ShearBehaviourofRCBeamsStrengthenedbyVariousUltrahigh...

Research ArticleShear Behaviour of RC Beams Strengthened by Various UltrahighPerformance Fibre-Reinforced Concrete Systems

Walid Mansour 1 and Bassam A Tayeh 2

1Civil Engineering Department Faculty of Engineering Kafrelsheikh University Kafr El-Sheikh Egypt2Civil Engineering Department Faculty of Engineering Islamic University of Gaza Gaza State of Palestine

Correspondence should be addressed to Bassam A Tayeh btayehiugazaedups

Received 20 January 2020 Revised 30 March 2020 Accepted 29 June 2020 Published 16 July 2020

Academic Editor Raffaele Landolfo

Copyright copy 2020 Walid Mansour and Bassam A Tayeh is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

is study presents a numerical investigation on the shear behaviour of shear-strengthened reinforced concrete (RC) beams byusing various ultrahigh performance fibre-reinforced concrete (UHPFRC) systemse proposed 3D finite element model (FEM)was verified by comparing its results with those of experimental studies in the literature e validated numerical model is used toanalyse the crucial parameters which are mainly related to the design of RC beams and shear-strengthened UHPFRC layers suchas the effect of shear span-to-depth ratio on the shear behaviour of the strengthened or nonstrengthened RC beams and the effectof geometry and length of UHPFRC layers Moreover the effect of the UHPFRC layersrsquo reinforcement ratio and strengthening ofone longitudinal vertical face on the mechanical performance of RC beams strengthened in shear with UHPFRC layers isinvestigated Results of the analysed beams show that the shear span-to-depth ratio significantly affects the shear behaviour of notonly the normal-strength RC beams but also the RC beams strengthened with UHPFRC layers However the effect of shear span-to-depth ratio has not been considered in existing design code equations Consequently this study suggests two formulas toestimate the shear strength of normal-strength RC beams and UHPFRC-strengthened RC beams considering the effect of theshear span-to-depth ratio

1 Introduction

Many reinforced concrete (RC) structures have to berepaired or strengthened to address their limitations instructural performance andor durability properties [1]e need to strengthen can be due to many reasons suchas change in service conditions corrosion of steel rein-forcement or upgradation of current design code pro-visions A promising material used in the strengthening ofRC structures is the ultrahigh performance fibre-rein-forced concrete (UHPFRC) because of its superior me-chanical properties very high strength in compressionand tension and extremely densified microstructure emechanical properties of UHPFRC have been extensivelyinvestigated [2ndash9]

In the last decade studies have experimentally usedUHPFRC for the flexural strengthening of RC beams

[10ndash14] ey showed that UHPFRC could increase stiffnessand resistance and delay the formation of localised cracks Inaddition Al-Osta et al [15] explored the effectiveness andefficiency of strengthening RC beams with UHPFRC by (a)roughening the surface of RC beams via sand blasting andcasting the UHPFRC in situ around the beams and (b)joining the prefabricated UHPFRC plates to the RC beamsusing epoxy However Tayeh et al [16] investigated thestrengthening of RC beams with UHPFRC laminates usingthe two different bonding methods of gluing with epoxy andmechanical anchoring e aforementioned techniquesemphasised that beams strengthened with a three-side jacketshowed the highest capacity enhancement whereas beamsstrengthened only at the bottom soffit showed lower en-hancement [15 16] Moreover the flexural response ofstrengthened RC beams improved when reinforcing barswere added within the laminates

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 2139054 18 pageshttpsdoiorg10115520202139054

e technique of flexural strengthening using UHPFRCwas investigated numerically in [17] by developing a nu-merical model for the extensive investigation of strength-ened RC beams with layers and jackets eir findings werecompared with those of beams strengthened with conven-tional RC layers and combinations of UHPFRC and steel-reinforcing bars eir results clearly showed that superiorperformance could be achieved by using the three-sideUHPFRC jackets

Shear failure is unfavourable for engineers because of itssudden occurrence with a brittle failure mode and manystudies have focused on improving the capacity and ductilityof RC beams strengthened in shear with UHPFRC[13 18ndash22] Sakr et al [23] proposed a 3D finite elementmodel (FEM) to investigate the behaviour of RC beamsstrengthened in shear with prefabricated UHPFRC plates byusing (a) one longitudinal vertical-side strengthening and(b) two longitudinal vertical-side strengthening eyconcluded that the prefabricated UHPFRC plates couldsignificantly enhance the ultimate load carrying capacityductility and strain of longitudinal reinforcement in thestrengthened RC beams compared with the control beamfailed in shear

Moreover Mohammed et al [24] experimentally andnumerically examined the effectiveness and efficiency ofUHPFRC-strengthened RC beam specimens without stir-rups by using three different strengthening techniques undertorsional moment e beam specimen strengthened on allfour sides obtained higher torsional strength compared withthe reference specimen

Despite the results of these studies using UHPFRC instrengthening and rehabilitating conventional RC beamslimited studies have considered the effect of the shear span-to-depth and UHPFRC layer reinforcement ratios on thebehaviour of RC beams strengthened in shear withUHPFRC Moreover information on the effect of UHPFRClayer length and geometry on the behaviour of the con-sidered structure is lacking Because of the difficulty ofstrengthening many structural elements on both sides es-pecially in exterior beams due to the neighbouring bordersstrengthening the RC beams using only one vertical lon-gitudinal side has been considered in the current researchStrengthening only one vertical longitudinal side of the RCbeams is rarely studied and evaluated in the literature

us a 3D FEM with the ability to simulate the be-haviour of RC beams strengthened in shear with UHPFRClayers is proposed in this study and validated using theexperiments available in the literature (Sections 2 and 3)Additionally the validated FEM is used in Section 4 todemonstrate the effects of the shear span-to-depth ratiolength and geometry of UHPFRC layers reinforcingUHPFRC layers and strengthening only one longitudinalvertical side on the behaviour of RC beams strengthenedin shear with UHPFRC layers

2 Numerical Investigation

e shear behaviour of simply supported RC beamsstrengthened with UHPFRC using different strengthening

schemes was investigated numerically e nonlinear finiteelement analysis software ABAQUS [25] was used to developa 3D model simulating the shear behaviour of UHPFRC-strengthened RC beams

21 Elements and Meshing Normal-strength concrete(NSC) and UHPFRC are modelled using the 3D stresseight-noded linear brick element (C3D8R) as shown inFigure 1 is figure also shows the two-noded linear 3Dtruss element (T3D2) which is used to model the steel-reinforcing bars and stirrups is element is suitable forstructural members that transmit only axial load

A mesh size of 40mmtimes 40mm was suggested to dividethe simulated RC beams to fine elements e proposed finemesh was required to obtain accurate results consistent withthose of the experimental response on the level of failureload and failure pattern

22 Materials e model of concrete damage plasticity wasused to simulate both concrete and UHPFRC although twoother models (concrete smeared and brittle cracking) wereavailable in ABAQUSe model of concrete damage plasticitywas used in this study due to its ability inmodelling the complexnonlinear properties of concrete and UHPFRC considering thesoftening behaviour under either compression or tension isapproach can also be used with a rebar to model concretereinforcement

e model of concrete damage plasticity assumes that theuniaxial tensile and compressive response of concrete ischaracterised by damaged plasticity as illustrated in Figure 2e damage variables in compression and tensionwere denotedby dc and dt respectively Such damage variables can take valuesfrom 0 (to represent the undamaged material) to 1 (to denotethe total loss of strength) In the case of uniaxial tension thestress-strain response followed a linear elastic relationship untilthe value of the failure stress σto was reached Beyond thefailure stress the formation of microcracks was representedmacroscopically with a softening stress-strain response whichinduced strain localisation in the concrete structure e re-sponse was linear under uniaxial compression until the value ofthe initial yield σco was reached e response in the plasticzone was typically characterised by stress hardening followedby strain softening beyond the ultimate stress σcu Birtel andMark [26] proposed the following equations to determine thecompressive and tensile damage parameters

(i) Compressive damage parameter (dc)

dc 1 minusσcEminus 1

c

εplc 1bc( 1113857 minus 1( 1113857 + σcEminus 1c

(1)

(ii) Tensile damage parameter (dt)

dt 1 minusσtEminus 1

c

εplt 1bt( 1113857 minus 1( 1113857 + σtEminus 1c

(2)

2 Advances in Civil Engineering

where dc and dt are the compressive and tensile damageparameters respectively σc and σt are the compressiveand tensile stresses of concrete respectively Ec is theelasticity modulus of concrete εplc and εplt are the plasticstrains corresponding to the compressive and tensilestrengths of concrete respectively and bc and bt areconstant parameters (they can take values from 0 to 1)

e reinforcement steel wasmodelled using elastic-perfectlyplastic material as suggested in [23] e relationship betweenthe reinforcement steel and concrete was modelled as a perfectbond (embedded region whereas the concrete was the hostelement)

3 Numerical Validation

e results of the proposed FEM were compared with theexperimental results available in the literature [21] to verifyits accuracy e experimental investigation consisted ofnine RC beams prepared considering the shear span-to-depth ratio (ad) and strengthening pattern as two variableparameters Two steel rebars with 20mm diameter wereplaced in the tension zone whilst two rebars with 12mmdiameter were provided in the compression zone of all thespecimens Moreover two-legged stirrups with 8mm di-ameter at a spacing of 120mm were used as shear rein-forcement Table 1 lists the details of the nine beamspecimens is table concluded that the beam specimens

were strengthened by applying a 30mm layer of UHPFRCover the longitudinal vertical faces of the RC beam speci-mens UHPFRC jacketing was executed in the followingschemes (a) two longitudinal vertical faces of the beams and(b) two longitudinal vertical faces in addition to the bottomface

e materials of concrete UHPFRC and steel rein-forcement were modelled using the data generatedthrough the experimental program as shown in Table 2

e model parameters of concrete damage plasticity forconcrete and UHPFRC materials are defined in Table 3whereas the simulated nonlinear properties of both con-crete and UHPFRC under tension and compression aredepicted in Figure 3

Table 4 shows the number of elements number ofdegrees of freedom and central processing unit time eprocessor type used for this study was 24 GHz with corei7

e bond between NSC and UHPFRC was considered aperfect bond (tie constraint the concrete and UHPFRC arethe master and slave surfaces respectively) becausedebonding was not observed in all the experimental tests[27ndash32]e control and strengthened beam specimens wereanalysed under a four-point loading arrangement All ex-perimental results including failure load failure mode andload-deflection responses were compared with those ob-tained through numerical modelling to check their validity

(a) (b) (c)

Figure 1 Finite element mesh of beam specimens (a) Concrete elements (b) Steel reinforcement elements (c) UHPFRC elements

σtσto

Eo

(1 ndash dt)Eo

ξtξt

elξt

pl

(a)

σcσc

σco

Eo (1 ndash dc)Eo

ξcξc

elξc

pl

(b)

Figure 2 Response of concrete to uniaxial loading in (a) tension and (b) compression [25]

Advances in Civil Engineering 3

31 Load-Deflection Responses e load-deflection re-sponses of FE obtained for the control beams beamsstrengthened using two layers and beams strengthenedusing three-side jackets with different shear span-to-depth ratios are shown in Figures 4ndash6 respectively andcompared with the experimental results

e results showed that FEM could simulate the behaviourof the RC control beams in addition to the RC beamsstrengthened with UHPFRC with acceptable accuracy

Table 5 presents a comparison between the experimentalresults of ultimate load and deflection at maximum load andtheir counterparts obtained using FE analysis For the first

Table 1 Details of the beam specimens tested by Bahraq et al [21]

Beam ID Strengthening pattern Dimensions (btimes htimes L) (mm) ad ratio Shear span (mm)CT-10 Control beam 140times 230times1120 10 200SB-2SJ-10 Two longitudinal vertical faces 200times 230times1120 10 200SB-3SJ-10 Jacket (two longitudinal vertical faces and the bottom face) 200times 260times1120 10 200CT-15 Control beam 140times 230times1120 15 280SB-2SJ-15 Two longitudinal vertical faces 200times 230times1120 15 280SB-3SJ-15 Jacket (two longitudinal vertical faces and the bottom face) 200times 260times1120 15 280CT-20 Control beam 140times 230times1120 20 384SB-2SJ-20 Two longitudinal vertical faces 200times 230times1120 20 384SB-3SJ-20 Jacket (two longitudinal vertical faces and the bottom face) 200times 260times1120 20 384

Table 2 Mechanical properties of concrete UHPFRC and shear reinforcement

Property Concrete UHPFRC Shear reinforcementCubical compressive strength (MPa) 65 1514 mdashModulus of elasticity (GPa) 31 41 2006Yield strength (MPa) mdash mdash 610Poissonrsquos ratio 02 022 03

Table 3 Concrete damage plasticity model parameters for concrete and UHPFRC

Material Dilation angle Eccentricity (fb0fc0) K Viscosity parameter

Concrete 20 01 116 0667 0UHPFRC 36 01 116 0667 0

ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

10

ndash0003 ndash0002 ndash0001 0 0001 0002

Stre

ss (M

Pa)

Plastic strain

(a)

ndash160

ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

ndash0006 ndash0004 ndash0002 0 0002 0004 0006

Stre

ss (M

Pa)

Plastic strain

(b)

Figure 3 Nonlinear behaviour of materials (a) concrete and (b) UHPFRC

Table 4 Model size and CPU time

Beam ID Number of elements Number of degree of freedom (DOF) CPU time (minutes)CT-10 5456 21000 35SB-2SJ-10 8016 33954 55SB-3SJ-10 9656 40323 70


group (control specimens) the experimental value of failureloads for CT-10 CT-15 and CT-20 were 383 286 and 276kNversus the predicted 379 295 and 285kN through the nu-merical model with a difference of only 1 3 and 3 re-spectively Additionally FEM could obtain the ultimate load forthe strengthened RC beams SB-2SJ-10 SB-3SJ-10 SB-2SJ-15SB-3SJ-15 SB-2SJ-20 and SB-3SJ-20 with a difference of 11 2 0 8 and 1 respectively compared with theexperimental results which had acceptable accuracy e nu-merical model can accurately estimate not only the ultimateload but also the midspan deflection at maximum load eexperimental midspan deflections for the tested RC beams werein the range of 217 to 750mm compared with 270 to 900mmin the case of FEM

32 Failure Mode e experimental and numerical in-vestigations showed that control beams CT-10 CT-15and CT-20 failed in shear compression by forming di-agonal cracks joining the points of the load applicationand support as shown in Figures 7ndash9 respectively In thecase of beam specimens SB-2SJ-10 SB-2SJ-15 and SB-2SJ-20 the vertical flexural cracks appeared at the beammidspan followed by the inclined crack as depicted inFigures 10ndash12 respectively However beam specimensSB-3SJ-10 SB-3SJ-15 and SB-3SJ-20 failed in theflexure by forming vertical cracks located in the maxi-mum bending moment zone as depicted inFigures 13ndash15 respectively is comparison concludedthat FEM could successfully simulate the majority offailure modes

4 Parametric Study

e validated FEM was used in the numerical investi-gation of the crucial parameters related to the design ofRC beams strengthened in shear with UHPFRC layerse effect of parameters and the geometry and length ofUHPFRC layers on the shear span-to-depth ratio andshear behaviour of RC beams were determined In ad-dition the effects of UHPFRC layersrsquo reinforcement ratioand one longitudinal vertical face strengthening on themechanical performance of RC beams strengthened inshear with UHPFRC layers were demonstrated

41 Shear Span-to-Depth Ratio411 Control Beam Specimens Previous studies [33ndash39]have shown that the shear span-to-depth ratio signifi-cantly affects the shear behaviour of RC elementsHowever this term has been ignored in current designcode equations [40 41] which estimate the shear capacityof RC beams Eleven normal-strength RC beams withshear span-to-depth ratios ranging from 10 to 35 at 025intervals were analysed using the validated FEM asshown in Table 6 Such samples helped not only to un-derstand the performance of RC members with differentratios of shear span-to-depth ratio but also derive anequation estimating the shear capacity of RC beamsconsidering the effect of shear span-to-depth ratio e

results presented in Table 6 including the ultimate loadbesides deflection at ultimate load reveal that the ulti-mate load decreases as the shear span-to-depth ratio anddeflection increase As the shear span-to-depth ratioincreased the shear failure mode gradually changed fromshear-compression failure to shear-tension failure Shearcracks propagated rapidly and violently in the shear-tension failure thereby causing the deterioration in ul-timate load with the increase in shear span-to-depthratio

0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)

Midspan deflection (mm)

CT-10 EXPCT-15 EXPCT-20 EXP

CT-10 FECT-15 FECT-20 FE

Figure 4 Experimental versus FE load-deflection responses forcontrol beam specimens


0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)

SB-2SJ-10 EXPSB-2SJ-15 EXPSB-2SJ-20 EXP

SB-2SJ-10 FESB-2SJ-15 FESB-2SJ-20 FE

Figure 5 Experimental versus FE load-deflection responses forstrengthened beam specimens using two vertical layers


e ultimate load of the analysed specimens wascalculated using the following design codes [40 41]

(1) Euro Code 2 (EC2) e Euro code estimates the shearresistance of beams with stirrups Vr(N) as follows

Vr 018K 100ρlfc( 111385713

bd +Asw

Szfyw d cot θd (3)

θd sinminus 1

Aswfyw d

bw sV1αccfc

1113971

(4)

where K 1 +200d

radicle 2 fc is the cylinder compressive

strength of concrete MPa d is the effective depth mm ρl is thelongitudinal reinforcement ratio b is the beam width mm Asw

is the cross-sectional area of shear reinforcement S is thespacing of stirrupsfyw d is the design value of the steel yieldstrength and θd is the design concrete strut angle

e value of V1 may be set to 09 minus (fc200) whereasthe internal lever arm may be set to z 09 d [42]

Additionally the long-term coefficient factor αcc is set to085 as recommended in [43]

(2) ACI Code ACI code considers both the concrete andshear reinforcement contributions when the shear capacityis calculated as

Vr

fc

1113968

6bd +

Asw

Sfywd d (5)

e obtained results in numerical ultimate load versusultimate load using the aforementioned design codes for the 11specimens are shown in Figure 16

e EC2 and ACI codes failed to capture the response ofthe RC beams compared with FEM eir values are alwaysconstant despite the change in shear span-to-depth ratiosbecause this term was ignored in their calculations Moreoverthe ACI code obtained lower estimates than EC2 in the ulti-mate load of the analysed RC beams because a diagonalconcrete strut (θd) of 45deg was adopted in the ACI modelcompared with 218deg le θd le 45deg in the case of the EC2model A

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)




Figure 6 Experimental versus FE load-deflection responses for strengthened beam specimens using three-side jacket

Table 5 Summary of the experimental and FE load-deflection responses

Beam IDExperimental results FE response

Ultimate load (kN) Deflection at ultimate load (mm) Ultimate load (kN) Deflection at ultimate load (mm)CT-10 383 217 379 270SB-2SJ-10 567 347 560 360SB-3SJ-10 628 310 631 325CT-15 286 440 295 470SB-2SJ-15 402 520 396 600SB-3SJ-15 482 410 482 600CT-20 276 700 285 690SB-2SJ-20 346 750 317 900SB-3SJ-20 353 414 356 720


(CT-10)

(a)

PE max principal(avg 75)

+2191e ndash 02+2008e ndash 02+1826e ndash 02+1643e ndash 02+1460e ndash 02+1278e ndash 02+1095e ndash 02+9128e ndash 03+7302e ndash 03+5477e ndash 03+3651e ndash 03+1826e ndash 03+0000e + 00

(b)

Figure 7 Failure mode for beam specimen CT-10 (a) experiment and (b) FE analysis

(CT-15)

(a)



(b)



(CT-20)

(a)


+2380e ndash 02+2181e ndash 02+1983e ndash 02

+7932e ndash 03+5949e ndash 03+3966e ndash 03+1983e ndash 03+0000e + 00

+1785e ndash 02+1586e ndash 02+1388e ndash 02+1190e ndash 02+9915e ndash 03

(b)


(SB-2SJ-10)

(a)



(b)

Figure 10 Failure mode for beam specimen SB-2SJ-10 (a) experiment and (b) FE analysis


(SB-2SJ-15)

(a)





(b)


(SB-2SJ-20)

(a)



(b)



(SB-3SJ-10)

(a)

+3628e ndash 03+0000e + 00





(b)


(SB-3SJ-15)

(a)



(b)



new equation that can predict the ultimate load of the RCbeams considering the effect of shear span-to-depth ratio isnecessary to improve the accuracy of the current design codeequations A new equation was derived on the basis of non-linear regression analysis of the numerical results using SPSSstatistics program and its results were compared with those ofthe numerical and analytical models as shown in Table 7

(3) New Equation e proposed new equation estimatesthe shear capacity of concrete members considering theconcrete compressive strength and effect of shear span-to-depth ratio (ad) as follows

Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)

e proposed new equation estimated the ultimate loadcapacity of RC control beamswell by using the numericalmodelwith an average error of 634 as shown in Table 7 Howeverfurther experimental and numerical studies are required toimprove the accuracy of the proposed equation

Error FEmodel minus new equation

FEmodellowast100 (7)

(SB-3SJ-20)

(a)





(b)


Table 6 Results of the control beam specimens with various shear span-to-depth ratios

Beam ID ad ratio Shear span (mm) Ultimate load (kN) Deflection at ultimate load (mm)CT-10 100 200 379 270CT-125 125 250 335 390CT-15 150 280 295 470CT-175 175 350 289 590CT-20 200 384 285 690CT-225 225 450 251 810CT-250 250 500 212 920CT-275 275 550 203 1000CT-30 300 600 178 1150CT-325 325 650 172 1290CT-350 350 700 167 1370


412 RC Beam Specimens Strengthened with UHPFRCLayers Table 8 presents the effect of shear span-to-depth ratioon the ultimate load and deflection at the ultimate load of RCbeams strengthened with UHPFRC on (a) two longitudinalvertical faces of beams (series SB-2SJ) and (b) two longitudinalvertical faces in addition to the bottom face (series SB-3SJ) e

ultimate load of the strengthened RC beams decreased sig-nificantly with the increase in shear span-to-depth ratio In thecase of SB-2SJ series the ultimate load decreased from560kN inthe case of SB-2SJ-10 specimen to 175kN in the case of SB-2SJ-35 with a decreasing ratio of 68 Strengthening the verticaland bottom faces of the RC beams (series SB-3SJ) still

Table 7 Results of new equations and numerical and analytical models for the ultimate load of the RC control beams with various shearspan-to-depth ratios

Beam ID ad ratioUltimate load (kN)

Error FE model EC2 ACI New equation

CT-10 100 379 281 141 428 minus 1293CT-125 125 335 281 141 351 minus 478CT-15 150 295 281 141 302 minus 237CT-175 175 289 281 141 269 692CT-20 200 285 281 141 244 1439CT-225 225 251 281 141 225 1036CT-250 250 212 281 141 211 047CT-275 275 203 281 141 199 197CT-30 300 178 281 141 189 minus 618CT-325 325 172 281 141 181 minus 523CT-350 350 167 281 141 174 minus 419Absolute average error 634

Table 8 Results of the RC beam specimens strengthened with UHPFRC with various shear span-to-depth ratios

Beam ID ad ratio Shear span (mm) Ultimate load (kN) Deflection at ultimate load (mm)SB-2SJ-10 10 200 560 360SB-2SJ-15 15 280 396 600SB-2SJ-20 20 384 317 900SB-2SJ-25 25 500 245 102SB-2SJ-30 30 600 200 113SB-2SJ-35 35 700 175 131SB-3SJ-10 10 200 631 325SB-3SJ-15 15 280 482 600SB-3SJ-20 20 384 356 720SB-3SJ-25 25 500 278 89SB-3SJ-30 30 600 226 101SB-3SJ-35 35 700 196 114

0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)

Shear span-to-depth ratio

FE modelACI code

EC2 codeNew equation

Figure 16 Total load capacity for the RC control beams with various shear span-to-depth ratios


deteriorated the ultimate load with the increase in shear span-to-depth ratio e ultimate load was 631 kN and 196kN in theSB-3SJ-10 and SB-3SJ-35 specimens respectively with a de-creasing ratio of 69 By contrast the shear span-to-depth ratio

increased as the deflection at ultimate load increased due to thesuperiormechanical properties of UHPFRC in tension from thecrack bridging phenomena which occurred because of thepresence of steel fibre

Table 9 Results of the RC beam specimens strengthened with UHPFRC with various lengths with constant shear span-to-depth ratio 20

Beam ID Ultimate load (kN) Ultimate load enhancement Deflection at ultimate load (mm)CT-20 285 mdash 690SB-2SJ-ST-100 299 490 525SB-2SJ-ST-200 309 840 870SB-2SJ-033L 287 070 240SB-2SJ-074L 301 560 590SB-2SJ-20 317 1130 900SB-3SJ-ST-100 331 1620 585SB-3SJ-ST-200 348 2220 695SB-3SJ-033L 314 1020 475SB-3SJ-074L 341 1970 615SB-3SJ-20 356 2500 720

(a) (b)

Figure 17 Strengthening configuration (a) specimen SB-2SJ-ST-100 and (b) specimen SB-3SJ-ST-100 (all dimensions in mm)

(a) (b)

Figure 18 Strengthening configuration (a) specimen SB-2SJ-033L and (b) specimen SB-3SJ-033L


42 Geometry and Length of UHPFRC Layers is sectioninvestigated the effect of the strengthening pattern andstrengthening length on the shear response of the RCbeams strengthened with UHPFRC layers Ten RC beamswere strengthened via (a) strengthening with UHPFRCstrips spaced every 100mm and (b) strengthening usingUHPFRC layers e results are listed in Table 9 efollowing nomenclature was used to distinguish betweenthe two technical specimens

SB-2SJ-ST-100 the specimen strengthened withUHPFRC strips where the third and fourth items wereSTstrips and width of the UHPFRC strip 100mmrespectively (Figure 17)SB-2SJ-033L the specimen strengthened with aUHPFRC layer where the third item is the length ofthe UHPFRC layer as a ratio from the beam length(L) and equal to 033L (Figure 18)

In the RC beams strengthened using two longitudinalvertical faces of UHPFRC as expected specimen SB-2SJ-20wasfully strengthened over its length and obtained the highestultimate load and deflection at 317kN and 900mm respec-tively However specimen SB-2SJ-033L with the loweststrengthening length realised the lowest ultimate load (287kN)with an increasing ratio equal to only 07 as compared withthe reference beam CT-20 Additionally specimen SB-2SJ-074L (strengthened along the shear zones only) improved thefailure load by 560 whereas the control beam CT-20 ob-tained 590mm deflection at the ultimate load

In the case of specimens strengthened on both verticalfaces and lower face using UHPFRC the ultimate loadcapacity increased as the strengthening length increasedSpecimen SB-3SJ-20 obtained the highest ultimate loadand deflection at 356 kN and 720 mm respectivelywhereas specimen SB-3SJ-033L achieved the lowest ul-timate load (314 kN) which was 1020 higher than that

Figure 19 Reinforcement assembly embedded in the UHPFRC vertical layers of specimen SB-2SJ-23-36

Table 10 Results of the RC beam specimens strengthened with reinforced UHPFRC layers with different reinforcement ratios with constantshear span-to-depth ratio 20

Beam ID Shear span (mm)Longitudinal reinforcement(ratioAsAUHPFRC )

Transversal reinforcement(ratioAstAUHPFRC ) Ultimate

load (kN)Deflection at ultimate

load (mm)Vertical face Lower face Vertical face

SB-2SJ-20 384 mdash mdash mdash 317 900SB-2SJ-23-36 384 2Oslash10 (230) mdash 5Oslash8m (360) 361 1100SB-2SJ-33-36 384 2Oslash12 (330) mdash 5Oslash8m (360) 400 1375SB-2SJ-58-36 384 2Oslash16 (580) mdash 5Oslash8m (360) 465 1425SB-2SJ-74-36 384 2Oslash18 (740) mdash 5Oslash8m (360) 511 1645SB-2SJ-74-57 384 2Oslash18 (740) 5Oslash10m (570) 515 1720SB-2SJ-74-73 384 2Oslash18 (740) 10Oslash8m (730) 516 1735SB-3SJ-20 384 mdash mdash mdash 356 720SB-3SJ-23-26 384 2Oslash10 (230) 2Oslash10 (26) 5Oslash8m (360) 490 935SB-3SJ-33-38 384 2Oslash12 (330) 2Oslash12 (38) 5Oslash8m (360) 560 1170SB-3SJ-58-67 384 2Oslash16 (580) 2Oslash16 (670) 5Oslash8m (360) 640 1330SB-3SJ-74-85 384 2Oslash18 (740) 2Oslash18 (85) 5Oslash8m (360) 673 1425As area of longitudinal reinforcement Ast area of transversal reinforcement and AUHPFRC area of UHPFRC layer


of specimen CT-20 Beam SB-3SJ-074L failed at 341 kNwith an increasing ratio of 1970 compared with that ofthe control specimen is finding indicated that thedesign engineers should strengthen the entire length ofthe RC beam with UHPFRC layers is strengtheningtechnique demonstrated the highest ultimate load withsufficient deflection

43 Reinforcing UHPFRC Layers To increase the ultimateload and ductility of the strengthened RC beams we usedUHPFRC layers with reinforcement bars (Figure 19) forexternal strengthening with different reinforcement ra-tios as shown in Table 10

As expected the first group (vertically strengthened)reinforcing the UHPFRC vertical layers in the case of beam SB-2SJ-23-36 increased not only the ultimate load by 14compared with specimen SB-2SJ-20 but also the deflection atultimate load by 22 Beam SB-2SJ-74-36 with the largestreinforcement ratio obtained the highest ultimate load at516kN whereas specimen SB-2SJ-20 obtained an ultimate loadof 317kNe use of reinforced UHPFRC layers improved notonly the ultimate load and deflection at ultimate load but alsothe failure mode manifested as flexural cracks as shown inFigure 20 As a result increasing the transversal reinforcementratio within the UHPFRC layers did not significantly improvethe ultimate load capacity of the strengthened specimensMoreover reinforcement helped in the uniform distribution of

Table 11 Results of the RC beam specimens strengthened with one vertical face of reinforced and nonreinforced UHPFRC layer withconstant shear span-to-depth ratio 20

Beam ID Longitudinal reinforcement(ratioAsAUHPFRC )

Transversal reinforcement(ratioAstAUHPFRC )

Ultimate load(kN)

Deflection at ultimateload (mm)

Stiffness (kNmm)

CT-20 mdash mdash 285 690 75SB-1SJ-ST-100 mdash mdash 289 203 226

SB-1SJ-ST-200 mdash mdash 290 238 235

SB-1SJ-033L mdash mdash 287 252 225

SB-1SJ-074 L mdash mdash 293 260 245

SB-1SJ-20 mdash mdash 300 221 276SB-1SJ-23-36 2Oslash10 (230) 5Oslash8m (360) 318 570 280

SB-1SJ-33-36 2Oslash12 (330) 5Oslash8m (360) 328 585 285



Figure 20 Flexural failure mode at failure of specimen SB-2SJ-74-36


stresses occurring on the surface of the strengthened RC beamsand resulted in large deformations at failure

However specimen SB-3SJ-74-85 from the second group(strengthening vertical faces in addition to the lower face)obtained the largest ultimate load amongst all the strengthenedRC specimens at 673kN whereas beam specimen SB-3SJ-20achieved an ultimate load of 356kN Moreover specimens SB-3SJ-23-26 SB-3SJ-33-38 and SB-3SJ-58-67 obtained higherultimate load at 38 58 and 80 respectively comparedwith specimen SB-3SJ-20

44 Strengthening of One Longitudinal Vertical FaceStrengthening two longitudinal vertical faces of the RC beamsmay not be available at all times especially in exterior beams dueto the neighbouring borders Nine strengthenedRC beamsweredivided into two groups e first contained five RC beamswhich were strengthened using a nonreinforced UHPFRC layerwith different strengthening lengths whereas the second groupadjoined four RC beams which were strengthened over theentire length by using a reinforcedUHPFRC layer with differentreinforcement ratios as demonstrated in Table 11 Additionally

0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)

CT-20SB-1SJ-ST-200SB-1SJ-074L

SB-1SJ-ST-100SB-1SJ-033LSB-1SJ-20


Figure 21 Load-deflection behaviour of the RC beams strengthened using nonreinforced UHPFRC layer

0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36

Figure 22 Load-deflection behaviour of the RC beams strengthened using reinforced UHPFRC layer


the RC control beam CT-20 was imported within the table forcomparison with the strengthened RC beams Notably only thesurface of the RC beam without the UHPFRC layer was loadedand supported to simulate the real structure case of thestrengthened RC beams

Regarding the first group beams SB-1SJ-ST-100 SB-1SJ-ST-200 SB-1SJ-033L SB-1SJ-074L and SB-1SJ-20 failedcompletely in shear (Figure 21) at a load of 289 290 287 293and 300kN compared with the control RC beam CT-20 at285kN No significant increase occurred in the ultimate loadbut stiffness improved significantly e use of a reinforcedUHPFRC layer in the second group improved the shear re-sponse and stiffness Beams SB-1SJ-23-36 SB-1SJ-33-36 SB-1SJ-58-36 and SB-1SJ-74-36 failed at the load values of 318328 352 and 376kN whereas the control RC beam withsufficient deflection at ultimate load obtained a load value of285kN as shown in Figure 22 Consequently if one longitu-dinal vertical face of the RC beam is strengthened then areinforced UHPFRC layer is used to improve the shearresponse

5 Conclusionsis study aims to propose FEM to simulate the behaviour ofRC beams strengthened in shear by using various UHPFRCsystems e results of the numerical model and a previousstudy in the literature are compared to check the validity of theproposed FEMe validated FEM is used to analyse the crucialparameters related to the design of RC beams strengthened inshear with UHPFRC layers e main conclusions of this studyare summarised as follows

(1) e shear behaviour of normal-strength RC beams andRCbeams strengthenedwithUHPFRC layers is affectedsignificantly by the change in the shear span-to-depthratio However the effect of shear span-to-depth ratiohas not been considered in current design codeequations Accordingly design formulas are proposedfor the estimation of shear strength of normal-strengthRC beams and RC beams strengthened with UHPFRCconsidering the effect of the shear span-to-depth ratio

(2) When the UHPFRC strengthening length is changedthe highest ultimate load is obtained by strengtheningthe entire length of RC beams e obtained ultimateload can be increased significantly by reinforcing thestrengthening UHPFRC layers Specimen SB-2SJ-74-57 failed at 511kN comparedwith 317kN in case of SB-2SJ-20 with sufficient ductility However the ultimateload of specimen SB-3SJ-74-85 was equal to 673 kNversus 356kN for specimen SB-3SJ-20 which wasstrengthened using nonreinforced UHPFRC layers

(3) Strengthening RC beams with one longitudinal verticalfacemust be executed using a reinforcedUHPFRC layerto improve the shear response of the strengthened RCbeams

Data Availability

e data used to support the findings of this study are includedin the article

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] D Baggio K Soudki and M Noel ldquoStrengthening of shearcritical RC beams with various FRP systemsrdquo Construction andBuilding Materials vol 66 pp 634ndash644 2014

[2] S-T Kang Y Lee Y-D Park and J-K Kim ldquoTensile fractureproperties of an ultra high performance fiber reinforcedconcrete (UHPFRC) with steel fiberrdquo Composite Structuresvol 92 no 1 pp 61ndash71 2010

[3] Y Yoo H O Shin J M Yang and Y S Yoon ldquoMaterial andbond properties of ultra high performance fiber reinforcedconcrete with micro steel fibersrdquo Composites Part B Engi-neering vol 58 pp 122ndash133 2013

[4] K Wille and A E Naaman ldquoFracture energy of UHP-FRCunder direct tensile loadingrdquo in Proceedings of FractureMechanics of Concrete and Concrete StructuresmdashRecent Ad-vances in Fracture Mechanics of Concrete Seoul Republic ofKorea May 2010

[5] O Tsioulou A Lampropoulos and S Paschalis ldquoCombinednon-destructive testing (NDT) method for the evaluation ofthe mechanical characteristics of ultra high performance fibrereinforced concrete (UHPFRC)rdquo Construction and BuildingMaterials vol 131 pp 66ndash77 2017

[6] K Habel M Viviani E Denarie and E Bruhwiler ldquoDe-velopment of the mechanical properties of an ultra-highperformance fiber reinforced concrete (UHPFRC)rdquo Cementand Concrete Research vol 36 no 7 pp 1362ndash1370 2006

[7] S D P Benson and B L Karihaloo ldquoCARDIFRCreg- devel-opment and mechanical properties Part III uniaxial tensileresponse and other mechanical propertiesrdquo Magazine ofConcrete Research vol 57 no 8 pp 433ndash443 2005

[8] S Paschalis and A Lampropoulos ldquoSize effect on the flexuralperformance of UHPFRCrdquo in Proceedings of the 7th HPFRCCConference Stuttgart Germany June 2015

[9] D Nicolaides A Kanellopoulos M Petrou P Savva andA Mina ldquoDevelopment of a new ultra high performance fibrereinforced cementitious composite (UHPFRCC) for impactand blast protection of structuresrdquo Construction and BuildingMaterials vol 95 pp 667ndash674 2015

[10] K Habel E Denarie and E Bruhwiler ldquoExperimental in-vestigation of composite ultra-high performance fiber-rein-forced concrete and conventional concrete membersrdquo ACIStructural Journal vol 104 pp 10ndash20 2007

[11] G Martinola A Meda G A Plizzari and Z RinaldildquoStrengthening and repair of RC beams with fiber reinforcedconcreterdquo Cement and Concrete Composites vol 32 no 9pp 731ndash739 2010

[12] P R Prem A Ramachandra Murthy G RameshB H Bharatkumar and N R Iyer ldquoFlexural behaviour ofdamaged RC beams strengthened with ultra high performanceconcreterdquo Advances in Structural Engineering vol 3pp 2057ndash2069 2015

[13] F J Alaee and B L Karihaloo ldquoRetrofitting of reinforcedconcrete beams with CARDIFRCrdquo Journal of Composites forConstruction vol 7 no 3 pp 174ndash186 2003

[14] T Noshiravani and E Bruhwiler ldquoExperimental investigationon reinforced ultrahigh performance fiber-reinforced con-crete composite beams subjected to combined bending andshearrdquo ACI Structural Journal vol 110 pp 251ndash262 2013


[15] M A Al-Osta M N Isa M H Baluch and M K RahmanldquoFlexural behavior of reinforced concrete beams strengthenedwith ultra-high performance fiber reinforced concreterdquoConstruction and Building Materials vol 134 pp 279ndash2962017

[16] B A Tayeh Z M EL dada S Shihada andM O Yusuf ldquoPull-out behavior of post installed rebar connections usingchemical adhesives and cement based bindersrdquo Journal ofKing Saud UniversitymdashEngineering Sciences vol 31 no 4pp 332ndash339 2019

[17] A P Lampropoulos S A Paschalis O T Tsioulou andS E Dritsos ldquoStrengthening of reinforced concrete beamsusing ultra high performance fibre reinforced concrete(UHPFRC)rdquo Engineering Structures vol 106 pp 370ndash3842016

[18] G Ruano F Isla D Sfer and B Luccioni ldquoNumericalmodeling of reinforced concrete beams repaired andstrengthened with SFRCrdquo Engineering Structures vol 86pp 168ndash181 2015

[19] C E Chalioris G E ermou and S J PantazopoulouldquoBehaviour of rehabilitated RC beams with self-compactingconcrete jacketingmdashanalytical model and test resultsrdquo Con-struction and Building Materials vol 55 pp 257ndash273 2014

[20] L Hussein and L Amleh ldquoStructural behavior of ultra-highperformance fiber reinforced concrete-normal strengthconcrete or high strength concrete composite membersrdquoConstruction and Building Materials vol 93 pp 1105ndash11162015

[21] A A Bahraq M A Al-Osta A Shamsad M A MesferS A Othman and M K Rahman ldquoExperimental and nu-merical investigation of shear behavior of RC beamsstrengthened by ultra-high performance concreterdquo Interna-tional Journal of Concrete Structures and Materials vol 13pp 1ndash19 2019

[22] S Mostosi A Meda P Riva and S Maringoni ldquoShearstrengthening of RC beams with high performance jacketrdquo inProceedings of the Fib Symposium in Prague Concrete Engi-neering for Excellence and Efficiency Prague Czech RepublicSeptember 2011

[23] M A Sakr A A Sleemah T M Khalifa andW N MansourldquoShear strengthening of reinforced concrete beams usingprefabricated ultra-high performance fiber reinforced con-crete plates experimental and numerical investigationrdquoStructural Concrete vol 20 no 3 pp 1137ndash1153 2019

[24] T J Mohammed B H Abu Bakar and N MuhamadBunnori ldquoTorsional improvement of reinforced concretebeams using ultra high-performance fiber reinforced concrete(UHPFC) jacketsmdashexperimental studyrdquo Construction andBuilding Materials vol 106 pp 533ndash542 2016

[25] K Hibbitt and I Sorensen ABAQUS Deory Manual UserManual and Example Manual Simulia Providence RI USA2000

[26] V Birtel and P Mark ldquoParameterised finite element mod-elling of RC beam shear failurerdquo in Proceedings of theABAQUS Usersrsquo Conference 2007 Boston MA USA May2006

[27] B A Tayeh B H Abu Bakar M A Megat Johari andY L Voo ldquoMechanical and permeability properties of theinterface between normal concrete substrate and ultra highperformance fiber concrete overlayrdquo Construction andBuilding Materials vol 36 pp 538ndash548 2012

[28] B A Tayeh B H Abu Bakar and M A Megat JoharildquoCharacterization of the interfacial bond between old concretesubstrate and ultra high performance fiber concrete repair

compositerdquo Materials and Structures vol 46 no 5pp 743ndash753 2013

[29] B A Tayeh B H A Bakar M A M Johari andM M Ratnam ldquoe relationship between substrate rough-ness parameters and bond strength of ultra high-performancefiber concreterdquo Journal of Adhesion Science and Technologyvol 27 no 16 pp 1790ndash1810 2013

[30] B A Tayeh B H A Bakar M A M Johari and Y L VooldquoEvaluation of bond strength between normal concretesubstrate and ultra high performance fiber concrete as a repairmaterialrdquo Procedia Engineering vol 54 pp 554ndash563 2013

[31] B A Tayeh B H A Bakar M A M Johari and Y L VooldquoUtilization of ultra-high performance fibre concrete(UHPFC) for rehabilitationmdasha reviewrdquo Procedia Engineeringvol 54 pp 525ndash538 2013

[32] B A Tayeh M A Naja S Shihada and M Arafa ldquoRepairingand strengthening of damaged RC columns using thin con-crete jacketingrdquo Advances in Civil Engineering vol 2019Article ID 2987412 16 pages 2019

[33] T C Zsutty ldquoShear strength prediction for separate categoriesof simple beam testsrdquo ACI Journal vol 68 pp 138ndash143 1971

[34] Z P Bazant and J K Kim ldquoSize effect in shear failure oflongitudinally reinforced beamsrdquo ACI Journal vol 81pp 456ndash466 1984

[35] J Niwa K Yamada K Yokozawa and H Okamura ldquoRe-valuation of the equation for shear strength of reinforcedconcrete beams without web reinforcementrdquo Translation fromProceedings of the JSCE vol 372 pp 65ndash84 1986

[36] W Li and C K Y Leung ldquoEffect of shear span-depth ratio onmechanical performance of RC beams strengthened in shearwith U-wrapping FRP stripsrdquo Composite Structures vol 177pp 141ndash157 2017

[37] K C Rajendra K Shailendra and M C Raob ldquoEffect ofshear-spandepth ratio on cohesive crack and double-Kfracture parameters of concreterdquo Advances in ConcreteConstruction vol 2 no 3 pp 229ndash247 2014

[38] H Kim M S Kim M J Ko and Y H Lee ldquoShear behavior ofconcrete beams reinforced with GFRP shear reinforcementrdquoInternational Journal of Polymer Science vol 2015 Article ID213583 8 pages 2015

[39] M K Svetlana and D S Biljana ldquoBending resistance ofcomposite sections with nonductile shear connectors andpartial shear connectionrdquo Advances in Civil Engineeringvol 2018 Article ID 5350315 14 pages 2018

[40] European Committee for Standardization EN 1992-1-1Eurocode2 Design of Concrete Structures-Part 1-1GeneralRules and Rules for Buildings European Committee forStandardization Brussels Belgium 2004

[41] ACI (American Concrete Institute) Building Code Require-ments for Reinforced Concrete (ACI 318-05) and Commentary(ACI 318R-05) American Concrete Institute Detroit MIUSA 2005

[42] O B Olalusi and C Viljoen ldquoAssessment of simplified andadvanced models for shear resistance prediction of stirrup-reinforced concrete beamsrdquo Engineering Structures vol 186pp 96ndash109 2019

[43] M Holicky J V Retief and J A Wium ldquoPartial factors forselected reinforced concrete members background to a re-vision of SANS 10100ndash1rdquo SAICE Journal vol 52 pp 36ndash442010


e technique of flexural strengthening using UHPFRCwas investigated numerically in [17] by developing a nu-merical model for the extensive investigation of strength-ened RC beams with layers and jackets eir findings werecompared with those of beams strengthened with conven-tional RC layers and combinations of UHPFRC and steel-reinforcing bars eir results clearly showed that superiorperformance could be achieved by using the three-sideUHPFRC jackets

Shear failure is unfavourable for engineers because of itssudden occurrence with a brittle failure mode and manystudies have focused on improving the capacity and ductilityof RC beams strengthened in shear with UHPFRC[13 18ndash22] Sakr et al [23] proposed a 3D finite elementmodel (FEM) to investigate the behaviour of RC beamsstrengthened in shear with prefabricated UHPFRC plates byusing (a) one longitudinal vertical-side strengthening and(b) two longitudinal vertical-side strengthening eyconcluded that the prefabricated UHPFRC plates couldsignificantly enhance the ultimate load carrying capacityductility and strain of longitudinal reinforcement in thestrengthened RC beams compared with the control beamfailed in shear

Moreover Mohammed et al [24] experimentally andnumerically examined the effectiveness and efficiency ofUHPFRC-strengthened RC beam specimens without stir-rups by using three different strengthening techniques undertorsional moment e beam specimen strengthened on allfour sides obtained higher torsional strength compared withthe reference specimen

Despite the results of these studies using UHPFRC instrengthening and rehabilitating conventional RC beamslimited studies have considered the effect of the shear span-to-depth and UHPFRC layer reinforcement ratios on thebehaviour of RC beams strengthened in shear withUHPFRC Moreover information on the effect of UHPFRClayer length and geometry on the behaviour of the con-sidered structure is lacking Because of the difficulty ofstrengthening many structural elements on both sides es-pecially in exterior beams due to the neighbouring bordersstrengthening the RC beams using only one vertical lon-gitudinal side has been considered in the current researchStrengthening only one vertical longitudinal side of the RCbeams is rarely studied and evaluated in the literature

us a 3D FEM with the ability to simulate the be-haviour of RC beams strengthened in shear with UHPFRClayers is proposed in this study and validated using theexperiments available in the literature (Sections 2 and 3)Additionally the validated FEM is used in Section 4 todemonstrate the effects of the shear span-to-depth ratiolength and geometry of UHPFRC layers reinforcingUHPFRC layers and strengthening only one longitudinalvertical side on the behaviour of RC beams strengthenedin shear with UHPFRC layers

2 Numerical Investigation

e shear behaviour of simply supported RC beamsstrengthened with UHPFRC using different strengthening

schemes was investigated numerically e nonlinear finiteelement analysis software ABAQUS [25] was used to developa 3D model simulating the shear behaviour of UHPFRC-strengthened RC beams

21 Elements and Meshing Normal-strength concrete(NSC) and UHPFRC are modelled using the 3D stresseight-noded linear brick element (C3D8R) as shown inFigure 1 is figure also shows the two-noded linear 3Dtruss element (T3D2) which is used to model the steel-reinforcing bars and stirrups is element is suitable forstructural members that transmit only axial load

A mesh size of 40mmtimes 40mm was suggested to dividethe simulated RC beams to fine elements e proposed finemesh was required to obtain accurate results consistent withthose of the experimental response on the level of failureload and failure pattern

22 Materials e model of concrete damage plasticity wasused to simulate both concrete and UHPFRC although twoother models (concrete smeared and brittle cracking) wereavailable in ABAQUSe model of concrete damage plasticitywas used in this study due to its ability inmodelling the complexnonlinear properties of concrete and UHPFRC considering thesoftening behaviour under either compression or tension isapproach can also be used with a rebar to model concretereinforcement

e model of concrete damage plasticity assumes that theuniaxial tensile and compressive response of concrete ischaracterised by damaged plasticity as illustrated in Figure 2e damage variables in compression and tensionwere denotedby dc and dt respectively Such damage variables can take valuesfrom 0 (to represent the undamaged material) to 1 (to denotethe total loss of strength) In the case of uniaxial tension thestress-strain response followed a linear elastic relationship untilthe value of the failure stress σto was reached Beyond thefailure stress the formation of microcracks was representedmacroscopically with a softening stress-strain response whichinduced strain localisation in the concrete structure e re-sponse was linear under uniaxial compression until the value ofthe initial yield σco was reached e response in the plasticzone was typically characterised by stress hardening followedby strain softening beyond the ultimate stress σcu Birtel andMark [26] proposed the following equations to determine thecompressive and tensile damage parameters

(i) Compressive damage parameter (dc)

dc 1 minusσcEminus 1

c

εplc 1bc( 1113857 minus 1( 1113857 + σcEminus 1c

(1)

(ii) Tensile damage parameter (dt)

dt 1 minusσtEminus 1

c

εplt 1bt( 1113857 minus 1( 1113857 + σtEminus 1c

(2)











(a) (b) (c)


σtσto

Eo

(1 ndash dt)Eo

ξtξt

elξt

pl

(a)

σcσc

σco

Eo (1 ndash dc)Eo

ξcξc

elξc

pl

(b)












Concrete 20 01 116 0667 0UHPFRC 36 01 116 0667 0

ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

10


Stre

ss (M

Pa)

Plastic strain

(a)

ndash160

ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20


Stre

ss (M

Pa)

Plastic strain

(b)







4 Parametric Study




0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)






0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)







Vr 018K 100ρlfc( 111385713

bd +Asw

Szfyw d cot θd (3)

θd sinminus 1

Aswfyw d

bw sV1αccfc

1113971

(4)

where K 1 +200d







Vr

fc

1113968

6bd +

Asw

Sfywd d (5)



0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)









(CT-10)

(a)



(b)


(CT-15)

(a)



(b)



(CT-20)

(a)





(b)


(SB-2SJ-10)

(a)



(b)



(SB-2SJ-15)

(a)





(b)


(SB-2SJ-20)

(a)



(b)



(SB-3SJ-10)

(a)

+3628e ndash 03+0000e + 00





(b)


(SB-3SJ-15)

(a)



(b)





Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)




(SB-3SJ-20)

(a)





(b)













0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References
























































(a) (b) (c)


σtσto

Eo

(1 ndash dt)Eo

ξtξt

elξt

pl

(a)

σcσc

σco

Eo (1 ndash dc)Eo

ξcξc

elξc

pl

(b)












Concrete 20 01 116 0667 0UHPFRC 36 01 116 0667 0

ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

10


Stre

ss (M

Pa)

Plastic strain

(a)

ndash160

ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20


Stre

ss (M

Pa)

Plastic strain

(b)







4 Parametric Study




0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)






0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)







Vr 018K 100ρlfc( 111385713

bd +Asw

Szfyw d cot θd (3)

θd sinminus 1

Aswfyw d

bw sV1αccfc

1113971

(4)

where K 1 +200d







Vr

fc

1113968

6bd +

Asw

Sfywd d (5)



0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)









(CT-10)

(a)



(b)


(CT-15)

(a)



(b)



(CT-20)

(a)





(b)


(SB-2SJ-10)

(a)



(b)



(SB-2SJ-15)

(a)





(b)


(SB-2SJ-20)

(a)



(b)



(SB-3SJ-10)

(a)

+3628e ndash 03+0000e + 00





(b)


(SB-3SJ-15)

(a)



(b)





Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)




(SB-3SJ-20)

(a)





(b)













0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References
























































Concrete 20 01 116 0667 0UHPFRC 36 01 116 0667 0

ndash60

ndash50

ndash40

ndash30

ndash20

ndash10

0

10


Stre

ss (M

Pa)

Plastic strain

(a)

ndash160

ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20


Stre

ss (M

Pa)

Plastic strain

(b)







4 Parametric Study




0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)






0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)







Vr 018K 100ρlfc( 111385713

bd +Asw

Szfyw d cot θd (3)

θd sinminus 1

Aswfyw d

bw sV1αccfc

1113971

(4)

where K 1 +200d







Vr

fc

1113968

6bd +

Asw

Sfywd d (5)



0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)









(CT-10)

(a)



(b)


(CT-15)

(a)



(b)



(CT-20)

(a)





(b)


(SB-2SJ-10)

(a)



(b)



(SB-2SJ-15)

(a)





(b)


(SB-2SJ-20)

(a)



(b)



(SB-3SJ-10)

(a)

+3628e ndash 03+0000e + 00





(b)


(SB-3SJ-15)

(a)



(b)





Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)




(SB-3SJ-20)

(a)





(b)













0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References

















































4 Parametric Study




0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)






0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)







Vr 018K 100ρlfc( 111385713

bd +Asw

Szfyw d cot θd (3)

θd sinminus 1

Aswfyw d

bw sV1αccfc

1113971

(4)

where K 1 +200d







Vr

fc

1113968

6bd +

Asw

Sfywd d (5)



0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)









(CT-10)

(a)



(b)


(CT-15)

(a)



(b)



(CT-20)

(a)





(b)


(SB-2SJ-10)

(a)



(b)



(SB-2SJ-15)

(a)





(b)


(SB-2SJ-20)

(a)



(b)



(SB-3SJ-10)

(a)

+3628e ndash 03+0000e + 00





(b)


(SB-3SJ-15)

(a)



(b)





Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)




(SB-3SJ-20)

(a)





(b)













0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References

















































Vr 018K 100ρlfc( 111385713

bd +Asw

Szfyw d cot θd (3)

θd sinminus 1

Aswfyw d

bw sV1αccfc

1113971

(4)

where K 1 +200d







Vr

fc

1113968

6bd +

Asw

Sfywd d (5)



0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tota

l loa

d (k

N)









(CT-10)

(a)



(b)


(CT-15)

(a)



(b)



(CT-20)

(a)





(b)


(SB-2SJ-10)

(a)



(b)



(SB-2SJ-15)

(a)





(b)


(SB-2SJ-20)

(a)



(b)



(SB-3SJ-10)

(a)

+3628e ndash 03+0000e + 00





(b)


(SB-3SJ-15)

(a)



(b)





Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)




(SB-3SJ-20)

(a)





(b)













0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References















































(CT-10)

(a)



(b)


(CT-15)

(a)



(b)



(CT-20)

(a)





(b)


(SB-2SJ-10)

(a)



(b)



(SB-2SJ-15)

(a)





(b)


(SB-2SJ-20)

(a)



(b)



(SB-3SJ-10)

(a)

+3628e ndash 03+0000e + 00





(b)


(SB-3SJ-15)

(a)



(b)





Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)




(SB-3SJ-20)

(a)





(b)













0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References















































(CT-20)

(a)





(b)


(SB-2SJ-10)

(a)



(b)



(SB-2SJ-15)

(a)





(b)


(SB-2SJ-20)

(a)



(b)



(SB-3SJ-10)

(a)

+3628e ndash 03+0000e + 00





(b)


(SB-3SJ-15)

(a)



(b)





Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)




(SB-3SJ-20)

(a)





(b)













0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References















































(SB-2SJ-15)

(a)





(b)


(SB-2SJ-20)

(a)



(b)



(SB-3SJ-10)

(a)

+3628e ndash 03+0000e + 00





(b)


(SB-3SJ-15)

(a)



(b)





Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)




(SB-3SJ-20)

(a)





(b)













0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References















































(SB-3SJ-10)

(a)

+3628e ndash 03+0000e + 00





(b)


(SB-3SJ-15)

(a)



(b)





Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)




(SB-3SJ-20)

(a)





(b)













0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References

















































Vc 144

fc

1113969a

d1113874 1113875

minus 1208b d +

Asw

Sfywd d (6)




(SB-3SJ-20)

(a)





(b)













0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References























































0

100

200

300

400

500

100 125 150 175 200 225 250 275 300 325 350

Tota

l loa

d (k

N)


FE modelACI code








(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References



















































(a) (b)


(a) (b)





















Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References

































































Ultimate load(kN)


Stiffness (kNmm)














0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References


















































0

100

200

300

0 1 2 3 4 5 6 7 8 9 10

Tota

l loa

d (k

N)





0

100

200

300

400

0 1 2 3 4 5 6 7 8 9

Tota

l loa

d (k

N)


SB-1SJ-23-36SB-1SJ-58-36

CT-20SB-1SJ-33-36SB-1SJ-74-36









Data Availability




References





















































Data Availability




References















































ShearBehaviourofRCBeamsStrengthenedbyVariousUltrahigh...

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