Materials and Design 61 (2014) 16–25

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Materials and Design

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Technical Report

Nonlinear behavior of shear deficient RC beams strengthened with nearsurface mounted glass fiber reinforcement under cyclic loading

http://dx.doi.org/10.1016/j.matdes.2014.04.0640261-3069/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +971 6 515 2496; fax: +971 6 515 2979.E-mail address: rhaweeleh@aus.edu (R.A. Hawileh).

G. Sakar a, R.A. Hawileh b,⇑, M.Z. Naser b, J.A. Abdalla b, M. Tanarslan a

a Dokuz Eylul University, Department of Civil Engineering, Buca, Izmir 35160, Turkeyb American University of Sharjah, Department of Civil Engineering, P.O. Box 26666, Sharjah, United Arab Emirates

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 February 2014Accepted 22 April 2014Available online 29 April 2014

The aim of this investigation is to evaluate experimentally and numerically the cyclic loading response ofreinforced concrete (RC) beams strengthened in shear with Glass Fiber Reinforced Polymer (GFRP) rodsusing the near surface mounted (NSM) technique. The experimental results indicated that the use of GFRProds as NSM strengthening systems can significantly enhance the overall capacity and ductility of sheardeficient RC members when subjected to cyclic loading. In particular, the increase in the load-carryingcapacity of the strengthened specimens over the unstrengthened control specimen was in the range of49–66%. Furthermore, the increase in the displacement over the control specimen ranged between112% and 172%. A 3D finite element (FE) model was also developed to simulate the response of the testedspecimens. The developed FE model integrates multiple simulation techniques, nonlinear material prop-erties and corresponding constitutive laws. The models incorporate concrete cracking, yielding of steelreinforcement, bond–slip behavior between NSM reinforcement and adhesive material and between steelreinforcement and adjacent concrete material, respectively. The load–deflection response envelopes andthe load–deflection hysteresis loops of the experimentally tested beams and those simulated by the FEmodels were compared. Good matching was observed between the predicted and measured results atall stages of cyclic loading.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Extensive experimental and numerical research studies hasbeen conducted recently to evaluate the response of externallybonded Fiber reinforced polymer (FRP) structural members includ-ing slabs, beams and columns [1–11]. FRP materials have highstrength to weight ratio and anti-corrosion properties and consid-ered to be the current most effective solutions in strengtheningand repairing reinforced concrete (RC) structural members. Rein-forced concrete beams are typically strengthened with externallybonded FRP sheets or laminates via epoxy adhesives. However, itwas observed in many cases that debonding of the FRP materialsfrom the concrete substrata occurs before achieving the theoreticalfull capacity of the strengthened member [12,13]. Debondingoccurs when maximum shear stresses at the FRP level reaches itsultimate bond strength. Hence, success of a conventionally exter-nally bonded FRP strengthening system is governed by the adhe-sion (bond) of the FRP and adjacent concrete surfaces.Furthermore, it should be noted that other factors might negativelyinfluence the performance of externally strengthened systems such

as temperature variations, freeze and thaw, and accidentalimpacts, among other factors.

FRP rods have been proposed as an alternative strengtheningsystem to overcome some of the drawbacks of the externallybonded FRP plates and sheets. The FRP rods will be attached to thestructural member using the near surface mounting (NSM) tech-nique. A typical NSM strengthening system consists of embeddingFRP rods into precut grooves in the concrete cover. The grooves usu-ally have square or rectangular cross sections and are usually filledwith epoxy adhesives and/or cement mortar. The major advantageof this strengthening system is that the possibility of the debondingof FRP from the concrete substrate will be reduced. In addition, thequality of the concrete inside the groove is typically better than thatof the surface concrete, in addition, NSM rods are protected by theconcrete cover such that they will not be exposed to environment,and concrete surface preparation will no longer be needed. The con-tribution of carbon fiber polymer (CFRP) bars to the flexural capacityof RC beams was examined earlier [14–16]. However, little researchhas been conducted on the use of FRP rods for shear-dominantapplications [17–19]. Those studies [17–19] showed that CFRP rodscan provide significant increase in load carrying capacity for sheardeficient beams. In particular, De Lorenzis and Nanni [17] evaluatedexperimentally two RC beam specimens deficient in shear and

Fig. 1. Detailing of control beam (BEAM-1).

G. Sakar et al. / Materials and Design 61 (2014) 16–25 17

strengthened with CFRP deformed rods using the NSM technique.The spacing between the vertical CFRP rods of the two strengthenedbeam specimens was 7 in. (178 mm) and 5 in. (127 mm), respec-tively. Test results had shown an increase, ranging from 28% to41%, in the load-carrying capacity of the strengthened specimensover the control beam. They concluded that the proposed NSMstrengthening technique considerably enhanced the shear carryingcapacity of RC beams. Similarly, Tanarslan [19] investigated, exper-imentally, the response of RC cantilever beams strengthened inshear using NSM–CFRP reinforcement under cyclic loading. A totalof eight RC beam specimens were casted and strengthened in shearwith CFRP rods using the NSM technique. The variables of the exper-imental program were the arrangement of the CFRP rods, spacingbetween the CFRP rods, and diameter of CFRP reinforcement. Theresults have shown an increase in the shear capacity of the strength-ened specimens over the control beam, ranging from 57% to 111%. Inaddition, the beams did not fail due to delamination, debonding orfracture of CFRP rod reinforcements.

Furthermore, additional parameters such as the length of FRProd, adhesive type and loading set-up, have been considered tostudy their influence in the overall behavior of NSM strengthenedsystems [20,21]. On the other hand, the use of GFRP reinforcementsfor shear strengthening has not been examined. This is mainly dueto alkali silica reaction that prohibits the use of GFRP bars. How-ever, test results confirmed that a properly designed and manufac-tured composite system of resin and glass can effectively protectthe glass fibers from degradation. Therefore, there is a need tobridge the knowledge gap in this research area and to investigatethe performance of RC beams strengthened with NSM GFRP bars.

Shear failure is brittle in nature and occurs without sufficientwarning. Therefore strengthening structures deficient in shear isof great importance, especially in active seismic regions. Conse-quently, experimental investigation should be conducted to resem-ble seismic events by testing NSM GFRP strengthened RC beamssubjected to cyclic loading. In addition, and to the best of theauthors’ knowledge, little research [22], if any has been publishedon finite element (FE) modeling of strengthened shear deficient RCbeams with NSM GFRP bars under cyclic loading.

The major objective of this paper is to experimentally andnumerically evaluate the response of shear deficient RC beamsstrengthened with NSM GFRP rods under cyclic loading. A totalof five cantilever beams specimens were strengthened using differ-ent spacing and diameter configurations of the NSM reinforcement.A finite element model has been developed which is capable ofpredicting the load–deflection envelope response and hysteresiscurves of the tested specimens with good accuracy.

Table 1Properties of tested specimens.

Specimen Topbars(mm)

Bot.bars(mm)

NSM GFRP reinforcement details

Diameter(mm)

Spacing(mm)

Arrangements

BEAM-1 (Control) 20 Ø 20 Ø – – –BEAM-2 (Strengthened) 20 Ø 20 Ø 6 Ø 160 Both sideBEAM-3 (Strengthened) 20 Ø 20 Ø 6 Ø 120 Both sideBEAM-4 (Strengthened) 20 Ø 20 Ø 10 Ø 160 Both sideBEAM-5 (Strengthened) 20 Ø 20 Ø 10 Ø 120 Both side

2. Experimental setup and procedure

A total of five rectangular RC cantilever beams with 200 mmwide and 350 mm deep were casted with a clear span of1700 mm. The beams were casted without stirrups in the beam’sspan as shown in Fig. 1 to fail in a shear mode. However, stirrupswere only provided at the loading support to prevent local cracksthat might occur due to applied load outside the shear span(Fig. 1). The beams were attached to a rigid RC column to simulatethe response of a fixed support. The column was heavily reinforcedto prevent cracking and pre-mature failure. Fig. 1 shows the geo-metrical details and the cross-sectional properties of the testedspecimens and rigid RC column.

All beams were casted from the same batch of concrete withwater, cement, sand and aggregate having a mass ratio of0.68:1:2:3, respectively. Four cylinder specimens were casted andtested at the same time of beam test to determine the compressivestrength of concrete. The measured average cylinder compressive

strength after 28-days was approximately 25 MPa. The main longi-tudinal reinforcement consisted of eight 20 mm diameter deformedsteel bars, four of which were located in the compression zone (topreinforcement) and the remaining four bars were located in the ten-sion zone (bottom reinforcement) of the members. A clear concretecover of 30 mm was kept constant for all the tested specimens toovercome any possible embedding problems. The reinforcing barsused in the experimental program were tested in tension to obtaintheir mechanical properties. The measured yield strength of thelongitudinal reinforcements was 414 MPa and 275 MPa,respectively.

The specimen designation, steel reinforcing and strengtheningscheme detailing are given in Table 1. BEAM-1 unstrengthenedand used as a control specimen to establish a reference for measur-ing the responses of the strengthened beams. The remaining fourshear deficient RC beams were strengthened with two legs ofNSM GFRP bars located on both vertical sides of the beams’cross-section as shown in Fig. 2 with different GFRP bar diametersand spacing. Beam specimens BEAM-2 and BEAM-3 were strength-ened with 6 mm diameter GFRP NSM rods spaced at 160, and120 mm, respectively. On the other hand, BEAM-4, and BEAM-5were strengthened with 10 mm diameter GFRP NSM rods spacedat 160, and 120 mm, respectively.

Uniaxial coupon tests were carried out in a servo-controlled testmachine to obtain the mechanical properties of the GFRP barsincluding the stress–strain relationship, tensile strength and mod-ulus of elasticity. It is observed from the tests that the stress–strainrelationships for the tested specimens were linear up to failure.The average obtained modulus of elasticity and tensile strengthwere found to be 40.6 GPa and 550 MPa, respectively. On the otherhand, the epoxy adhesive used to bond the NSM GFRP bars to

(b) BEAM-3 and BEAM-5 (All Dimensions are in mm.)

(a) BEAM-2 and BEAM-4 (All Dimensions are in mm.)

Fig. 2. Strengthening schemes of strengthened beam specimens.

Rigid Floor

LVDT

Rig

id W

all

Hinge

Hinge

Load Cell

Hydraulic Jack

Fig. 3. Schematic of test setup.

0 2 4 6 8 10 12-80

-60

-40

-20

0

20

40

60

80

cycle number

Shea

r for

ce (K

N)

Fig. 4. Cyclic applied load history.

18 G. Sakar et al. / Materials and Design 61 (2014) 16–25

concrete surfaces had a tensile strength and secant tensile elasticmodulus of epoxy as 30 and 3800 MPa, respectively.

BEAM-1 was used as a benchmark and tested without any addi-tional FRP strengthening to establish a reference response. Theremaining shear deficient RC beams were strengthened with GFRPbars with different diameters and spacing as shown in Table 1. Theparameters varied herein were diameter of FRP rod as well as spac-ing used in between FRP reinforcement. Thus, specimens BEAM-2,and BEAM-3 were strengthened with 6 Ø diameter GFRP NSM rodsspaced at 160, and 120 mm, respectively. On the other hand,BEAM-4, and BEAM-5 were strengthened with 10 Ø diameter GFRPNSM rods spaced at 160, and 120 mm, respectively.

In order to install the NSM GFRP rods, grooves were cut into theconcrete cover. The dimensions of these grooves are a function ofthe bar diameter. The width of the groove is one and a half timesthe diameter of GFRP bar reinforcement. The vertical length of eachgroove was 350 mm, which is equal to the depth of the beam asshown in Fig. 2. The grooves were half-filled with the bondingepoxy adhesive. The GFRP reinforcement were subsequentlyinserted and lightly pressed to allow the adhesive to flow aroundthe GFRP bar and avoid any pores between the bars and the sidesof the groove. Afterwards, the grooves were filled with more epoxyadhesive and the surface was leveled by removing any additionalepoxy. All applications were performed in a controlled lab environ-ment at room temperature. The strengthened specimens were leftto cure at room temperature for at least two weeks before testing.

A schematic view of the experimental set-up and arrangementof the measurement devices, including the loading column, aredepicted in Fig. 3. The loading column has two hinges, a loadingcell with 500 kN capacity and a hydraulic jack with 400 kN capac-ity. Four linear variable differential transformers (LVDTs) wereused to monitor displacements. The LVTD’s are located at the endof the beam specimens for maximum vertical displacement underthe rigid support to calculate the undesired displacement and

finally on the rigid support to calculate the rotation. In addition,cycles of loading and unloading were applied at the free end ofthe cantilever beam. Load cycles were selected to evaluate flexuraland shear cracks propagations. Fig. 4 shows a sample of the appliedloading history. Loading was steadily increased up to yielding ofthe flexural top or bottom steel reinforcements or failure of thetested specimen.

3. Experimental results and observations

The load–deflection hysteresis curves for the tested specimensmeasured at the free end of the cantilever beams are shown inFig. 5. It should be noted that the first crack appeared as a flexuralcrack at a load between 33.18 kN and 39.65 kN for all the testedspecimens, regardless of the strengthening scheme. As the loadincrement was increased, the initially developed flexural crackswere advanced through the member’s sides and caused shear crackpropagations. Similarly, shear cracks were also developed at theunstrengthened part of the specimens, between the GFRP bars.Thereafter, the behavior of the strengthened beams specimensshowed deviation according to the strengthening scheme.

Fig. 6 shows the load–deflection response envelop curves forthe tested specimens. These curves were plotted by connecting

Fig. 5. Load–deflection hysteresis curves for the tested specimens.

G. Sakar et al. / Materials and Design 61 (2014) 16–25 19

the peak loading values for each cycle versus their correspondingdeflection values. It is clear from Fig. 6 that all the tested specimenshave similar trend up to a load of about 30 kN. Afterwards, thebehavior tends to deviate based on the strengthening scheme.Table 2 lists the ultimate attained load prior to failure along withthe vertical deflection, and the increase in both the displacementand ultimate capacities compared to the unstrengthened specimen(BEAM-1).

It can be observed from Figs. 5, 6 and Table 2 that the use of theproposed NSM shear strengthening system with GRRP rods has sig-nificantly enhanced the cyclic load carrying capacity of the testedspecimens. The increase in load carrying capacity ranged between49% and 66% of the control beam specimen (BEAM-1), dependingon the rod diameter and rod spacing. The range of increase of loadcarrying capacity observed in this study and their trends agreesvery well with that of previous studies [17,19,22]. In addition,the displacements at failure (ductility) of the strengthened

specimens were more than that of the control specimen. Theincrease in the displacement over the control specimen rangedbetween 112% and 172%. Furthermore, the load carrying capacityhas been slightly improved with increasing bar size from 6 mmto 10 mm and with reducing the spacing from 160 mm to120 mm by less than 5.0%.

Three different failure mechanisms were observed in thisexperimental investigation. The observed failure mechanisms ofthe tested specimens were shear failure, shear failure due to con-crete cover separation and flexural failure followed with shear fail-ure. Fig. 7 shows the failure of the unstrengthened BEAM-1specimen which failed at a load of 61.90 kN due to the formationof a major shear crack.

BEAM-2 and BEAM-4 were strengthened with similar spacedGFRP bars at 160 mm (3/4d) center-to-center. The two specimensapproximately depicted the same behavior where both failed dueto concrete cover separation near the longitudinal tension

Fig. 7. Failure of control specimen.

Fig. 6. Load–deflection envelope curves of the tested specimens.

Beam 2

Fig. 8. Failure mode, Be

Table 2Measured experimental results.

Specimen Ultimateload (kN)

Ratio loadincrease toBEAM-1

Failuredisplacement(mm)

Ratio displacementincrease to BEAM-1

BEAM-1 61.90 – 9.46 –BEAM-2 92.68 1.49 22.68 2.40BEAM-3 98.11 1.58 20.08 2.12BEAM-4 96.29 1.56 22.64 2.39BEAM-5 102.50 1.66 25.70 2.72

20 G. Sakar et al. / Materials and Design 61 (2014) 16–25

reinforcement at the bottom of the beam as shown in Fig. 8. At15 kN, flexural cracks appeared at the tension face. Then at approx-imately 35 kN, shear cracks occurred at the unstrengthened partbetween the GFRP rods. When the load exceeded 45 kN, shearcracks started to develop faster and wider and propagated toexhaust the body of the beam’s web. This behavior continued untilthe load level reached 80 kN. BEAM-2, which was strengthenedwith 6 mm diameter GFRP bars, had sustained the 90 kN loadingcycle but failed in the subsequent cycle at a load of 92.68 kN.BEAM-4 also sustained the forward loading of the 90 kN cycle suc-cessfully and gained a slight increase in strength due to larger-sized GFRP bar diameter. However the BEAM-4 specimen failedat a load level of 96.29 kN.

BEAM-3 and BEAM-5 were strengthened with 6 mm and 10 mmGFRP bars, respectively with 120 mm center-to-center (d/4)spacing. The behavior of both strengthened beams was similarup to a load level of 80 kN. Decreasing the spacing similar toBEAM-2 and BEAM-4 improved the behavior and the specimenfailed at a load level of 98.11 kN. However, an abrupt shear failureoccurred as shown in Fig. 9. It was expected that BEAM-5 would beable to achieve a better behavior and reach its flexural capacity.However, multiple cracks were visually observed in that cycle. Inthe next load cycle, BEAM-5 specimen exceed the 100 kN and theflexural steel reinforcement have yielded, larger cracks wereobserved when the load was 95 kN that led to flexural failure fol-lowed by a shear failure at a load level of 102.50 kN.

Beam 4

am 2 and Beam 4.

Shear CrackShear Crack

Fig. 9. Sample of the failure modes observed in the experimental program.

G. Sakar et al. / Materials and Design 61 (2014) 16–25 21

4. Finite element modeling

In previous studies [11,22–27], the authors developed finite ele-ment (FE) models that predicted the response of unstrengthenedand externally strengthened members under static, fire and cyclicloading. One of the objectives of this study is to develop 3D nonlin-ear FE models to predict the performance of RC beams strength-ened with NSM GFRP rods. In order to validate the results, thedeveloped models have the same geometric and material proper-ties of that of the five tested specimens presented in the precedingsections. Taking advantage of symmetry in the beam’s transversedirection, one-half 3D model is developed using the FE software,ANSYS 11.0 [28]. The cyclic loading was applied to the free endof the cantilever beams as shown in Fig. 10. Fig. 10(a and b) showsa representative detailed sample of the developed model for astrengthened specimen with NSM GFRP rods.

The ANSYS SOLID65 [28] element was used to model the con-crete and epoxy adhesives materials. The element is capable ofsimulating cracking in tension and crushing in compression andit has three degrees of freedom per node. The column was heavilyreinforced and did not exhibit any cracking during loading [22].Thus, it was modeled with elastic material properties usingSOLID45 element [28] which is very similar to SOLID65 but with-out the cracking or crushing capabilities. On the other hand, thespar LINK8 [28] element is used to model the reinforcing GFRPand steel bars [22]. The element is defined by two nodes that hasthree translational degrees of freedom per node and is capable ofsimulating elastic–plastic deformation.

ANSYS spring COMBIN14 [28] was used to simulate the bond–slip behavior between the GFRP rods and surrounding epoxymaterials. The spring element is a uniaxial tension–compressionelement and is defined by its stiffness and has two nodes withup to three degrees of freedom per node. Determining the stiffnessof the spring will be discussed in the subsequent section.Additional information on the properties of the used element types

(a) Side view

(b) Isometric view of RC beam

Rigid column

Fig. 10. Details of the d

in FE simulation along with their nonlinear capabilities and desiredparameters (geometrical and material) is given in Table 3.

The mechanical material properties used as inputs in the devel-oped FE model were similar to those used in measured the exper-imental program and given in Table 4.

In order to numerically model the nonlinear behavior of con-crete material, the concrete constitutive material model in ANSYS[28] is used. The concrete constitutive material model is basedon the developed plastic model by William and Warnke [29]. Avalue of 0.2 [22,23] is taken for the open and closed shear inputcoefficients for the William and Warnke model. The William andWarnke model also assumes a tri-linear behavior to simulate theresponse of the concrete elements in tension. The tri-linear modelstarts with linear elastic segment up to the tensile strength of con-crete (Table 4). Once the concrete reaches its maximum tensilestress, a stiffness multiplier of 0.6 is used to simulate a softeningin the tensile stress to 60% of the concrete maximum tensile stressft. In other words, in a given concrete element, once the maximumtensile strength is achieved, the cracked element experiences asudden drop of strength equals to 0.6ft that represents the loss ofstiffness induced by the cracks development. Further, this soften-ing is followed by a linearly descending tensile response to zerostress at a strain equals to six times the maximum tensile strain.The conventional Hognestad [30] model is used to simulate theresponse of the concrete elements in compression.

The inelastic kinematic hardening von-Misses plasticity elastic-fully plastic model was used to simulate the nonlinear behavior ofthe steel bars. The modulus of elasticity and yield strength of thesteel reinforcement are reported in Table 4. On the other hand,the GFRP rod NSM reinforcement was modeled as a brittle linearelastic material up to its tensile strength. The modulus of elasticityand tensile strength of the GFRP rods are shown in Table 4. Fur-thermore, the epoxy adhesive material was defined as an elasticmaterial with the properties given in Table 4 up to its tensilestrength. The epoxy material will crack and fails according to

specimen

Concrete

Steel rebars

Epoxy ResinP

GFRP rebar

GFRP rebar

eveloped FE model.

Table 3Element types used in FE simulation.

Elementtype

No. ofnodes perelement

Material Numerical capabilities

SOLID65 8 Concrete Capable of cracking in tension andcrushing in compression, plasticdeformation, and creep

SOLID45 8 Epoxy Plasticity, creep, large deflection, andlarge strain

LINK8 2 Steel andGFRProds

Plasticity, creep, stress stiffening, andlarge deflection

COMBIN14 2 Bond–slip

Longitudinal or torsional spring

Fig. 11. Predicted and measured lo

Table 4Material properties used in the FE simulation.

Material Compressivestrength(MPa)

Yieldstrength(MPa)

Tensilestrength(MPa)

Elasticmodulus(GPa)

Poissonratio

Concrete 25.0 – 3.1a 24.0b 0.20Steel – 414.0 – 200.0 0.30GFRP – – 550.0 40.8 0.28Epoxy – – 30.0 3.80 0.29

a ft ¼ 0:62ffiffiffiffif 0c

p(MPa).

b Ex ¼ 4800ffiffiffiffif 0c

p(MPa).

22 G. Sakar et al. / Materials and Design 61 (2014) 16–25

William and Wranke model, defined above, upon reaching its ten-sile strength. The elastic modulus and tensile strength of the epoxymaterial are also reported in Table 4.

The developed models take into account the bond–slip behaviorbetween the bar reinforcement and surrounding material. Thebond–slip action between the steel reinforcement and surroundingconcrete material, as well as between the NSM GFRP rods andbonding material (epoxy) is simulated and it follows a set of rela-tionships presented in CEB-FIP model [31]. The bond–slip relation-ship used in this study is described by Eq. (1).

s ¼ sus

sm

� �0:4

ð1Þ

where s is the bond stress at a given slip s (MPa); su is the maxi-mum bond stress (MPa); s is the relative slip at a given shear stress(mm); sm is the maximum slip at sm (mm).

The bond–slip behavior is used to calculate the stiffness of thespring COMBIN14 elements that follows the ascending segmentof CEB-FIP model. Then, a horizontal plateau is set to equal themaximum bond stress (sm since the embedded reinforcement can-not completely debond from their substrates [32–34].

According to the CEB-FIB provisions, the value of the maximumbond stress depends on reinforcement bar type and adjoiningmaterial. According to the model [31], the values of

ffiffiffiffif 0c

pand

0.6 mm were taken to simulate the values of su and sm respectively

ad–deflection envelope results.

Fig. 12. Measured and predicted load–deflection hysteresis curves.

Table 5Comparison between the FE predicted and experimental measured results.

Specimen FE model Failure load (kN) Percentage difference (FE/Exp.) Maximum deflection (mm) Percentage difference

Exp. FE Exp. FE (FE/Exp.)

BEAM-1 FE BEAM-1 61.90 62.1 0.32% 11.69 12.2 4.3%BEAM-2 FE BEAM-2 92.68 95.05 2.55% 20.68 21.6 1.04%BEAM-3 FE BEAM-3 98.11 100.0 1.92% 20.08 21.67 7.90%BEAM-4 FE BEAM-4 96.29 96.0 �0.30% 22.64 23.4 3.35%BEAM-5 FE BEAM-5 102.50 103.0 0.49% 25.70 24.5 �4.67%

G. Sakar et al. / Materials and Design 61 (2014) 16–25 23

for the steel reinforcement. On the other hand, the values of su andsu of the GFRP rods were assumed based on the experimental pro-grams of [35] to be 20.25 MPa, and 0.42 mm, respectively.

COMBIN14 elements require an input stiffness parameter (k)defined as the longitudinal stiffness. The longitudinal stiffness (k)of the spring element (COMBIN14) is calculated using Eq. (2) [36].

k ¼ psu

pdrNrsuL1 þ L2

2

� �ð2Þ

where p is the horizontal distance between the tension steel rein-forcement bars in (mm), dr is the diameter of the bars in (mm), Nr

is the number of bars and L1 and L2 are the lengths of two adjacent

24 G. Sakar et al. / Materials and Design 61 (2014) 16–25

bar elements in (mm). It should be noted that the adjacent nodesbetween the bars and epoxy or concrete materials are coupled inthe transverse directions of the bar reinforcement.

In this study, the force convergence criterion controls the con-vergence of Newton–Raphson solution scheme. After several trials,it was found that a convergence tolerance limit of 0.1 [22–24] led toconvenient and optimum solution processing time. In addition, deb-onding of the NSM GFRP rod from the epoxy (GFRP bar pull-out) wasalso considered as a failure criteria. Divergence in solution is definedwhen the solution for a 1 N load increment does not converge. Oncedivergence take place, the ultimate load-carrying capacity of eachbeam specimen was traced and checked against the obtained testdata.

5. Finite element results and validation

Five FE models were developed and have been numerically val-idated against the experimental data tested herein. The developednumerical models were distinguished using the prefix ‘‘FE’’ fol-lowed by the tested specimen designation BEAM-1, BEAM-2,BEAM-3, BEAM-4, and BEAM-5, respectively.

Fig. 11 shows the predicted and measured load–deflectionresponse envelope results of the tested specimens. The load–deflection response envelopes were developed by connecting peakedge deflection and loading values for the entire cyclic loadinghistory.

Fig. 12 displays the measured and the predicted load–deflectionhysteresis curves. In addition, Table 5 shows a comparisonbetween the predicted and the measured failure load and its corre-sponding deflection. It is clear from Figs. 11 and 12 and Table 5 thatthe developed FE model managed to successfully predict theresponse of the tested specimens at all stages of loading till failureof the specimens. The maximum deviation between the predictedand measured data is less than 10% as shown in Table 5. The accu-racy of the developed FE models are in agreement with previousstudies conducted by the authors [11,22–27,34] of FRP strength-ened beams using different techniques and tested under static,cyclic and fire loading.

6. Conclusions

This paper presented experimental results and numerical simu-lation of shear deficient rectangular RC beams strengthened withNSM GFRP rods when subjected to cyclic loading. The followingconclusions could be drawn from the results of this research:

� The tested NSM GRRP shear strengthening system has sig-nificantly enhanced the cyclic load carrying capacity of thetested specimens within a range of 49% and 66% (of thecontrol beam specimen) depending on the strengtheningscheme.

� The use of the proposed NSM shear strengthening systemwith GRRP rods has also significantly enhanced the ductil-ity of the beam by increasing the displacement. The dis-placements at failure (ductility) of the strengthenedspecimens were more than that of the control unstrength-ened specimen and ranged between 112% and 172%.

� The load carrying capacity has been slightly improved (lessthan 5%) when increasing the GFRP bar size from 6 mm to10 mm and reducing the spacing from 160 mm to 120 mm.

� The predicted results from the developed FE models in thisstudy correlated very well with the measured data of thetested specimens at all stages of the cyclic loading. Themaximum deviation between the numerical and testresults is less than 10%.

� The developed FE model could be used as a valid tool forfuture investigations of the cyclic performance of RC beamsstrengthened in shear with NSM GFRP reinforcement usingdifferent schemes and configurations.

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