research article shear behavior of concrete beams...

Research ArticleShear Behavior of Concrete Beams Reinforced withGFRP Shear Reinforcement

Heecheul Kim Min Sook Kim Myung Joon Ko and Young Hak Lee

Department of Architectural Engineering Kyung Hee University 1732 Deogyeong-daero Giheung-gu Yongin-siGyeonggi-do 446-701 Republic of Korea

Correspondence should be addressed to Young Hak Lee leeyhkhuackr

Received 5 August 2015 Revised 23 September 2015 Accepted 27 September 2015

Academic Editor Gonzalo Martınez-Barrera

Copyright copy 2015 Heecheul Kim 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 the shear capacities of concrete beams reinforced with glass fiber reinforced polymer (GFRP) plates as shearreinforcement To examine the shear performance we manufactured and tested a total of eight specimens Test variables includedtheGFRP strip-width-to-spacing ratio and type of opening arrayThe specimenwith aGFRP plate with a 3times2 opening array showedthe highest shear strength From the test results the shear strength increased as the strip-width-to-strip-spacing ratio increasedAlso we used the experimental results to evaluate whether the shear strength equations of ACI 318-14 and ACI 4401R can beapplied to the design of GFRP shear reinforcement In the results the ACI 440 equation underestimated the experimental resultsmore than that of ACI 318

1 Introduction

Several studies have been carried out on the flexural behaviorof concrete beamswith fiber reinforced polymer (FRP) tensilereinforcement because FRPmaterials have advantages such ascorrosion resistance light weight machinability workabilityand high strength [1ndash5] Most FRP shear reinforcement forconcretemembers has been studied as ameans of retrofittingHawileh et al [6] and Al-Tamimi et al [7] suggested tech-niques that involved externally bonding carbon fiber rein-forced polymer (CFRP) laminates or sheets to reinforcedconcrete members Hassan and Rizkalla [8] researched thebonding strength of FRP plates that were either embeddedor attached to the exterior of concrete members Howevertypical shear reinforcement (stirrup) for concrete members isdifficult to fabricate with FRP materials because of their brit-tle nature and unidirectional characteristics Therefore FRPshear reinforcement has not yet been sufficiently investigatedThe strength of the bent portion is significantly less than thatof the straight part of FRP rods hence several codes anddesign guidelines have specified the reduced capacity of FRPstirrups caused by bending the bars [9ndash12] Recent studiesinvestigated the shear capacities of FRP stirrups andproposedan equation of shear strength [12ndash15] Kim et al proposed

a new type of FRP shear reinforcement as a substitute for steelstirrups [16] Plate-type FRP shear reinforcement has betterconstructability and easier fabrication than FRP stirrupsAlso plate shear reinforcement does not reduce the strengthby concentrating stress in the bent portion In an earlierpaper the types of FRP and shape of reinforcement did notsignificantly affect the shear strength

In this paper considering economics and ease of fab-rication we use a lattice shaped GFRP material for shearreinforcement To evaluate the applicability of FRP plates forshear reinforcement shear tests were conducted using con-crete beams embedded with GFRP plates with openings con-sidering the array of the openings and the GFRP strip-width-to-spacing ratio as the main variables We also analyzed thefailure modes and strain distributions

2 Experimental Investigation

21 Experimental Materials Following ASTM C39 [17] wetested seven cylindrical specimens of 150mm diameter and300mm height The average compressive strength of the 28-day concrete was 446MPa Ten deformed steel bars withdiameter of 25mm and yield strength of 500MPa were used

Hindawi Publishing CorporationInternational Journal of Polymer ScienceVolume 2015 Article ID 213583 8 pageshttpdxdoiorg1011552015213583

2 International Journal of Polymer Science

Table 1 Details of the experimental variations of the GFRP plate designs

SpecimenGFRP plate

Type 119891119891119906 Width (119908119891) Thickness (119905) Center-to-center spacing of vertical strips (119904)(MPa) (mm) (mm) (mm)

A-1 A 480 20 4 340A-2 A 480 30 4 340A-3 A 480 50 4 340A-4 A 480 70 4 340A-5 A 480 65 4 170A-6 A 480 70 4 110B-3 B 480 375 4 230C-3 C 480 375 4 230

Figure 1 Schematic view of a concrete beam reinforced with GFRPplates

as longitudinal reinforcement We used GFRP plates withopenings embedded in the concrete as shear reinforcementThe tensile test of the FRP was conducted based on CSAS806-02 [10]The tensile stress was 480MPa Figure 1 shows aschematic view of a specimen

22 Specimen Details We considered the array of openingsGFRP strip-width-to-spacing ratio and the amount of rein-forcement as variables The GFRP plates were manufacturedin three shapes as shown in Figures 2 and 3 Each platehad the same total area (119887119891 times ℎ119891) the A-Type had a 2 times 2opening array B-Type a 3times2 opening array andC-Type a 3times3opening array All the intersections of the horizontal (0∘) andvertical (90∘) components made right angles The differencein thewidth of the horizontal and vertical components of eachplate provided variants within each type of opening arrayDetails of the three plate designs and the variations withineach type are given in Table 1

We tested a total of eight concrete beams embeddedwith GFRP plates with openings Figure 4 illustrates how weplaced GFRP plates in the specimens depending on theirshapes The anchorage length (119897119889) was 300mm far from thepoints of support The total span (119871) and clear span (119897119899)were 2700mm and 2100mm respectively The thickness ofthe concrete cover was 40mm and the shear span-to-depthratio was 24 All the specimens were reinforced using tendeformed steel bars with a diameter of 25mm in two layers toensure shear failure prior to flexural failure in the beam tests

23 Test Setup Load was applied to each specimen at a rateof 5 kNmin using a hydraulic jack with a maximum capacityof 5000 kN as shown in Figure 5 The force generated by thehydraulic jackwas transmitted to the center of a steel spreaderbeam installed to apply two-point loading to the beam

specimen A load cell attached to the bottom of the jackmeasured the magnitude of the loading A linear variable-differential transducer (LVDT) installed at the bottom centerof the specimenmeasured the vertical displacement As illus-trated in Figure 5 we installed four strain gauges at the centerof the horizontal and vertical components of each FRP plateA data logger collected load displacement and strain data

3 Shear Strength Equation

Figure 6 defines the width of the GFRP strip (119908119891) effectivedepth (119889) and spacing (119904)

Several mechanisms contribute to the shear capacities ofreinforced concrete beams such as the concrete shear rein-forcement mechanical aggregates interlocking and dowelaction of the tensile reinforcement Shear reinforcement hasa mechanism for resistance to shear as shown in Figure 7For this paper we replaced the stirrup with a vertical strip ofthe FRP shear reinforcement The function of the horizontalstrip is to anchor the vertical stripsThe horizontal projectionof the crack is taken as 119889 The number of FRP vertical stripscrossing the crack is 119889119904 Assuming that all FRP vertical stripsreach their failure the shear strength of the shear reinforce-ment can be obtained from

119881119904 =

119860119891119891119891119906119889

119904 (1)

We assume the crack angle to be 45∘ when calculatingthe shear strength of the shear reinforcement The tensilebehavior of the FRP is characterized by a linearly elasticstress-strain relationship up to failure Hence shear failure isassumed to occur after fracture of the shear reinforcement

31 Shear Strength Equation in ACI 318-14 As shown in (2)the shear strength equation in ACI 318-14 [15] provides thesum of the shear strength of the concrete and the shearreinforcementThe shear strength of concrete can be obtainedfrom (3) which includes the longitudinal steel ratio (120588119908) andshear span-to-depth ratio (119886119889) Equation (4) calculates theshear strength of the shear reinforcement material based onthe concept of the shear strength of a steel stirrup in ACI 318-14 Calculating the shear strength of FRP plates requires thearea of the vertical components (119860119891) the number of vertical

International Journal of Polymer Science 3

(a) A-Type (b) B-Type

(c) C-Type

Figure 2 Designs of the three experimental GFRP plates

bf

x

s

y

hf

wf

Figure 3 Notation of geometry for a GFRP plate

components (119899) and the tensile strength in the critical shearspan as in (4)The area of the plate (119860119891) can be obtained from(5) and the number of vertical components in the criticalshear span can be obtained from (6)

119881119899 = 119881119888 + 119881119891 (2)

119881119888 = (016radic1198911015840119888 +17120588119908119889

119886) 119887119908119889 (3)

119881119891318 = 119899119860119891119891119891119906 sin120572 (4)

119860119891 = 2119905119891119908119891 (5)

119899 =119889

119904(1 + cot120572) (6)

32 Shear Strength Equation in ACI 4401R-06 ACI 4401Rprovides a shear strength equation for concrete with FRPrebar flexural reinforcement However in this paper weadopted the shear strength equation for concrete in ACI318 because we used steel flexural reinforcement The shearstrength of the shear reinforcement can be calculatedwith (7)Equation (8) gives the stress level in the FRP shear reinforce-ment at its utmost for use in design ACI 4401R addresses thereduced shear strength of stirrups caused by bending the FRPbars as shown in (9) Because our GFRP shear reinforcementis a plate type we did not consider the bend portion Consider

119881119891440 = 119899119860119891119891119891V119889 sin120572 (7)

119891119891V119889 = 0004119864119891 le 119891119891119887 (8)

119891119891119887 = (005119903119887

119889+ 03)119891119891119906V (9)

4 Experimental Test Results

41 Failure Mode As shown in Figure 8 flexural cracksoccurred at the tension surface in the middle of the spanfollowed by the formation of inclined cracks As the inclined


P P

813 474 340 3002700

4025

4042

0

(a) A-1

P P

813 474 340 3002700

4025

4042

0

(b) A-2

P P

813 474 3002700

4025

4042

0

340

(c) A-3

P P

813 474 340 3002700

4040

420

(d) A-4

P P

813 474 3002700

4025

4042

0170

(e) A-5

P P

813 474 340 3002700

4025

4042

0

(f) A-6

P P

813 474 231 3002700

4025

4042

0

(g) B-3

P P

813 474 231 3002700

4025

4042

0

(h) C-3

Figure 4 Arrangement of GFRP plates in specimens

2700

300

3425

350

813

Steel straingauge FRP strain

gauge

Figure 5 Test setup of typical specimen

cracks propagated toward the loading point concrete crush-ing occurred in the upper end region of the inclined crack atthe final stage of failure In other words shear-compressionfailure (shear failure from the diagonal crack) occurred Theinitial crack appeared at a load of approximately 150 kN in themiddle of the beam It appeared to be a flexural crack causedby tensile stress due to bending At approximately 200 kNa flexural shear crack appeared at effective depth far from

wf

d

sVertical

component

Figure 6 Definitions of 119908119891 119889 and 119904

the point of support At approximately 450 kN the diagonalcrack appeared and then a flexural shear crack followedThereinforcement of the GFRP plates increased resistance to theshear force as the diagonal crack occurred and elongated


A B

CVc

d

s

T

Afffu

Figure 7 Shear resistance by FRP shear reinforcement

(a) A-2

(b) A-3

(c) B-3

(d) C-3

Figure 8 Shear-compression failure in specimens

When the GFRP plate reached the limit of its tensile strengthit fractured and specimen failure occurred

We observed two typical failure modes in response to theamount of reinforcement provided First all the specimensexcept A-5 and A-6 fractured and the plates ruptured afterthey had demonstrated their maximum shear strength Theconcrete cover of specimens A-5 and A-6 on the otherhand fractured before the plate reached its maximum shearstrength The specimens showed two different failure modesbecause the size of the openings in the plates and the ratioof the area of the openings varied This result could also becaused by a lack of concrete coverageTherefore if the openingsize ratio of the area of openings and sufficient concrete

Table 2 Maximum loading and shear strength test results

Specimen 119875max 119881max Failure mode(kN) (kN)

A-1 57320 28660 ShearA-2 59173 29587 ShearA-3 77683 38842 ShearA-4 89976 44988 ShearA-5 74874 37437 ShearA-6 95027 47514 ShearB-3 87264 43632 ShearC-3 75793 37897 Shear

Table 3 Size and opening dimensions of FRP reinforcements

Specimen 119887119891 ℎ119891 119909 119910 OpeningFRP plate ()A-1 700 340 320 125 6723A-2 710 340 310 125 6421A-3 730 340 290 125 5842A-4 750 340 270 125 5294A-5 405 340 975 125 3540A-6 290 340 40 125 2028B-3 730 340 1933 125 5842C-3 730 340 1933 83 5819

coverage conditions are met the plate will demonstratemaximum shear strength and the specimen will provideeffective shear performance The test results for maximumloading and maximum shear strength are summarized inTable 2

42 Array of Openings and Ratio of Openings Figure 9 showsthe measurements used for each plate type and the variationsof those types The total width and height of the plates aremarked as 119887119891 and ℎ119891 respectively the width and heightof each opening are marked as 119909 and 119910 respectively Theopening size and ratio of the area of openings are listed inTable 3 Ratio of the area of openings is the area of all openingsdivided by the total area of the plate We designed the plate tomeet the following conditions both the width (119909) and depth(119910) of theGFRPplate openings described in Table 3 should beat least 100mm and ratio of the area of openings should behigher than 50

In specimens A-5 and A-6 which did not meet thoseconditions the concrete exhibited brittle failure before theplate reached the limit of its maximum strength SpecimenC-3 whichmet the ratio condition but not the size conditionshowed lower maximum shear strength than Specimen B-3 did which met both conditions Therefore if the openingsize is larger than 100mm and ratio of the area of openings ishigher than 50 sufficient integration between the FRP shearreinforcement and the concrete can be expected

Figure 10 shows the load-deflection relations for threespecimens (A-3 B-3 and C-3) with the same ratio of the areaof openings All three specimens exhibited the same behaviorbefore shear failure This test result indicates that Specimen


bf

hf

xy

Figure 9 Dimensions of a GFRP plate and its openings

A-3B-3C-3

0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)

5 10 15 200Deflection (mm)

Figure 10 Load-deflection curves for three different arrays ofopenings in GFRP shear reinforcement

B-3 had more effective integration than A-3 because ofa larger bonded area between the concrete and the B-3plate Although C-3 had the largest bonded area among thethree its depth (119910) was less than 100mm Specimen B-3showed the largest shear strengthTherefore to increase shearcapacity the bonded area between the FRP plate and the con-crete should be maximized while meeting the conditions ofopening size and ratio of the area of openings

43 Amount of Shear Reinforcement To examine the influ-ence of the amount of shear reinforcement on shear strengthwe designed each specimen with different amounts of rein-forcement The amount of shear reinforcement was theproduct of the number of vertical components in the criticalshear span (119899) the width of the vertical components (119908119891)and the thickness of the vertical components (119905119891) that is(119899 times 119908119891 times 119905119891) Figure 11 shows the load-deflection relationsfor specimens with various shear reinforcement areas Theamount of shear reinforcement for the experimental variants

0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)

5 10 15 20 25 300Deflection (mm)

A-1A-2A-3

A-4A-5A-6

Figure 11 Load-deflection curves for amount of shear reinforce-ment

ACI 318ACI 4401R

Vex

pVn

minus1

minus05

0

05

1

15

2

25

3

A-4 A-5A-1 A-3 A-6A-2Specimens

Figure 12 Ratio of test results to theoretical predictions of shearstrength (119881exp119881119899)

A-1 to A-4 was controlled by the different widths of thevertical strips for A-5 and A-6 it was controlled by differentspacing of the vertical strips Figure 12 shows the ratio ofshear strength for six specimens (A-1 A-2 A-3 A-4 A-5and A-6) according to the amount of shear reinforcement119881exp was obtained from the experiment that measured shearstrength and 119881119899 was obtained from the equation by whichshear strength was calculated

All of the specimens except A-5 and A-6 showed similarratios of shear strength In contrast specimens A-5 and A-6 showed only 80ndash90 of the calculated value Because theplate had insufficient opening size and ratio of the area ofopenings brittle failure occurred in specimens A-5 and A-6before the shear reinforcement reached the limit of its maxi-mum strength


Table 4 Experimental results and ratio of shear strength

Specimen 119881119888 119881119891318 119881119891440 119881exp 119881exp119881119899318 119881exp119881119899440(kN) (kN) (kN) (kN)A-1 16455 3868 1612 28860 141 160A-2 16455 5802 2418 29587 133 157A-3 16455 9671 4029 38842 149 190A-4 16455 13539 5641 44988 150 204A-5 16455 25144 10476 37437 090 139A-6 16455 41847 17436 47514 081 140B-3 16455 10722 4467 43632 161 209C-3 16455 10722 4467 37897 139 181

Vex

p(k

N)

050

100150200250300350400450500

005 01 015 02 0250GFRP strip-width-to-strip-spacing ratio (wfs)

Figure 13 Effect of the GFRP strip-width-to-spacing ratio on shearstrength

Figure 13 shows shear strength according to the width-to-spacing ratio of the strip for all of the specimens except thetwo that did not meet the opening size and ratio conditions(A-5 and A-6) The results indicate that the shear strengthincreases as the spacing-width ratio of a strip increases Asexpected effective shear-crack control is established by pro-viding a larger bonded area to resist shear cracksThis bondedarea increases as the width-to-spacing ratio increases

5 Comparison of Experimental Results andShear Strength Equations

Table 4 shows the shear strength of the concrete (119881119888) shearstrength of the plate (119881119891) and maximum shear strength (119881119899)which is the sum of the shear strength of the concrete and ofthe plate of the beam designed using the shear strength equa-tions of ACI 318 and ACI 440-1R The ratio of shear strength(119881exp119881119899) which compares the maximum calculated shearstrength (119881119899) and the experimental shear strength (119881exp) isalso included in Table 4 The shear strength equation in ACI318-14 calculates the shear strength of concrete as a constantAs shown in Table 4 the mean value of the shear strengthratio (119881exp119881119899) is 146 with a standard deviation of 010 usingACI 318 and the shear strength ratio (119881exp119881119899) of two valueswas between 133 and 161 On the other hand ACI 4401Rgives a mean value 183 with a standard deviation of 021 with

a shear strength ratio of two values between 157 and 209This verifies that the shear strength equation in ACI 318 canbe used to predict the shear strength of concrete beams withembedded GFRP plates with openings as long as the platemeets the minimum conditions for opening size and ratio ofthe area of openings On the other hand when using ACI4401R only 40 of the design strength was applied as tensilestrength therefore the test results were underestimated

6 Conclusions

In this study to analyze the shear performance of concretebeams with embedded GFRP plates with openings weselected the array of openings ratio of the area of openingsamounts of shear reinforcement and GFRP strip-width-to-strip-spacing ratio as variables We used the shear strengthequations in ACI 318-14 and ACI 4401R to compare theexperimental and theoretical shear strengths We draw thefollowing conclusions

(1) The width and height of the opening should be largerthan 100mm and the ratio of the area of openingsshould be greater than 50 to obtain effective shearperformance

(2) Three different results from three different shapes ofreinforcing plates show that increasing the bondedarea between the GFRP plate and the concreteincreases the performance of the shear reinforcementprovided the basic conditions are met

(3) Analysis of the GFRP strip-width-to-spacing ratioshowed that as the ratio increased the bonded areaincreased which improved resistance to shear cracks

(4) The equations in ACI 318 and ACI 4401R yieldedgenerally conservative shear strength resultsTheACI318 code gives a mean value of 146 with a standarddeviation of 01 The ACI 4401R code gives a meanvalue of 183 with a standard deviation of 02 There-fore the shear strength equation in ACI 318 was moreapplicable than that in ACI 4401R to the GFRP plate-reinforced concrete beams

Notations

119886119889 Shear span-to-depth ratios119860119891 Sectional area of a vertical strip of FRP plate (mm2)119887119908 Web width (mm)119889 Distance from extreme compression fiber to centroid

of longitudinal tension reinforcement (mm)1198911015840119888 Specified compressive strength of concrete (MPa)119891119891119906 Specified tensile strength of FRP plate (MPa)119899 Number of vertical components of the FRP plate

within the critical shear span119904 Center-to-center spacing of longitudinal shear

reinforcement (mm)119905119891 Thickness of FRP plate (mm)119881119888 Nominal shear strength provided by concrete (kN)119881exp Shear strength provided by experiment (kN)119881119891 Nominal shear strength provided by FRP plate (kN)


119881119899 Nominal shear strength (kN)119908119891 Width of FRP plate (mm)120572 Angle between shear reinforcement and longitudinal

axis of the member (∘)120588119908 Ratio of 119860 119904 to 119887119908119889

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by a National Research Foundationof Korea (NRF) grant funded by the Korea government(MSIP) (NRF-2011-0016332)

References

[1] C Higgins G T Williams M M Mitchell M R Dawson andD Howell ldquoShear strength of reinforced concrete girders withcarbon fiber-reinforced polymer experimental resultsrdquo ACIStructural Journal vol 109 no 6 pp 805ndash814 2012

[2] F-Y Yeh and K-C Chang ldquoSize and shape effects on strengthand ultimate strain in FRP confined rectangular concretecolumnsrdquo Journal ofMechanics vol 28 no 4 pp 677ndash690 2012

[3] A Mofidi and O Chaallal ldquoShear strengthening of RC beamswith externally bonded FRP composites effect of strip-width-to-strip-spacing ratiordquo Journal of Composites for Constructionvol 15 no 5 pp 732ndash742 2011

[4] M M R Taha M J Masia K-K Choi P L Shrive and NG Shrive ldquoCreep effects in plain and fiber-reinforced polymer-strengthened reinforced concrete beamsrdquo ACI Structural Jour-nal vol 107 no 6 pp 627ndash635 2010

[5] C Mazzotti M Savoia and B Ferracuti ldquoAn experimentalstudy on delamination of FRP plates bonded to concreterdquoConstruction and Building Materials vol 22 no 7 pp 1409ndash1421 2008

[6] R A Hawileh H A Rasheed J A Abdalla and A K Al-Tamimi ldquoBehavior of reinforced concrete beams strengthenedwith externally bonded hybrid fiber reinforced polymer sys-temsrdquoMaterials and Design vol 53 pp 972ndash982 2014

[7] A K Al-Tamimi R Hawileh J Abdalla and H A RasheedldquoEffects of ratio of CFRP plate length to shear span and endanchorage on flexural behavior of SCC RC beamsrdquo Journal ofComposites for Construction vol 15 no 6 pp 908ndash919 2011

[8] 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

[9] ACI Committee 4401R Guide for the Design and Constructionof Concrete Reinforced with FRP Bars (ACI 4401R-06) Ameri-can Concrete Institute Farmington Hills Mich USA 2006

[10] Canadian Standard Association (CSA) Design and Construc-tion of Building Components with Fiber Reinforced Polymers(CSA S806-02) Canadian Standard Association (CSA) Missis-sauga Canada 2002

[11] Intelligent Sensing for Innovative Structures (ISIS) CanadaReinforcing Concrete Structures with Fibre Reinforced Poly-mers (ISIS-M03-01) ISIS Canada Resource Centre WinnipegCanada 2001

[12] M R Ehsani H Saadatmanesh and S Tao ldquoBond of hookedglass fiber reinforced plastic (GFRP) reinforcing bars to con-creterdquo ACI Materials Journal vol 92 no 4 pp 391ndash400 1995

[13] K Ishihara T Obara Y Satao T Ueda and Y KakutaldquoEvaluation of ultimate strength of FRP rods at bent up portionrdquoin Proceedings of the 3rd International Symposium on Non-Metallic (FRP) Reinforcement for Concrete Structures pp 27ndash34Sapporo Japan 1997

[14] E Shehata R Morphy and S Rizkalla ldquoFibre reinforced poly-mer shear reinforcement for concrete members behaviour anddesign guidelinesrdquo Canadian Journal of Civil Engineering vol27 no 5 pp 859ndash872 2000

[15] A K El-Sayed E El-Salakawy and B Benmokrane ldquoMechani-cal and structural characterization of new carbon FRP stirrupsfor concrete membersrdquo Journal of Composites for Constructionvol 11 no 4 pp 352ndash362 2007

[16] D-J Kim M S Kim J Choi H Kim A Scanlon and Y HLee ldquoConcrete beams with fiber-reinforced polymer shear rein-forcementrdquo ACI Structural Journal vol 111 no 4 pp 903ndash9112014

[17] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTMC 39 ASTMInternational West Conshohocken Pa USA 2001

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Table 1 Details of the experimental variations of the GFRP plate designs

SpecimenGFRP plate

Type 119891119891119906 Width (119908119891) Thickness (119905) Center-to-center spacing of vertical strips (119904)(MPa) (mm) (mm) (mm)

A-1 A 480 20 4 340A-2 A 480 30 4 340A-3 A 480 50 4 340A-4 A 480 70 4 340A-5 A 480 65 4 170A-6 A 480 70 4 110B-3 B 480 375 4 230C-3 C 480 375 4 230

Figure 1 Schematic view of a concrete beam reinforced with GFRPplates

as longitudinal reinforcement We used GFRP plates withopenings embedded in the concrete as shear reinforcementThe tensile test of the FRP was conducted based on CSAS806-02 [10]The tensile stress was 480MPa Figure 1 shows aschematic view of a specimen

22 Specimen Details We considered the array of openingsGFRP strip-width-to-spacing ratio and the amount of rein-forcement as variables The GFRP plates were manufacturedin three shapes as shown in Figures 2 and 3 Each platehad the same total area (119887119891 times ℎ119891) the A-Type had a 2 times 2opening array B-Type a 3times2 opening array andC-Type a 3times3opening array All the intersections of the horizontal (0∘) andvertical (90∘) components made right angles The differencein thewidth of the horizontal and vertical components of eachplate provided variants within each type of opening arrayDetails of the three plate designs and the variations withineach type are given in Table 1

We tested a total of eight concrete beams embeddedwith GFRP plates with openings Figure 4 illustrates how weplaced GFRP plates in the specimens depending on theirshapes The anchorage length (119897119889) was 300mm far from thepoints of support The total span (119871) and clear span (119897119899)were 2700mm and 2100mm respectively The thickness ofthe concrete cover was 40mm and the shear span-to-depthratio was 24 All the specimens were reinforced using tendeformed steel bars with a diameter of 25mm in two layers toensure shear failure prior to flexural failure in the beam tests

23 Test Setup Load was applied to each specimen at a rateof 5 kNmin using a hydraulic jack with a maximum capacityof 5000 kN as shown in Figure 5 The force generated by thehydraulic jackwas transmitted to the center of a steel spreaderbeam installed to apply two-point loading to the beam

specimen A load cell attached to the bottom of the jackmeasured the magnitude of the loading A linear variable-differential transducer (LVDT) installed at the bottom centerof the specimenmeasured the vertical displacement As illus-trated in Figure 5 we installed four strain gauges at the centerof the horizontal and vertical components of each FRP plateA data logger collected load displacement and strain data

3 Shear Strength Equation

Figure 6 defines the width of the GFRP strip (119908119891) effectivedepth (119889) and spacing (119904)

Several mechanisms contribute to the shear capacities ofreinforced concrete beams such as the concrete shear rein-forcement mechanical aggregates interlocking and dowelaction of the tensile reinforcement Shear reinforcement hasa mechanism for resistance to shear as shown in Figure 7For this paper we replaced the stirrup with a vertical strip ofthe FRP shear reinforcement The function of the horizontalstrip is to anchor the vertical stripsThe horizontal projectionof the crack is taken as 119889 The number of FRP vertical stripscrossing the crack is 119889119904 Assuming that all FRP vertical stripsreach their failure the shear strength of the shear reinforce-ment can be obtained from

119881119904 =

119860119891119891119891119906119889

119904 (1)

We assume the crack angle to be 45∘ when calculatingthe shear strength of the shear reinforcement The tensilebehavior of the FRP is characterized by a linearly elasticstress-strain relationship up to failure Hence shear failure isassumed to occur after fracture of the shear reinforcement

31 Shear Strength Equation in ACI 318-14 As shown in (2)the shear strength equation in ACI 318-14 [15] provides thesum of the shear strength of the concrete and the shearreinforcementThe shear strength of concrete can be obtainedfrom (3) which includes the longitudinal steel ratio (120588119908) andshear span-to-depth ratio (119886119889) Equation (4) calculates theshear strength of the shear reinforcement material based onthe concept of the shear strength of a steel stirrup in ACI 318-14 Calculating the shear strength of FRP plates requires thearea of the vertical components (119860119891) the number of vertical



(c) C-Type


bf

x

s

y

hf

wf



119881119899 = 119881119888 + 119881119891 (2)

119881119888 = (016radic1198911015840119888 +17120588119908119889

119886) 119887119908119889 (3)

119881119891318 = 119899119860119891119891119891119906 sin120572 (4)

119860119891 = 2119905119891119908119891 (5)

119899 =119889

119904(1 + cot120572) (6)


119881119891440 = 119899119860119891119891119891V119889 sin120572 (7)

119891119891V119889 = 0004119864119891 le 119891119891119887 (8)

119891119891119887 = (005119903119887

119889+ 03)119891119891119906V (9)




P P

813 474 340 3002700

4025

4042

0

(a) A-1

P P

813 474 340 3002700

4025

4042

0

(b) A-2

P P

813 474 3002700

4025

4042

0

340

(c) A-3

P P

813 474 340 3002700

4040

420

(d) A-4

P P

813 474 3002700

4025

4042

0170

(e) A-5

P P

813 474 340 3002700

4025

4042

0

(f) A-6

P P

813 474 231 3002700

4025

4042

0

(g) B-3

P P

813 474 231 3002700

4025

4042

0

(h) C-3


2700

300

3425

350

813


gauge



wf

d

sVertical

component




A B

CVc

d

s

T

Afffu


(a) A-2

(b) A-3

(c) B-3

(d) C-3














bf

hf

xy


A-3B-3C-3

0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)





0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)

5 10 15 20 25 300Deflection (mm)

A-1A-2A-3

A-4A-5A-6


ACI 318ACI 4401R

Vex

pVn

minus1

minus05

0

05

1

15

2

25

3








Vex

p(k

N)

050

100150200250300350400450500







6 Conclusions






Notations










Acknowledgment


References

























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





(c) C-Type


bf

x

s

y

hf

wf



119881119899 = 119881119888 + 119881119891 (2)

119881119888 = (016radic1198911015840119888 +17120588119908119889

119886) 119887119908119889 (3)

119881119891318 = 119899119860119891119891119891119906 sin120572 (4)

119860119891 = 2119905119891119908119891 (5)

119899 =119889

119904(1 + cot120572) (6)


119881119891440 = 119899119860119891119891119891V119889 sin120572 (7)

119891119891V119889 = 0004119864119891 le 119891119891119887 (8)

119891119891119887 = (005119903119887

119889+ 03)119891119891119906V (9)




P P

813 474 340 3002700

4025

4042

0

(a) A-1

P P

813 474 340 3002700

4025

4042

0

(b) A-2

P P

813 474 3002700

4025

4042

0

340

(c) A-3

P P

813 474 340 3002700

4040

420

(d) A-4

P P

813 474 3002700

4025

4042

0170

(e) A-5

P P

813 474 340 3002700

4025

4042

0

(f) A-6

P P

813 474 231 3002700

4025

4042

0

(g) B-3

P P

813 474 231 3002700

4025

4042

0

(h) C-3


2700

300

3425

350

813


gauge



wf

d

sVertical

component




A B

CVc

d

s

T

Afffu


(a) A-2

(b) A-3

(c) B-3

(d) C-3














bf

hf

xy


A-3B-3C-3

0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)





0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)

5 10 15 20 25 300Deflection (mm)

A-1A-2A-3

A-4A-5A-6


ACI 318ACI 4401R

Vex

pVn

minus1

minus05

0

05

1

15

2

25

3








Vex

p(k

N)

050

100150200250300350400450500







6 Conclusions






Notations










Acknowledgment


References

























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




P P

813 474 340 3002700

4025

4042

0

(a) A-1

P P

813 474 340 3002700

4025

4042

0

(b) A-2

P P

813 474 3002700

4025

4042

0

340

(c) A-3

P P

813 474 340 3002700

4040

420

(d) A-4

P P

813 474 3002700

4025

4042

0170

(e) A-5

P P

813 474 340 3002700

4025

4042

0

(f) A-6

P P

813 474 231 3002700

4025

4042

0

(g) B-3

P P

813 474 231 3002700

4025

4042

0

(h) C-3


2700

300

3425

350

813


gauge



wf

d

sVertical

component




A B

CVc

d

s

T

Afffu


(a) A-2

(b) A-3

(c) B-3

(d) C-3














bf

hf

xy


A-3B-3C-3

0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)





0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)

5 10 15 20 25 300Deflection (mm)

A-1A-2A-3

A-4A-5A-6


ACI 318ACI 4401R

Vex

pVn

minus1

minus05

0

05

1

15

2

25

3








Vex

p(k

N)

050

100150200250300350400450500







6 Conclusions






Notations










Acknowledgment


References

























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




A B

CVc

d

s

T

Afffu


(a) A-2

(b) A-3

(c) B-3

(d) C-3














bf

hf

xy


A-3B-3C-3

0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)





0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)

5 10 15 20 25 300Deflection (mm)

A-1A-2A-3

A-4A-5A-6


ACI 318ACI 4401R

Vex

pVn

minus1

minus05

0

05

1

15

2

25

3








Vex

p(k

N)

050

100150200250300350400450500







6 Conclusions






Notations










Acknowledgment


References

























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




bf

hf

xy


A-3B-3C-3

0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)





0

100

200

300

400

500

600

700

800

900

1000

Load

(kN

)

5 10 15 20 25 300Deflection (mm)

A-1A-2A-3

A-4A-5A-6


ACI 318ACI 4401R

Vex

pVn

minus1

minus05

0

05

1

15

2

25

3








Vex

p(k

N)

050

100150200250300350400450500







6 Conclusions






Notations










Acknowledgment


References

























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






Vex

p(k

N)

050

100150200250300350400450500







6 Conclusions






Notations










Acknowledgment


References

























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








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



research article shear behavior of concrete beams...

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