FE modeling of concrete beams and columns reinforced with FRP composites

Frid Abed .Chhmi Oucif .Yousef Awer .Hy H.Mhnn .Hkem Alkhrish

a Department of Civil Engineering.American University of Sharjah.P.O.Box 26666.United Arab Emirates

b Institute of Structural Mechanics (ISM).Bauhaus-Universit¨at Weimar.Marienstra?e 15.D-99423.Weimar.Germany

Keywords: Numerical analysis BRFP GFRP CFRP Columns Beams xperimental tests

ABSTRACT Compression and flexure members such as columns and beams are critical in a structure as its failure could lead to the collapse of the structure.In the present work.numerical analysis of square and circle short columns,and reinforced concrete(RC)beams reinforced with fiber reinforced polymer composites are carried out.This work is divided into two parts.In the first part,numerical study of axial behavior of square and circular concrete columns reinforced with Glass Fiber Reinforced Polymer (GFRP) and Basalt Fiber Reinforced Polymer (BFRP)bars and spiral.and Carbon Fiber Reinforced Polymer (CFRP) wraps is conducted.The results of the first part showed that the axial capacity of the circular RC columns reinforced with GFRP increases with the increase of the longitudinal reinforcement ratio.In addition.the results of the numerical analysis showed good correlation with the experimental ones.An interaction diagram for BFRP RC columns is also developed with considering various eccentricities.The results of numerical modeling of RC columns strengthened with CFRP wraps revealed that the number and the spacing between the CFRP wraps provide different levels of ductility enhancement to the column.For the cases considered in this study.column with two middle closely spaced CFRP wraps demonstrated the best performance.In the second part of this research,flexural behavior of RC beams reinforced with BFRP,GFRP and CFRP bars is investigated along with validation of the numerical model with the experimental tests.The results resembled the experimental observations that indicate significant effect of the FRP bar diameter and type ont he flexural capacity of the RC beams.It was also shown that Increasing the number of bars while keeping the same reinforcement ratio enhanced the stiffness of the RC beam.

1.Introduction

Existing reinforced concrete structures are subject to damage and performance degradation under external loads.It is then indispensable to improve their performance using appropriate strengthening techniques.Fiber Reinforced Polymer (FRP) composites have been recently utilized in the field of structural engineering.FRP materials have many advantages including a onequarter to one-fifth density of that of steel.greater tensile strength than steel.and most importantly there is no corrosion even in harsh environments [1-3].FRP strengthening undergoes different production procedures and exhibits different failure mechanism structures conventionally reinforced with steel bars.Consequently.the conventional design philosophies of reinforced concrete had to be changed to account for the different mechanical behavior of FRP strengthening.There are various FRP materials that were utilized such as: GFRP.AFRP.CFRP and BFRP[4-7].

Concrete columns and beams are usually reinforced with conventional steel that is prone to corrosion which lead to high maintenance costs and short service life.Strengthening of these elements is necessary to increase their compressive[8],flexural[9]and shear strengths [10].Numerical analysis of reinforced concrete structures is a challenging task as it necessitates accurate definition of material model in order to describe the structural and material behaviors under external loading [11-15].Various attempts and experimental programs have been conducted to improve the ductility of RC columns and beams using FRP materials.Saljoughian and Mostofinejad (2018) [16]investigated the enhancement of compressive strength and ductility of square reinforced concretecolumns under cyclic and axial compression using longitudinally aligned CFRP.Two strengthening techniques were used,namely the externally bonded reinforcement on grooves (EBROG) and the externally bonded reinforcement in grooves (EBRIG).The results revealed that the grooving method could enhance the ductility and compressive strength of the columns comparing to the externally bonded reinforcement using conventional surface preparation method.In another investigation,the authors in Ref.[17]presented a new strengthening technique of rectangular cross-section RC columns.This method consists of the application of CFRP strips wet layup sheets along with the application of prestress level.The influence of the cross-section aspect ratio on the strengthened column behavior under axial compression loading was also investigated.The results showed that the proposed technique has a significant effect on the increase of the load carrying capacity of rectangular RC columns.It was also observed that the maximum axial strength and axial strain decrease with the increase of the aspect ratio.In Ref.[18].the authors studied experimentally the strengthening of RC columns with post-compressed steel plates under high axial load ratios and lateral reversed cyclic loads.The results demonstrated that the lateral displacement ductility capacity of the columns increases due to the effectiveness of the applied approach.

Kissman and Sundar (2019) [19]investigated the effect GFRP wrapping on the existing circular RC columns.It was demonstrated that the GFRP wrapping affects significantly the compressive and tensile strengths of RC columns.The same wrapping technique using CFRP was used in Ref.[20]in combination with shape memory alloy (SMA) and GFRP bars to study the RC columns behavior under axial compressive load and cyclic lateral displacements.The results showed that the lateral load capacity.energy dissipation capacity.stiffness and ductility of the columns were improved due to the strengthening using GFRP bars.In addition,it was found that the SMA strengthening reduced the residual deformation of the connections.Jiang et al.(2016)[21]proposed a new strengthening of circular bridge columns using near-surfacemounted (NSM) BFRP bars and sheets jacketing under cyclic lateral loads.The comparison of the repaired columns with the original columns revealed an improvement in the flexural capacity of the repaired columns.

Many studies had,also,been conducted to evaluate the behavior of concrete beams reinforced with FRP bars[22-27].BFRP reinforcement.being a more recent development.has fewer studies about its flexural behavior [28-30].Few studies investigated the flexural behavior of RC beams reinforced with BFRP bars.The authors in Ref.[28]conducted experimental tests on over-reinforced beams designed to fail by concrete crushing under static loads.The results indicated that the increase in reinforcement ratio caused a non-linear increase in the flexural capacity of the beams.In Ref.[29],the authors studied the performance of beams reinforced with BFRP in flexure and shear.Nine beams with reinforcement ratio ranging from 0.28 to 1.60 were casted.The results showed that the ultimate and service loads were proportionally impacted by the reinforcement ratio.Some researchers investigated the effect of exposure on the bond behavior between BFRP bars and concrete.For instance.the authors in Ref.[31]studied the impact of alkali conditions on the properties of BFRP bars.The bars were immersed in alkaline solution with elevated temperature.All the bars failed in a pullout mode in shear.One of the studies conducted in the GFRP reinforcement was a study conducted by Ref.[32]where the authors evaluated the flexural behavior of continuous beams reinforced with GFRP bars with a special focus of the effect of reinforcement ratio.In another study [5],six concrete beams reinforced with GFRP and steel bars were tested in flexure.The results showed that a hybrid GFRP and steel design improved the behavior of the concrete beams in terms of enhancing load carrying capacity,cracking stiffness and deformability.Finite element modeling of composite materials is not an easy task as accurate definition of material model is required.As a brittle material.concrete has received much attention in terms of cracking modeling [33-38]and fracture behavior [39-44].

Due to the lack of research on FRP bars used in concrete members particularly under compression.the ACI 440.1R-15 [45]code for the design of FRPs does not provide design criteria for FRPs reinforced columns.Therefore.in order to understand the compressive behaviors of RC columns reinforced with different types of FRP bars,it is very crucial to be able to predict and simulate their failure mechanisms.The objective of this paper is to develop finite elements models to investigate the compressive behavior of RC columns reinforced with FRP bars and wraps.The FE modeling is also extended to simulate and study the flexural response of FRP RC beams.Different reinforcement ratios and detailing will be investigated in the present paper.

2.Modeling of RC columns reinforced with FRP bars and wraps

In this section.the axial behavior of circular RC columns reinforced with GFRP bars and spirals.square RC columns reinforced with BFRP bars.and square RC columns strengthened with CFRP wraps is experimentally and numerically investigated.Nonlinear finite element models are developed to predict the axial behavior of RC columns under concentric and eccentric loading.Different parameters such as longitudinal and transverse reinforcement GFRP ratios.and number of CFRP wraps along with the development of interaction diagram for RC columns reinforced with BFRP are considered.

2.1.Description of experimental program

2.1.1.RC columns reinforced with GFRP bars and spirals

The experimental program given in Ref.[46]is used in the modeling of circular RC columns reinforced with GFRP bars and spirals.The tests consisted of a monotonically increasing pure axial load on 9 full scale circular columns reinforced with GFRP longitudinal and transverse (spirals) bars.2 columns reinforced with steel bars.and one plain concrete column.GFRP bars have diameters of 6.4.9.5.12.7 and 15.9 mm with their corresponding tensile elastic moduli of 52.5.53.4.53.6 and 55.4 GPa.tensile strengths of 938.889 941 and 934 MPa.and tensile strains of 1.9,1.89,1.7 and 1.56%,respectively[46].

For concrete.all columns are cast with normal weight.ready mixed concrete with average compressive strength of 41.9 MPa.All the materials properties are incorporated in the FE model,and have a diameter of 30 cm and length of 1.5 m.Strain gauges are attached on 3 bars at the middle height for each column while 4 strain gauges are mounted on spirals at 90°apart.Table 1 presents the test matrix with the axial capacity for the columns [46].

The columns labels from Table 1represent the reinforcement type and quantity.For example.the first column in group 2,(G8V-3H80).indicates GFRP reinforcement with 8 longitudinal bars and #3 spiral with 80 mm pitch.All longitudinal bars are #5 with 15.9 mm diameter.In this paper.a numerical study will be focused on the 9 GFRP columns where the longitudinal reinforcement ratios.spirals diameters and pitches or both are varying.

2.1.2.RC columns reinforced with BFRP bars

The experimental program consists of two columns reinforced with BFRP bars of diameters 16 mm and 20 mm and a control column specimen reinforced with conventional steel bars ofdiameter 16 mm.More details about arrangement of the reinforcement and spacing of the ties are illustrated in Fig.1.

Table 1 Test matrix.specimens details and results [46].

2.2.Finite element modeling

2.2.1.RC column reinforced with GFRP and BRFP bars

Commercial software package ABAQUS is used to create the nonlinear finite element model in which the axial behavior of the GFRP and BFRP reinforced columns are accurately simulated.The first column reinforced with GFRP bars in the second group which has#8,#5 bars and#3 spiral with 80 mm pitch is used to verify the FE model.The actual materials properties mentioned earlier that were tested in the experimental program,are incorporated into the finite element model.The nonlinear behavior of the concrete material is accounted in the modeling by introducing the actual inelastic properties of the concrete in the model.Moreover.to account for large deformation.the nonlinear analysis (NLGEOM)option is activated.Various load-eccentricities are applied on the columns and the load-displacement graphs are retrieved for all eccentricities applied.The load versus axial strain graphs are obtained from the FE analysis.The modeling of RC columns reinforced with GFRP bars is carried out under the effect of the longitudinal reinforcement ratios through varying the number of longitudinal bars while keeping the same diameter of 15.9 mm.

Fig.1.Geometric description of the column specimen (all dimensions are in mm).

2.2.1.1.Model geometry and materials properties.GFRP.BRFP.steel and concrete are the major materials used in the model.For the concrete material,the elastic behavior is defined through the elastic modulus and Poisson’s ratio while the inelastic behavior is defined using the concrete damage plasticity (CDP) model.Utilizing the CDP approach allows introducing both the compressive and tensile properties of the concrete material in the FE analysis.Figs.2 and 3 illustrate.respectively.the compressive and tensile properties for concrete used in the present FE analysis.The plasticity parameters for the CDP model are represented by the dilation angle of 36.eccentricity of 0.1.the ratio fb0/fc0of 1.16.the parameter K of 0.667 and viscosity parameter of 1.0×10-5.The GFRP and BRFP materials are modeled using the elastic modulus and strength.The GFRP material properties are defined with an average of 900 MPa tensile strength.300 MPa compressive strength.while for the BFRP,rupture strength is defined as 1100 MPa under tension and 400 MPa under compression as the compressive strength of the BFRP and GFRP is assumed to be 35% of the tensile strength as suggested in the literature.The plastic behavior for the steel ties is defined using the yield strength for the steel reinforcement (420 MPa).

The geometry of the column and the reinforcement is modeled using eight-node linear brick three-dimensional solid elements with reduced integration.The concrete column is modeled as a 3D solid deformable part whereas the reinforcement.including the ties.are modeled using deformable truss element.which only carries axial load during bending.In the experiment tests of RC columns reinforced with GFRP bars and spirals.all spirals at both ends of the column which is 250 mm of the total 1500 mm length have fixed pitch of 50 mm which is different than the middle pitch.Then.the spiral in the FE model is modeled as three parts: the middle part and both ends.Fig.3 shows the full model and the reinforcements with the chosen mesh.Fig.5 shows the assembly of the model of BFRP RC column.The form of interaction between the concrete part and the reinforcement,including the ties,is modeled as perfect bonding as the reinforcement is embedded inside the concrete part.As shown in Fig.4(b).rigid plates are added to the model to ensure the uniformity of the load applied on the top and bottom surfaces.Moreover.normal and tangential surface-tosurface contact defined the interaction between the rigid plates and concrete surfaces using the penalty contact approach.Boundary conditions and loadings are assigned on the plates through reference points defined on the center of each rigid plate.

A mesh sensitivity analysis is done to reach the appropriate mesh in which there is no significant change in results using a smaller mesh.The mesh sensitivity analysis of GFRP-RC columns is applied on the column G8V-3H80 that was verified with the experimental data.Mesh sizes of 52 mm.42 mm.32 mm and 22 mm are examined to reach the appropriate size.The model with a mesh size of 32 mm is considered as it gave the most accurate results.Regarding the BFRP-RC columns it was found that the model with mesh size of 30 mm gave the most accurate results.

2.2.2.RC column strengthened with CFRP wraps

In this section.four finite element models of square concrete columns (200 × 200 x 1000) mm reinforced with 4#10 steel bars and 6#8 steel ties are analyzed.one with no CFRP and the other three with different layers of CFRP wraps.The purpose of thissection is to study the compressive behavior of the reinforced column with different numbers and locations of CFRP sheets along the column height.

Fig.2.(a) Inelastic compressive and (b) tensile behaviors of concrete used in the FE model.

Fig.3.(a)FE Mesh configuration and(b)GFRP reinforcement cage of GFRP-RC column.

Fig.4.BFRP-RC column used in the FE analysis(a)reinforcement using truss element,(b) concrete part using solid elements.and (c) mesh configuration.

2.2.2.1.Model geometry and material properties.Concrete with a compressive strengthof 50 MPa is used considering elasticity and concrete damaged plasticity properties.Reinforcement was assumed as elastic perfectly plastic with a yield stress value of 420 MPa.Details of the square RC column are shown in Fig.5.CFRP wraps are defined in this section with elastic orthotropic properties as shown in Table 2.with a tensile strength of 3900 MPa.

Four square RC columns are modeled in ABAQUS with different numbers of CFRP wraps and different spacing (Fig.6).Two rigid plates are placed at the top and bottom ends to provide uniform loading to the column.A concentric displacement of 4.0 mm is applied on the top pinned plate.The reinforcement is defnied as an embedded region inside the concrete column which is considered as the host.Moreover,CFRP wraps are defined as shell homogenous with a thickness value of 0.17 mm using 3-points Gauss integration rule for the analysis.Friction tangential behavior is assigned in thecontact property for the interaction between each CFRP wrap and concrete,also a similar interaction property is defined between the rigid plates and the concrete.Different mesh configurations were considered and examined before selecting the appropriate mesh size for each part.and a finer mesh is used for the CFRP wraps to allow for accurate simulation.

Fig.5.RC column details:(a)cross-section,(b)CFRP wrap,(c)column dimensions,(d)FE geometry of steel cage.

Table 2 CFRP elastic orthotropic properties.

2.3.Results and discussions

2.3.1.Circular RC column reinforced with GFRP bars and spirals

2.3.1.1.FE model verification.The developed FE model for the circular column reinforced with GFRP is verified against its experimental counterpart through matching the total load applied,calculated as the reaction force on the rigid plate.versus the axial strain.at the middle of the column.The load vs strain results predicted using the FE model in ABAQUS for the column G8V-3H80 showed very good correlation with the experimental results as shown in Fig.7.Moreover.the failure mode obtained from the FE simulation of the same column captured the localized deformation at the top 1/3 of the column height.which resembles the spalling location observed experimentally.as shown in Fig.8.

Fig.7.FE model verification of G8V-3H80.

First.the verified model is used to compare the other experimentally tested columns with equivalent models with changing the reinforcement ratios to match the experimental ones.Fig.9(a)shows the comparison between the three experimentally tested columns with the FE models when changing the longitudinal bar reinforcement ratio.Whereas.the comparison of the next three columns with FE models done with changing the spirals’diameters is shown in Fig.9(b).Fig.9(c) illustrates the comparison when changing the spirals’pitches.Column G8V-3H80 was chosen to be the verified model because it was used in the experiment as the main column for doing the comparisons when changing the parameters.This column is shown as the middle column in Fig.9.From these figures,it is clearly shown that the FE results are in good correlation with the experimental ones.However.in each of these figures.the two new columns other than the verified model are slightly different than the experimental columns.This difference is due to the small differences and imperfection of the materials’properties in general and concrete specifically.Fig.10 shows the failure modes obtained from the FE simulations and comparison with the spalling location observed experimentally.From these figures.it is observed that all of the columns have close failure modes comparing the experimental columns with the FE models.

2.3.1.2.FE parametric analysis.Next.a parametric study is conducted to observe the effect of changing the longitudinalreinforcement ratios.spirals diameters and pitches.First.different longitudinal reinforcements are used to study their effect on the axial behavior.Fig.11(a) shows the load versus axial strain for different numbers of longitudinal GFRP bars of 4.6.8.10 and 12 bars.corresponding to reinforcement ratios of 1.1.1.7.2.2.2.8,and 3.2%,respectively.The results reveal that as the reinforcement ratio increases the compressive capacity and the ductility of the column increase.Second.studying the effect of varying the diameter of the spirals using#2.#3.#4.#5.and#6 diameters.it is observed that as the volumetric ratio of transverse reinforcement increases,the peak load increases as well as the ductility as shown in Fig.11(b).It is also observed that the column reinforced with#2 spiral has a brittle behavior as the load decay faster unlike the column with#6 spiral in which the load decay much slower.

Fig.6.CFRP-RC columns details: (a) without CFRP wraps.(b) with 1 middle CFRP wrap.(c) with 2 CFRP wraps.(d) with 3 CFRP wraps.

Fig.8.Comparison between the failure modes by the FE model and the spalling of the concrete in the experiment of G8V-3H80[46].

Finally.the FE parametric analysis considered the columns reinforced with#3 spirals but with varying pitches from 40 mm to 120 mm adding 20 mm at each column.As illustrated in Fig.11(c),the smaller pitch which means higher volumetric ratio provides better and efficient confinement.The graph shows that for small pitch.40 mm.a second load peak encountered before the load started to decay indicating noticeable ductile behavior.For the case of larger pitch.the peak load was reduced.and less ductility is observed as the load decayed faster.

Fig.9.Comparison between the experimental GFRP-RC columns and FE with varying (a)number of longitudinal bars.(b) spirals diameters and (c) spirals pitches.

Fig.10.Comparison between the failure modes by the FE model and the spalling of the concrete in the experiment [46]for (a) G4V-3H80.(b) G12V-3H80.(c) G8V-2H80.(d)G8V-4H80.(e) G8V-3H40 and (f) G8V-3H120.

2.3.2.Square RC column reinforced with BFRP bars

2.3.2.1.FE model verification using steel RC columns.In order to verify the accuracy of the model under various eccentricities,the FE model is utilized to develop an interaction diagram for a steel reinforced column.Various load eccentricities are applied on the steel reinforced concrete column.For each eccentricity,the load vs.displacement graphs are recorded to acquire the maximum capacity.Fig.12 shows an example of a load vs.displacement graph predicted using the FE model.The corresponding moment for each eccentricity is also recorded for each eccentricity to plot the interaction diagram.Table 3 displays a summary of the eccentricities applied on the column.

The FE developed interaction diagram is compared with an interaction diagram that was developed analytically using the ACI318 [47]code procedure for the same short column.The comparison is displayed in Fig.13.The procedure provided by ACI318 code includes analysis of pure axial compression and pure bending which represent the unique values of Pnand Mnon the y- and xaxes of the diagram.respectively.The other intermediate points represent the combinations of axial compression and bending depending on loading eccentricities.The developed FE model is observed to exhibit the same behavior throughout the various eccentricities applied on the column.Both interaction diagrams exhibit identical capacities at the pure axial loading (e = 0).the eccentricity corresponding to the balance point.and the pure flexural capacity.However,the other applied eccentricity exhibits a small error when compared to the analytically developed interaction diagram.

2.3.2.2.Developing interaction diagram for BFRP-RC column.After verifying the FE model.the procedure conducted to develop an interaction diagram for a steel reinforced concrete column is repeated using the properties of BFRP bars as the main reinforcement.Various eccentricities are applied on the column reinforced with BFRP bars.Table 4 displays the summary of the eccentricities considered in the FE analysis and the corresponding ultimate loads and moments.Fig.14 displays the interaction diagram developed for the BFRP reinforced concrete column.Unlike steel.it is preferable to design a BFRP reinforced concrete beam to fail in a compression-controlled mode.Thus.for the case of pure moment,BFRP-RC column is still under compression-controlled condition.Therefore.when developing an interaction diagram for FRP-RC column.the results beyond the balanced condition may not be considered.

Fig.11.Effect of(a) the longitudinal reinforcement ratio.(b) spiral diameters and (c) spirals pitches applied on the column G8V-3H80.

Fig.12.A sample of load-displacement results for e = 15 predicted by the FE model.

Table 3 Eccentricities used for the steel reinforced column.

The mode of failure throughout the various eccentricities is the crushing of concrete due to the buckling of the column.Fig.15 displays the mode of failure for one eccentricity case.which shows the contours of the equivalent plastic strains (PEMAG) for the concrete part and the reinforcements at ultimate load.At failure,the concrete exhibited high plastic strain values,beyond 0.003.On the other hand.the reinforcement did not develop any plastic strain,which indicate that the BFRP bars,unlike steel,did not yield.

Fig.13.Comparison of interaction diagrams developed using the present FE model and the ACI318 [47]code procedure.

Table 4 Eccentricities used for the BFRP reinforced Column.

Fig.14.Interaction diagram for a BFRP-RC column developed using the proposed FE model.

2.3.3.RC column strengthened with CFRP wraps

Fig.16(a)represents the relation between the load and the axial displacement applied on each of the four columns.The curve of the unwrapped column shows that it has the lowest ductility to undergo the applied displacement; it failed before reaching the maximum increment.One of the solutions to strengthen the concrete was adding the CFRP wraps.Three other models are applied controlling the number and spacing of wraps in order to specify the best assortment of parameters that would increase the ductility of the RC column.The results showed that the model including one middle CFRP wrap is a good option for strengthening but did not reach the intended displacement.However.models including 2 middle CFRP wraps and 3 middle CFRP wraps are the most sufficient since both exceeded the assigned displacement value.According to the models,the best arrangement is adding two middle spaced CFRP wraps.

Fig.15.Contours of equivalent plastic strains at ultimate force in (a)concrete and (b)reinforcement.

Based on finite element analysis.the strengthened concrete column crushed just before reaching the ultimate concrete strain(0.003).Similar behavior was encountered for all three strengthened columns up to the ultimate strain point on the curve since they have the same properties.but different parametric arrangements.As shown in Fig.16(b).all strengthened columns exceeded the ultimate strain limit; however.the best results are for the column with the two middle closely spaced CFRP wraps.

3.Modeling of concrete beams reinforced with GFRP.CFRP and BFRP bars

In this section.flexural behavior of concrete beams reinforced longitudinally with FRP bars is numerically investigated.The FE mode in validated using published experimental data.The effect of reinforcement ratio and number of reinforcement bars on the flexural behavior of BFRP reinforced beams is studied.In addition,BFRP reinforced beam is compared with GFRP and CFRP reinforced beams with similar reinforcement ratio.

3.1.Description of experimental program

Three beams were casted and tested in Ref.[27]to investigate the effect of reinforcing RC beams in flexure with BFRP bars.The beams have dimensions of 230 mm × 180 mm and span for 2200 mm,as shown in Fig.17.To prevent shear failure,all beams are reinforced in the transverse direction with φ 8 stirrups placed at 100 mm c/c.In addition.the beams are reinforced with 2φ10 steel bars in the compression zone.and longitudinally reinforced with 2φ10.2φ12 and 3φ16 BFRP bars in the tension zone.respectively.Table 5 shows the experimental test matrix.The beams are loaded using four-point bending test at a displacement control mode rate of 1 mm per minute.

The average concrete compressive strength (f’c) of thespecimens is found to be 30 MPa.In addition.tensile tests are performed on BFRP bars and the average tensile strength and Young’s modulus are found to be 1190 MPa and 50 GPa.respectively.In addition.the steel bars have a yield strength of 460 MPa,and a Young’s modulus of 200 GPa.

Fig.17.Geometry and reinforcement details of the beams (dimensions in mm).

Table 5 Test matrix[27].

Table 6 FEM matrix.

3.2.Finite element modeling

Commercial software (ABAQUS) is used to perform nonlinear finite element analysis on the RC beams presented in.Full beams are modeled using material properties specified in Ref.[27].In addition.the parameter (*NLGEOM) is incorporated in the model to capture the geometric and material nonlinearities.i.e.to capture the true stress-strain response of all materials used in the model and consider large deformations.Post processing includes finding the displacement at midspan and the reactions at the supports(the total value of the reactions represents the experimental load applied on the beams).In addition,crack propagation and internal stresses are obtained.The accuracy of FEM results is validated by comparing them tothe experimental results in Ref.[27].Following that.a parametric study is performed to investigate the effect of changing the area of BFRP bars.In addition.FEM results of two beams with 2 bars are compared with beams having the same area but different number of bars.Finally.the effect of using different FRP bar types in flexural reinforcement of RC beams is investigated.The FRP types explored in this study are BFRP.CFRP and GFRP.Table 6 presents the properties of the modeled beams in this section.

3.3.Materials properties

Steel bars used in top reinforcement and stirrups,are defined to have an elastic modulus of 200 GPa.Poisson’s ratio of 0.3.and a yield strength of 460 MPa.It is worth noting that the true stressstrain curve for steel used in the experimental study could not be obtained.Hence.elastic-perfectly plastic behavior is assumed and only yield strength is input in Abaqus to define the inelastic deformation of steel.Concrete Damaged Plasticity model is used to define the non-linearity of concrete material.Table 7 shows the values of concrete plasticity parameters as defined in Abaqus.Compressive and tensile stress-strain curves are obtained based on the compressive strength of concrete as shown in Fig.2.According to Ref.[27].the failure of all specimens is dominated by concrete crushing.Hence.FRP bars did not reach the ultimate tensile capacity.For that reason.BFRP.CFRP and GFRP bars are modeled in Abaqus as elastic materials with elastic modulus of 59,000 GPa,131,000 GPa.and 48,000 GPa.respectively.and Poisson’s ratio of 0.2.

Table 7 Concrete plasticity parameters.

3.4.Beam geometry and mesh sensitivity analysis

Steel and FRP bars are modeled as 2-node linear 3-D trusselements (T3D2) that are embedded in the concrete region.The concrete part is modeled as an 8-node linear 3D solid element with reduced integration (C3D8R).Mesh sensitivity analysis is carried out to select the appropriate mesh size and simulate the experimental results with minimum computational time.In this analysis,a mesh size of 30 mm is considered ideal for all beams.Fig.18 shows the reinforcement cage for a beam with 2 BFRP bars and mesh configuration for the beams modeled in this study.Four rigid plates are introduced to the model to apply onto the boundary conditions and reduce stress concentration on the beam in those areas.The interaction between the plates and the beam is modeled as surfaceto-surface contact.with the beam being the slave surface and the plates as master surface.The boundary conditions at the bottom plates are a pin and a roller.In addition.a vertical displacement is applied at the top plates to mimic the applied load on the beam.

3.5.Results and discussion

3.5.1.FE model verification and validation

The experimental results of the three beams presented in Ref.[27]are used to validate the developed FE models.Fig.19 shows the experimental and FE generated load-displacement curves for beams 2T10B,2T12B and 3T16B,respectively.It is clear from Fig.19 that all FEM results are in good agreement with the experimental results.In particular.the initial stiffness.load at first crack.and degradation trend of the FE curves generally matches that of the experimental curves.In addition.cracks distribution along the beam length is accurately captured by the FE models.Fig.20 shows the crack pattern of beam 3T16B obtained from the experimental test[27],and the effective plastic strain(PEEQT)obtained from the FE model.

Fig.19.Model verification of the beams 2T10B.2T12B and 3T16B.

3.5.2.Parametric study

The verified models are utilized to carry out multiple parametric studies.Variations in the ratio,detailing,and type of reinforcement are implemented and the flexural behavior of the varying models are observed.Fig.21(a)presents the load versus midspan deflection behavior of the FE models examining the effect of reinforcement ratio on the flexural behavior of the beams.The beams are reinforced with 2T8,2T10,2T12,and 2T16 BFRP bars corresponding to reinforcement ratios of 0.003.0.0047.0.0068.and 0.0123.respectively.The beams show the same pre-cracking stiffness due to the fact that concrete is controlling the behavior of the beam until the first crack.After the first crack beams with higher reinforcement ratios showed higher stiffness.The increase of stiffness,however,is not proportional to the reinforcement ratio.

Fig.21(b)presents the load versus midspan deflection behavior of the FE models examining the effect of reinforcement detailing on the flexural behavior of the beams.As expected.beams with the same axial stiffness (i.e.3T8-2T10 and 3T10-2T12) have the same flexural capacity.The only differentiating factor is the maximum deflection.where beams with more reinforcement bars in the tension zone experience less maximum midspan deflection and would fail at lower displacement values.

Fig.21(c) presents the load versus midspan deflection of behavior of the FE models examining the effect of reinforcement type on the flexural behavior of the beams.FRP types with higher modulus and tensile strength of elasticity.such as CFRP.exhibitlarger flexural capacity.Until the first cracking load,the stiffness of the beams is the same.After which.the strength of the FRP reinforcement control the stiffness.BFRP and GFRP reinforcement show similar stiffness trend with BFRP reinforced beams have larger reinforcement.The CFRP reinforced beam have much higher stiffness that BFRP and GFRP one.The behavior of the CFRP reinforced beam can be traced back to the high strength properties of CFRP bars.

Fig.18.FEM geometry: (a) reinforcement cage; (b) mesh configuration.

Fig.20.Crack distribution for beam 3T16 B at failure: (a) experimental[27]; (b) deformed shape of FE model (PEEQT).

Fig.21.Load-Deflection curves for (a) Group 1.(b) Group 2 and (c) Group 3.

4.Conclusions

The axial behavior of columns and flexural behavior of beams reinforced with FRPs were numerically investigated in the present paper.The results of the numerical modeling of columns reinforced with GFRP bars and spirals showed good agreement with the experimental results.It was shown that the axial capacity and ductility of the column increase as longitudinal reinforcement ratio increases.The capacity and ductility also increase as spiral diameter(i.e.volumetric ratio) increases.while keeping the pitch at a value in which confinement happens.When the pitch of the spirals decreases.i.e.the volumetric ratio increases.the peak load and ductility increase because of better confinement.A nonlinear FE model was also developed to simulate the ductility performance RC columns strengthened with CFRP sheets.The results revealed that the CFRP wraps play a major role in strengthening the concrete columns.Changing some parameters related to the number and the spacing between the wraps have achieved different levels of ductility enhancement in the column.According to the FEM.the column with two middle closely spaced CFRP wraps demonstrated the best performance.

The results of the numerical modeling of beams reinforced with BRFP bars also showed good agreement with the experimental results.The results revealed that increasing bar diameter leads to the increase in the ultimate load-carrying capacity of the beams and to the decrease in its ductility.In addition.increasing the number of bars.while keeping the total area of bars constant.results in a similar load-displacement pattern.However,beams with more bars fail at a lower displacement.The results also revealed that varying FRP type has a large impact on the overall beams behavior.CFRP bars have the best performance.in terms of increasing the beam’s capacity.followed by BFRP bars thenGFRP bars.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.