Flexural Behavior of Concrete Beam Strengthened by Near ...downloads.hindawi.com/journals/amse/2017/9180624.pdf6 AdvancesinMaterialsScienceandEngineering ℎ d f d s c b 𝜀 s 𝜀

Research ArticleFlexural Behavior of Concrete Beam Strengthened byNear-Surface Mounted CFRP Reinforcement Using EquivalentSection Model

Woo-tai Jung Jong-sup Park Jae-yoon Kang and Moon-seoung Keum

Structural Engineering Research Institute Korea Institute of Civil Engineering and Building Technology Goyang Republic of Korea

Correspondence should be addressed to Woo-tai Jung woodykictrekr

Received 26 August 2016 Accepted 4 December 2016 Published 12 February 2017

Academic Editor Carlo Santulli

Copyright copy 2017 Woo-tai Jung et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

FRP (fiber reinforced polymer) has found wide applications as an alternative to steel rebar not only for the repair and strengtheningof existing structures but also for the erection of new structures Near-surface mounted (NSM) strengthening was introduced asan alternative of externally bonded reinforcement (EBR) but this method also experiences early bond failure which stresses theimportance of predicting accurately the bond failure behavior in order to evaluate precisely the performance ofNSM reinforcementThis study proposes the equivalent section model assuming monolithic behavior of the filler and CFRP reinforcement Thisequivalent section model enables establishing a bond failure model applicable independently of the sectional shape of the CFRPreinforcement This so-derived bond failure model is then validated experimentally by means of beams flexure-strengthened byNSM CFRP reinforcements with various cross-sections Finally analytical analysis applying the bond failure model consideringthe equivalent section and defined failure criteria is performedThe results show the accuracy of the prediction of the failure modeas well as the accurate prediction of the experimental results regardless of the sectional shape of the CFRP reinforcement

1 Introduction

Despite its excellence as construction material concretedegrades with time and the serviceability deteriorates follow-ing the ongoing performance loss of the concrete memberand the material itself caused by environmental actions Thewidth of the cracks developed in concrete enlarges graduallywith time and favors the penetration of impurities whichaccelerate the degradation of the structure Steel plate bond-ing external tendons prestressing and FRP (fiber reinforcedpolymer) bonding are some of the common strengthen-ing methods for degraded concrete structures Steel platebonding offers poor workability on site due to its heavyweight and is susceptible to corrosion External tendonsprestressing can improve the serviceability by controlling thecracks and restoring the deflection but requires anchoringdevices that are designed to have substantial size to meetthe tensile strength of the reinforcement All three methodspresent the inconvenience of being vulnerable to external

damage because of external reinforcements factual exposureat the surface of the reinforced section Besides FRP bondingimproves the performance of the structure by bonding theCFRP (carbon fiber reinforced polymer) sheet or plate on thetensile face of the concretememberOwing to the lightweightcorrosion-resistant and high strength properties of CFRPFRP bonding is gaining wider applications as an alternativeto steel plate bonding [1ndash6]

The structure strengthened by externally bonded CFRPsheet or plate experiences bond failure of the interfacebetween the FRP reinforcement and concrete which makesthe CFRP reinforcement unable to develop 100 of itscapacity The risk of bond failure increases with shorterreinforced length and larger amount of reinforcement Alsothis risk depends sensitively on the skill of the technician exe-cuting the strengthening work [2] Another drawback of theexternal bonding is the exposure of the reinforcement whichincreases the risk of damage caused by vehicle impact or fireand makes it difficult to achieve strengthening effect without

HindawiAdvances in Materials Science and EngineeringVolume 2017 Article ID 9180624 16 pageshttpsdoiorg10115520179180624

2 Advances in Materials Science and Engineering

sufficient protection Accordingly Near-Surface Mounted(NSM) strengthening was introduced to minimize suchproblems and improve the utilization of the reinforcingmaterial [2] NSM strengthening using CFRP reinforcementstarted since 1990s and designates the strengthening methodembedding the CFRP reinforcement and the filler inside theslot dug in the tensile zone of the concrete cover The NSMstrengthening is known to reduce the tasks executed on sitecompared to the external bonding and to decrease the effectsof early bond failure [3 4]

Similarly to external bonding NSM strengthening alsoexperiences bond failure This topic is being studied untilnow and necessitates deeper investigation since differentbond failuremodels were proposed according to the sectionalshape of the reinforcement or stochastic data There is a needis thus to provide a bond failure model for each shape ofCFRP reinforcement to predict the flexural behavior of themember strengthened by NSM reinforcement (NSMR) [5ndash8] Bond failure may theoretically occur in diverse mannerslike the interfacial failure between the CFRP reinforcementand filler the failure of the filler-concrete interface and soon Because the bond failure induced experimentally may bedifferent than that predicted theoretically the bond failuremodel should rely on actual failure patterns Accordingly theproposed bond failure model should be applicable regardlessof the sectional shape of the CFRP reinforcement based uponthe close analysis of the bond failure occurring actually in theflexure-strengthened behavior

This study intends to propose a bond failure modelconsidering the equivalent section through the analysis of thefailure patterns of specimens flexure-strengthened by NSMCFRP reinforcement and to validate this model with regardto the flexural behavior of NSM-strengthened specimenswith various CFRP reinforcement shapes Other studies havedeficiencies such as complicated analysis and various failureswith FRP shapes because they have used the data which is notflexural test but pull-out test This study offers new failuremodel with equivalent section which results from failuremode of flexural test

2 Major Failure Modes of Flexure-Strengthened Specimens by NSMR

The common failure modes experienced by the RC (rein-forced concrete) member strengthened by NSM CFRP arevarious like failure at the interface FRP-filler cohesive failureon filler failure at the interface filler-concrete and cohesivefailure on concrete [8] Since bond failure is an importantfactor affecting the performance of the member studieswere carried out to predict experimentally and analyticallythe bond failure characteristics Even if bond failure bypull-out test occurs in various ways like failure of CFRPreinforcement-filler interface inside the filler or of thefiller-concrete interface the bond failure of the flexure-strengthenedmember byNSMreinforcementmay lack diver-sity compared to that of the pull-out test [4] Accordinglythere is a need is to examine the major failure modes through

Concreteinterface

55

FRPrupture

35

Fillerinterface

10

Figure 1 Distribution of the types of failure mode of flexure-strengthened concrete beams (2004ndash2016 106 beams strengthenedwith NSM reinforcement) [5ndash8 10 23ndash40]

bending test in order to evaluate the flexural behavior of theNSM reinforcement

The investigated results until 2016 on the failure modesobserved in 106 concrete beams flexure-strengthened byNSM FRP reinforcement and shown in Figure 1 reveal thatfailure occurred mainly by rupture of the FRP reinforcementand failure of the filler-concrete interface (including theconcrete cover) This indicates that about 90 of the failuresexperienced by the flexure-strengthened members by NSMFRP occur through the rupture of FRP or the failure of theconcrete interface which represent the major failure modesdetermining the strengthened performance of the flexuralmembers

This means that the bond failure in NSM strengthen-ing depends on cohesive concrete around the slot becausestrength of cohesive filler is better than that of cohesiveconcrete generally Therefore the filler-CFRP reinforcementensemble behaves like a unique reinforcement Accordinglythis study assumes the filler-CFRP reinforcement ensemble asan equivalent section to propose the bond failure model Theequivalent section illustrated in Figure 2 is defined as the sec-tion including the sections of the filler and reinforcement andbehaving monolithically Under this assumption the stressdeveloped at the filler-reinforcement interface is transferredto the filler-concrete interface by means of the filler whichwill enable us to propose a bond failure model independentof the sectional shape of the reinforcement

3 Proposal of Bond Failure Model

The following assumptions are adopted to establish the bondfailure model applying the equivalent section derived aboveFirst bond failure occurs at the concrete-equivalent sectioninterface Second the shear force that occurred at the CFRP-filler interface is transferred to the filler-concrete interface

Advances in Materials Science and Engineering 3

Rod

P

A

A

Plate

Equivalent reinforcement

Section A-A

P

P P

Figure 2 Concept of equivalent section

CFRP

CFRP

τ

(a) Malek et al

(b) Hassan and Rizkalla

ConcreteFiller

CFRP

Af

hg

y yx

x

x

z

z

CFRP Concrete

wg

120591 f

dx

dx

ff

ff

dx

dx

120591

120591

ff +dff

dx

dx

ff +dff

dx

dx

ff

Filler

Figure 3 Shear stress developed at the interface [5 9]

Third the filler is considered only as a mean to transfer theshear force and the deformation of the filler is ignored (see(1))

Based upon these assumptions the equilibrium of theforces acting on the infinitesimal element 119889119909 of Figure 3(b)can be expressed as follows

119860119891119889119891119891 = 120591119888 (2ℎ119892 + 119908119892) 119889119909 (1)

where 120591119888 is shear stress developed at the epoxy-concreteinterface ℎ119892 is depth of slot 119908119892 is width of slot and 119860119891 iscross-sectional area of CFRP reinforcement

Rearranging (1) with respect to 120591119888 gives (2) The formu-lations derived by Malek et al [9] and Hassan and Rizkalla[5] from the infinitesimal element shown in Figure 3 areexpressed in (3) and (4) respectively

120591119888 = 119860119891(2ℎ119892 + 119908119892)

119889119891119891119889119909 (2)

120591119888 = 119889119891119891119889119909 119905119891 [9] (3)

120591119888 = 12119889119891119891119889119909 119905119891 [5] (4)

where 119905119891 is thickness of CFRP plate and 119891119891 is tensile stress ofCFRP plate

The shear stress 120591119888 proposed in this study for the infinites-imal element is expressed in terms of the dimensions of theslot and the cross-sectional area of the CFRP reinforcementsince the equivalent section is assumed The formulations

for 120591119888 provided in (3) and (4) are expressed in terms ofthe dimensions of the CFRP reinforcement Equation (5)reformulates 120591119888 of (2) proposed in this study for the 4-pointloading condition shown in Figure 4 The derivation of (5) isskipped here since it is similar to that reported by Hassan andRizkalla [5]

120591119888 = 119860119891(2ℎ119892 + 119908119892) (

1198991198751198970119910119890119868119890 120601119890minus120601119909 + 119899119875119910119890119868119890 )

1206012 = (2ℎ119892 + 119908119892)119866119886119860119891119905119886119864119891

119899 = 119864119891119864119888

(5)

where 119875 is applied load 1198970 is distance from support to endof reinforcement 119909 is distance from end of reinforcement 119910119890is distance from reinforcement to neutral axis 119868119890 is effectivemoment of inertia 119864119891 is elastic modulus of CFRP reinforce-ment 119864119888 is elastic modulus of concrete 119905119886 is thickness ofepoxy and 119866119886 is shear elastic modulus of epoxy

31 Failure Criteria It is primordial to establish failurecriteria to simulate bond failure using the analyticalmodel Inparticular the bond failure of the flexure-strengthened speci-mens by NSM reinforcement is similar to that of the externalbonding since it occurs at the concrete-filler interface and notin the filler nor at the reinforcement-filler interface [5 10]

A survey of the research on the bond characteristicsof External Bonding Reinforcement (EBR) reveals that the


ConcreteGroove

P

l0 x

a CL

Figure 4 Four-point loading

bond failure criterion at the end of the reinforcement is setas the concrete failure coefficient (flexure-tensile strength)which when exceeded means that failure has occurred [9 1112] Moreover since bond failure occurs along the concretesurface many researchers define the strength of the concretesurface as the interfacial bond failure criterion [13 14] Thebond failure occurring at the concrete interface is closelyrelated to the cracking strength of concrete and is assumedto occur when the shear stress developed at the concreteinterface exceeds the cracking strength of concrete [12]

Accordingly since cracking at the concrete interface hasdecisive effect on the propagation of the cracks and onthe bond failure this study adopts the concrete flexure-tensile strength (failure coefficient) proposed by numerousresearchers like Malek et al [9] and Tumialan et al [12] asfailure criterion The cracking stress of normal concrete iscalculated as the following failure coefficient (flexure-tensilestrength) [15] and it is assumed that bond failure occurs whenthe value of the cracking stress exceeds the failure criterion of

120591max = 119891119903 = 063radic119891119888119896 (MPa) = 75radic119891119888119896 (psi) (6)

32 Concrete Material Model The stress-strain curve ofconcrete is represented using the parabolic material modelshown in Figure 5(a) This model is assumed to exhibitnonlinear elastic behavior with a parabolic shape until theultimate compressive strain (120576119888119906) [16]

119891119888 = 119891119888119896 [21205761198881205761015840119888 minus (1205761198881205761015840119888)2] (7)

where 119891119888 is stress of concrete 119891119888119896 is compressive strength ofconcrete 120576119888 is strain of concrete 1205761015840119888 is strain when the concretestress 119891119888 reaches the compressive strength 119891119888119896 The value of 1205761015840119888is assumed to be 0002 in this study Note that the ultimatecompressive strain of concrete is assumed to 0003

33 Material Model of Steel Reinforcement As shown inFigure 5(b) the stress-strain curve of the steel reinforcementis assumed to be bilinear exhibiting linear elastic behaviorbefore the yield stress (119891119910) and perfect plastic behaviorbeyond the yield stress The elastic modulus in the plasticregion is set as 1198641015840119904 = 001119864119904 [17]

119891119904 = 119864119904120576119904 for 120576119904 le 120576119910119891119904 = 119891119910 + 1198641015840119904 (120576119904 minus 120576119910) for 120576119904 ge 120576119910 (8)

where 119891119904 is stress of steel rebar 120576119904 is strain of steel rebar 120576119910 isyield strain of steel rebar 119864119904 is elastic modulus of steel rebarand 1198641015840119904 is elastic modulus in plastic zone

34 Material Model of CFRP Reinforcement The stress-straincurve of CFRP reinforcement shown in Figure 5(c) assumeslinear elastic behavior until rupture In Figure 5(c) 119891119891119906designates the rupture stress of the CFRP reinforcement and120576119891119906 is the rupture strain of the CFRP reinforcement

119891119891 = 119864119891120576119891 (9)

where 119891119891 is stress of CFRP reinforcement 120576119891 is strain ofCFRP reinforcement and 119864119891 is elastic modulus of CFRPreinforcement

4 Computation of Deflection

The deflection of an ordinary RC member can be classifiedinto three zones delimited by the initiation of cracks and theyielding of the tensile rebar The effective moment of inertia(119868119890) is calculated according to this classification and appliedin the formula computing the deflection [18] In generalthe whole section is considered to be effective prior to theinitiation of cracks and the corresponding moment of inertiaof thewhole section (119868119892) is applied For the zone after crackingand before yielding of the tensile rebar the effective momentof inertia of Branson [19] is adopted and for the zone afteryielding of the tensile rebar the cracked section momentof inertia (119868119888119903) is used In this study the flexural rigidityis calculated by applying the moment-curvature curve fromearly loading and used to compute the deflection per loadingstage [19 20]The curvature (120601) at an arbitrary loading stage iscomputed as follows using the concrete strain (120576119888) and neutralaxis (119888)

120601 = 120576119888119888 (10)

Here the flexural rigidity (EI)119890 at any loading stage canbe expressed as follows from the moment-curvature (119872-120601)relation

(EI)119890 = 119872120601 (11)

Once the flexural rigidity is calculated the deflection (Δ) atmidspan can be computed as follows according to the loadingcondition that is 4-point loading here

Δ = Pa24 (EI)119890 (31198712 minus 41198862) (12)

5 Section Analysis of Beam Strengthenedby NSMR

Section analysis is conducted using the strain compatibilitycondition and equilibrium of the forces to predict the flexuralbehavior of the reinforced specimensThemoment-curvaturedistribution of ordinary RC specimens can be classified into


fc

fck

120576998400c120576cu 120576c

(a) Concrete

fs

fy

Es

120576y 120576s

E998400s

(b) Steel reinforcement

Ef

120576f

ff

ffu

120576fu

(c) CFRP reinforcement

Figure 5 Material models

three zones delimited by the initiation of cracks in concreteand the yielding of rebar Therefore the section analysisis performed considering three different cases that are asfollows the precracking stage when the acting moment 119872119886due to the load is smaller than the cracking moment thepreyielding stage after cracking and before yielding of therebar and the postyielding case [14 20] The calculation foreach case uses the equilibrium of the forces and momentsFigure 6 describes the strain and stress distributions in eachcase

(a) Precracking stage 0 le 119872119886 le 11987211988811990312119891119888119887119888 + 11986010158401199041198911015840119904 minus 12 (ℎ minus 119888) 119891119888119905119887 minus 119860 119904119891119904 minus 119860119891119891119891119890 = 0119872119886

= 13119891119888119905119887ℎ (ℎ minus 119888) + 119860 119904119891119904 (119889119904 minus 13119888)+ 119860119891119891119891119890 (119889119891 minus 13119888) minus 11986010158401199041198911015840119904 (13119888 minus 1198891015840119904)

(13)

(b) Preyielding stage119872119888119903 le 119872119886 le 11987211991012057211205731119891119888119896119887119888 + 11986010158401199041198911015840119904 minus 119860 119904119891119904 minus 119860119891119891119891119890 = 0119872119886

= 119860 119904119891119904 (119889119904 minus 121205731119888) + 119860119891119891119891119890 (119889119891 minus 121205731119888)minus 11986010158401199041198911015840119904 (121205731119888 minus 1198891015840119904)

(14)

(c) Postyielding stage119872119910 le 119872119886 le 11987211990612057211205731119891119888119896119887119888 + 11986010158401199041198911015840119904 minus 119860 119904 [119891119910 + 1198641015840119904 (120576119904 minus 120576119910)] minus 119860119891119891119891119890

= 0119872119886

= 119860 119904 [119891119910 + 1198641015840119904 (120576119904 minus 120576119910)] (119889119904 minus 121205731119888)+ 119860119891119891119891119890 (119889119891 minus 121205731119888) minus 11986010158401199041198911015840119904 (121205731119888 minus 1198891015840119904)

(15)

51 Determination of Bond Failure The common failuremodes in NSMRwith 1 line of reinforcement are known to bethe rupture of the CFRP reinforcement and the bond failureof the concrete-filler interface (bond model I) When NSMRis done with more than 1 line of reinforcement the failuremode varies according to the interval between the slots or thedistance to the corners If the space of slots is sufficiently wideor the distance from slot to the corners is larger than a definitevalue rupture of the CFRP reinforcement or bond failure ofthe concrete interfacemay occur similarly to the 1-lineNSMR(bond model II-1) However when it is not the case failuremay occur not only through the concrete interface but alsoby failure of concrete between the slots or spalling of theconcrete between the slots and the corners (bond model II-2) Accordingly this study simplifies the failure pattern asshown in Figure 7 to simulate analytically such failures InFigure 7 even if different from the bond failure of the cornerconcrete only the failure of two lines of reinforcement isconsidered to occur through the bond failure between theslots In such case this simplified pattern appears to remainapplicable if failure of the corners occurs after the bond failurebetween the slots During the section analysis since it isdifficult to model the amount of reinforcement in the 2 linesthe simplification assumes that the 2 lines of reinforcementand the filler behave as one unique reinforcement and fillerensemble as shown in Figure 7 Accordingly in case of NSMRwith 2 lines of reinforcement the width of the slot theamount of reinforcement and the width of the filler aredoubled to compute the shear stress developed at the end ofthe reinforcement

52 Calculation Procedure In order to predict the nonlinearbehavior of the specimens strengthened by NSMR usingCFRP the analysis is conducted in three different stagesFigure 8 presents the flowchart of the calculation procedureadopted in the analysis The calculation procedure deter-mines the load the position of the neutral axis the strain ineachmaterial and the deflection using the strain compatibilitycondition the constitutive equations of each material andthe equilibrium of the internal forces by increasing the strainaccording to the material model of the steel rebar Finalfailure is decided at bond failure using the bond failuremodelproposed in this study when the shear stress developed atthe end of the CFRP reinforcement exceeds the maximum


ℎ df

ds

c

b

120576998400s

120576feffe

NAConcrete

Steel

CFRP

d998400s

120576s

120576t

120576c

fs

ft

fc

f998400s

(a)

ℎ df

ds

c

b

120576998400s

120576fe ffe

NA

ConcreteCFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(b)

ℎ dfds

c

b

120576998400s

120576feffe

NA

Concrete

CFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(c)

Figure 6 Strain and stress distributions per analysis stage

shear strength at compressive failure of concrete when thecompressive strain at the top of concrete exceeds 0003 and atrupture of the reinforcement when the rupture strain of theCFRP reinforcement is exceeded

6 Validation Test of Bond FailureModel for NSMR

61 Test Variables When the filler and FRP reinforcementbehave as an equivalent reinforcement the equivalent rein-forcement can be modeled using the equivalent sectionduring the section analysis In such case it is acceptable toskip the consideration of the concrete-filler interface andfiller-FRP reinforcement interface Therefore it is necessaryto check the behavior of this equivalent reinforcement byexamining the failure mode of beams flexure-strengthenedby FRP reinforcements exhibiting various sectional shapesTo that goal a series of tests were conducted to validate thebehavior of the equivalent section using CFRP reinforce-ments presenting rectangular round and trapezoidal shapes

It is necessary to understand the arrangement details ofthe reinforcement in the reinforced section to mount it at thebottom of the beam To that goal two lines of reinforcementare arranged as shown in Figure 9 and the test variablesare set as the spacing between the two lines (119878 = 60mmand 2119878 = 120mm) and as the embedded depth (25mmand 15mm) to evaluate their influence on the section failuremode and strengthening effectThe same reinforced length of2700mm is applied in all the specimens Table 1 summarizesthe designation of the specimens with the test variablesFigure 9 depicts the cross-section of each of the specimensdesignated in Table 1 and corresponding reinforced areas(119860119891)62 Fabrication of Specimens Strengthened by NSMR A totalof 9 specimens were fabricated as shown in Figure 10 toverify the reliability of the bond failure model used in theanalysis The fabrication used ready-mixed concrete withdesign strength of 27MPa D10 SD40 tensile rebar werearranged with reinforcement ratio of 00041 and three D13


ConcreteFillerCFRP reinforcement

Failure mode Failure mode

Simplify

wg

ℎg ℎg

Af

ta 2wg2Af

2ta

Figure 7 Simplification of failure mode of 2-line reinforcement [bond model II-2]

Table 1 Designation of specimens and corresponding test variables

Specimen CFRP area(mm2) CFRP type Slot depth (mm) CFRP cross-sectional shape 120588119891

CONTROL mdash mdash mdash Nonstrengthened mdashR-TR-10 350 Rod 25 Trapezoidal 00003R-PL-15 210 Strip 15 Rectangular 00003R-PL-25 350 Strip 25 Rectangular 00005R-RD-9 636 Rod 25 Round 00007R-PL-25lowast2-S 700 Strip 25 Rectangular 00010R-PL-25lowast2-2S 700 Strip 25 Rectangular 00010R-RD-9lowast2-S 1272 Rod 25 Round 00014R-RD-9lowast2-2S 1272 Rod 25 Round 00014

compressive reinforcements were disposed D10 shear rein-forcements were disposed at spacing of 100mm to preventshear failure Strain gauges (T1 T2 B1 and B3) were bondedat midspan on the upper and lower steel reinforcements andat the quarters (B2 B4) on the lower rebar to measure thestrain of the reinforcements according to loading (Figure 10)

The reinforcement ratio of the CONTROL beam wasset to 00041 between the minimum ratio of 00032 andmaximum ratio of 0033 to induce ductile failure and notcompressive failure of concrete and to increase the differencein the reinforcing performanceThe equivalent reinforcementratio of FRP is calculated using (16) for the conversion of the

FRP reinforcement ratio into steel reinforcement ratio andthe corresponding values are listed in Table 1

120588119891 = 119860119891119887119889119891 times119864119891119864119904 (16)

where 119860119891 is cross-sectional area of CFRP reinforcement(mm2) 119887 is width of section (mm)119889119891 is effective depth (mm)119864119891 is elastic modulus of CFRP reinforcement (MPa) and 119864119904is elastic modulus of steel reinforcement (MPa)

Similarly to the CONTROL beam the flexure-strengthened specimens are reinforced by an amount of


Start

Data input(i) Dimensions of the beam(ii) The material properties

Force equilibriumΝΑ

Strain compatibility

No

No

Yes

Yes

No

No

Yes

End

Yes

Calculate Mcr Pcr

Assume 120576998400ct 120576s

Strain compatibility1205721 1205731 120576ct 120576cb 120576fe

|120576998400ct minus 120576ct| = 0

120576ct 120576cb 120576fe

OutputMa Pa 120601a (EI)a Δ a 120591c

Ma gt Mcr

Ma gt My

120576ct gt 120576cu120576fe gt 120576fu120591c gt 120591max

120576998400ct = 120576ct120576s = 120576s + Δ120576s

Figure 8 Flowchart of calculation procedure

25 25

20

251525

20

R-TR-10 R-PL-15 R-PL-25 R-RD-9

Af =

35 mm2

Af = Af = Af =Af =

Af =

21 mm235 mm2 70 mm2

S

SS

= 60mm S = 60mm636 mm21272 mm2

R-PL-25lowast2-SR-PL-25lowast2-2S

R-RD-9lowast2-SR-RD-9lowast2-2S

Figure 9 Cross-section of specimens strengthened by NSMR [unit mm]


30

20

300 300 300

200 3000 200

Top

T2Bottom

B3B2

T1

B1

B4

200

300

40

30

Stirrup

9001700

12100 = 1200 12100 = 1200 3ea-D13

3ea-D10

D10100

Figure 10 Dimensions and details of specimens [unit mm]

Making slot

(a)

Epoxy adhesive

Filling epoxy adhesive

(b)

FRP reinforcement(laminate rebar etc)

Insert FRP into the slot

(c)

Curing

(d)

Figure 11 Specimen strengthening process by NSMR

reinforcement smaller than the maximum reinforcementratio to induce ductile failure For the NSM strengthening aslot was grinded using a grinder at midspan on the bottomof the beam and the fine dust was removed by air-brushingThen primer was applied in the slot and cured for more than1 day The filler for NSMR adopted an epoxy matrix mixedwith hardener at a proportion of 2 1 and was applied in theslot The reinforcement was finally embedded with respectto the considered test variable and curing was conducted formore than 3 days prior to the test (Figure 11)

Table 2 summarizes the material properties The rectan-gular and trapezoidal CFRP reinforcements present smoothsurface without particular surface treatment whereas theround CFRP reinforcement is deformed by wrapping thesurface by fabrics

63 Loading and Measurement Methods Four-point loadingtest was conducted using UTM (Universal Testing Machine)with capacity of 980 kN (Figure 12) Loading was applied

Figure 12 Test setup

through displacement control at speed of 002mms untila displacement of 15mm and speed of 005mms beyondthat displacement until failure The data were measured atintervals of 1 s and recorded using a static data logger and acomputer


R-TR-10 R-PL-15CFRP rupture

R-PL-25Bond failure

R-RD-9Bond failureCFRP rupture

Bond failureR-PL-25lowast2-S

Bond failure Bond failure Bond failureR-PL-25lowast2-2S R-RD-9lowast2-S R-RD-9lowast2-2S

Figure 13 Failure patterns of specimens strengthened by NSMR

The load-displacement curves were drawn using the loadgiven by the actuator and the displacements measured byLVDTs disposed at the center and quarter points of thespecimens

7 Results of Validation Test

71 Failure Modes Figure 13 shows the failure pattern of thespecimens strengthened by NSMR Failure occurred throughrupture of CFRP or bond failure First the specimens thatexperienced CFRP rupture pertain to the specimens withrelatively smaller amount of reinforcement and the specimenswith trapezoidal reinforcement In this failure mode cracksperpendicular to the slots were observed without failureof epoxy reinforcement or concrete Second for the bondfailure cracks parallel to the slots were observed and failureof the epoxy and reinforcement occurred around the slotsentraining the concrete around the slots The occurrence ofbond failure at the epoxy-concrete interface was observednot only in this study but also in most of the experimentalstudies related to the specimens flexure-strengthened byNSMR The epoxy and the reinforcement are seen to behavemonolithically as a unique reinforcement similarly to thefailure mode (equivalent section behavior) suggested above

In case of narrow spaced NSMR the P-PL-25lowast2-S speci-men strengthened by strip reinforcement experienced bondfailure of the reinforcement and filler together with failurenot only of the concrete between the slots but also of thecorners Besides the P-RD-9lowast2-S specimen strengthenedby rod reinforcement experienced failure of the concretebetween the slots only

In case of widely spaced NSMR the P-PL-25lowast2-2S speci-men strengthened by strip reinforcement experienced bondfailure of the reinforcement and filler together with thequasi-disappearance of the corners On the other hand theP-RD-9lowast2-2S specimen strengthened by rod reinforcementexperienced partial failure of the concrete corners due to theshock provoked by the bond failure of the reinforcement andfiller

In case of identical spacing the different failure patternsobserved according to the reinforcement can be attributedto the effect of the amount of reinforcement and moment ofinertia of the cross-sectional shape

72 Analysis of Strengthening Effect Table 3 summarizesthe experimental results for the specimens strengthened byNSMRThemoment load and deflection are represented foreach instance of early cracking rebar yielding andmaximumload 119875119875con the load ratio of strengthened specimen tothe nonstrengthened specimen (CONTROL) indicates thestrengthening effect The efficiency of CFRP is expressed interms of the ratio of the maximum strain measured in theCFRP reinforcement of the specimen to the strain at rupture(120576max120576119906) as a matter of fact a ratio closer to 100means thatthe reinforcement develops its best performance In strength-ening effect analysis since the load ratio does not giveinformation on the cross-sectional area and physical prop-erties of the CFRP reinforcement this indicator is valid onlywhen the same reinforcement and strengthening method areused and not good when they are different Accordinglythis study adopts the dimensionless strengthening effect peraxial rigidity obtained by dividing the maximum load by thestiffness of the reinforcement to compare the strengthening


Table 2 Material properties

Material PropertiesConcrete1 Compressive strength (MPa) 313

Tension steel reinforcement (D10)1Yield strength (MPa) 436Tensile strength (MPa) 562

Diameter (mm) 953Area (mm2) 7133

Compression steel reinforcement (D13)1Yield strength (MPa) 481Tensile strength (MPa) 608


CFRP strip (PL smooth surface)1Thickness (mm) 14

Tensile strength (MPa) 24825Elastic modulus (GPa) 167Ultimate strain () 148

CFRP rod (TR smooth surface)1Design thickness (mm) 10Tensile strength (MPa) 1500Elastic modulus (GPa) 100Ultimate strain () 15

CFRP rod (RD deformed surface)2Diameter (mm) 9


1 from supplier 2 from tests performed by authors according to [22]

effect brought by CFRP reinforcements exhibiting differentsections and physical properties Since the strengtheningeffect per axial rigidity (119875119906EA times 103) considers not onlythe efficiency of FRP but also the physical properties of thereinforcement this indicator becomes effective when analyz-ing the strengthening effect according to the strengtheningmethod and sectional details If the value of this indicator ishigh it means that the strengthening effect is good

The experimental results show that the yield load andmaximum load increase with larger cross-sectional area ofthe reinforcement However specimens R-PL-25 and R-TR-10 present identical reinforced area but different flexuralbehaviors This can be explained by the fact that thesetwo specimens have different stiffness of the reinforcementsTherefore it appears that the comparison of the strengtheningeffect should consider not only the reinforced area but also theeffect of the reinforcement stiffness Accordingly the obser-vation of the strengthening effect per axial rigidity revealsthat specimens R-TR-10 and R-PL-15 experiencing CFRPrupture have better strengthening effect than specimens R-PL-25 and R-RD-9 featured by bond failure In case of NSMRusing reinforcements with identical shape the strengtheningeffect per axial rigidity tends to reduce with larger amountof reinforcement The reduction of the strengthening effectper axial rigidity even if the reinforced area increases asmuch as the increase of the amount of reinforcement can beattributed to the fact that the reinforcement could not develop100 of its performance due to bond failure Such tendencyis more apparent in the specimens strengthened by 2 linesof reinforcement and seems to be caused by the premature

occurrence of bond failure following the overlapping of thefailed surfaces

The comparison of the strengthening effects brought by1-line and 2-line reinforcement shows that the strengtheningeffects of specimens R-PL-25lowast2-S and R-PL-25lowast2-2S reachrespectively 69 and 75 which is lower than the 83of specimen R-PL-25 with 1-line reinforcement Moreoverspecimen R-PL-25lowast2-S with smaller spacing than specimenR-PL-25lowast2-2S is more vulnerable to failure Specimen R-RD-9lowast2-S with round reinforcement and narrow spacing showsreduced strengthening effect compared to the specimenswith1-line reinforcement and indicates that the failure of the slotspacing affects the bond failure The strengthening effectof specimen R-RD-9lowast2-2S with large spacing reaches 91which is higher than the specimens with 1-line reinforcementand indicates that this specimen is less influenced by thespacing Failure modes are affected by the position of slotswhen the distance between slots or the distance from slot tocorner is less than 40mm [21] R-PL-25lowast2-S2S specimenshave 40mm space between slots and corner and thereforeone slotrsquos failure affects the other slotsrsquo failure and cornersThe comparison of strengthening effects per axial rigidityshows that R-PL-25lowast2-S specimen is larger than R-RD-9lowast2-Sspecimen because the distance between slots of R-PL-25lowast2-Sspecimen is wider than that of R-RD-9lowast2-S specimen

73 Comparison of Experimental and Analytical ResultsFigure 14 plots concurrently the load-displacement curvemeasured at midspan and the analytical values derived fromthe analytic model of this study together with the failure


Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969


ExperimentalAnalytical

Bond failure

20 40 60 800Deflection (mm)

020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo

(f) R-RD-9lowast2-2S


Bond failure


020406080

100120140

Load

(kN

)

(g) R-PL-25lowast2-S(2S)

Figure 14 Comparison of experimental and analytical load-deflection curves


Table 4 Comparison of experimental and analytical results

Specimens R-TR-10 R-PL-15 R-PL-25 R-RD-9 R-PL-25lowast2-S R-PL-25lowast2-2S R-RD-9lowast2-S R-RD-9lowast2-2SMoment atyielding(kNsdotmm)

Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111

Maximummoment(kNsdotmm)

Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1

Deflection atyielding(mm)

Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125

Maximumdeflection(mm)

Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102

mode Table 4 compares the experimental and analyticalvalues of the moment and displacement at each stage Theanalytic model proposed in this study is seen to predictthe experimental maximum load within an error of 8for all strengthened beams and shows perfect concordancewith the final failure mode The analysis of the specimensstrengthened with 1-line reinforcement applied the bondfailure model I Among the specimens strengthened with2-line reinforcement for the cases where failure occurredbetween the slots (Figure 14(e)) and the cases experiencingfailure between the slots and additional failure of the concretecorners (Figure 14(g)) analysis was performed using thebond failure model II-2 simplifying the failure mode For thespecimens that experienced failure of the concrete corners(Figure 14(f)) the bond failure model II-1 was applied in theanalysis similarly to the 1-line failure mode

In view of the analytical results the bond failure modelproposed in this study appears to predict accurately thefailure mode of the 1-line NSMR as well as of the 2-lineNSMR specimens and to simulate appropriately the load-displacement behavior

8 Conclusions

This study examined the failure modes reported in previ-ous studies to propose a bond failure model consideringthe equivalent section Tests were performed on specimensstrengthened by NMSR with various shapes of CFRP rein-forcement The following conclusions can be drawn

The survey of the failure modes observed in former spec-imens flexure-strengthened by NSMR revealed that failureoccurred mainly through rupture of CFRP reinforcementfailure of filler-concrete interface and failure of filler-CFRPreinforcement interface with larger occurrence of the failureof filler-concrete interface than the failure of filler-CFRPreinforcement interface

Based upon this inventory of the major failure modes ofthe flexure-strengthened specimens the failed surface was

assumed as an equivalent section representing the filler-concrete interface and a bond failure model was derived so asto be applicable regardless of the sectional shape of the CFRPreinforcement

Tests were then conducted on flexure-strengthened spec-imens by NSMR to validate the proposed bond failure modelThe experimental results showed that the yield load andmaximum load increased with larger cross-sectional area ofthe CFRP reinforcement and that the strengthening effect peraxial rigidity reduced even if the bonded area enlarged asmuch as the increase of the amount of reinforcement Thiswas explained by the fact that the reinforcement could notdevelop 100 of its performance due to bond failure

In the case of the specimens strengthened with 2-linereinforcement premature bond failure occurred due to theoverlapping of the failed surface caused by the reinforcementspacing Accordingly further studies should be conducted onthe details of the reinforced section to compute theminimumspacing enabling the slots to behave independently during theNSMR design

Analytical analysis was finally carried out by settingfailure criteria for the bond failure model considering theequivalent section proposed in this study The results vali-dated the failure mode in which the CFRP reinforcement andfiller behaved monolithically and regardless of the sectionalshape of the CFRP reinforcementMoreover the failuremodeand flexure-strengthened behavior could be predicted withinan error of 8

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research was supported by a grant from ldquoA StrategicResearch Project Funded by the Korea Institute of CivilEngineering and Building Technologyrdquo and ldquoUpgrading


Technology of Prestressed NSM Reinforcement System withCFRP Tendonrdquo

References

[1] W T Jung Flexural behavior of reinforced concrete beamsstrengthened with NSM CFRP reinforcements considering theequivalent section [PhD thesis] Myongji University SeoulSouth Korea 2009

[2] R EI-Hacha ldquoEffectiveness of near surface mounted FRP rein-forcement for flexural strengthening of reinforced concretebeamsrdquo in Proceedings of the 4th International Conferenceon Advanced Composite Materials in Bridges and StructuresAlberta Canada July 2004

[3] KICT Development of Strengthening Methods for DeterioratedConcrete Bridges Report 2004

[4] L De Lorenzis and J G Teng ldquoNear-surface mounted FRPreinforcement an emerging technique for strengthening struc-turesrdquoComposites Part B Engineering vol 38 no 2 pp 119ndash1432007

[5] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003

[6] T Hassan and S H Rizkalla ldquoBond mechanism of near-surface-mounted fiber-reinforced polymer bars for flexuralstrengthening of concrete structuresrdquo ACI Structural Journalvol 101 no 6 pp 830ndash839 2004

[7] I Del Prete A Bilotta L Bisby and E Nigro ldquoBond testson NSM FRP strengthening using cementitious matrices forconcrete structuresrdquo in Proceedings of the 4 Contributo in Attidi Convegno FRPRCS-12 amp APFIS-2015 Joint Conference 2015

[8] M R F Coelho J M Sena-Cruz and L A C Neves ldquoAreview on the bond behavior of FRP NSM systems in concreterdquoConstruction and BuildingMaterials vol 93 pp 1157ndash1169 2015

[9] A M Malek H Saadatmanesh and M R Ehsani ldquoPredictionof failure load of RC beams strengthened with FRP plate dueto stress concentration at the plate endrdquo ACI Structural Journalvol 95 no 2 pp 142ndash152 1998

[10] I A Sharaky L Torres J Comas and C Barris ldquoFlexuralresponse of reinforced concrete (RC) beams strengthened withnear surface mounted (NSM) fibre reinforced polymer (FRP)barsrdquo Composite Structures vol 109 no 1 pp 8ndash22 2014

[11] S A Mirza M Hatzinikolas and J G MacGregor ldquoStatisticaldescriptions of strength of concreterdquoASCE J Struct Div vol 105no 6 pp 1021ndash1037 1979

[12] G Tumialan P Serra A Nanni and A Belarbi ldquoConcretecover delamination in RC beams strengthened with FRP sheetsSP-188rdquo in Proceedings of the 4th International Symposium onFRP for Reinforcement of Concrete Structures (FRPRCS4 rsquo99)pp 725ndash735 AmericanConcrete Institute BaltimoreMdUSANovember 1999

[13] U Neubauer and F S Rostasy ldquoDesign aspects of concretestructures strengthened with externally bonded CFRP platesrdquoin Proceedings of the 7th International Conference on StructuralFaults and Repairs vol 2 pp 109ndash118 ECS PublicationsEdinburgh UK 1997

[14] J S Park Flexural behavior of RC beam strengthened with pre-stressed CFRP plates considering bond characteristics [PhDthesis] Myongji University Seoul Republic of Korea 2007

[15] ACI Committee 318 Building Code Requirements for StructuralConcrete (318-05) and Commentary-(318R-05) American Con-crete Institute 2005

[16] M P Collins and D Mitchell Prestressed Concrete StructuresPrentice Hall 1991

[17] H E-D M Sallam A-A M Saba H H Shahin and H Abdel-Raouf ldquoPrevention of peeling failure in plated beamsrdquo Journal ofAdvanced Concrete Technology vol 2 no 3 pp 419ndash429 2004

[18] S B Lee M Y Park S Y Jang K S Kim and S S KimldquoInvestigation on the effective moment of inertia of reinforcedconcrete flexural members under service loadrdquo Journal of theKorea Concrete Institute vol 20 no 3 pp 393ndash404 2008

[19] D E Branson ldquoInstantaneous and time-dependent deflectionsof simple and continuous reinforced concrete beamsrdquo HPRReport 7 part 1 Alabama Highway Department Bureau ofPublic Roads 1963

[20] J Y Park H D Cho and S H Han ldquoPrediction of non-linearbehavior for RC beam flexural strengthened with CFRP platerdquoKSCE Journal of Civil Engineering vol 24 no 1 pp 9ndash16 2004

[21] J Y Kang Y H Park J S Park Y J You and W T JungldquoAnalytical evaluation of RC beams strengthened with nearsurface mounted CFRP laminatesrdquo in Proceedings of the 7thInternational Symposium on Fiber-Reinforced Polymer Rein-forcement for Reinforced Concrete Structures (FRPRCS rsquo05)November 2005

[22] ACI 4403R-04 ldquoGuide test methods for fiber-reinforced poly-mer(FRPs) for reinforcing and strengthening concrete struc-turesrdquo American Concrete Institute 2004

[23] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswith CFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005

[24] R El-Hacha and S H Rizkalla ldquoNear-surface-mounted fiber-reinforced polymer reinforcements for flexural strengthening ofconcrete structuresrdquo ACI Structural Journal vol 101 no 5 pp717ndash726 2004

[25] A Carolin B Taljsten and A Hejll ldquoConcrete beams exposedto live loading during carbon fiber reinforced polymer strength-eningrdquo Journal of Composites for Construction vol 9 no 2 pp178ndash186 2005

[26] J G Teng L De Lorenzis B Wang R Li T N Wong andL Lam ldquoDebonding failures of RC beams strengthened withnear surface mounted CFRP stripsrdquo Journal of Composites forConstruction vol 10 no 2 pp 92ndash105 2006

[27] J A O Barros S J E Dias and J L T Lima ldquoEfficacy of CFRP-based techniques for the flexural and shear strengthening ofconcrete beamsrdquo Cement and Concrete Composites vol 29 no3 pp 203ndash217 2007

[28] J R Yost S P Gross D W Dinehart and J J MildenbergldquoFlexural behavior of concrete beams strengthened with near-surface-mounted CFRP stripsrdquo ACI Structural Journal vol 104no 4 pp 430ndash437 2007

[29] H Nordin and B Taljsten ldquoConcrete beams strengthened withprestressed near surface mounted CFRPrdquo Journal of Compositesfor Construction vol 10 no 1 pp 60ndash68 2006

[30] H T Choi J S West and K A Soudki ldquoPartially bondednear-surface-mounted CFRP bars for strengthened concrete T-beamsrdquo Construction and Building Materials vol 25 no 5 pp2441ndash2449 2011

[31] A M Khalifa ldquoFlexural performance of RC beams strength-ened with near surface mounted CFRP stripsrdquo AlexandriaEngineering Journal vol 55 no 2 pp 1497ndash1505 2016


[32] S E El-Gamal A Al-Nuaimi A Al-Saidy and A Al-LawatildquoEfficiency of near surface mounted technique using fiber rein-forced polymers for the flexural strengthening of RC beamsrdquoConstruction and Building Materials vol 118 pp 52ndash62 2016

[33] S-Y Seo K-B Choi Y-S Kwon and K-S Lee ldquoFlexuralstrength of rc beam strengthened by partially de-bonded nearsurface-mounted FRP Striprdquo International Journal of ConcreteStructures and Materials vol 10 no 2 pp 149ndash161 2016

[34] S Foubert K Mahmoud and E El-Salakawy ldquoBehavior ofprestressed hollow-core slabs strengthened in flexurewith near-surface mounted carbon fiber-reinforced polymer reinforce-mentrdquo ASCE Composite Construction Journal vol 20 no 62016

[35] A Bilotta F Ceroni ENigro andMPecce ldquoEfficiency ofCFRPNSM strips and EBR plates for flexural strengthening of RCbeams and loading pattern influencerdquoComposite Structures vol124 pp 163ndash175 2015

[36] A A Khalil E E Etman and A H El-Masry ldquoBehavior ofreinforced concrete continuous beams strenghened with nearsurface mounted reinforcementrdquo in Proceedings of the Interna-tional Conference on Advances in Structural and GeotechnicalEngineering Hurghada Egypt April 2015

[37] H Zhang L He and G Li ldquoBond failure performancesbetween near-surface mounted FRP bars and concrete forflexural strengthening concrete structuresrdquo Engineering FailureAnalysis vol 56 pp 39ndash50 2015

[38] B Almassri A Kreit F A Mahmoud and R FrancoisldquoMechanical behaviour of corroded RC beams strengthened byNSM CFRP rodsrdquo Composites Part B Engineering vol 64 pp97ndash107 2014

[39] W Ibrahim W A Fattah A Kotb and M A Mjeed ldquoFlexuralbehavior of RC beams strengthened with CFRP stripsrdquo in Pro-ceedings of the 7th International Conference on FRP Compositesin Civil Engineering (CICE rsquo14) Canada August 2014

[40] A Laraba N Chikh H Mesbah N Djebbar and A BelouarldquoExperimental evaluation of damaged rectangular reinforcedconcrete beams repaired with near surface mounted carbonfibre reinforced polymerrdquo Materials Research Innovations vol18 no 6 pp S6ndashS13 2014

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


sufficient protection Accordingly Near-Surface Mounted(NSM) strengthening was introduced to minimize suchproblems and improve the utilization of the reinforcingmaterial [2] NSM strengthening using CFRP reinforcementstarted since 1990s and designates the strengthening methodembedding the CFRP reinforcement and the filler inside theslot dug in the tensile zone of the concrete cover The NSMstrengthening is known to reduce the tasks executed on sitecompared to the external bonding and to decrease the effectsof early bond failure [3 4]

Similarly to external bonding NSM strengthening alsoexperiences bond failure This topic is being studied untilnow and necessitates deeper investigation since differentbond failuremodels were proposed according to the sectionalshape of the reinforcement or stochastic data There is a needis thus to provide a bond failure model for each shape ofCFRP reinforcement to predict the flexural behavior of themember strengthened by NSM reinforcement (NSMR) [5ndash8] Bond failure may theoretically occur in diverse mannerslike the interfacial failure between the CFRP reinforcementand filler the failure of the filler-concrete interface and soon Because the bond failure induced experimentally may bedifferent than that predicted theoretically the bond failuremodel should rely on actual failure patterns Accordingly theproposed bond failure model should be applicable regardlessof the sectional shape of the CFRP reinforcement based uponthe close analysis of the bond failure occurring actually in theflexure-strengthened behavior

This study intends to propose a bond failure modelconsidering the equivalent section through the analysis of thefailure patterns of specimens flexure-strengthened by NSMCFRP reinforcement and to validate this model with regardto the flexural behavior of NSM-strengthened specimenswith various CFRP reinforcement shapes Other studies havedeficiencies such as complicated analysis and various failureswith FRP shapes because they have used the data which is notflexural test but pull-out test This study offers new failuremodel with equivalent section which results from failuremode of flexural test

2 Major Failure Modes of Flexure-Strengthened Specimens by NSMR

The common failure modes experienced by the RC (rein-forced concrete) member strengthened by NSM CFRP arevarious like failure at the interface FRP-filler cohesive failureon filler failure at the interface filler-concrete and cohesivefailure on concrete [8] Since bond failure is an importantfactor affecting the performance of the member studieswere carried out to predict experimentally and analyticallythe bond failure characteristics Even if bond failure bypull-out test occurs in various ways like failure of CFRPreinforcement-filler interface inside the filler or of thefiller-concrete interface the bond failure of the flexure-strengthenedmember byNSMreinforcementmay lack diver-sity compared to that of the pull-out test [4] Accordinglythere is a need is to examine the major failure modes through

Concreteinterface

55

FRPrupture

35

Fillerinterface

10

Figure 1 Distribution of the types of failure mode of flexure-strengthened concrete beams (2004ndash2016 106 beams strengthenedwith NSM reinforcement) [5ndash8 10 23ndash40]

bending test in order to evaluate the flexural behavior of theNSM reinforcement

The investigated results until 2016 on the failure modesobserved in 106 concrete beams flexure-strengthened byNSM FRP reinforcement and shown in Figure 1 reveal thatfailure occurred mainly by rupture of the FRP reinforcementand failure of the filler-concrete interface (including theconcrete cover) This indicates that about 90 of the failuresexperienced by the flexure-strengthened members by NSMFRP occur through the rupture of FRP or the failure of theconcrete interface which represent the major failure modesdetermining the strengthened performance of the flexuralmembers

This means that the bond failure in NSM strengthen-ing depends on cohesive concrete around the slot becausestrength of cohesive filler is better than that of cohesiveconcrete generally Therefore the filler-CFRP reinforcementensemble behaves like a unique reinforcement Accordinglythis study assumes the filler-CFRP reinforcement ensemble asan equivalent section to propose the bond failure model Theequivalent section illustrated in Figure 2 is defined as the sec-tion including the sections of the filler and reinforcement andbehaving monolithically Under this assumption the stressdeveloped at the filler-reinforcement interface is transferredto the filler-concrete interface by means of the filler whichwill enable us to propose a bond failure model independentof the sectional shape of the reinforcement

3 Proposal of Bond Failure Model

The following assumptions are adopted to establish the bondfailure model applying the equivalent section derived aboveFirst bond failure occurs at the concrete-equivalent sectioninterface Second the shear force that occurred at the CFRP-filler interface is transferred to the filler-concrete interface


Rod

P

A

A

Plate


Section A-A

P

P P


CFRP

CFRP

τ

(a) Malek et al


ConcreteFiller

CFRP

Af

hg

y yx

x

x

z

z

CFRP Concrete

wg

120591 f

dx

dx

ff

ff

dx

dx

120591

120591

ff +dff

dx

dx

ff +dff

dx

dx

ff

Filler




119860119891119889119891119891 = 120591119888 (2ℎ119892 + 119908119892) 119889119909 (1)



120591119888 = 119860119891(2ℎ119892 + 119908119892)

119889119891119891119889119909 (2)

120591119888 = 119889119891119891119889119909 119905119891 [9] (3)

120591119888 = 12119889119891119891119889119909 119905119891 [5] (4)




120591119888 = 119860119891(2ℎ119892 + 119908119892) (

1198991198751198970119910119890119868119890 120601119890minus120601119909 + 119899119875119910119890119868119890 )

1206012 = (2ℎ119892 + 119908119892)119866119886119860119891119905119886119864119891

119899 = 119864119891119864119888

(5)





ConcreteGroove

P

l0 x

a CL






119891119888 = 119891119888119896 [21205761198881205761015840119888 minus (1205761198881205761015840119888)2] (7)






119891119891 = 119864119891120576119891 (9)




120601 = 120576119888119888 (10)


(EI)119890 = 119872120601 (11)


Δ = Pa24 (EI)119890 (31198712 minus 41198862) (12)




fc

fck

120576998400c120576cu 120576c

(a) Concrete

fs

fy

Es

120576y 120576s

E998400s


Ef

120576f

ff

ffu

120576fu






(13)



(14)


= 0119872119886


(15)




ℎ df

ds

c

b

120576998400s

120576feffe

NAConcrete

Steel

CFRP

d998400s

120576s

120576t

120576c

fs

ft

fc

f998400s

(a)

ℎ df

ds

c

b

120576998400s

120576fe ffe

NA

ConcreteCFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(b)

ℎ dfds

c

b

120576998400s

120576feffe

NA

Concrete

CFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(c)









Simplify

wg

ℎg ℎg

Af

ta 2wg2Af

2ta








120588119891 = 119860119891119887119889119891 times119864119891119864119904 (16)




Start




No

No

Yes

Yes

No

No

Yes

End

Yes

Calculate Mcr Pcr

Assume 120576998400ct 120576s


|120576998400ct minus 120576ct| = 0

120576ct 120576cb 120576fe


Ma gt Mcr

Ma gt My


120576998400ct = 120576ct120576s = 120576s + Δ120576s


25 25

20

251525

20


Af =

35 mm2

Af = Af = Af =Af =

Af =

21 mm235 mm2 70 mm2

S

SS

= 60mm S = 60mm636 mm21272 mm2





30

20

300 300 300

200 3000 200

Top

T2Bottom

B3B2

T1

B1

B4

200

300

40

30

Stirrup

9001700

12100 = 1200 12100 = 1200 3ea-D13

3ea-D10

D10100


Making slot

(a)

Epoxy adhesive


(b)



(c)

Curing

(d)









R-PL-25Bond failure































Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Rod

P

A

A

Plate


Section A-A

P

P P


CFRP

CFRP

τ

(a) Malek et al


ConcreteFiller

CFRP

Af

hg

y yx

x

x

z

z

CFRP Concrete

wg

120591 f

dx

dx

ff

ff

dx

dx

120591

120591

ff +dff

dx

dx

ff +dff

dx

dx

ff

Filler




119860119891119889119891119891 = 120591119888 (2ℎ119892 + 119908119892) 119889119909 (1)



120591119888 = 119860119891(2ℎ119892 + 119908119892)

119889119891119891119889119909 (2)

120591119888 = 119889119891119891119889119909 119905119891 [9] (3)

120591119888 = 12119889119891119891119889119909 119905119891 [5] (4)




120591119888 = 119860119891(2ℎ119892 + 119908119892) (

1198991198751198970119910119890119868119890 120601119890minus120601119909 + 119899119875119910119890119868119890 )

1206012 = (2ℎ119892 + 119908119892)119866119886119860119891119905119886119864119891

119899 = 119864119891119864119888

(5)





ConcreteGroove

P

l0 x

a CL






119891119888 = 119891119888119896 [21205761198881205761015840119888 minus (1205761198881205761015840119888)2] (7)






119891119891 = 119864119891120576119891 (9)




120601 = 120576119888119888 (10)


(EI)119890 = 119872120601 (11)


Δ = Pa24 (EI)119890 (31198712 minus 41198862) (12)




fc

fck

120576998400c120576cu 120576c

(a) Concrete

fs

fy

Es

120576y 120576s

E998400s


Ef

120576f

ff

ffu

120576fu






(13)



(14)


= 0119872119886


(15)




ℎ df

ds

c

b

120576998400s

120576feffe

NAConcrete

Steel

CFRP

d998400s

120576s

120576t

120576c

fs

ft

fc

f998400s

(a)

ℎ df

ds

c

b

120576998400s

120576fe ffe

NA

ConcreteCFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(b)

ℎ dfds

c

b

120576998400s

120576feffe

NA

Concrete

CFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(c)









Simplify

wg

ℎg ℎg

Af

ta 2wg2Af

2ta








120588119891 = 119860119891119887119889119891 times119864119891119864119904 (16)




Start




No

No

Yes

Yes

No

No

Yes

End

Yes

Calculate Mcr Pcr

Assume 120576998400ct 120576s


|120576998400ct minus 120576ct| = 0

120576ct 120576cb 120576fe


Ma gt Mcr

Ma gt My


120576998400ct = 120576ct120576s = 120576s + Δ120576s


25 25

20

251525

20


Af =

35 mm2

Af = Af = Af =Af =

Af =

21 mm235 mm2 70 mm2

S

SS

= 60mm S = 60mm636 mm21272 mm2





30

20

300 300 300

200 3000 200

Top

T2Bottom

B3B2

T1

B1

B4

200

300

40

30

Stirrup

9001700

12100 = 1200 12100 = 1200 3ea-D13

3ea-D10

D10100


Making slot

(a)

Epoxy adhesive


(b)



(c)

Curing

(d)









R-PL-25Bond failure































Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




ConcreteGroove

P

l0 x

a CL






119891119888 = 119891119888119896 [21205761198881205761015840119888 minus (1205761198881205761015840119888)2] (7)






119891119891 = 119864119891120576119891 (9)




120601 = 120576119888119888 (10)


(EI)119890 = 119872120601 (11)


Δ = Pa24 (EI)119890 (31198712 minus 41198862) (12)




fc

fck

120576998400c120576cu 120576c

(a) Concrete

fs

fy

Es

120576y 120576s

E998400s


Ef

120576f

ff

ffu

120576fu






(13)



(14)


= 0119872119886


(15)




ℎ df

ds

c

b

120576998400s

120576feffe

NAConcrete

Steel

CFRP

d998400s

120576s

120576t

120576c

fs

ft

fc

f998400s

(a)

ℎ df

ds

c

b

120576998400s

120576fe ffe

NA

ConcreteCFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(b)

ℎ dfds

c

b

120576998400s

120576feffe

NA

Concrete

CFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(c)









Simplify

wg

ℎg ℎg

Af

ta 2wg2Af

2ta








120588119891 = 119860119891119887119889119891 times119864119891119864119904 (16)




Start




No

No

Yes

Yes

No

No

Yes

End

Yes

Calculate Mcr Pcr

Assume 120576998400ct 120576s


|120576998400ct minus 120576ct| = 0

120576ct 120576cb 120576fe


Ma gt Mcr

Ma gt My


120576998400ct = 120576ct120576s = 120576s + Δ120576s


25 25

20

251525

20


Af =

35 mm2

Af = Af = Af =Af =

Af =

21 mm235 mm2 70 mm2

S

SS

= 60mm S = 60mm636 mm21272 mm2





30

20

300 300 300

200 3000 200

Top

T2Bottom

B3B2

T1

B1

B4

200

300

40

30

Stirrup

9001700

12100 = 1200 12100 = 1200 3ea-D13

3ea-D10

D10100


Making slot

(a)

Epoxy adhesive


(b)



(c)

Curing

(d)









R-PL-25Bond failure































Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




fc

fck

120576998400c120576cu 120576c

(a) Concrete

fs

fy

Es

120576y 120576s

E998400s


Ef

120576f

ff

ffu

120576fu






(13)



(14)


= 0119872119886


(15)




ℎ df

ds

c

b

120576998400s

120576feffe

NAConcrete

Steel

CFRP

d998400s

120576s

120576t

120576c

fs

ft

fc

f998400s

(a)

ℎ df

ds

c

b

120576998400s

120576fe ffe

NA

ConcreteCFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(b)

ℎ dfds

c

b

120576998400s

120576feffe

NA

Concrete

CFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(c)









Simplify

wg

ℎg ℎg

Af

ta 2wg2Af

2ta








120588119891 = 119860119891119887119889119891 times119864119891119864119904 (16)




Start




No

No

Yes

Yes

No

No

Yes

End

Yes

Calculate Mcr Pcr

Assume 120576998400ct 120576s


|120576998400ct minus 120576ct| = 0

120576ct 120576cb 120576fe


Ma gt Mcr

Ma gt My


120576998400ct = 120576ct120576s = 120576s + Δ120576s


25 25

20

251525

20


Af =

35 mm2

Af = Af = Af =Af =

Af =

21 mm235 mm2 70 mm2

S

SS

= 60mm S = 60mm636 mm21272 mm2





30

20

300 300 300

200 3000 200

Top

T2Bottom

B3B2

T1

B1

B4

200

300

40

30

Stirrup

9001700

12100 = 1200 12100 = 1200 3ea-D13

3ea-D10

D10100


Making slot

(a)

Epoxy adhesive


(b)



(c)

Curing

(d)









R-PL-25Bond failure































Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




ℎ df

ds

c

b

120576998400s

120576feffe

NAConcrete

Steel

CFRP

d998400s

120576s

120576t

120576c

fs

ft

fc

f998400s

(a)

ℎ df

ds

c

b

120576998400s

120576fe ffe

NA

ConcreteCFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(b)

ℎ dfds

c

b

120576998400s

120576feffe

NA

Concrete

CFRP

Steel

d998400s

120576s

120576c

fs

fc

f998400s

(c)









Simplify

wg

ℎg ℎg

Af

ta 2wg2Af

2ta








120588119891 = 119860119891119887119889119891 times119864119891119864119904 (16)




Start




No

No

Yes

Yes

No

No

Yes

End

Yes

Calculate Mcr Pcr

Assume 120576998400ct 120576s


|120576998400ct minus 120576ct| = 0

120576ct 120576cb 120576fe


Ma gt Mcr

Ma gt My


120576998400ct = 120576ct120576s = 120576s + Δ120576s


25 25

20

251525

20


Af =

35 mm2

Af = Af = Af =Af =

Af =

21 mm235 mm2 70 mm2

S

SS

= 60mm S = 60mm636 mm21272 mm2





30

20

300 300 300

200 3000 200

Top

T2Bottom

B3B2

T1

B1

B4

200

300

40

30

Stirrup

9001700

12100 = 1200 12100 = 1200 3ea-D13

3ea-D10

D10100


Making slot

(a)

Epoxy adhesive


(b)



(c)

Curing

(d)









R-PL-25Bond failure































Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






Simplify

wg

ℎg ℎg

Af

ta 2wg2Af

2ta








120588119891 = 119860119891119887119889119891 times119864119891119864119904 (16)




Start




No

No

Yes

Yes

No

No

Yes

End

Yes

Calculate Mcr Pcr

Assume 120576998400ct 120576s


|120576998400ct minus 120576ct| = 0

120576ct 120576cb 120576fe


Ma gt Mcr

Ma gt My


120576998400ct = 120576ct120576s = 120576s + Δ120576s


25 25

20

251525

20


Af =

35 mm2

Af = Af = Af =Af =

Af =

21 mm235 mm2 70 mm2

S

SS

= 60mm S = 60mm636 mm21272 mm2





30

20

300 300 300

200 3000 200

Top

T2Bottom

B3B2

T1

B1

B4

200

300

40

30

Stirrup

9001700

12100 = 1200 12100 = 1200 3ea-D13

3ea-D10

D10100


Making slot

(a)

Epoxy adhesive


(b)



(c)

Curing

(d)









R-PL-25Bond failure































Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Start




No

No

Yes

Yes

No

No

Yes

End

Yes

Calculate Mcr Pcr

Assume 120576998400ct 120576s


|120576998400ct minus 120576ct| = 0

120576ct 120576cb 120576fe


Ma gt Mcr

Ma gt My


120576998400ct = 120576ct120576s = 120576s + Δ120576s


25 25

20

251525

20


Af =

35 mm2

Af = Af = Af =Af =

Af =

21 mm235 mm2 70 mm2

S

SS

= 60mm S = 60mm636 mm21272 mm2





30

20

300 300 300

200 3000 200

Top

T2Bottom

B3B2

T1

B1

B4

200

300

40

30

Stirrup

9001700

12100 = 1200 12100 = 1200 3ea-D13

3ea-D10

D10100


Making slot

(a)

Epoxy adhesive


(b)



(c)

Curing

(d)









R-PL-25Bond failure































Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




30

20

300 300 300

200 3000 200

Top

T2Bottom

B3B2

T1

B1

B4

200

300

40

30

Stirrup

9001700

12100 = 1200 12100 = 1200 3ea-D13

3ea-D10

D10100


Making slot

(a)

Epoxy adhesive


(b)



(c)

Curing

(d)









R-PL-25Bond failure































Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





R-PL-25Bond failure































Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






















Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Table3Ex

perim

entalresults

Specim

ens

CONTR

OL

R-TR

-10

R-PL

-15

R-PL

-25

R-RD

-9R-PL

-25lowast2-S

R-PL

-25lowast2-2S

R-RD

-9lowast2-S

R-RD

-9lowast2-2S

Cracking

119872 119888119903(Nsdotmm

lowast103)

8930

8705

8122

8663

8652

9466

11240

10164

10883

119875 119888119903 (kN)

1598

1658

1547

165

1648

1803

2141

1936

2073

Δ 119888119903 (mm)

138

174

172

198

166

188

284

166

184

119875 119888119903119875 119888119903c

on1

104

097

103

103

113

134

121

13

Yielding

119872 119910(Nsdotmm

lowast103)

24512

28859

30172

32387

32855

37779

37007

40724

40562

119875 119910 (kN)

4669

5497

5747

6169

6258

7196

7049

7757

7726

Δ 119910 (mm)

1248

1336

155

1606

1536

1646

1416

1522

154

119875 119910119875119910co

n1

118

123

132

134

154

151

166

165

Maxim

um

119872 119906(Nsdotmm

lowast103)

29500

41533

41160

45245

48631

57572

56191

59036

78556

119875 119906 (kN)

5619

7911

7840

8618

9263

1096

61070

3112

45

1496

3

Δ 119906 (mm)

7168

5868

5894

5398

4388

4692

4444

395

5419

119875 119906119875119906co

n1

141

1415

316

519

519

2266

Ductility

Δ 119906Δ 119910

574

439

38

336

286

285

314

26

352

CFRP

efficiency

120576 max120576 119906

()

mdash100

100

8384

6975

7091

Streng

theffectp

eraxialrigidity

119875 119906EAtimes103

mdash226

2232

1472

1293

6914

728

969



Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Bond failure


020406080

100120140

Load

(kN

)

(a) R-RD-9


Bond failure


020406080

100120140

Load

(kN

)

(b) R-PL-25


FRP rupture

020406080

100120140

Load

(kN

)


(c) R-PL-15


FRP rupture

020406080

100120140

Load

(kN

)


(d) R-TR-10


Bond failure

020406080

100120140

Load

(kN

)


B

(e) R-RD-9lowast2-S


Bond failure

020406080

100120140160

Load

(kN

)


Bo



Bond failure


020406080

100120140

Load

(kN

)






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






Test 28859 30172 32855 32387 37779 37007 40724 40562Analysis 27698 27783 30821 29667 34198 34198 36480 36480

Analysistest 104 109 107 109 110 108 112 111


Test 41533 41160 48631 45245 57572 56191 59036 78556Analysis 40613 41054 49652 48584 54259 54259 59089 78372

Analysistest 102 1 098 093 106 104 1 1


Test 1336 155 1536 1606 1646 1416 1522 154Analysis 1196 1196 121 1204 1224 1224 1235 1235

Analysistest 112 13 127 133 134 116 123 125


Test 5868 5894 4388 5398 4692 4444 395 5419Analysis 5783 5785 4478 5256 3516 3516 3353 5339

Analysistest 101 102 098 103 133 126 118 102



8 Conclusions








Competing Interests


Acknowledgments




References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



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