Effect of reinforcement ratio on the flexural performance of hybrid FRPreinforced concrete beams
Renyuan Qin a, Ao Zhou a, Denvid Lau a, b, *
a Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kongb Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
a r t i c l e i n f o
Article history:Received 22 July 2016Received in revised form30 August 2016Accepted 17 September 2016Available online 19 September 2016
Keywords:Glass fibresHybridMechanical propertiesFinite element analysis (FEA)
* Corresponding author. Department of ArchitecturUniversity of Hong Kong, Hong Kong.
Fiber reinforced polymer (FRP) is widely used in concrete structures due to its high tensile strength andsuperior corrosion resistance. However, the FRP reinforced concrete (FRPRC) shows a less ductilebehavior compared to the conventional steel reinforced concrete. In order to improve the strength andflexural ductility simultaneously, a hybrid reinforcement system composed of FRP and steel bars hasbeen proposed and adopted in design recently. In hybrid FRPRC beams, FRP and steel reinforcements playdifferent roles in improving strength and ductility. The hybrid reinforcement ratio between FRP and steel,Af/As, has a significant influence on the flexural performance of hybrid FRPRC beams as it affects thebalance between strength and ductility in the flexural design. Here, the effect of hybrid reinforcementratio on the flexural performance of concrete beams in both under- and over- reinforced scenarios isstudied using three-dimensional finite element models. The results from the finite element models showthat a preferable strength and ductility performance can be obtained through an appropriate design ofhybrid reinforcement ratio. Such information helps us determine an appropriate range of hybrid rein-forcement ratio and provide a design guideline for hybrid FRPRC beams for optimizing the strength andductility performance.
Fiber reinforced polymer (FRP) has been considered as analternative material to steel reinforcement in the reinforced con-crete structures with the advantages of corrosion resistance, non-conductivity and high strength-to-weight ratio. Numerous studieshave been carried out to evaluate the performance of using FRP barto substitute steel bar in order to solve the durability problem ofreinforced concrete structures in an aggressive environment, suchas bridge decks and roadbeds which may encounter a seriouscorrosion of steel reinforcement [1e15]. Moreover, the lifespan ofFRP materials has been demonstrated to be much longer than thatof the traditional steel reinforcement. It is reported that theembodied energy of FRP is 68% lower than that of steel [7]. Owingto these characteristics, FRP can be regarded as a sustainable con-struction material with a less environmental impact compared tosteel.
e and Civil Engineering, City
Despite the aforementioned advantages, FRP exhibits a linearelastic behavior up to failure and possesses no ductility in generalcompared to conventional steel bars, which is a drawback when itserves as an internal reinforcement in concrete structures [16e18].In order to increase the ductility of FRP reinforced concrete (FRPRC)flexural members, many researchers have experimentally investi-gated the design of adding steel longitudinal bars to FRPRC beams[19e25]. Through adding the steel bars, the ductility of hybridFRPRC beam is significantly improved compared to that of pureFRPRC beam. Such ductility improvement is necessary because itcan provide ample warning before structural collapse, especiallywhen the structure is under seismic attack. The additional steelbars can ensure that the ductile behavior of flexural member ismaintained. In hybrid reinforcement scenario, the strength can bemainly provided by FRP reinforcement and the ductility can beprovided by the addition of steel reinforcement. Since the addi-tional steel reinforcement is not designed for load bearing capacityof the beam, a certain extent of steel corrosion could be acceptable,especially in the aggressive environment. The optimized structuralperformance can be achieved by designing the hybrid reinforce-ment appropriately [24,25]. Moreover, the deformation and the
Fig. 1. Sample representation of our developed finite element models. C3D8R elementis used to model concrete and steel support, and T3D2 element is used to build FRP andsteel reinforcements in the model.
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crack width of hybrid FRPRC beams are reduced compared to thoseof pure FRPRC beams [26e29]. Previous studies of FRPRC have ledto the development of design formulas in various standards andguidelines such as ACI 440.1R-15, CSA S806-12, Fib Bulletin No. 40,and JSCE 1997 [30e33]. However, these standards and guidelinesonly provide the indication on pure FRPRCmembers and only a fewstandards on hybrid FRPRC design have been developed. In hybridFRPRC beam, two kinds of reinforcement, i.e. FRP and steel bars,play different roles in improving strength and ductility. Althoughthe additional steel reinforcement in hybrid FRPRC can improve theflexural ductility, the load-carrying capacity of hybrid FRPRC maydrastically decrease due to the brittle failure of FRP reinforcement ifthe hybrid reinforcement ratio is not well designed. Hybrid rein-forcement ratio, Af/As, is a key factor to optimize the balance be-tween improving ductility and retaining high load-carryingcapacity.
The objective of this study is to investigate the effect of hybridreinforcement ratio, Af/As, on the flexural performance of hybridFRPRC beams, and to provide design guidelines on hybrid rein-forcement ratio which can optimize the ductility and the load-carrying capacity. In order to study the contributions of FRP andsteel reinforcement towards the structural performance of FRPRCwith different hybrid reinforcement ratios, finite element modelsare built to predict the structural behavior of hybrid FRPRC beams.Finite element method is a powerful numerical tool in simulatingthe flexural behavior of FRPRC beams, and it can provide satisfac-tory predictions for linear and nonlinear behavior of FRPRC beams[27,34e37]. Moreover, the variation of hybrid reinforcement ratiocan be easily achieved in finite element models by changing thecross-sectional area of each reinforcement bar, which is an efficientway to obtain credible results. Six specimens including steel rein-forced concrete (SRC), pure FRPRC and hybrid FRPRC beams areused to validate the developed finite element models [7,11]. Afterthe validation of finite element models, a parametric study ofhybrid reinforcement ratio, Af/As, is carried out to investigate thecontributions of FRP and steel reinforcement to the overall struc-tural performance and mechanical properties of the beam. Anappropriate range of hybrid reinforcement ratio can be determinedthrough optimizing the structural performance of hybrid FRPRCbeam. Such information can enrich our understanding of the rela-tionship between hybrid reinforcement ratio and flexural behaviorof hybrid FRPRC. Furthermore, it can be easily adopted in hybridFRPRC design practice so as to optimize the ductility and load-carrying capacity performance according to different serviceconditions.
2. Finite element models
The ABAQUS Finite Element Code is used to carry out numericalanalysis in a three-dimensional manner [38]. The geometry, me-chanical properties, boundary conditions and static loads in thefinite element models are set according to the tested specimens inour experiment [7,11]. The sample representation of our developedthree-dimensional finite element model is given in Fig. 1.
2.1. Element types
The element type C3D8R (3D 8-node linear with reduced inte-gration) in the continuous (solid) element of ABAQUS is used tosimulate the nonlinear behavior of concrete. The continuous (solid)unit can be used to analyze complex linear and nonlinear problems,including plastic and large deformation, heat transfer, acoustics,etc. The C3D8R unit is a reduced integration for eight-node solidelements with three translational degrees of freedom per node. Thereduced integration is obtained by integrating with the lower-order
rigidity of the unit, while the mass matrix and distributed loads areobtained from full integration. It can be used to reduce the calcu-lation time, and to getmore accurate displacement and stress fields.The C3D8R element is also employed tomodel the loading and rigidsteel supports as bricks with elastic steel material properties inorder to avoid the stress concentration at corresponding locationsand the non-convergence in the solution. Both FRP and steel rein-forcement bars are modeled by three-dimensional 2-node firstorder truss elements (T3D2) with the use of linear interpolationmethod to determine the position and the displacement. The crosssection is defined as solid section and the cross section is updatedby assuming that the unit is incompressible when the model issubjected to a nonlinear large displacement analysis.
As the objective of this work is to investigate the overall struc-tural performance rather than the local behavior at concrete-reinforcement interface, a perfect bond between FRP-concreteand steel-concrete is assumed here with an appropriate tensilebehavior of concrete after cracking. The bond-slip behavior of FRP-concrete joint has certain effect on external FRP bonded systems,but it has limited influence on the structural response of beaminternally reinforced with FRP/steel bars as the failure of FRPRC iscaused by concrete crushing or rupture of FRP bars instead. Theembedded constraint is used to simulate the reinforcingconfiguration.
2.2. Material properties
The mechanical properties of concrete, FRP and steel re-inforcements used in the finite element models are based on thetest results as shown in the literature [7,11]. The concrete damagedplasticity model is used to simulate the nonlinear response of thetensile and compressive stress-strain relationship of concrete ele-ments. The mechanical properties of concrete are adopted fromexperimental data, which are shown in Table 1. For plain concreteunder uniaxial compression, the stress-strain relationship isdefined in both elastic range and plastic range. Within the linearelastic range, the compressive behavior is defined by the elasticmodulus (Ec) and the Poisson's ratio (0.167). In the plastic range, thecompressive stress is defined as a function of non-elastic strain.
Hongestad model, which is one of the most commonly usedmodels, is adopted to define the uniaxial compression behavior ofconcrete [39]. The stress-strain relationship suggested by Hon-gnestad is shown in Fig. 2 (a). It consists of a parabolic ascent stageand a linear descent stage, namely:
sc ¼ s0
�2�εc
ε0
���εc
ε0
�2 �ε � ε0 (1)
sc ¼ s0
�1� 0:15
�ε� εc
εc � ε0
��ε0 � ε � εu (2)
Table 1Material properties of specimens.
Specimen name fc (MPa) fy (MPa) ffu (MPa) Es (GPa) Ef (GPa) rs rf
MD1.3 39.0 341 e 189.0 e 1.180G0.8 30.0 e 593 e 40.0 e 0.756G2.1 41.3 e 582 e 38.0 e 1.845G1.0-T0.7 39.8 597 582 190.0 38.0 0.591 0.923G0.6-T1.0 44.6 550 588 196.4 39.5 0.923 0.533T0.2 35.3 507 e 220.5 e 0.213 e
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The tensile behavior of concrete is defined as linear elastic up tothe concrete tensile strength (fct). The tension-stiffening modelfor pure FRP and hybrid FRP reinforcements is used to define thepost-failure behavior of cracked concrete, which is shown inFig. 2(b) [40].
The post-failure tension stiffening model of concrete in FRPRC isdetermined by the tension stiffening factor b and tensile strengthfct. The tension stiffening factor b is related to the stiffness ofreinforcement regardless of the reinforcement ratio or concretestrength.
For concrete reinforced by steel or FRP bars solely, the tensionstiffening factor b is given as:
b ¼ exp½ � 1100ðεm � εcrÞðEb=200Þ � (3)
where Eb is the elastic modulus of the reinforcement, εcr is theconcrete strain at cracking, and εm is the corresponding tensilestrain.
When it comes to the hybrid FRPRC scenario, the relative rigidityshould be adjusted using the following equation:
Fig. 2. (a) Hognestad model for concrete uniaxial compression and (b) concrete ten-sion softening model are used to define the stress-strain relationship in finite elementmodeling.
b ¼ exph� 1100ðεm � εcrÞ
�XEbAb=200
XAb
� i(4)
where Ab is the total area of reinforcements (FRP and steel).The post-cracking tensile stress-strain relationship can then be
determined by the following equation:
sct ¼ bfct (5)
where sct is the tensile stress corresponding to the tensile strain εm.The stress-strain relationship of FRP is shown as below:
sf ¼ Efεf (6)
where sf, Ef and εf are the stress, the elastic modulus and the strainof FRP reinforcement respectively. The nonlinear behavior of steelreinforcement is modeled as linear elastic up to yield stage, beyondwhich it is fully plastic. The stress-strain curves of steel and FRP areshown in Fig. 3.
2.3. Specimen design
In total, fifteen beam specimens which can be divided into threegroups are modeled using ABAQUS Finite Element Software. Vali-dation group (Group V) consists of six beams covering SRC beams,pure FRPRC beams and hybrid FRPRC beams, which are used tovalidate our finite elementmodels against the experimental results.Four beams in Group A and five beams in Group B are designedbased on the balanced reinforcement ratio in order to study theeffect of hybrid reinforcement ratio on the flexural performance ofhybrid FRPRC beams in both under- and over- reinforced scenarios.The balanced reinforcement ratio for SRC beam, rbs, is a conditionthat beams fail through concrete crushing with steel reinforcementyielding simultaneously. For pure FRPRC beam, the balanced FRPreinforcement ratio, rbf, is a case that the rupture of FRP rein-forcement occurs simultaneously with the concrete crushing,
Fig. 3. Stress-strain relationship of longitudinal FRP and steel reinforcement.
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which results in the beam failure. Considering the balanced rein-forcement ratio of both SRC and pure FRPRC beams, a balancedreinforcement ratio for hybrid FRPRC beams is proposed as thecondition that concrete crushing in compression zone and ruptureof FRP reinforcement occurs synchronously. The equivalent rect-angular stress block of concrete recommended in ACI 318M-08 [41]is used to calculate the balanced reinforcement ratio for both pureand hybrid FRPRC beams. The balanced reinforcement ratio for pureFRPRC beam, rbf, is shown in following equation according to ACI440. 1R-15 [33]:
rbf ¼ 0:85b1f 0cffu
Efε0c
ffu þ Efε0c(7)
where b1 is the ratio between the depth of the equivalent rectan-gular concrete stress block and that of the neutral axis, εc 0 ¼ 0:003which is the extreme concrete strain in compression. The effectivereinforcement ratio, req, for hybrid FRPRC beam is calculatedthrough the following equation:
req ¼ rs þ rfffufy
(8)
where rs is the steel reinforcement ratio and rf is the FRP rein-forcement ratio. Hence, the balanced reinforced ratio for hybridFRPRC beam can be obtained by combining Equations (7) and (8).The theoretical moment capacity of Group A and Group B is100 kNm and 210 kNm respectively. For the beam specimens inGroup A and B, the diameters of FRP and steel reinforcement aredesigned using typical sizes, and the hybrid reinforcement ratiobetween FRP and steel reinforcements is then designed (i.e. withinthe range which can fulfill the scope of our parametric study). Itshould be noted that all beam specimens are designed to failthrough bending at around midspan in order to investigate thecontribution of FRP reinforcement to the flexural performance ofFRPRC. To avoid shear failure, an excessive amount of shear rein-forcement (i.e. twice of the required amount) is provided. In Table 2,the reinforcement details and the hybrid reinforcement ratios of allsimulated beam specimens are listed.
3. Experimental program
Six beam specimens consisted of SRC, pure FRPRC and hybridFRPRC were tested experimentally in order to validate the devel-oped finite element models [7,11]. The tested specimens weresimply supported and loaded in load-control mode to 0.75Pn andthen in displacement-control mode until failure. The load was
Table 2Reinforcement details and hybrid reinforcement ratio of beam specimens.
applied to a point at midspan. Tested specimens included oneconcrete beam (MD1.3) reinforced with four mild steel bars, oneconcrete beam (T0.2) reinforced with two high yield steel bars, twobeams (G0.8 and G2.1) reinforced with GFRP bars and two beams(G1.0-T0.7 and G0.6-T1.0) reinforced with hybrid GFRP and steelbars. It should be noted that the numbers after particular symbols(MDx, Tx and Gx) refer to the corresponding reinforcementratio. All longitudinal reinforcement including steel, GFRP orthe combination of both were placed in one layer. The beamspecimens were identical with a rectangular cross-section of280 mm � 380 mm (width � depth) and a nominal length of4600 mm. Two steel barswith the diameter of 6 mmwere arrangedin the compressive zone and stirrups with the diameter of 8 mmwere spaced at 50 mm at beam-ends and spaced at 100 mm in restpart. In addition, the clear cover of concrete at each side was20 mm.
Fig. 4 shows the cross section of tested beam specimens withreinforcement design. The diameters of steel bars in MD1.3 andT0.2 were 20 mm and 12 mm, and the diameters of GFRP bars inG0.8 and G2.1 were 16 mm and 25 mm. In beam specimenG1.0-T0.7 and G0.6-T1.0, the diameters of steel bars were 20 mmand 25 mm while the diameters of GFRP bars were 25 mm and19 mm respectively. The details of transverse reinforcementarrangement along beam specimen and schematic diagram ofexperiment set-up are also shown in Fig. 4.
4. Results and discussion
Failure in finite element models is defined through either con-crete crushing (i.e. by reaching the concrete compressive strainlimit) or rupture of FRP reinforcement (i.e. by reaching the tensilestrength of FRP). Table 3 lists the load-carrying capacities and thefailure modes of all fifteen beam specimens in our finite elementsimulation. Beams reinforced with only steel bars, i.e. MD1.3 andT0.2, fail in ductile flexure with yielding of steel reinforcementfollowed by concrete crushing at the compressive zone. Whenfocusing the beams reinforced with FRP bars solely or hybrid FRPand steel bars, it is noticed that the failure is not simply caused byconcrete crushing, instead the failure is initiated by the excessivedeformation in the reinforcement layer due to the rupture of FRPreinforcement after steel yielding. It is also noticed that when theeffective reinforcement ratio is less than balanced reinforcementratio, FRP reinforcement reaches its strength before concrete rea-ches its compressive strain limit, which causes the beam failureinitiated by FRP rupture. However, when the effective reinforce-ment ratio is greater than the balanced reinforcement ratio, allbeams fail through concrete crushing without reaching the
Over-/under-reinforcement Hybrid reinforcement ratio Af/As
Fig. 4. (a) Transverse reinforcement arrangement and (b) cross-section of beam specimens in experiment.
Table 3Load-carrying capacity and failure mode of simulated beam specimens.
Unit Load-carrying capacity P (kN) Over-/under-reinforcement Hybrid reinforcement ratio Af/As Failure mode
MD1.3 142.7 Under e Steel yielding and concrete crushingT0.2 42.9 Under e Steel yielding and concrete crushingG0.8 150.4 Balanced e GFRP ruptureG2.1 219.6 Over e Concrete crushingG1.0-T0.7 230.5 Over 5:3 Steel yielding and concrete crushingG0.6-T1.0 222.6 Over 3:5 Steel yielding and concrete crushingA1 99.4 Under 1:1 GFRP ruptureA2 104.7 Under 2:1A3 108.6 Under 1:2A4 116.9 Under 1:4B1 209.4 Over 1:1 Steel yielding and concrete crushingB2 228.1 Over 5:3B3 224.8 Over 3:5B4 205.8 Over 2:5B5 200.6 Over 5:2
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strength limit of FRP reinforcement. Under this situation, the hybridreinforcement ratio has limited influence on the failure mode ofhybrid FRPRC beam. In what follows, the simulation results and thestructural performance of the fifteen beam specimens are discussedin following two aspects. The first section is to evaluate the accu-racy between our developed finite element models and theexperimental results. The second section is to study the effect ofhybrid reinforcement ratio on the flexural performance in under-and over- reinforced scenarios with validated models.
4.1. Validation of finite element models
The predicted load-displacement responses at midspan, theload-carrying capacities and the deflections at failure of the finiteelement models in Group V are validated by comparing with the
experimental results [7,11]. Fig. 5 shows the comparisons betweenthe simulation and the experimental results. In addition, thesimulated and experimental results for the maximum load and themidspan displacement at failure are listed in Table 4. The resultsfrom the developed finite element models and the experiment arein a good agreement, with a maximum deviation less than 10%. Thecrack width in pure FRPRC beam is larger than that in hybrid FRPRCbeam due to the low stiffness of FRP. The crack initiation andpropagation can result in a reduction of beam stiffness and an in-crease of midspan displacement significantly. This behavior agreeswell with the experimental finding in terms of crack width andbeam displacement in pure and hybrid FRPRC beams [7].
However, it is also shown that the load-displacement curvesfrom the finite element simulation are stiffer than those from theexperiment. The major reason is that microcracks generated by
Fig. 5. Comparison of load-displacement relationship between experimental specimens and finite element models. (a) and (f) are results from steel reinforced concrete beams; (b)and (e) are results from FRP reinforced concrete beams; (c) and (d) are results from hybrid FRP reinforced concrete beams. All the errors in terms of the load-carrying capacity andthe ultimate displacement for these six specimens are less than 10%.
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shrinkage and temperature effect are not included in the finiteelement models. In addition, the hypothesis of perfect bond
between reinforcement and concrete in the simulation may not beable to reflect the real situation. With the reasonable accuracy, it
Table 4A comparison of maximum load and displacement between experimental program and finite element model.
Beam specimen Maximum load P (kN) Difference Displacement (mm) Difference
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can be concluded that the developed finite element models in thisstudy can well predict the structural performance of SRC, pureFRPRC and hybrid FRPRC beams.
From the load-displacement curves, it can be observed thatduring the loading process, the state of hybrid FRPRC beams can bedivided into three stages: elastic stage, cracking stage and ultimatestage. Numerical result of sample G1.0-T0.7 is chosen for the dis-cussion related to the stress state of both concrete and reinforce-mentmaterials during the loading process, which is shown in Fig. 6.
Fig. 6. Finite element results of beam specimen in (a) elastic stage, where all material incluconcrete cracks in tension, steel and reinforcement are in elastic; and (c) ultimate stage whfailure.
4.1.1. Elastic stageIn this stage, the stress of concrete at tension zone is small and
linear. With the increase of displacement at midspan, concrete attension zone reaches its stress limit, and cracks occur at midspan.Because the elastic modulus of steel is much larger than that ofGFRP, the tensile stress of steel bars is also larger than that of FRPbars, which is shown in Fig. 6 (a).
ding concrete, FRP and steel reinforcement remain in elastic; (b) cracking stage, whereere steel reinforcement is yielded and FRP reinforcement continues to carry loading to
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4.1.2. Cracking stageDue to cracking, the strength of concrete at tensile zone is
insufficient, and the tensile stress at the bottom of beam is mainlytaken by the reinforcement bars. With the increase of load, steelreinforcement bars reach the yield strength. As the elastic modulusof FRP is lower, the stiffness of the beam reduces significantly.Concrete at compressive zone has not reached the failure strain atthis stage. It can be observed in Fig. 6 (b) that the cracks at midspanextend to the top of beam and more cracks occur and developuniformly towards the end of beam.
Fig. 8. Load-displacement curves of beam specimens B1, B2, B3, B4 and B5, and theassociated hybrid reinforcement ratios Af/As are 1:1, 5:3, 3:5, 2:5 and 5:2 respectively.The load-carrying capacity of beam specimen can be enhanced on the expense of a lessductile behavior with a higher hybrid reinforcement ratio Af/As. All the beams fail
4.1.3. Ultimate stageIt can be observed from Fig. 6 (c) that the load level of beam at
this stage shows a small increase, while the displacement at mid-span, as well as the stress of FRP bars, increases significantly. Thestiffness of the beam reduces significantly after yielding of steelreinforcement and complete development of cracks at this stage.With the increase of load, the failure of beam specimen occurs byeither rupture of FRP bars or concrete crushing at the compressivezone, while both failuremodes provide safer characteristics with animproved ductility compared to pure FRPRC beam.
through concrete crushing in compression in over-reinforced scenario.
4.2. Effect of hybrid reinforcement ratio between FRP and steel
To study the effect of hybrid reinforcement ratio between FRPand steel on the flexural performance of hybrid FRPRC, nine finiteelement models with different hybrid reinforcement ratios aredesigned to investigate its flexural strength and ductility perfor-mance. The load-displacement curves of beam specimens obtainedfrom finite element models in Groups A and B are shown in Figs. 7and 8, respectively.
It is observed in Figs. 7 and 8 that there are always three stagesin the load-displacement curves for the hybrid FRPRC specimensregardless of their failure modes. A clear yield point can be foundfor calculating the ductility factor. Flexural ductility is definedbased on displacement ductility factor (m) in this study, which is theratio of ultimate midspan displacement ( Δu) to midspandisplacement at yield point ( Δy). The yielding point refers to thepoint in the load-displacement curve where steel reinforcement
Fig. 7. Load-displacement curves of beam specimens A1, A2, A3 and A4, and theassociated hybrid reinforcement ratios Af/As are 1:1, 2:1, 1:2 and 1:4 respectively.Ductility of beam specimen is reduced by decreasing the hybrid reinforcement ratioAf/As, while it has a mild influence on the load-carrying capacity of hybrid FRPRC beamin under-reinforced scenario. All the beams fail through the rupture of FRP re-inforcements in this group.
reaches plastic phase. Displacement ductility factor (m) is adimensionless number to characterize the flexural ductility ofhybrid beam specimens.
In Fig. 7 and Table 5, there is a clear correlation between theload-carrying capacity and the hybrid reinforcement ratio in under-reinforced hybrid FRPRC scenario. With the increase of FRP rein-forcement, the load-carrying capacity increases by 5.33% and theductility improves by 15.78% compared to those of specimens A1and A2. However, with the interchanged amount of FRP and steelreinforcement, the load-carrying capacity increases by 9.26%,whereas the ductility reduces by 18.69% compared to those of beamspecimen A1. When further adjusting the hybrid reinforcementratio between FRP and steel reinforcement to 1:4, the load-carryingcapacity increases by 17.61%, while the ductility decreases by33.98% compared to those of beam specimen A1. It is obvious thatthe stiffness is governed by the ratio of FRP and steel reinforcement(Af/As). A higher hybrid reinforcement ratio Af/As results in a lowerstiffness, whereas the plastic stage and the ultimate deformation ofbeam specimen are in proportion to this ratio in the under-rein-forced hybrid FRPRC scenario. Since under-reinforced hybrid FRPRCbeams fail through the rupture of FRP bars, tensile stress is mainlycarried by FRP bars after the yielding of steel reinforcement. LessFRP reinforcement leads to the FRP rupture rapidlywhen the beamsare at the ultimate stage, which reduces the ductility of beamspecimen significantly. However, with a reasonable hybrid rein-forcement ratio Af/As, an under-reinforced hybrid FRPRC beampossesses a good flexural performance and a good serviceabilitymore economically.
For Group B, all five hybrid FRPRC beam specimens are designedin balanced-/over- reinforced scenarios. With the increase of FRPreinforcement amount, the load-carrying capacity increases by7.93% and the ductility improves by 3.55% compared to those ofspecimens B1 and B2, which is shown in Fig. 8 and Table 6. Throughinterchanging the amount of FRP and steel reinforcement, the load-carrying capacity increases by 9.26%, and ductility increases by6.24% compared to those of specimen B1. One more group ofcrossover design, i.e. B4 and B5, is carried out to further investigatethe effect of hybrid reinforcement ratio Af/As on the flexural per-formance of over-reinforced hybrid FRPRC beam. By adjusting thisparameter to 2:5, the load-carrying capacity reduces by 1.72% while
Table 5Comparison of flexural behavior in Group A.
Beam specimen Af/As Load capacity P (kN) Difference % Displacement (mm) Ductility factor m Difference
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the ductility improves by 10.89%. For specimen B5, the load-carrying capacity and the ductility factor reduce by 4.2% and14.76% respectively, when compared to those of the reference beamB1. It is noticed that in over-reinforced hybrid FRPRC beams, theload-carrying capacity of beam specimen can be enhanced on theexpense of a less ductile behavior with a higher hybrid reinforce-ment ratio Af/As. Moreover, with the increase of Af/As, the yieldingpoint is indistinct and strain energy of beam specimen is reducedobviously, which is shown in Fig. 8.
Based on above observations, with the decrease of hybrid rein-forcement ratio Af/As, the failure of under-reinforced beam specimenoccurs rapidly after yielding of steel reinforcement. When the hybridreinforcement ratio of the specimen is smaller than 1:2, the ductilityfactor is less than 3.0, possessing a less ductile behavior than therequirement of normal service condition. For over-reinforced design,with the same reinforcement content, beam specimens with ahigher hybrid reinforcement ratio show a better load-carrying ca-pacity on the expense of a less ductile behavior, which can beconcluded from the comparison between B2 and B3, as well as B4and B5. It should be noticed that when Af/As is equal to 5:2 (i.e. thebeam specimen B5), the ductility factor is reduced to 2.63 and thedeflection of B5 at midspan is much larger than that of the otherspecimens in Group B. For specimens in Group B, the slope of load-displacement curve at post-elastic stage is positive only when thehybrid reinforcement ratio is larger than 1, whereas the load levelalways increases after yielding of steel reinforcement for specimensin Group A. This phenomenon should attribute to the fact that theFRP reinforcement tends to suffer higher tensile forces after the steelbars have reached the yield strength. However, for the over-reinforced design, if the amount of FRP reinforcement is less thanthe requirement, it cannot provide enough strength to resist thedecay of concrete after the yielding of steel reinforcement, leading tothe reduction of load-carrying capacity. In addition, it is noticed thatthe stiffness can be enhanced by increasing the reinforcement de-gree by comparing the results of Group A and Group B. Over-reinforced hybrid FRPRC beams possess not only a higher load-carrying capacity, but also a good ductile behavior. These resultsagree well with the findings in the literature [7,11,35].
5. Recommendations on hybrid FRPRC flexural design
Based on the finite element simulation in this study, over-reinforced hybrid FRPRC beams possess higher strength and stiff-ness on expense of a less ductile behavior, which is still sufficient tofulfill the safety requirement. Thus, it is recommended that theover-reinforced beam design should be adopted in hybrid FRPRCbeam design. It should be noticed that the hybrid reinforcementratio, Af/As, should be designed larger than 1 to ensure the strengthof hybrid FRPRC beam after yielding of steel reinforcement. How-ever, this ratio should be smaller than 2.5 to meet the ductilityrequirement in normal service conditionwith a reasonable stiffnessand deformation resistance. Under-reinforced beam design can alsobe adopted as an economical method in hybrid FRPRC design.However, the load-carrying capacity of under-reinforced design isgenerally lower since beams fail through rupture of FRP rein-forcement and concrete does not reach its material limit. Ductilityimprovement can be achieved by steel yielding in under-reinforcedhybrid FRPRC beam on the expense of strength. In order to preventexcessive elongation that may cause the rupture of FRP reinforce-ment, the amount of FRP reinforcement should be larger than thatof steel reinforcement. The recommendations on hybrid FRPRCdesign are listed as follows:
� Over-reinforced beam design is recommended in hybrid FRPRCbeamwith higher strength, stiffness and sufficient ductility. Thehybrid reinforcement ratio, Af/As, should be designed in therange of 1e2.5 to provide enough post-elastic strength andstiffness for meeting the ductility requirement.
� Under-reinforced beam design can also be adopted in hybridFRPRC beam as an economical method. The hybrid reinforce-ment ratio, Af/As, should be larger than 1 to prevent excessiveelongation which may cause the rupture of FRP reinforcement,further leading to reduced strength and ductility.
� In hybrid FRPRC beam, FRP reinforcement is used to take upstrength while steel reinforcement is mainly responsible forductility improvement. It is recommended that beam membersshould be firstly designed as pure FRPRC beams according to ACI440.1R-15 [33]. Then, the amount of additional steel
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reinforcement can be designed in accordance with the afore-mentioned range of hybrid reinforcement ratio to obtain suffi-cient ductility and load-carrying capacity performance.
6. Conclusions
A total of fifteen 3D nonlinear finite element models aredeveloped in this study to simulate the response of concrete beamsinternally reinforced with a hybrid system consisted of FRP andsteel reinforcement bars. Six models are used to validate the ac-curacy of simulation scheme by comparing the predicted resultswith the experimental observations. Furthermore, the finiteelement models are used to investigate the effect of hybrid rein-forcement ratio between FRP and steel in both under- and over-reinforced designs and provide guidelines for determining thehybrid reinforcement ratio in FRPRC beams. It is concluded that thedeveloped finite elementmodels can be applied to predict the load-displacement behavior of the FRPRC beams accurately as the de-viation between the experimental and simulation results is smallerthan 10%. Engineers and researchers can use the developed finiteelement models as a powerful tool to investigate the performanceof FRPRC. In the over-reinforced scenario, the hybrid reinforcementratio, Af/As, should be designed within the range from 1 to 2.5 toensure the post-elastic strength of beam with sufficient ductilityand stiffness. Ductility improvement can be achieved by steelyielding in under-reinforced hybrid FRPRC beam on the expense ofultimate strength, and the amount of FRP reinforcement should belarger than that of steel reinforcement to prevent an excessiveelongation. Over-reinforced design for hybrid FRPRC is demon-strated as a preferable choice possessing high stiffness, high load-carrying capacity and good ductility behavior. Under-reinforceddesign can also be used as an economical way provided that theAf/As is carefully controlled.
Acknowledgements
The authors are grateful to the support from Croucher Founda-tion through the Start-up Allowance for Croucher Scholars throughgrant number 9500012, and the support from the Research GrantsCouncil (RGC) in Hong Kong through the Early Career Scheme (ECS)through grant number 139113.
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