Research Article Prediction of Flexural Capacity of RC ...

Research ArticlePrediction of Flexural Capacity of RC Beams Strengthened inFlexure with FRP Fabric and Cementitious Matrix

Kyusan Jung Kinam Hong Sanghoon Han Jaekyu Park and Jaehyun Kim

Department of Civil Engineering Chungbuk National University 1 Chungdae-ro Seowon-gu CheongjuChungbuk 362-763 Republic of Korea

Correspondence should be addressed to Kinam Hong hongcbnuackr

Received 1 August 2015 Revised 28 September 2015 Accepted 28 September 2015

Academic Editor Osman Gencel

Copyright copy 2015 Kyusan 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

This paper presents both experimental and analytical research results for predicting the flexural capacity of reinforced concrete(RC) beams strengthened in flexure with fabric reinforced cementitious matrix (FRCM) In order to assess the efficiency of theFRCM-strengthening method six beams were strengthened in flexure with FRCM composite having different amounts and layersof FRP fabric and were tested under four-point loading From test results it was confirmed that the slippage between the FRPfabric and matrix occurs at a high strain level and all of the FRCM-strengthened beams failed by the debonding of the FRCMAdditionally a new bond strength model for FRCM considering the slippage between fabric and matrix was proposed using a testdatabase to predict the strengthening performance of the FRCM composite The prediction of the proposed bond strength modelagreed well with the debonding loads of the test database

1 Introduction

Fabric reinforced cementitious matrix (FRCM) compositeswere developed to strengthen deteriorated reinforced con-crete structures and have been employed during the lasttwo decades [1] Unlike externally bonded fiber reinforcedpolymer (FRP) systems epoxy resin is not used for theFRCM-strengthening method The FRP fabric used in theFRCM-strengthening method is attached by using a cemen-titious matrix an inorganic material instead of epoxy resin[2] The use of an inorganic material can solve variousproblems that result from the use of epoxy resin [3] Themajor problems associated with epoxy resin are its lowglass transition temperature difficulty of application at lowtemperatures inability to apply to humid surfaces and lackof vapor permeability [1] Additionally FRCM compositehas higher fire resistance than externally bonded FRP sheetsand laminates [4] However the mechanical properties ofa cementitious matrix such as bond strength are generallylower than those of epoxy resin Thus the FRP materials inthe FRCM-strengthening method are shaped like fabric ortextile to improve the bond strength of the FRP reinforcement[5]

Many experimental studies have been performed to verifythe efficiency of the FRCM-strengtheningmethod DrsquoAmbrisiand Focacci [3] investigated the flexural performance ofRC beams strengthened with FRCM composite using twodifferent FRP net materials carbon fiber net and polypara-phenylene benzobisoxazole (PBO) fiber net and shapes Itwas confirmed from their study that PBO-FRCM performsbetter than carbon-FRCMand the variation of the debondingstrain with the number of layers is more gradual than thatof FRP materials [3] Additionally they insisted that it isnecessary to identify more representative material parame-ters which can describe the mechanical behavior of differenttypes of matrices in relation to the adapted type of fibers[3] Ombres [6] investigated the flexural performance of RCbeams strengthened with PBO-FRCM composite and pre-dicted their flexural behavior by using various existing bondstrength models for externally bonded reinforced FRP Basedon his research results he suggested that when debondingfailures occur the predictions of the existing bond strengthmodel are not accurate and a more accurate and reliabledebonding model for FRCM-strengthened RC beams shouldbe developed [6] Loreto et al [7] evaluated the performanceof RC slab strengthened with PBO-FRCM composite by

Hindawi Publishing CorporationInternational Journal of Polymer ScienceVolume 2015 Article ID 868541 11 pageshttpdxdoiorg1011552015868541

2 International Journal of Polymer Science

Strain gages

FRCM composite materialsR (support) R (support)900mm 900mm 900mm

3000mm

2-D10mm

2-D10mm

300mm

170mm

P2 (load) P2 (load)

Figure 1 Test specimen layout

three-point bending test and performed an analytical study toverify the level of accuracy of the ultimate capacity predictionaccording to the ACI 549 [8] guide where the proposedequations are based on the conventional reinforced concretetheory Through the results of their study they reportedthat the ultimate capacity prediction according to the ACI549 [8] guide was satisfactory because the tensile propertiesused in the analysis did not depend on fiber rupture butare based on the performance of the FRCM tensile couponduring the crack formation zone [7] Babaeidarabad et al[1] tested FRCM-strengthened beams having 1-ply and 4-ply PBO fabric and predicted the efficiency of the FRCM-strengthening method through a section analysis followingmethodology in accordancewithACI 549 [8] andACI 318 [9]Their research results showed that the strain compatibility ofa beam with 1-ply fabric was no longer satisfied due to fabricslippage within the matrix after steel yielding They notedthat the slippage behavior can be captured in the analysis bythe tensile characteristic parameters obtained from FRCMcoupon testing [1]

Meanwhile several studies to identify the bond-slipbehavior between the fibermatrix and FRCMconcrete inter-face have been performed by a few researchers Ombres[4] carried out an experimental and theoretical study onthe bond-slip behavior between concrete and PBO-FRCMcomposite and proposed a nonlinear bond-slip model forFRCMusing the experimental data However the parametersof his model should be calibrated using more experimentaldata DrsquoAmbrisi et al [10] experimentally and analyticallyevaluated the bond stress between CFRP-FRCM materialsand masonry and reported that the debonding occurs at thefibersmatrix interface after a considerable fibersmatrix slipAlso DrsquoAmbrisi et al [11] performed an experimental studyon the bond-slip between PBO-FRCM and concrete andreported that the debonding strain in PBOfibers decreased inproportion to 1radic119899 with an increase in the number of layers119899

Although some studies on the bond-slip behavior offibermatrix and FRCMconcrete interface have been per-formed a bond strengthmodel for FRCMhas not been estab-lished yet Moreover the ACI 549 [8] guideline applicable forpredicting the strengthening efficiency of FRCM compositealso requires an additional FRCM coupon test to define thetensile characteristic parameters of the FRCM compositeThus this study aimed to perform the flexural tests including

Table 1 Mixture properties of concrete

WC () Sa () Unit weight (kgm3)W C S G Ad(a)

484 481 168 345 860 949 207(a)AE water-reducing admixture

Table 2 Mechanical properties of rebar used

Nominaldiameter(mm)

Modulus ofelasticity(MPa)

Yieldstrength(MPa)

Ultimatestrength(MPa)

Elongation()

953 20 times 105 480 590 171

the number of plies and the amount of FRP fabric as testvariables and to develop a bond strengthmodel to predict theflexural behavior of FRCM-strengthened beams without anadditional test

2 Experimental Program

21 Test Specimens The experimental program consisted ofseven beams of 3000mm and a cross section of 170 times

300mm Two deformed bars were placed on the tension andcompression faces respectively Shear reinforcements wereplaced in a center-to-center spacing of 150mm to preventshear failure in all specimens Steel reinforcement of D10with a nominal diameter of 953mm was used for tensioncompression and shear reinforcement The side and verticalconcrete cover was kept at 30mm for all beamsThe details ofthe test specimens are presented in Figure 1

22 Materials Ready-mix concrete was used to fabricatethe beams The mixture properties of the concrete used aretabulated in Table 1

Six standard concrete cylinders with dimensions ofΦ100mm times 200mmwere cast and tested according to ASTMC39C39M [12] The average compressive strength of theconcrete obtained from the compressive tests for the cylinderswas 280MPa at the age of 28 days Mechanical propertiesof rebar were determined by the direct tensile tests forthree coupons in accordance with ASTM A370 [13] in thelaboratory Material properties of the rebar used were takenfrom tests and are given in Table 2

International Journal of Polymer Science 3

(a) Cementitious matrix

CFRP

GFRP

(b) FRP fabric

Figure 2 Components of FRCM composite

Table 3 Mechanical properties of cementitious matrix

Elastic modulus(GPa)

Compression strength(MPa)

Cementitiousmatrix 40 45

The cementitious matrix and FRP fabric used for flexuralstrengthening of RC specimens are shown in Figures 2(a)and 2(b) respectively The cementitious matrix consisted ofmicrocement fine aggregate polypropylene staple fiber andadmixtures The compressive strength of the cementitiousmatrix was determined from a compression test of five cubesof 50mm size according to ASTM C109C109M [14] andmeasured as 45MPa at the age of 28 days Table 3 presents themechanical properties of the cementitious matrix obtainedfrom the compression test

As shown in Figure 2(b) the FRP fabric consisted ofCFRP and GFRP strips Black CFRP and white GFRP stripswere laid in the warp direction and weft direction respec-tively at spacings of 17mm and 33mm The FRP fabric wasdivided into Type A and Type B by the amount of CFRP fiberper strip The cross-sectional areas of a CFRP strip for TypesA and B were 18 and 27mm2 respectively Additionallythe nominal thicknesses of FRP fabric for Types A and Bwere 00107mmand 00162mm respectivelyThemechanicalproperties of the FRP fabric offered by manufacturers arepresented in Table 4

23 Test Program The test variables included the number ofplies and the amount of FRP fabric An unstrengthened spec-imen used to relatively assess the strengthening performanceof FRCM was labeled as Control Specimens strengthenedwith FRP fabric were labeled using a one-letter abbreviationand an Arabic number The first letter A or B representsType A or B of the FRP fabric respectively The followingArabic number 1 2 or 3 represents the application of 1-ply

Table 4 Mechanical properties of FRP fabric

TypeNominalthickness(mm)

Elasticmodulus(GPa)

Ultimatetensile strength

(MPa)

Ultimatetensile strain

()A 0107 240 4300 175B 0162 240 4300 175

Table 5 Test variables

Group Specimen ID Type of FRP fabric Number of pliesControl mdash mdash

AA1

Type A1

A2 2A3 3

BB1

Type B1

B2 2B3 3

2-ply or 3-ply FRP fabric on the bottom face of the specimenrespectively Table 5 illustrates the test variables

24 Strengthening Procedure The strengthening procedureof the FRCM composite was as follows (1) The first layerof cementitious matrix with a nominal thickness of 2mmwas applied on the bottom surface of the specimen (2) Theprecut FRP fabric was laid on the cementitious matrix (3)The second layer of cementitious matrix with a nominalthickness of 2mm was applied on the FRP fabric In the caseof strengthening with 2-ply and 3-ply FRP fabric the aboveprocedurewas repeated two and three times respectivelyThenominal thickness of FRCM with 1-ply FRP fabric was takenas approximately 5mm The bond length of FRP fabric was2600mm regardless of the number of FRP fabric layers Flex-ural tests were performed after 28 days of strengthening toallow the cementitious matrix to develop sufficient strength


Table 6 Summary of experimental results

Specimen ID Ultimate load (kN) Deflection at ultimateload (mm)

Percent increaseover Control () Failure mode

Control 445 110 mdash FlexureA1 586 180 1317 DebondingA2 627 155 1410 DebondingA3 836 220 1879 DebondingB1 655 229 1472 DebondingB2 737 156 1656 DebondingB3 978 216 2198 Debonding

Figure 3 Test setup

25 Test Setup All beams were tested using a simply sup-ported system with a net span of 2700mm The tests for allbeams were performed under four-point loading as shownin Figure 3

Load was applied at a stroke rate of 04mmmin by ahydraulic actuator with a maximum capacity of 2000 kNThe load was measured by a load cell The deflectionswere measured by Linear Variable Differential Transducers(LVDTs) at midspan As shown in Figure 1 the strains ofFRP fabric were measured by seven strain gauges attachedon CFRP strip at the spacing of 200mm The strains in theconcrete and steel rebars at the midspan of each beam weremeasured by strain gauges The strain in the concrete wasmeasured by a strain gauge placed on the top of each beambefore testing For steel rebar strain was measured by a straingauge mounted in each tension rebar before concrete castingThe load and strains were recorded by using a data loggerDuring the test the propagation of crack and damage ofFRCM composite were visually inspected and recorded onthe surface of the beam

3 Test Results and Discussion

31 Summary of Test Results Thetest results for ultimate loaddeflection and failure mode of each specimen are presentedin Table 6The flexural strengths of beams strengthened withFRCM composite increased from 1317 to 2198 relativeto the Control specimen The ultimate load of the FRCM-strengthened beams increased with a higher amount of FRP

(a) Control

(b) A3

(c) B3

Figure 4 Failure modes of specimens

fabric and all of them failed by the debonding of the FRCMcomposite

32 Failure Mode Figure 4 shows the failure modes ofrepresentative specimens in each group The initial crack ofthe Control specimen occurred at the midspan under a loadof 218 kN New vertical cracks occurred with the increase inapplied load and the initial cracks were progressed towardthe compressive zone With the increase of applied loadthe vertical cracks extended about 90 of the height of thecross section Finally the Control specimen failed due to theyielding of tensile reinforcement followed by crushing of theconcrete compressive zone (see Figure 4(a))

In the case of specimen A3 strengthened with 3-ply FRPfabric an initial crack occurred at the load of 259 kN andthen the crack pattern produced by the increase of appliedload was similar to that of the Control The average spacingof vertical flexural cracks was approximately 100mm andmuch closer than that of Control The interfacial debondingof the FRCM composite started at the vertical crack undera loading point and gradually progressed toward a rightsupport (see Figure 4(b)) However failure began with theconcrete cover ripping-off before complete debonding ofthe FRCM composite happened Eventually it failed byFRCM composite debonding followed by the crushing of theconcrete compressive zone between two loading points

The initial crack load of specimen B3 with the FRPfabric of Type B occurred at the load of 309 kN Until theapplied load attained approximately 95 kN no debonding of


0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90100

Load

(kN

)

Displacement (mm)

ControlA1

A2A3

(a) Group A

0

10

20

30

40

50

60

70

80

90

100

Load

(kN

)

ControlB1

B2B3

0 5 10 15 20 25 30Displacement (mm)

(b) Group B

Figure 5 Load-displacement curves of specimens

the FRCM composite was observed in the specimen How-ever once the load reached the maximum load of 978 kNthe debonding of FRCM composite suddenly occurred at theright side of the specimen (see Figure 4(c))The crack patternof specimen B3 was similar to that of specimen A3 but thedebonding process of the FRCM composite was different

33 Comparison of Load-Deflection Curves Figures 5(a) and5(b) show the load-deflection curves of specimens in GroupsA and B respectively

The initial flexural stiffness of specimens in Groups Aand B was higher than that of the Control specimen but wasnot proportional to the amount of FRP fabric This is due tothe fact that the strengthening effect of an externally bondedreinforced system is exhibited after the occurrence of aninitial crack Flexural stiffness after the yielding of tensile steelrepresents the effect of the amount of FRP fabric as shownin Figures 5(a) and 5(b) Additionally the maximum load ofthe specimens significantly increased with a greater numberof FRP fabric layers The maximum loads of specimens A1A2 and A3 in Group A were 586 kN 627 kN and 836 kNrespectively The maximum loads of specimens B1 B2 andB3 were 655 kN 737 kN and 978 kN respectively Howeverthe maximum loads were not proportional to the number ofFRP fabric layers in both Group A andGroup B On the otherhand the strengthening performances of B1 B2 and B3 withType B of FRP fabric were higher than those of A1 A2 andA3with Type A respectivelyThis resulted from the difference inthe amount of FRP fiber As mentioned before the nominalthicknesses of the FRP fabric layer for Types A and B were00107mm and 00162mm respectively Therefore it can beconcluded that Type B is more effective than Type A for theFRCM-strengthening method

34 Relationship of Load-FRP Fabric Strain Figures 6(a) and6(b) show comparisons of load-FRP fabric strain curvesmeasured at the midspan of specimens in Groups A and BThe load-strain curves of all specimens in Groups A andB exhibited a trend in which the tensile strain of the FRPfabric rapidly increased after the occurrence of an initialcrack In particular the FRP fabric strain of specimen A1increased much rapidly compared to those of other speci-mens It is because the contribution of cementitious matrixto the tensile strength is transferred to FRP fabric after theformation of initial crack at midspan so that the FRP fabricof specimen A1 with the lowest fabric amount contributesmuch higher tensile strength than other specimens Thestrains of specimens in Groups A and B ultimately reachedapproximately 8000120583120576 and 12000120583120576 respectively Althoughthe maximum strains of specimens in Group B were higherthan those of specimens in GroupA these were less than 70of the strain corresponding to FRP fabric rupture 17500120583120576Before initial crack occurrence the relationship of load-FRCM fabric strain was linear However the relationshipafter initial crack became nonlinear resulting from the bond-slip behavior between the FRCM fabric and cementitiousmatrix

35 Strain Distribution at a Midspan Cross Section Figures7(a) and 7(b) show the strain distribution along the depthat a midspan cross section of representative specimens ofGroups A and B The strains of concrete tensile rebar andFRP fabric were checked at representative load stages It canbe observed from Figure 7 that the neutral axis rises andthe slippage between FRP fabric and the cementitious matrixincreases with the higher load Consequently it should benoted that the strain distribution of a section at low strain canbe assumed to be linear but it cannot be regarded as linear at


A1A2A3

0

20

40

60

80

100

Load

(kN

)

3000 6000 9000 12000 150000Strain (times10minus6)

(a) Group A

B1B2B3

0

20

40

60

80

100

Load

(kN

)


(b) Group B

Figure 6 Comparisons of load-FRP fabric strain curves

0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

836kN73kN65kN60kN

52kN40kN32kN14kN

(a) A3

0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

977 kN83kN80kN74kN

71kN50kN33kN20kN

(b) B3

Figure 7 Strain distributions at a midspan section

the high strain level due to the slippage between FRP fabricand cementitious matrix

4 Numerical Analysis

41 Proposition of Bond Strength Model The bond strengthmodel proposed by Teng et al [15] has been well known as amodel for externally bonded reinforcement (EBR) Althoughthe bond-slip behavior of the FRCM composite is differentfrom that of EBR due to the adhesive being used it was

considered that the bond-slip concept based on fracturemechanics was similar in both cases Therefore a new bondstrength model which was based on the model by Teng etal [15] was used to evaluate the effective stress of the FRCMcomposite in this study Equation (1) shows themodel byTenget al [15]

120590119901= 120572120573119901120573119871

radic119864119901radic1198911015840

119888

119905119901

(1)


Table 7 Database for RC beams strengthened with FRCM composite

Reference Specimen ID 119887119888(mm) 119889 (mm) ℎ (mm) 119860

119904(mm2) 119891

119910(MPa) 119891

1015840

119888(MPa) 119864

119891(GPa) 119905

1(mm) Number of plies

Project study

A1 170 270 300 1426 480 280 240 0107 1A2 170 270 300 1426 480 280 240 0107 2A3 170 270 300 1426 480 280 240 0107 3B1 170 270 300 1426 480 280 240 0162 1B2 170 270 300 1426 480 280 240 0162 2B3 170 270 300 1426 480 280 240 0162 3

Babaeidarabad et al [1]

L 1 152 260 305 258 276 291 280 005 1L 4 152 260 305 258 276 291 280 005 4H 1 152 260 305 258 276 4291 280 005 1H 4 152 260 305 258 276 4291 280 005 4

Ombres [6]

S2 T1 P2 150 230 250 157 5259 2302 270 0045 2S2 T1 P3 150 230 250 157 5259 2302 270 0045 3S2 T2 P2 150 230 250 157 5259 2239 270 0045 2S2 T2 P3 150 230 250 157 5259 2239 270 0045 3

Loreto et al [7]

L 1 X 305 129 152 2139 414 291 280 005 1L 4 X 305 129 152 2139 414 291 280 005 4H 1 X 305 129 152 2139 414 4291 280 005 1H 4 X 305 129 152 2139 414 4291 280 005 4

where

120573119901= radic

2 minus 119887119901119887119888

1 + 119887119901119887119888

120573119871=

1 if 119871 ge 119871119890

sin 120587119871

2119871119890

if 119871 lt 119871119890

119871119890= radic

119864119901119905119901

radic1198911015840

119888

(2)

where 119887119901is the width of the bonded plate 119887

119888is the width of the

concrete block 119871 is the bond length 119871119890is the effective bond

length 119864119901is the elastic modulus of plate 119905

119901is the thickness

of the bonded plate 1198911015840119888is the cylinder compressive strength

for concrete and 120572 is the reduction factor and given as 0427by Teng et al [15]

In the FRCM composite the total nominal thickness ofFRP fabric 119905

119901is defined by

119905119901= 1199051times 119899 (3)

where 1199051is the nominal thickness of 1-ply FRP fabric and 119899 is

the number of layersMeanwhile DrsquoAmbrisi et al [11] suggested through the

experimental study for bond-slip behavior between an FRCMcomposite and concrete that the FRP fabric strain corre-sponding to its debonding 120576

119891deb decreases at the rate of 1radicnwith the higher amount of FRP fabric Therefore (3) canbe modified into (4) in the bond strength model for FRCM

composite considering the slippage between FRP fabric andmatrix

119905119901= 1199051times radic119899 (4)

Finally the bond strength model for the FRCM composite isproposed as

120590FRCM = 120572120573119901120573119871

radic119864119901radic1198911015840

119888

1199051radic119899

(5)

where 120590FRCM is the stress in the FRCM composite at debond-ing

In addition the coefficient 120572 should be calibrated toaccount for the difference between FRCM and EBR Thetest data of RC beams strengthened with FRCM compositewere collected to calibrate the 120572 value Table 7 shows thecollected test database for RC beams strengthened withFRCM composite The database consists of the geometriesand material properties of 18 RC beams tested under four-point or three-point loading

For the database given in Table 7 as the strain in the FRPfabric at the critical section was not reported the experimen-tal value of stress in the FRP fabric at debonding 119891

119891deb wasdeduced from the experimental debonding moment 119872

119906debusing the conventional reinforced concrete theory Figure 8shows the analytical model to deduce the experimentalstress in the FRP fabric at debonding from the experimentaldebondingmoment It illustrates the assumed basic analyticalconditions of internal strain stress and resultant force fora FRCM-strengthened section at ultimate stage Both straincompatibility and internal force equilibrium in the analyticalmodel were assumed to relate the stress in the FRP fabric tothe applied moment


Compression

Tension hd

C

CL

As

Af

b

120576c

cu

120576y

120576fdeb

f998400c

TS

Tf

1205721f998400c

C = 1205721f998400c 1205731cub

Ts = Asfy

Tf = Afffdeb

1205731cu

Figure 8 Analytical model at the ultimate stage

In Figure 8 the experimental debondingmoment119872119906deb

is expressed according to (6a) (6b) (6c) (6d) (6e) (6f) (6g)and (6h)The tensile steel was assumed to be yielded based onthe test results in the section analysis

119872119906deb = 119872

119904+ 119872119891 (6a)

where

119872119904= 119860119904119891119910(119889 minus

1205731119888119906

2) (6b)

119872119891

= 119899119860119891119891119891deb (ℎ minus

1205731119888119906

2) (6c)

1205731(119888119906) =

41205761015840

119888minus 120576119888(119888119906)

61205761015840

119888minus 2120576119888(119888119906) (6d)

1205761015840

119888=

171198911015840

119888

119864119888

(6e)

119864119888= 4 700radic119891

1015840

119888 (6f)

119891119891deb = 119864

119891120576119891deb (6g)

120576119888=

119888119906

ℎ minus 119888119906

120576119891deb (6h)

where 119872119904is the contribution of steel reinforcement to

nominal flexural strength 119872119891is the contribution of FRP

reinforcement to nominal flexural strength 119860119904is the area of

steel reinforcement 119872119891is the area of FRP reinforcement 119889

is the distance from extreme compression fiber to centroidof tension reinforcement ℎ is the long side cross-sectionaldimension of rectangular 119891

119910is the yield stress of steel

reinforcement 1205761015840

119888is the compressive strain corresponding

to 1198911015840

119888 119864119888is the modulus of elasticity of concrete 119864

119891is the

modulus of elasticity of FRP fabric 120576119891deb is the strain in the

FRCM composite at debonding 119888119906is the neutral axis depth

at the ultimate moment 1205731is the concrete stress block factor

and 120576119888is the concrete compressive strain

The stress 119891119891deb can be expressed as (7) by using (6a)ndash

(6c)

119891119891deb =

119872119906deb minus 119860

119904119891119910(119889 minus 120573

11198881199062)

119899119860119891(ℎ minus 120573

11198881199062)

(7)

Also the stress 119891119891deb should satisfy the internal force equilib-

rium expressed as (8a) (8b) (8c) (8d) and (8e)

119879119904+ 119879119891

= 119862 (8a)

where

119879119904= 119860119904119891119910 (8b)

119879119891

= 119899119860119891119891119891deb (8c)

119862 = 12057211198911015840

1198881205731119888119906119887 (8d)

1205721(119888119906) =

31205761015840

119888120576119888(119888119906) minus [120576119888(119888119906)]2

31205731(119888119906) 1205761015840

119888

2 (8e)

where 119879119904is the tensile force for steel reinforcement 119879

119891is the

tensile force for FRCM composite 119862 is the compressive forcefor concrete and 120572

1is the concrete stress block factor

The stress 119891119891deb was computed with the trial and error

method using (7) and (8a)ndash(8e)The value of 120572 for each beamgiven in Table 7 was calculated with (9) derived from 119891

119891deband (5)

120572 =

119891119891deb

120573119901120573119871radic119864119901radic1198911015840

1198881199051radic119899

(9)

Finally Figure 9 shows the 120572 values calculated for test beamspresented in Table 7 The average 120572 value for total beams wastaken as 0729 from a regression analysis

In order to verify the proposed bond strength modelfor FRCM it was used to numerically predict the flexuralcapacity of the FRCM-strengthenedRCbeams Table 8 showsthe comparison between test results and analytical resultsThe ratio of test results to predicted values ranged from


Table 8 Comparisons between test results and analytical results

Reference Specimen ID 119875119906test (kN) 119875

119906analysis (kN) 119875119906test119875119906analysis

Project study

A1 5858 5857 100A2 6270 7126 088A3 8360 8225 102B1 6552 6270 105B2 7368 7814 094B3 9776 9146 107


L 1 6770 6251 108L 4 9900 9076 109H 1 6300 6476 097H 4 9680 9651 100

Ombres [6]

S2 T1 P2 6600 5510 120S2 T1 P3 7139 6037 118S2 T2 P2 5286 5489 096S2 T2 P3 5571 6010 093

Loreto et al [7]

L 1 X 4501 4425 102L 4 X 6530 7150 091H 1 X 4200 4648 090H 4 X 6576 7748 085

Mean 100Standard deviation 0094

Average 120572 = 0729

00

02

04

06120572

08

10

12

14

50 100 150 200 250 300 350 400 450 5000Ef120588f (MPa)

Figure 9 Computed 120572 values

085 to 120 The average and standard deviation of theratios were 100 and 0094 respectively It should be notedfrom comparison that the proposed bond strength modelfor FRCM can be used to predict the flexural capacity ofthe FRCM-strengthened beam because test results agree wellwith the predicted values

42 Load-Deflection Curve The comparisons of load-deflection curves for representative beams of Table 7are presented in Figure 10 Theoretical curves consisted of atrilinear diagramThus the corresponding load andmidspan

deflection at three stages namely cracking yielding andultimate stage were calculated using the moment capacityand strain compatibility The midspan deflection Δ offlexural beam with simple supports under three- and four-point load was calculated from the following equationsrespectively

Δ3119901

=1

12

1198721198712

119864119888119868

(10)

Δ4119901

=69

648

1198721198712

119864119888119868

(11)

where 119872 is the applied moment 119871 is the beam net span and119868 is the corresponding moment of inertia The term 119872119864

119888119868

is the curvature of the cross section at midspan 120594 calculatedfrom

120594 =120576119904

119889 minus 119888 (12)

where 119888 is the corresponding neutral axis depth and 120576119904is the

corresponding stress of tensile rebarThe corresponding load at ultimate stage was derived

from the moment computed using the proposed bondstrength model As shown in Figure 10 the predicted load-deflection response of FRCM-strengthened beams is in sat-isfactory agreement with experimental results In particularthe slope between yielding and ultimate stage namely thedebonding in the predicted diagram agrees with test resultswell It results from the accuracy of the proposed bondstrength model predicting the FRP fabric stress at debond-ing


0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

L_1_expAnalytical

(a) L 1

0 5 10 15 20 25 30 35 400

20

40

60

80

120

100

Load

(kN

)

Displacement (mm)

L_1_X_expAnalytical

(b) L 1 X

0 10 20 30 40 50 60 700

20

40

60

80

100

120

Load

(kN

)

Displacement (mm) S2_T2_P3_exp

Analytical

(c) S2 T2 P3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

A3_expAnalytical

(d) A3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B1_expAnalytical

(e) B1

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B2_expAnalytical

(f) B2

Figure 10 Comparisons of load-displacement curves


5 Conclusion

The following conclusions are drawn from the results

(1) The flexural strengths of beams strengthened withFRCM composite ranged from 1317 to 2198 rel-ative to a Control specimen increasing with a higheramount of FRP fabric Also all of them failed by thedebonding of the FRCM composite

(2) Before initial crack occurrence the relationship ofload-FRCM fabric strain was linear However theslippage between FRP fabric and cementitious matrixincreased with the higher load after crack formationConsequently it should be noted that the straindistribution of a section at low strain can be assumedto be linear but it cannot be regarded as linear at thehigh strain level due to the slippage between FRPfabric and cementitious matrix

(3) Although the maximum strains of specimens inGroup B were higher than those of specimens inGroup A these were less than 70 of the straincorresponding to FRP fabric rupture 17500120583120576 Thesepremature failures were due to the debonding of theFRCM composite

(4) A new bond strength model which was based onthe model by Teng et al [15] and which consideredthe slippage between the FRP fabric and matrix wasproposed to predict the strengthening performanceof the FRCM composite The ratios of collected testresults to predicted values ranged from 085 to 120The average and standard deviation of the ratioswere 100 and 0094 respectively Thus it could beconcluded that the proposed bond strengthmodel forFRCM can be used to predict the flexural capacity ofthe FRCM-strengthened beam

(5) The predicted load-deflection response of FRCM-strengthened beams at cracking yielding and ulti-mate stage was in satisfactory agreement with exper-imental results confirming the accuracy of the pro-posed bond strength model

Conflict of Interests

The authors declare no conflict of interests

Acknowledgment

This research was supported by Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (NRF-2013R1A1A2012521)

References

[1] S Babaeidarabad G Loreto and A Nanni ldquoFlexural strength-ening of RC beams with an externally bonded fabric-reinforcedcementitious matrixrdquo Journal of Composites for Constructionvol 18 no 5 2014

[2] Y A Al-Salloum H M Elsanadedy S H Alsayed and RA Iqbal ldquoExperimental and numerical study for the shearstrengthening of reinforced concrete beams using textile-reinforced mortarrdquo Journal of Composites for Construction vol16 no 1 pp 74ndash90 2012

[3] A DrsquoAmbrisi and F Focacci ldquoFlexural strengthening of RCbeams with cement-based compositesrdquo Journal of Compositesfor Construction vol 15 no 5 pp 707ndash720 2011

[4] L Ombres ldquoAnalysis of the bond between fabric reinforcedcementitious mortar (FRCM) strengthening systems and con-creterdquoComposites Part B Engineering vol 69 pp 418ndash426 2015

[5] C G Papanicolaou T C Triantafillou M Papathanasiouand K Karlos ldquoTextile reinforced mortar (TRM) versus FRPas strengthening material of URM walls out-of-plane cyclicloadingrdquo Materials and Structures vol 41 no 1 pp 143ndash1572008

[6] L Ombres ldquoFlexural analysis of reinforced concrete beamsstrengthened with a cement based high strength compositematerialrdquo Composite Structures vol 94 no 1 pp 143ndash155 2011

[7] G Loreto L Leardini D Arboleda and A Nanni ldquoPerfor-mance of RC slab-type elements strengthened with fabric-reinforced cementitious-matrix compositesrdquo Journal of Com-posites for Construction vol 18 no 3 2014

[8] American Concrete Institute ldquoDesign and construction guideof externally bonded FRCM system for concrete and masonryrepair and strengtheningrdquo ACI 549 American Concrete Insti-tute Farmington Hills Mich USA 2013

[9] American Concrete Institute (ACI) ldquoBuilding code require-ments for reinforced concreterdquo ACI 318 American ConcreteInstitute Farmington Hills Mich USA 2011

[10] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013

[11] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental analysison bond between PBO-FRCM strengthening materials andconcreterdquo Composites B Engineering vol 44 no 1 pp 524ndash5322013

[12] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39C39MASTM International West Conshohocken Pa USA 2013

[13] ASTM ldquoStandard test methods and definitions for mechanicaltesting of steel productsrdquo ASTM A370 ASTM InternationalWest Conshohocken Pa USA 2013

[14] ASTM International ldquoStandard test method for compressivestrength of hydraulic cement mortarsrdquo ASTM C109C109MASTM International West Conshohocken Pa USA 2013

[15] J G Teng S T Smith J Yao and J F Chen ldquoIntermediatecrack-induced debonding in RC beams and slabsrdquo Journal ofConstruction and Building Materials vol 17 no 6-7 pp 447ndash462 2003

Submit your manuscripts athttpwwwhindawicom

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


Strain gages

FRCM composite materialsR (support) R (support)900mm 900mm 900mm

3000mm

2-D10mm

2-D10mm

300mm

170mm

P2 (load) P2 (load)

Figure 1 Test specimen layout

three-point bending test and performed an analytical study toverify the level of accuracy of the ultimate capacity predictionaccording to the ACI 549 [8] guide where the proposedequations are based on the conventional reinforced concretetheory Through the results of their study they reportedthat the ultimate capacity prediction according to the ACI549 [8] guide was satisfactory because the tensile propertiesused in the analysis did not depend on fiber rupture butare based on the performance of the FRCM tensile couponduring the crack formation zone [7] Babaeidarabad et al[1] tested FRCM-strengthened beams having 1-ply and 4-ply PBO fabric and predicted the efficiency of the FRCM-strengthening method through a section analysis followingmethodology in accordancewithACI 549 [8] andACI 318 [9]Their research results showed that the strain compatibility ofa beam with 1-ply fabric was no longer satisfied due to fabricslippage within the matrix after steel yielding They notedthat the slippage behavior can be captured in the analysis bythe tensile characteristic parameters obtained from FRCMcoupon testing [1]

Meanwhile several studies to identify the bond-slipbehavior between the fibermatrix and FRCMconcrete inter-face have been performed by a few researchers Ombres[4] carried out an experimental and theoretical study onthe bond-slip behavior between concrete and PBO-FRCMcomposite and proposed a nonlinear bond-slip model forFRCMusing the experimental data However the parametersof his model should be calibrated using more experimentaldata DrsquoAmbrisi et al [10] experimentally and analyticallyevaluated the bond stress between CFRP-FRCM materialsand masonry and reported that the debonding occurs at thefibersmatrix interface after a considerable fibersmatrix slipAlso DrsquoAmbrisi et al [11] performed an experimental studyon the bond-slip between PBO-FRCM and concrete andreported that the debonding strain in PBOfibers decreased inproportion to 1radic119899 with an increase in the number of layers119899

Although some studies on the bond-slip behavior offibermatrix and FRCMconcrete interface have been per-formed a bond strengthmodel for FRCMhas not been estab-lished yet Moreover the ACI 549 [8] guideline applicable forpredicting the strengthening efficiency of FRCM compositealso requires an additional FRCM coupon test to define thetensile characteristic parameters of the FRCM compositeThus this study aimed to perform the flexural tests including

Table 1 Mixture properties of concrete

WC () Sa () Unit weight (kgm3)W C S G Ad(a)

484 481 168 345 860 949 207(a)AE water-reducing admixture

Table 2 Mechanical properties of rebar used

Nominaldiameter(mm)

Modulus ofelasticity(MPa)

Yieldstrength(MPa)

Ultimatestrength(MPa)

Elongation()

953 20 times 105 480 590 171

the number of plies and the amount of FRP fabric as testvariables and to develop a bond strengthmodel to predict theflexural behavior of FRCM-strengthened beams without anadditional test

2 Experimental Program

21 Test Specimens The experimental program consisted ofseven beams of 3000mm and a cross section of 170 times

300mm Two deformed bars were placed on the tension andcompression faces respectively Shear reinforcements wereplaced in a center-to-center spacing of 150mm to preventshear failure in all specimens Steel reinforcement of D10with a nominal diameter of 953mm was used for tensioncompression and shear reinforcement The side and verticalconcrete cover was kept at 30mm for all beamsThe details ofthe test specimens are presented in Figure 1

22 Materials Ready-mix concrete was used to fabricatethe beams The mixture properties of the concrete used aretabulated in Table 1

Six standard concrete cylinders with dimensions ofΦ100mm times 200mmwere cast and tested according to ASTMC39C39M [12] The average compressive strength of theconcrete obtained from the compressive tests for the cylinderswas 280MPa at the age of 28 days Mechanical propertiesof rebar were determined by the direct tensile tests forthree coupons in accordance with ASTM A370 [13] in thelaboratory Material properties of the rebar used were takenfrom tests and are given in Table 2



CFRP

GFRP

(b) FRP fabric











Elasticmodulus(GPa)


(MPa)


()A 0107 240 4300 175B 0162 240 4300 175



AA1

Type A1

A2 2A3 3

BB1

Type B1

B2 2B3 3








Figure 3 Test setup





(a) Control

(b) A3

(c) B3







0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90100

Load

(kN

)

Displacement (mm)

ControlA1

A2A3

(a) Group A

0

10

20

30

40

50

60

70

80

90

100

Load

(kN

)

ControlB1

B2B3


(b) Group B








A1A2A3

0

20

40

60

80

100

Load

(kN

)


(a) Group A

B1B2B3

0

20

40

60

80

100

Load

(kN

)


(b) Group B


0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

836kN73kN65kN60kN

52kN40kN32kN14kN

(a) A3

0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

977 kN83kN80kN74kN

71kN50kN33kN20kN

(b) B3






120590119901= 120572120573119901120573119871

radic119864119901radic1198911015840

119888

119905119901

(1)




119904(mm2) 119891

119910(MPa) 119891

1015840

119888(MPa) 119864

119891(GPa) 119905


Project study

A1 170 270 300 1426 480 280 240 0107 1A2 170 270 300 1426 480 280 240 0107 2A3 170 270 300 1426 480 280 240 0107 3B1 170 270 300 1426 480 280 240 0162 1B2 170 270 300 1426 480 280 240 0162 2B3 170 270 300 1426 480 280 240 0162 3


L 1 152 260 305 258 276 291 280 005 1L 4 152 260 305 258 276 291 280 005 4H 1 152 260 305 258 276 4291 280 005 1H 4 152 260 305 258 276 4291 280 005 4

Ombres [6]

S2 T1 P2 150 230 250 157 5259 2302 270 0045 2S2 T1 P3 150 230 250 157 5259 2302 270 0045 3S2 T2 P2 150 230 250 157 5259 2239 270 0045 2S2 T2 P3 150 230 250 157 5259 2239 270 0045 3

Loreto et al [7]

L 1 X 305 129 152 2139 414 291 280 005 1L 4 X 305 129 152 2139 414 291 280 005 4H 1 X 305 129 152 2139 414 4291 280 005 1H 4 X 305 129 152 2139 414 4291 280 005 4

where

120573119901= radic

2 minus 119887119901119887119888

1 + 119887119901119887119888

120573119871=

1 if 119871 ge 119871119890

sin 120587119871

2119871119890

if 119871 lt 119871119890

119871119890= radic

119864119901119905119901

radic1198911015840

119888

(2)









119901is defined by

119905119901= 1199051times 119899 (3)






119905119901= 1199051times radic119899 (4)


120590FRCM = 120572120573119901120573119871

radic119864119901radic1198911015840

119888

1199051radic119899

(5)







Compression

Tension hd

C

CL

As

Af

b

120576c

cu

120576y

120576fdeb

f998400c

TS

Tf

1205721f998400c

C = 1205721f998400c 1205731cub

Ts = Asfy

Tf = Afffdeb

1205731cu




119872119906deb = 119872

119904+ 119872119891 (6a)

where

119872119904= 119860119904119891119910(119889 minus

1205731119888119906

2) (6b)

119872119891

= 119899119860119891119891119891deb (ℎ minus

1205731119888119906

2) (6c)

1205731(119888119906) =

41205761015840

119888minus 120576119888(119888119906)

61205761015840

119888minus 2120576119888(119888119906) (6d)

1205761015840

119888=

171198911015840

119888

119864119888

(6e)

119864119888= 4 700radic119891

1015840

119888 (6f)

119891119891deb = 119864

119891120576119891deb (6g)

120576119888=

119888119906

ℎ minus 119888119906

120576119891deb (6h)









to 1198911015840


119891is the






(6c)

119891119891deb =

119872119906deb minus 119860

119904119891119910(119889 minus 120573

11198881199062)

119899119860119891(ℎ minus 120573

11198881199062)

(7)



119879119904+ 119879119891

= 119862 (8a)

where

119879119904= 119860119904119891119910 (8b)

119879119891

= 119899119860119891119891119891deb (8c)

119862 = 12057211198911015840

1198881205731119888119906119887 (8d)

1205721(119888119906) =

31205761015840

119888120576119888(119888119906) minus [120576119888(119888119906)]2

31205731(119888119906) 1205761015840

119888

2 (8e)


119891is the





119891deband (5)

120572 =

119891119891deb

120573119901120573119871radic119864119901radic1198911015840

1198881199051radic119899

(9)







Project study

A1 5858 5857 100A2 6270 7126 088A3 8360 8225 102B1 6552 6270 105B2 7368 7814 094B3 9776 9146 107


L 1 6770 6251 108L 4 9900 9076 109H 1 6300 6476 097H 4 9680 9651 100

Ombres [6]

S2 T1 P2 6600 5510 120S2 T1 P3 7139 6037 118S2 T2 P2 5286 5489 096S2 T2 P3 5571 6010 093

Loreto et al [7]

L 1 X 4501 4425 102L 4 X 6530 7150 091H 1 X 4200 4648 090H 4 X 6576 7748 085


Average 120572 = 0729

00

02

04

06120572

08

10

12

14

50 100 150 200 250 300 350 400 450 5000Ef120588f (MPa)





Δ3119901

=1

12

1198721198712

119864119888119868

(10)

Δ4119901

=69

648

1198721198712

119864119888119868

(11)


119888119868


120594 =120576119904

119889 minus 119888 (12)





0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

L_1_expAnalytical

(a) L 1

0 5 10 15 20 25 30 35 400

20

40

60

80

120

100

Load

(kN

)

Displacement (mm)

L_1_X_expAnalytical

(b) L 1 X

0 10 20 30 40 50 60 700

20

40

60

80

100

120

Load

(kN

)


Analytical

(c) S2 T2 P3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

A3_expAnalytical

(d) A3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B1_expAnalytical

(e) B1

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B2_expAnalytical

(f) B2



5 Conclusion









Acknowledgment


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





CFRP

GFRP

(b) FRP fabric











Elasticmodulus(GPa)


(MPa)


()A 0107 240 4300 175B 0162 240 4300 175



AA1

Type A1

A2 2A3 3

BB1

Type B1

B2 2B3 3








Figure 3 Test setup





(a) Control

(b) A3

(c) B3







0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90100

Load

(kN

)

Displacement (mm)

ControlA1

A2A3

(a) Group A

0

10

20

30

40

50

60

70

80

90

100

Load

(kN

)

ControlB1

B2B3


(b) Group B








A1A2A3

0

20

40

60

80

100

Load

(kN

)


(a) Group A

B1B2B3

0

20

40

60

80

100

Load

(kN

)


(b) Group B


0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

836kN73kN65kN60kN

52kN40kN32kN14kN

(a) A3

0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

977 kN83kN80kN74kN

71kN50kN33kN20kN

(b) B3






120590119901= 120572120573119901120573119871

radic119864119901radic1198911015840

119888

119905119901

(1)




119904(mm2) 119891

119910(MPa) 119891

1015840

119888(MPa) 119864

119891(GPa) 119905


Project study

A1 170 270 300 1426 480 280 240 0107 1A2 170 270 300 1426 480 280 240 0107 2A3 170 270 300 1426 480 280 240 0107 3B1 170 270 300 1426 480 280 240 0162 1B2 170 270 300 1426 480 280 240 0162 2B3 170 270 300 1426 480 280 240 0162 3


L 1 152 260 305 258 276 291 280 005 1L 4 152 260 305 258 276 291 280 005 4H 1 152 260 305 258 276 4291 280 005 1H 4 152 260 305 258 276 4291 280 005 4

Ombres [6]

S2 T1 P2 150 230 250 157 5259 2302 270 0045 2S2 T1 P3 150 230 250 157 5259 2302 270 0045 3S2 T2 P2 150 230 250 157 5259 2239 270 0045 2S2 T2 P3 150 230 250 157 5259 2239 270 0045 3

Loreto et al [7]

L 1 X 305 129 152 2139 414 291 280 005 1L 4 X 305 129 152 2139 414 291 280 005 4H 1 X 305 129 152 2139 414 4291 280 005 1H 4 X 305 129 152 2139 414 4291 280 005 4

where

120573119901= radic

2 minus 119887119901119887119888

1 + 119887119901119887119888

120573119871=

1 if 119871 ge 119871119890

sin 120587119871

2119871119890

if 119871 lt 119871119890

119871119890= radic

119864119901119905119901

radic1198911015840

119888

(2)









119901is defined by

119905119901= 1199051times 119899 (3)






119905119901= 1199051times radic119899 (4)


120590FRCM = 120572120573119901120573119871

radic119864119901radic1198911015840

119888

1199051radic119899

(5)







Compression

Tension hd

C

CL

As

Af

b

120576c

cu

120576y

120576fdeb

f998400c

TS

Tf

1205721f998400c

C = 1205721f998400c 1205731cub

Ts = Asfy

Tf = Afffdeb

1205731cu




119872119906deb = 119872

119904+ 119872119891 (6a)

where

119872119904= 119860119904119891119910(119889 minus

1205731119888119906

2) (6b)

119872119891

= 119899119860119891119891119891deb (ℎ minus

1205731119888119906

2) (6c)

1205731(119888119906) =

41205761015840

119888minus 120576119888(119888119906)

61205761015840

119888minus 2120576119888(119888119906) (6d)

1205761015840

119888=

171198911015840

119888

119864119888

(6e)

119864119888= 4 700radic119891

1015840

119888 (6f)

119891119891deb = 119864

119891120576119891deb (6g)

120576119888=

119888119906

ℎ minus 119888119906

120576119891deb (6h)









to 1198911015840


119891is the






(6c)

119891119891deb =

119872119906deb minus 119860

119904119891119910(119889 minus 120573

11198881199062)

119899119860119891(ℎ minus 120573

11198881199062)

(7)



119879119904+ 119879119891

= 119862 (8a)

where

119879119904= 119860119904119891119910 (8b)

119879119891

= 119899119860119891119891119891deb (8c)

119862 = 12057211198911015840

1198881205731119888119906119887 (8d)

1205721(119888119906) =

31205761015840

119888120576119888(119888119906) minus [120576119888(119888119906)]2

31205731(119888119906) 1205761015840

119888

2 (8e)


119891is the





119891deband (5)

120572 =

119891119891deb

120573119901120573119871radic119864119901radic1198911015840

1198881199051radic119899

(9)







Project study

A1 5858 5857 100A2 6270 7126 088A3 8360 8225 102B1 6552 6270 105B2 7368 7814 094B3 9776 9146 107


L 1 6770 6251 108L 4 9900 9076 109H 1 6300 6476 097H 4 9680 9651 100

Ombres [6]

S2 T1 P2 6600 5510 120S2 T1 P3 7139 6037 118S2 T2 P2 5286 5489 096S2 T2 P3 5571 6010 093

Loreto et al [7]

L 1 X 4501 4425 102L 4 X 6530 7150 091H 1 X 4200 4648 090H 4 X 6576 7748 085


Average 120572 = 0729

00

02

04

06120572

08

10

12

14

50 100 150 200 250 300 350 400 450 5000Ef120588f (MPa)





Δ3119901

=1

12

1198721198712

119864119888119868

(10)

Δ4119901

=69

648

1198721198712

119864119888119868

(11)


119888119868


120594 =120576119904

119889 minus 119888 (12)





0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

L_1_expAnalytical

(a) L 1

0 5 10 15 20 25 30 35 400

20

40

60

80

120

100

Load

(kN

)

Displacement (mm)

L_1_X_expAnalytical

(b) L 1 X

0 10 20 30 40 50 60 700

20

40

60

80

100

120

Load

(kN

)


Analytical

(c) S2 T2 P3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

A3_expAnalytical

(d) A3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B1_expAnalytical

(e) B1

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B2_expAnalytical

(f) B2



5 Conclusion









Acknowledgment


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








Figure 3 Test setup





(a) Control

(b) A3

(c) B3







0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90100

Load

(kN

)

Displacement (mm)

ControlA1

A2A3

(a) Group A

0

10

20

30

40

50

60

70

80

90

100

Load

(kN

)

ControlB1

B2B3


(b) Group B








A1A2A3

0

20

40

60

80

100

Load

(kN

)


(a) Group A

B1B2B3

0

20

40

60

80

100

Load

(kN

)


(b) Group B


0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

836kN73kN65kN60kN

52kN40kN32kN14kN

(a) A3

0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

977 kN83kN80kN74kN

71kN50kN33kN20kN

(b) B3






120590119901= 120572120573119901120573119871

radic119864119901radic1198911015840

119888

119905119901

(1)




119904(mm2) 119891

119910(MPa) 119891

1015840

119888(MPa) 119864

119891(GPa) 119905


Project study

A1 170 270 300 1426 480 280 240 0107 1A2 170 270 300 1426 480 280 240 0107 2A3 170 270 300 1426 480 280 240 0107 3B1 170 270 300 1426 480 280 240 0162 1B2 170 270 300 1426 480 280 240 0162 2B3 170 270 300 1426 480 280 240 0162 3


L 1 152 260 305 258 276 291 280 005 1L 4 152 260 305 258 276 291 280 005 4H 1 152 260 305 258 276 4291 280 005 1H 4 152 260 305 258 276 4291 280 005 4

Ombres [6]

S2 T1 P2 150 230 250 157 5259 2302 270 0045 2S2 T1 P3 150 230 250 157 5259 2302 270 0045 3S2 T2 P2 150 230 250 157 5259 2239 270 0045 2S2 T2 P3 150 230 250 157 5259 2239 270 0045 3

Loreto et al [7]

L 1 X 305 129 152 2139 414 291 280 005 1L 4 X 305 129 152 2139 414 291 280 005 4H 1 X 305 129 152 2139 414 4291 280 005 1H 4 X 305 129 152 2139 414 4291 280 005 4

where

120573119901= radic

2 minus 119887119901119887119888

1 + 119887119901119887119888

120573119871=

1 if 119871 ge 119871119890

sin 120587119871

2119871119890

if 119871 lt 119871119890

119871119890= radic

119864119901119905119901

radic1198911015840

119888

(2)









119901is defined by

119905119901= 1199051times 119899 (3)






119905119901= 1199051times radic119899 (4)


120590FRCM = 120572120573119901120573119871

radic119864119901radic1198911015840

119888

1199051radic119899

(5)







Compression

Tension hd

C

CL

As

Af

b

120576c

cu

120576y

120576fdeb

f998400c

TS

Tf

1205721f998400c

C = 1205721f998400c 1205731cub

Ts = Asfy

Tf = Afffdeb

1205731cu




119872119906deb = 119872

119904+ 119872119891 (6a)

where

119872119904= 119860119904119891119910(119889 minus

1205731119888119906

2) (6b)

119872119891

= 119899119860119891119891119891deb (ℎ minus

1205731119888119906

2) (6c)

1205731(119888119906) =

41205761015840

119888minus 120576119888(119888119906)

61205761015840

119888minus 2120576119888(119888119906) (6d)

1205761015840

119888=

171198911015840

119888

119864119888

(6e)

119864119888= 4 700radic119891

1015840

119888 (6f)

119891119891deb = 119864

119891120576119891deb (6g)

120576119888=

119888119906

ℎ minus 119888119906

120576119891deb (6h)









to 1198911015840


119891is the






(6c)

119891119891deb =

119872119906deb minus 119860

119904119891119910(119889 minus 120573

11198881199062)

119899119860119891(ℎ minus 120573

11198881199062)

(7)



119879119904+ 119879119891

= 119862 (8a)

where

119879119904= 119860119904119891119910 (8b)

119879119891

= 119899119860119891119891119891deb (8c)

119862 = 12057211198911015840

1198881205731119888119906119887 (8d)

1205721(119888119906) =

31205761015840

119888120576119888(119888119906) minus [120576119888(119888119906)]2

31205731(119888119906) 1205761015840

119888

2 (8e)


119891is the





119891deband (5)

120572 =

119891119891deb

120573119901120573119871radic119864119901radic1198911015840

1198881199051radic119899

(9)







Project study

A1 5858 5857 100A2 6270 7126 088A3 8360 8225 102B1 6552 6270 105B2 7368 7814 094B3 9776 9146 107


L 1 6770 6251 108L 4 9900 9076 109H 1 6300 6476 097H 4 9680 9651 100

Ombres [6]

S2 T1 P2 6600 5510 120S2 T1 P3 7139 6037 118S2 T2 P2 5286 5489 096S2 T2 P3 5571 6010 093

Loreto et al [7]

L 1 X 4501 4425 102L 4 X 6530 7150 091H 1 X 4200 4648 090H 4 X 6576 7748 085


Average 120572 = 0729

00

02

04

06120572

08

10

12

14

50 100 150 200 250 300 350 400 450 5000Ef120588f (MPa)





Δ3119901

=1

12

1198721198712

119864119888119868

(10)

Δ4119901

=69

648

1198721198712

119864119888119868

(11)


119888119868


120594 =120576119904

119889 minus 119888 (12)





0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

L_1_expAnalytical

(a) L 1

0 5 10 15 20 25 30 35 400

20

40

60

80

120

100

Load

(kN

)

Displacement (mm)

L_1_X_expAnalytical

(b) L 1 X

0 10 20 30 40 50 60 700

20

40

60

80

100

120

Load

(kN

)


Analytical

(c) S2 T2 P3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

A3_expAnalytical

(d) A3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B1_expAnalytical

(e) B1

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B2_expAnalytical

(f) B2



5 Conclusion









Acknowledgment


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90100

Load

(kN

)

Displacement (mm)

ControlA1

A2A3

(a) Group A

0

10

20

30

40

50

60

70

80

90

100

Load

(kN

)

ControlB1

B2B3


(b) Group B








A1A2A3

0

20

40

60

80

100

Load

(kN

)


(a) Group A

B1B2B3

0

20

40

60

80

100

Load

(kN

)


(b) Group B


0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

836kN73kN65kN60kN

52kN40kN32kN14kN

(a) A3

0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

977 kN83kN80kN74kN

71kN50kN33kN20kN

(b) B3






120590119901= 120572120573119901120573119871

radic119864119901radic1198911015840

119888

119905119901

(1)




119904(mm2) 119891

119910(MPa) 119891

1015840

119888(MPa) 119864

119891(GPa) 119905


Project study

A1 170 270 300 1426 480 280 240 0107 1A2 170 270 300 1426 480 280 240 0107 2A3 170 270 300 1426 480 280 240 0107 3B1 170 270 300 1426 480 280 240 0162 1B2 170 270 300 1426 480 280 240 0162 2B3 170 270 300 1426 480 280 240 0162 3


L 1 152 260 305 258 276 291 280 005 1L 4 152 260 305 258 276 291 280 005 4H 1 152 260 305 258 276 4291 280 005 1H 4 152 260 305 258 276 4291 280 005 4

Ombres [6]

S2 T1 P2 150 230 250 157 5259 2302 270 0045 2S2 T1 P3 150 230 250 157 5259 2302 270 0045 3S2 T2 P2 150 230 250 157 5259 2239 270 0045 2S2 T2 P3 150 230 250 157 5259 2239 270 0045 3

Loreto et al [7]

L 1 X 305 129 152 2139 414 291 280 005 1L 4 X 305 129 152 2139 414 291 280 005 4H 1 X 305 129 152 2139 414 4291 280 005 1H 4 X 305 129 152 2139 414 4291 280 005 4

where

120573119901= radic

2 minus 119887119901119887119888

1 + 119887119901119887119888

120573119871=

1 if 119871 ge 119871119890

sin 120587119871

2119871119890

if 119871 lt 119871119890

119871119890= radic

119864119901119905119901

radic1198911015840

119888

(2)









119901is defined by

119905119901= 1199051times 119899 (3)






119905119901= 1199051times radic119899 (4)


120590FRCM = 120572120573119901120573119871

radic119864119901radic1198911015840

119888

1199051radic119899

(5)







Compression

Tension hd

C

CL

As

Af

b

120576c

cu

120576y

120576fdeb

f998400c

TS

Tf

1205721f998400c

C = 1205721f998400c 1205731cub

Ts = Asfy

Tf = Afffdeb

1205731cu




119872119906deb = 119872

119904+ 119872119891 (6a)

where

119872119904= 119860119904119891119910(119889 minus

1205731119888119906

2) (6b)

119872119891

= 119899119860119891119891119891deb (ℎ minus

1205731119888119906

2) (6c)

1205731(119888119906) =

41205761015840

119888minus 120576119888(119888119906)

61205761015840

119888minus 2120576119888(119888119906) (6d)

1205761015840

119888=

171198911015840

119888

119864119888

(6e)

119864119888= 4 700radic119891

1015840

119888 (6f)

119891119891deb = 119864

119891120576119891deb (6g)

120576119888=

119888119906

ℎ minus 119888119906

120576119891deb (6h)









to 1198911015840


119891is the






(6c)

119891119891deb =

119872119906deb minus 119860

119904119891119910(119889 minus 120573

11198881199062)

119899119860119891(ℎ minus 120573

11198881199062)

(7)



119879119904+ 119879119891

= 119862 (8a)

where

119879119904= 119860119904119891119910 (8b)

119879119891

= 119899119860119891119891119891deb (8c)

119862 = 12057211198911015840

1198881205731119888119906119887 (8d)

1205721(119888119906) =

31205761015840

119888120576119888(119888119906) minus [120576119888(119888119906)]2

31205731(119888119906) 1205761015840

119888

2 (8e)


119891is the





119891deband (5)

120572 =

119891119891deb

120573119901120573119871radic119864119901radic1198911015840

1198881199051radic119899

(9)







Project study

A1 5858 5857 100A2 6270 7126 088A3 8360 8225 102B1 6552 6270 105B2 7368 7814 094B3 9776 9146 107


L 1 6770 6251 108L 4 9900 9076 109H 1 6300 6476 097H 4 9680 9651 100

Ombres [6]

S2 T1 P2 6600 5510 120S2 T1 P3 7139 6037 118S2 T2 P2 5286 5489 096S2 T2 P3 5571 6010 093

Loreto et al [7]

L 1 X 4501 4425 102L 4 X 6530 7150 091H 1 X 4200 4648 090H 4 X 6576 7748 085


Average 120572 = 0729

00

02

04

06120572

08

10

12

14

50 100 150 200 250 300 350 400 450 5000Ef120588f (MPa)





Δ3119901

=1

12

1198721198712

119864119888119868

(10)

Δ4119901

=69

648

1198721198712

119864119888119868

(11)


119888119868


120594 =120576119904

119889 minus 119888 (12)





0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

L_1_expAnalytical

(a) L 1

0 5 10 15 20 25 30 35 400

20

40

60

80

120

100

Load

(kN

)

Displacement (mm)

L_1_X_expAnalytical

(b) L 1 X

0 10 20 30 40 50 60 700

20

40

60

80

100

120

Load

(kN

)


Analytical

(c) S2 T2 P3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

A3_expAnalytical

(d) A3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B1_expAnalytical

(e) B1

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B2_expAnalytical

(f) B2



5 Conclusion









Acknowledgment


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




A1A2A3

0

20

40

60

80

100

Load

(kN

)


(a) Group A

B1B2B3

0

20

40

60

80

100

Load

(kN

)


(b) Group B


0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

836kN73kN65kN60kN

52kN40kN32kN14kN

(a) A3

0

50

100

150

200

250

300

Dep

th o

f sec

tion

(mm

)

4000 8000 12000 16000 200000Strain (120583120576)

977 kN83kN80kN74kN

71kN50kN33kN20kN

(b) B3






120590119901= 120572120573119901120573119871

radic119864119901radic1198911015840

119888

119905119901

(1)




119904(mm2) 119891

119910(MPa) 119891

1015840

119888(MPa) 119864

119891(GPa) 119905


Project study

A1 170 270 300 1426 480 280 240 0107 1A2 170 270 300 1426 480 280 240 0107 2A3 170 270 300 1426 480 280 240 0107 3B1 170 270 300 1426 480 280 240 0162 1B2 170 270 300 1426 480 280 240 0162 2B3 170 270 300 1426 480 280 240 0162 3


L 1 152 260 305 258 276 291 280 005 1L 4 152 260 305 258 276 291 280 005 4H 1 152 260 305 258 276 4291 280 005 1H 4 152 260 305 258 276 4291 280 005 4

Ombres [6]

S2 T1 P2 150 230 250 157 5259 2302 270 0045 2S2 T1 P3 150 230 250 157 5259 2302 270 0045 3S2 T2 P2 150 230 250 157 5259 2239 270 0045 2S2 T2 P3 150 230 250 157 5259 2239 270 0045 3

Loreto et al [7]

L 1 X 305 129 152 2139 414 291 280 005 1L 4 X 305 129 152 2139 414 291 280 005 4H 1 X 305 129 152 2139 414 4291 280 005 1H 4 X 305 129 152 2139 414 4291 280 005 4

where

120573119901= radic

2 minus 119887119901119887119888

1 + 119887119901119887119888

120573119871=

1 if 119871 ge 119871119890

sin 120587119871

2119871119890

if 119871 lt 119871119890

119871119890= radic

119864119901119905119901

radic1198911015840

119888

(2)









119901is defined by

119905119901= 1199051times 119899 (3)






119905119901= 1199051times radic119899 (4)


120590FRCM = 120572120573119901120573119871

radic119864119901radic1198911015840

119888

1199051radic119899

(5)







Compression

Tension hd

C

CL

As

Af

b

120576c

cu

120576y

120576fdeb

f998400c

TS

Tf

1205721f998400c

C = 1205721f998400c 1205731cub

Ts = Asfy

Tf = Afffdeb

1205731cu




119872119906deb = 119872

119904+ 119872119891 (6a)

where

119872119904= 119860119904119891119910(119889 minus

1205731119888119906

2) (6b)

119872119891

= 119899119860119891119891119891deb (ℎ minus

1205731119888119906

2) (6c)

1205731(119888119906) =

41205761015840

119888minus 120576119888(119888119906)

61205761015840

119888minus 2120576119888(119888119906) (6d)

1205761015840

119888=

171198911015840

119888

119864119888

(6e)

119864119888= 4 700radic119891

1015840

119888 (6f)

119891119891deb = 119864

119891120576119891deb (6g)

120576119888=

119888119906

ℎ minus 119888119906

120576119891deb (6h)









to 1198911015840


119891is the






(6c)

119891119891deb =

119872119906deb minus 119860

119904119891119910(119889 minus 120573

11198881199062)

119899119860119891(ℎ minus 120573

11198881199062)

(7)



119879119904+ 119879119891

= 119862 (8a)

where

119879119904= 119860119904119891119910 (8b)

119879119891

= 119899119860119891119891119891deb (8c)

119862 = 12057211198911015840

1198881205731119888119906119887 (8d)

1205721(119888119906) =

31205761015840

119888120576119888(119888119906) minus [120576119888(119888119906)]2

31205731(119888119906) 1205761015840

119888

2 (8e)


119891is the





119891deband (5)

120572 =

119891119891deb

120573119901120573119871radic119864119901radic1198911015840

1198881199051radic119899

(9)







Project study

A1 5858 5857 100A2 6270 7126 088A3 8360 8225 102B1 6552 6270 105B2 7368 7814 094B3 9776 9146 107


L 1 6770 6251 108L 4 9900 9076 109H 1 6300 6476 097H 4 9680 9651 100

Ombres [6]

S2 T1 P2 6600 5510 120S2 T1 P3 7139 6037 118S2 T2 P2 5286 5489 096S2 T2 P3 5571 6010 093

Loreto et al [7]

L 1 X 4501 4425 102L 4 X 6530 7150 091H 1 X 4200 4648 090H 4 X 6576 7748 085


Average 120572 = 0729

00

02

04

06120572

08

10

12

14

50 100 150 200 250 300 350 400 450 5000Ef120588f (MPa)





Δ3119901

=1

12

1198721198712

119864119888119868

(10)

Δ4119901

=69

648

1198721198712

119864119888119868

(11)


119888119868


120594 =120576119904

119889 minus 119888 (12)





0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

L_1_expAnalytical

(a) L 1

0 5 10 15 20 25 30 35 400

20

40

60

80

120

100

Load

(kN

)

Displacement (mm)

L_1_X_expAnalytical

(b) L 1 X

0 10 20 30 40 50 60 700

20

40

60

80

100

120

Load

(kN

)


Analytical

(c) S2 T2 P3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

A3_expAnalytical

(d) A3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B1_expAnalytical

(e) B1

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B2_expAnalytical

(f) B2



5 Conclusion









Acknowledgment


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






119904(mm2) 119891

119910(MPa) 119891

1015840

119888(MPa) 119864

119891(GPa) 119905


Project study

A1 170 270 300 1426 480 280 240 0107 1A2 170 270 300 1426 480 280 240 0107 2A3 170 270 300 1426 480 280 240 0107 3B1 170 270 300 1426 480 280 240 0162 1B2 170 270 300 1426 480 280 240 0162 2B3 170 270 300 1426 480 280 240 0162 3


L 1 152 260 305 258 276 291 280 005 1L 4 152 260 305 258 276 291 280 005 4H 1 152 260 305 258 276 4291 280 005 1H 4 152 260 305 258 276 4291 280 005 4

Ombres [6]

S2 T1 P2 150 230 250 157 5259 2302 270 0045 2S2 T1 P3 150 230 250 157 5259 2302 270 0045 3S2 T2 P2 150 230 250 157 5259 2239 270 0045 2S2 T2 P3 150 230 250 157 5259 2239 270 0045 3

Loreto et al [7]

L 1 X 305 129 152 2139 414 291 280 005 1L 4 X 305 129 152 2139 414 291 280 005 4H 1 X 305 129 152 2139 414 4291 280 005 1H 4 X 305 129 152 2139 414 4291 280 005 4

where

120573119901= radic

2 minus 119887119901119887119888

1 + 119887119901119887119888

120573119871=

1 if 119871 ge 119871119890

sin 120587119871

2119871119890

if 119871 lt 119871119890

119871119890= radic

119864119901119905119901

radic1198911015840

119888

(2)









119901is defined by

119905119901= 1199051times 119899 (3)






119905119901= 1199051times radic119899 (4)


120590FRCM = 120572120573119901120573119871

radic119864119901radic1198911015840

119888

1199051radic119899

(5)







Compression

Tension hd

C

CL

As

Af

b

120576c

cu

120576y

120576fdeb

f998400c

TS

Tf

1205721f998400c

C = 1205721f998400c 1205731cub

Ts = Asfy

Tf = Afffdeb

1205731cu




119872119906deb = 119872

119904+ 119872119891 (6a)

where

119872119904= 119860119904119891119910(119889 minus

1205731119888119906

2) (6b)

119872119891

= 119899119860119891119891119891deb (ℎ minus

1205731119888119906

2) (6c)

1205731(119888119906) =

41205761015840

119888minus 120576119888(119888119906)

61205761015840

119888minus 2120576119888(119888119906) (6d)

1205761015840

119888=

171198911015840

119888

119864119888

(6e)

119864119888= 4 700radic119891

1015840

119888 (6f)

119891119891deb = 119864

119891120576119891deb (6g)

120576119888=

119888119906

ℎ minus 119888119906

120576119891deb (6h)









to 1198911015840


119891is the






(6c)

119891119891deb =

119872119906deb minus 119860

119904119891119910(119889 minus 120573

11198881199062)

119899119860119891(ℎ minus 120573

11198881199062)

(7)



119879119904+ 119879119891

= 119862 (8a)

where

119879119904= 119860119904119891119910 (8b)

119879119891

= 119899119860119891119891119891deb (8c)

119862 = 12057211198911015840

1198881205731119888119906119887 (8d)

1205721(119888119906) =

31205761015840

119888120576119888(119888119906) minus [120576119888(119888119906)]2

31205731(119888119906) 1205761015840

119888

2 (8e)


119891is the





119891deband (5)

120572 =

119891119891deb

120573119901120573119871radic119864119901radic1198911015840

1198881199051radic119899

(9)







Project study

A1 5858 5857 100A2 6270 7126 088A3 8360 8225 102B1 6552 6270 105B2 7368 7814 094B3 9776 9146 107


L 1 6770 6251 108L 4 9900 9076 109H 1 6300 6476 097H 4 9680 9651 100

Ombres [6]

S2 T1 P2 6600 5510 120S2 T1 P3 7139 6037 118S2 T2 P2 5286 5489 096S2 T2 P3 5571 6010 093

Loreto et al [7]

L 1 X 4501 4425 102L 4 X 6530 7150 091H 1 X 4200 4648 090H 4 X 6576 7748 085


Average 120572 = 0729

00

02

04

06120572

08

10

12

14

50 100 150 200 250 300 350 400 450 5000Ef120588f (MPa)





Δ3119901

=1

12

1198721198712

119864119888119868

(10)

Δ4119901

=69

648

1198721198712

119864119888119868

(11)


119888119868


120594 =120576119904

119889 minus 119888 (12)





0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

L_1_expAnalytical

(a) L 1

0 5 10 15 20 25 30 35 400

20

40

60

80

120

100

Load

(kN

)

Displacement (mm)

L_1_X_expAnalytical

(b) L 1 X

0 10 20 30 40 50 60 700

20

40

60

80

100

120

Load

(kN

)


Analytical

(c) S2 T2 P3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

A3_expAnalytical

(d) A3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B1_expAnalytical

(e) B1

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B2_expAnalytical

(f) B2



5 Conclusion









Acknowledgment


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Compression

Tension hd

C

CL

As

Af

b

120576c

cu

120576y

120576fdeb

f998400c

TS

Tf

1205721f998400c

C = 1205721f998400c 1205731cub

Ts = Asfy

Tf = Afffdeb

1205731cu




119872119906deb = 119872

119904+ 119872119891 (6a)

where

119872119904= 119860119904119891119910(119889 minus

1205731119888119906

2) (6b)

119872119891

= 119899119860119891119891119891deb (ℎ minus

1205731119888119906

2) (6c)

1205731(119888119906) =

41205761015840

119888minus 120576119888(119888119906)

61205761015840

119888minus 2120576119888(119888119906) (6d)

1205761015840

119888=

171198911015840

119888

119864119888

(6e)

119864119888= 4 700radic119891

1015840

119888 (6f)

119891119891deb = 119864

119891120576119891deb (6g)

120576119888=

119888119906

ℎ minus 119888119906

120576119891deb (6h)









to 1198911015840


119891is the






(6c)

119891119891deb =

119872119906deb minus 119860

119904119891119910(119889 minus 120573

11198881199062)

119899119860119891(ℎ minus 120573

11198881199062)

(7)



119879119904+ 119879119891

= 119862 (8a)

where

119879119904= 119860119904119891119910 (8b)

119879119891

= 119899119860119891119891119891deb (8c)

119862 = 12057211198911015840

1198881205731119888119906119887 (8d)

1205721(119888119906) =

31205761015840

119888120576119888(119888119906) minus [120576119888(119888119906)]2

31205731(119888119906) 1205761015840

119888

2 (8e)


119891is the





119891deband (5)

120572 =

119891119891deb

120573119901120573119871radic119864119901radic1198911015840

1198881199051radic119899

(9)







Project study

A1 5858 5857 100A2 6270 7126 088A3 8360 8225 102B1 6552 6270 105B2 7368 7814 094B3 9776 9146 107


L 1 6770 6251 108L 4 9900 9076 109H 1 6300 6476 097H 4 9680 9651 100

Ombres [6]

S2 T1 P2 6600 5510 120S2 T1 P3 7139 6037 118S2 T2 P2 5286 5489 096S2 T2 P3 5571 6010 093

Loreto et al [7]

L 1 X 4501 4425 102L 4 X 6530 7150 091H 1 X 4200 4648 090H 4 X 6576 7748 085


Average 120572 = 0729

00

02

04

06120572

08

10

12

14

50 100 150 200 250 300 350 400 450 5000Ef120588f (MPa)





Δ3119901

=1

12

1198721198712

119864119888119868

(10)

Δ4119901

=69

648

1198721198712

119864119888119868

(11)


119888119868


120594 =120576119904

119889 minus 119888 (12)





0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

L_1_expAnalytical

(a) L 1

0 5 10 15 20 25 30 35 400

20

40

60

80

120

100

Load

(kN

)

Displacement (mm)

L_1_X_expAnalytical

(b) L 1 X

0 10 20 30 40 50 60 700

20

40

60

80

100

120

Load

(kN

)


Analytical

(c) S2 T2 P3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

A3_expAnalytical

(d) A3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B1_expAnalytical

(e) B1

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B2_expAnalytical

(f) B2



5 Conclusion









Acknowledgment


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials







Project study

A1 5858 5857 100A2 6270 7126 088A3 8360 8225 102B1 6552 6270 105B2 7368 7814 094B3 9776 9146 107


L 1 6770 6251 108L 4 9900 9076 109H 1 6300 6476 097H 4 9680 9651 100

Ombres [6]

S2 T1 P2 6600 5510 120S2 T1 P3 7139 6037 118S2 T2 P2 5286 5489 096S2 T2 P3 5571 6010 093

Loreto et al [7]

L 1 X 4501 4425 102L 4 X 6530 7150 091H 1 X 4200 4648 090H 4 X 6576 7748 085


Average 120572 = 0729

00

02

04

06120572

08

10

12

14

50 100 150 200 250 300 350 400 450 5000Ef120588f (MPa)





Δ3119901

=1

12

1198721198712

119864119888119868

(10)

Δ4119901

=69

648

1198721198712

119864119888119868

(11)


119888119868


120594 =120576119904

119889 minus 119888 (12)





0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

L_1_expAnalytical

(a) L 1

0 5 10 15 20 25 30 35 400

20

40

60

80

120

100

Load

(kN

)

Displacement (mm)

L_1_X_expAnalytical

(b) L 1 X

0 10 20 30 40 50 60 700

20

40

60

80

100

120

Load

(kN

)


Analytical

(c) S2 T2 P3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

A3_expAnalytical

(d) A3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B1_expAnalytical

(e) B1

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B2_expAnalytical

(f) B2



5 Conclusion









Acknowledgment


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

L_1_expAnalytical

(a) L 1

0 5 10 15 20 25 30 35 400

20

40

60

80

120

100

Load

(kN

)

Displacement (mm)

L_1_X_expAnalytical

(b) L 1 X

0 10 20 30 40 50 60 700

20

40

60

80

100

120

Load

(kN

)


Analytical

(c) S2 T2 P3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120Lo

ad (k

N)

Displacement (mm)

A3_expAnalytical

(d) A3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B1_expAnalytical

(e) B1

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Load

(kN

)

Displacement (mm)

B2_expAnalytical

(f) B2



5 Conclusion









Acknowledgment


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




5 Conclusion









Acknowledgment


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



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