nominally unaffected by thepresence of the polypropylene fibers.
The bond coefficients found for the three GPRP beamswere larger than 1, meaning that the GPRP bars had bondcharacteristics worse than that of steel, despite the fact thatthc bars had Jugs and a coarse sand-epoxy coating meant toimprove the bond characteristics. The bond coefficientvalues are shown in Table 3. Research has shown that thebond between PRP bars and concrete is highly dependent onand can be *~~atJy ir.nproved ?y the ~ug geom:try an.d .resinpropertles 2 .~. Studies on vanous GFRP bars 1rom dIfferentmanufacturers have shown bond coefficients ranging from0.71 (0 1.83, meaning that the bars can have bond characteristicssuperior to or inferior to steel. 14 The bond coefficient for theGFRP-reinforced beams with FRC were reduced by approximately 57% for the (1)6 (No.2) and (plO (No.3) beams andby approximately 45% for the (Id 3 (No.4) beam as comparedto their counterpart beams with plain concrete. The significantdecrease in the maximum crack widths observed is a resultof this considerable decrease in the bond coefficient.
The bond coefficients for the CPRP-reinforced beamswith plain concrete were also greuter than I. The bondcoefficients are presented in Table 3. The values are muchhigher than those found for the beams with steel reinforcement,which indicates a significant reduction in the bond quality ofthe CFRP reinforcing bars. The CFRP bars used in this studywere very smooth, with no physical deformations or coatingsto improve its bond to concrete. The high value of the bondcoetJicient that was found was not unexpected.
Like Ule GFRP-reinforced specimens, the addition of polypropylene fibers to the concrete leads to a large reduction inthe bond coe1Ticient. The bond coefficient is reduced byapproximately 47, 39, and 74% for the beams with 416 (No.2),(ldO(No. 3), and ~l3 (No.4) bars, respectively. The reductionil1 maximum crack widths observed is the most pronouncedin 111c specimens with the CPRP bars, which are smooth andhave no deformations. The presence of fibers has a greatereffeoton reducing crack widths when used with reinforcingbarswit11 pm)!'· bond chm·acteristics.
CONCLUSIONSThe ct'acJ6ng 'behavior of pillin lUl,djJolypropyleile PRC
beams witheithcl' steel,'GPRP, orGFRP reinfbi'cingbarswas measured llsij.1g a digit/it imaging system. Thef01lowing
328
conclusions can be drawn from the results of the experimental investigation:
J. The addition of polypropylene fibers to the concreteimproves the cracking behavior (reduced crack widths andspacing) of beams reinforced with PRP bars, with moreimprovement seen in beams with CFRP reinforcing bars thanin beams with GPRP reinforcing bars.
2. The addition of polypropylene fibers to the concretedoes not significantly improve the preyield crackingbehavior of beams reinforced with steel bars.
3. A modification to the Gergely-Lutz equation given byACI Committee 440 for predicting crack widths in PRPreinforced beams is implemented and was used to calculatebond coefficients for FRP-reinforced beams with plainconcrete and PRe. The bond coefficients were used as aproxy to quantify the improvements to the crack widthresponse of the beams, where reduced bond coefficientssignified reductions in maximum crack width. The use ofPRC was found to reduce the bond coefficient on the orderof 45 to 55% for the GPRP-reinforced beams, 45 to 75% forthe CPRP-reinforced beams, and 1 to 15% for the steelreinforced beams. Based on the data found in this set of tests,no clear correlation between bond coefficient and bar size/reinforcement ratio was found.
ACKNOWLEDGMENTSThe authors wish to thank Hughes Brothers, Inc., Blue Circle Cement,
W.R. Grace, and Wakefield Materials for providing the FRP reinforcingbars. cement and slag, admixtures and fiber reinforcement, and aggregates,respectively. The authors would also like to thank 1. Kelble for hisassistance with the experimental testing.
NOTATION.II,. concrete area surrounding one tension bm' equal to total effective
tension area of concrete surrounding reinforcement and havingsame centroid, divided by number of bars
d depth to centroid of tension reinforcementde thickness of concrete cover measured from tension face to center
of bar closest to that faceEe elastic modulus of concreteEf etastic modulus of FRP reinforcement.Ii stress in FRP reinforcementler moment of inertia of cracked sectionkb corrective bond coefficientM applied momentMer cracking momentIV crack widthYer depth to centroid of cracked section£f strain in FRP reinforcementy ratio of distance from tension face to neutrat axis to distance from
centroid of reinforcement to neutral axis
REFERENCESI. Nanni, A., "Flexural Behavior and Design of RC Members Using FRP
Reinforcement," Journal of Structural Engineering, V. I t9, No. II, 1993,pp, 3344-3359.
2. Nanni, A.,"North American Design Guidelines for ConcreteReinforcement and Strengthening Using FRP: Principles, Applications andUnresolved lssues," Construction aJ1(1 Building Materials, V. 17, No. 6-7,2003, pp. 439-446.
3. Benmokrane, B.; Chaallal, 0.; and Masmoudi, R., "Flexural Responseof Concrete Beams Reinforced with FRP Reinforcing Bm'S," ACI StructuralJournal, V. 93, No. I, Jan.-Feb: 1996, pp. 46-55.
4. Masmoudi, R.; Benmok:rane, R; and Chaallal, 0., "Cracking Behaviourof Concrete Beams Reinforced with FRP Rebars," Canadian Journal ofCivil Engineering, V. 23, No.6, 1996, pp. 1172-1179.
5. Masmoudi, R.; Theriault, M.; and Benmokrane. B., "FlexuralBehavior ofConcrete Beams Reinfprced with Defonned Fiber ReinforcedPlastic Reinforcing Rpds," ACI Structural Journal, V. 95, No.6, Nov.-Dec.1998, pp. 665-676.
5. Tomanji, H. A., and Saafi, M .. "Flexural Behavior of Concrete BeamsReinforced with Glass Fiber:Reinforced Potymer (GFRP) Bars," ACI
;p,.r;.;.a~;trLICtLjralJournal/May-June 201 0
•�
Slrucl!irai Joumal, V. 97, No.5. Nov.-Dec" 1998. pp. 71.2-71.9. 6. TMriault, M., and Benmokrane, B., "Effects of ERP Reinfon:emelll
Ratio and Concrete Stre.ngth on Flexural Behavior of Concrele Beams." Journal ofColllposilesfor COIJ.Slruclwn, V. 2. No. 1. 1998, pp. 7-16.
7. Razaqpur. A. G.: Svecova, D.: and Cheung. M. S.. "A Rational Method of Deflection Calculation for FRP Reinforced Concrete Beams," ACI SlrllClUml Joui1lal, V. 97, No. 1. Jan.-Feb. 2000. pp. 175-184.
8. Micelli, F.. and Nanni. A., "Durability of FRP Rods for Concrete Str\lClUres," Con5rniclion and Building Malt'fifJls. V. 18. No.7. 2004. pp. 491-503.
9. Zollo, R.. "Fiber-Reinforced Coucrele: An Overview after 30 Years of Development," Cemenl and Concrete Composiles, V. 19. No.2. 1997, pp. 107-122
10. ACI Comminee 544. "Repon on Fiber-Reinforced Concrete (ACI 544.IR-96)." American Concrete InslilUle. Farmington Hills. Ml, 1996 (reapproved 2009). 66 pp.
II. Lee, W. K.. "Flexural Behavior of Fiber-Reinforced Concrete Beams Reinforced with FRP Bars," masler's thesis. Tufts University, Medford. MA, 2003. 161 pp.
12. Jansen, D. C: Choi, S.: and Shah, S., "Studying Shear Crack Initiation and Growth of Reinforced Concrete Beams Using Full-Field Digital Imaging," Proceedings of the 2nd lntemaJional Conference on Nonde.l'lruetil'e Tesling o{ConcreJe in the In{rastmclUre, NasllVille, TN, 1996, pp. 195-203.
13. Wang, H.. and Bciarbi, A., "Flexural Behavior of Fiber-ReinforcedConcrete Beams Reinforced with FRP Rebars," 71h inlernational Symposium on Fiber-Rein/im:ed (FRP) Polymer Rein/orcement jor ConCl~~le Slructures. SP-230, C. K. Shield, J. P. Bllsel, S. L Walkup, and D. D. Gremel, eds.. American Concrete Institute, Farmington Hills, MI, 2005, pp. 895-914.
14. ACI Committee 440, "Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars IACI 440.1 R-06)." American Concrete Institute, Farmington Hills. MI, 2006, 44 pp.
15. Gergely, P., and Lutz. L.. "Maximum Crack Width in Reinforced Concrete Flexural Members." Causes, Mecllflnisms. and Con/lvl of Crocking in Concrete, SP-20, American Concrete Institute, Farmington Hills, MI, 1968, pp. 87-i 17.
16, Faz.a. S. S",and G(lJ)g~~Ub,.H. V. S., "Theoreti~al!anciEt'perim"ntal Correlation of Behavior of.(!;:,:,nQrete Be,ulls R{~nfofGed !¥itbJ:;iber ReLufo{ced Plastic Rebat'S," FiIJer-Reinfon:ed-Plaslic, Reil,forcemell1 fO;' Concrete Siruciures. SP-138. A. N3nni and C. W. Dolan. .ods., AmeJican Concrete Institute.. Farmington Hills, MI, 1993. pp. 599-614.
17. Masmoudi. R.: Benmokrane. B.: and Chaalal. 0., "Cracking Behavior of Beams Rcjnforced with FRP Rebars," "'irsl hllemational COIl(enmce on Composires in b!(mS/I1ICllUr3S, H. Saadutmune.,h ,utd M. Ehsani, cds .. Tucson, AZ. 1996. pp. 374-388.
18. Tighioll(ln, B.: Benmoh'Tfllle. B.; lutd Gao, D" "InveStigation on the Bond of Fiber Reinforced Polymer (FRP) Rebars in Concrete," S,'cond inlernmional Conference on Composires in In./i'a.\·trtiClUreS, V. n. H. Saadannanesh and M. Ehsl111i, ecls" Tucson, AZ, 1998, pp. 102-112.
19. Masmoudi, R.; Benllloknme. B.: and CluwllaJ. 0., "Cracking Bch'l\'iour of Concrete Beam, Reinforced with FRJ' Rebars," Canadian Journal of Civil Engineering. V. 23. No.6, 1996, pp. 1172-1179.
20. Salib. S. R.. and Abdei-Sayed, G., "Precliction of Crack Width for Fiber-Reinforced Polymer-Reinforced Coucrete Beams." ACl Stl'llclUral .10uI'lla I. V. 101. No.4, july-Aug. 2004, pp. 532-536.
21. Harajli. M.: l-!out, M.; and Jalkh, W.. "Local Bond Stress-Slip Behavior of Reinforcing Bars Embedded in Plaiu and Fiber Concrete," ACI Malerials Journal, V. 92. No.4, July-Aug, 1995, pp. 343-354.
22. Harnjli, M. H., and Mabsout, M. E., "Evalulltion of Bond Strength of Steel Reinforcing Bar;; in Plain and Fiber-Reinforced Concrete," ACI Slruclllral.1ourt/al. V. 99. No.4, July-Aug, 2002, pp. 509-517.
23. Harajli, 111.: H:lInad. 13.: aud Karam, K" "Bond-Slip Response or Reinforcing Bars Embedded in Plain und Fiber Concrete," Journal of Mllterials in Civil Engineering, V. 14. No.6, 2002, pp. 503-511.
24. Mal\>ar, L. J., "Tensile find Bond Properties of GFRP Reinforcing Bars." ACi MOlaials Journal, V. 92, No.3, May-June 1995, JlJl. 276-285.
25. AI-ZlIhrnni, M. M.: AI-Dulaijan, S. U.; Nanni, A.; Bakis, C. E.: and Boothby, T. E., "Evalulltion of Bond Using FRP Rods with Axisymmetric Deformations," ConsJrlu:lion IJnd Building Mm",-ials, V. 13, No.6, 1999, PI). 299-309.
329ACI Structural Journal/May-June 2010
Slrucl!irai Joumal, V. 97, No.5. Nov.-Dec" 1998. pp. 71.2-71.9.6. TMriault, M., and Benmokrane, B., "Effects of ERP Reinfon:emelll
Ratio and Concrete Stre.ngth on Flexural Behavior of Concrele Beams."Journal ofComposilesfor COIJ.Slruclwn, V. 2. No. 1. 1998, pp. 7-16.
7. Razaqpur. A. G.: Svecova, D.: and Cheung. M. S.. "A RationalMethod of Deflection Calculation for FRP Reinforced Concrete Beams,"ACI SlrllClUml Joui1lal, V. 97, No. 1. Jan.-Feb. 2000. pp. 175-184.
8. Micelli, F.. and Nanni. A., "Durability of FRP Rods for ConcreteStr\lClUres," Con5rniclion and Building Malt'fials. V. 18. No.7. 2004.pp. 491-503.
9. Zollo, R.. "Fiber-Reinforced Coucrele: An Overview after 30 Years ofDevelopment," Cemenl and Concrete Composiles, V. 19. No.2. 1997,pp. 107-122-
10. ACI Comminee 544. "Repon on Fiber-Reinforced Concrete(ACI 544.IR-96)." American Concrete InslilUle. Farmington Hills. Ml,1996 (reapproved 2009). 66 pp.
II. Lee, W. K.. "Flexural Behavior of Fiber-Reinforced Concrete BeamsReinforced with FRP Bars," masler's thesis. Tufts University, Medford.MA, 2003. 161 pp.
12. Jansen, D. C: Choi, S.: and Shah, S., "Studying Shear Crack Initiationand Growth of Reinforced Concrete Beams Using Full-Field DigitalImaging," Proceedings of the 2nd lntemaJional Conference on Nonde.l'lruetil'eTesling o{ConcreJe in the In{rastmclUre, NasllVille, TN, 1996, pp. 195-203.
13. Wang, H.. and Bciarbi, A., "Flexural Behavior of Fiber-ReinforcedConcrete Beams Reinforced with FRP Rebars," 71h inlemational Symposiumon Fiber-Reinjim:ed (FRP) Polymer Reinjorcement jor ConCl~~le Slructures.SP-230, C. K. Shield, J. P. Bllsel, S. L Walkup, and D. D. Gremel, eds..American Concrete Institute, Farmington Hills, MI, 2005, pp. 895-914.
14. ACI Committee 440, "Guide for the Design and Construction ofStructural Concrete Reinforced with FRP Bars IACI 440.1 R-06)." AmericanConcrete Institute, Farmington Hills. MI, 2006, 44 pp.
15. Gergely, P., and Lutz. L.. "Maximum Crack Width in ReinforcedConcrete Flexural Members." Causes, Mecllflnisms. and Con/lvl ofCrocking in Concrete, SP-20, American Concrete Institute, FarmingtonHills, MI, 1968, pp. 87-i 17.
ACI Structural Journal/May-June 2010
16. Faz.a. S. S",and G(lJ)g~~Ub,.H. V. S., "Theoreti~al!anciEt'perimental
Correlation of Behavior of.(!;:,:,nQrete Bc,ulls R{~nfofGed !¥itbJ:;iber ReLufo{cedPlastic Rebat'S," FiIJer-Reinfim:ed-PlaSlic, Reil!toreemell1 fo;' ConcreteSiruciures. SP-138. A. Nanni and C. W. Dolan. .ods., AmeJican ConcreteInstitute.. Farmington Hills, MI, 1993. pp. 599-614.
17. Masmoudi. R.: Benmokrane. B.: and Chaalal. 0., "CrackingBehavior of Beams Rcjnforced with FRP Rebars," "'irsl hllemationalCOIl(enmce on Composires in b!(mS/I1ICllUr3S, H. Saadutmune.,h (utd M. Ehsani,cds .. Tucson, AZ. 1996. pp. 374-388.
18. Tighioll(ln, B.: Benmoh'Tfllle. B.; lutd Gao, D" "Investigation on theBond of Fiber Reinforced Polymer (FRP) Rebars in Concrete,"S,'cond inlernmional Conference on Composires in In./i'a.\·trtiClUreS,V. n. H. Saadannanesh and M. Ehsl111i, ecls" Tucson, AZ, 1998, pp. 102-112.
19. Masmoudi, R.; Benllloknme. B.: and CluwllaJ. 0 .. "Cracking Bch'l\'iourof Concrete Beam, Reinforced with FRJ' Robars," Canadian Journal ofCivil Engineering. V. 23. No.6, 1996, pp. 1172-1179.
20. Salib. S. R.. and Abdei-Sayed, G .. "Precliction of Crack Width forFiber-Reinforced Polymer-Reinforced Coucrele Beams." ACl Stl'llclUral.10uI'lla I. V. 101. No.4, July-Aug. 2004, pp. 532-536.
21. Harajli. M.: l-!out, M.; and Jalkh, W.. "Local Bond Stress-SlipBehavior of Reinforcing Bars Embedded in Plaiu and Fiber Concrete," ACIMarerials Journal, V. 92. No.4, July-Aug, 1995, pp. 343-354.
22. Harnjli, M. H.• and Mabsoul, M. E., "Evalulltion of Bond Strength ofSteel Reinforcing Bars in Plain and Fiber-Reinforced Concrete," ACISlruclllral.1ourt/al. V. 99. No.4, July-Aug, 2002, pp. 509-517.
23. Harajli, 111.: H:lInad. 13.; aud Karam, K,. "Bond-Slip Response orReinforcing Bars Embedded in Plain und Fiber Concrete," Journal ofMllterials in Civil Engineering, V. 14. No.6, 2002, pp. 503-511.
24. Mal\'ar, L. J., "Tensile and Bond Propertios of GFRP ReinforcingBars." ACi MOlN'ials Journal, V. 92, No.3, May-June 1995, JlJl. 276-285.
25. AI-ZlIhrnni, M. M.: AI-Dulaijan, S. U.; Nanni, A.; Bakis, C. E.: andBoothby, T. E., "Evalulltion of Bond Using FRP Rods with AxisymmetricDeformations," ConsJrlu:lion IJnd Building Mil/",-ials, V. 13. No.6, 1999,PI). 299-309.
329
•