Numerical Investigations of GFRC beams strengthened in shear Numerical Investigations of GFRC beams strengthened in shear with innovative techniques with innovative techniques

This paper discusses the ﬁ nite element (FE) analysis to predict the behavior of glass ﬁ ber-reinforced concrete beams without shear reinforcement (stirrups) and strengthening them with proposed techniques to increase their shear strength. For this study, 18 (120 £ 300 £ 2200 mm) specimens were modeled using Ansys mechanical. The main variables were the percentage of discrete glass ﬁ ber in the concrete (0.0, 0.6, and 1.2%), the type of main reinforcing bars (steel or GFRP), the shear strengthening material (GFRP or steel) links, the strengthening systems (side near-surface mounted bars, externally bonded sheet, or both), various near-surface mounted GFRP bar con ﬁ gurations (side-bonded links, full wrapped stirrups, side C-shaped stirrups, and side bent bars), the link spacing, the link inclination angle, and the number of bent bars. Each model had a free span of 2000 mm with a constant shear span-to-depth ratio (a/d) of 2.0. The numerical models were veri ﬁ ed against experimental results presented in the earlier publication. These results were analyzed to investigate the effect of main variables on shear strength. Increasing the ratio of discrete glass ﬁ ber-reinforced concrete beam to 0.6 and 1.2% enhanced the ductility and increase the shear strength by 24 and 32% for steel reinforcement and by 16 and 29% for GFRP reinforcement, respectively. The use of GFRP bars instead of steel bars as the main reinforcement slightly enhanced the shear strength and ductility but decreased the stiffness. The use of various strengthening systems enhanced the shear capacity by a ratio of up to 115%. A new strengthening technique (side near surface mounted bent bars with strips) produced better improvements in terms of shear capacity, ductility, and crack propagation compared with other strengthening techniques. The results of numerical analyses and the experimental results for 18 beams were considered, and the ratio between them is equivalent by a factor of 0.96 e 1.04.


Introduction
S hear failure in concrete elements is especially harmful because it happens without sufficient warning as a result of insufficient shear reinforcement, steel corrosion, damaging environmental effects, freezeethaw cycles, or corrosive chemicals (Noel and Soudki, 2011).Fiber-reinforced concrete (FRC) is a common construction material that is used in a variety of structural applications, including slabs in industrial buildings and concrete sewer pipes because of its advantages in shear resistance, such as reduction in the crack number and shear crack width as reported by many research studies (Elkareim and Moustafa, 2011;Soliman and Osman, 2011;Abdul-Zaher et al., 2016;Ahmadi et al., 2020).Fiber-reinforced polymer (FRP) in the form of bars for reinforcement and bars or sheets for strengthening beams is gaining credibility as a concrete rehabilitation material.This is due to its advantages such as corrosion resistance, longer service life, humidity resistance, high tensile strength, lightweight, durability, low maintenance, ease of application, and nonmagnetic properties (Al-Rousan and Issa, 2016;Medhlom, 2016;Ibrahim et al., 2017;Karzad et al., 2019;Siddika et al., 2019;Thamrin et al., 2019;Jin et al., 2020).The use of FRP bars rather than steel bars for reinforcing structures solves the issue of durability in aggressive environments such as roadbeds and bridge decks, where substantial corrosion of steel reinforcement may occur (Pang et al., 2016).Many researchers (El-Sayed et al., 2005;Monika et al., 2017) have examined ratios and various types of FRP bars in reinforced concrete beams without web reinforcement and evaluated their effects on shear capacity as compared with beams with conventional steel.Without adding discrete glass fiber in concrete, the near-surface mounted (NSM) and externally bonded reinforcement (EBR) techniques were used to investigate the shear capacity in studies (Sharaky et al., 2015;Seo et al., 2016;Panahi and Izadinia, 2018).The NSM FRP method does not require surface preparation (Khalifa, 2016;Zhanga et al., 2017); is faster to install; protects against external factors like mechanical damage, vandalism, and fire; increases the load-carrying capacity of RC elements; generates greater strain in FRP (De Lorenzis and Teng, 2007); raises confinement provided by the surrounding concrete and epoxy, and reduces the risk of debonding (El-Hacha and Rizkalla, 2004), making NSM an effective substitute for traditional methods (EBR) for RC structures.This paper summarizes the shear results of FE analysis modeling of 18 glass fiber-reinforced concrete (GFRC) beams without stirrups using Ansys, version 21.The GFRC beams without web reinforcement were divided into four groups: in the first group, the volume ratio of glass fiber added in concrete mixes was 0, 0.6, or 1.2% by weight of cement with steel or GFRP bars the as main reinforcement.In the other three groups, all GFRC beams that included a fiber ratio of 1.2% only were reinforced with steel bars as the main reinforcement and strengthened using variable proposed strengthening techniques.Beam strengths in shear are listed in groups second, third, and fourth.In the second group, steel or GFRP side near-surface mounted (SNSM) links were used as vertical or inclined links with variable spacing for steel vertical links.In the third group, GFRP NSM C shape stirrups, GFRP NSM full wrap stirrups, or GFRP EBR sheets were used.In the fourth group, a newly proposed strengthening technique (GFRP side NSM bent bars) was used in one or two rows, or combined GFRP SNSM bent bars and GFRP EBR sheets were used together.Although experimental work has been used in numerous studies to test the shear strength of FRP and steel-reinforced concrete beams, there are no sufficient analytical studies on steel-GFRC beams without stirrups.Several software packages, including Ansys, have been used to idealize theoretical investigations using FE for modeling beams (Ibrahim and Wissam, 2009;Dawari and Vesmawala, 2014;Elmezaini and Ashour, 2015;Ahmad et al., 2021;Tahenni et al., 2021;Barour et al., 2022).Ansys mechanical APDL software is used to construct an analytical model of simply supported GFRC beams without stirrups under four-point bending.The results of the failure load, deflection, and load-midspan displacement relationships were presented from modeling runs.Crack development of the analyzed GFRC beams was carefully investigated.The loadedeflection curve is an important presentation in analyzing beam shear response.The numerical analysis results showed the ultimate shear capacity for all beams, the maximum deflection with increasing glass fiber ratio, the behavior of beams reinforced with steel and GFRP bars, and the behavior of GFRC beams without web reinforcement strengthened with proposed techniques in shear.To confirm the FE models, the results of the numerical analysis were compared with experimental investigations by the authors (Hany et al., 2022).These results of numerical analysis models were proven to achieve good agreement with corresponding experimental investigation results.As a result, the developed models are considered useful for laboratory investigations, particularly in parametric studies.A parametric study was carried out on beams to illustrate the viability of the finite element (FE) model by comparing FE results with the experimental results.

Research significance
The main objectives of this research were as follows: (1) Developing FE models of GFRC beams without stirrups.
(2) Analyze GFRC beams without stirrups that have been externally strengthened using various proposed techniques using the FE modeling software (Ansys).
(3) Investigate the influence of important parameters on the behavior of strengthened GFRC beams in shear.(4) Verify the accuracy of the numerical analysis models against the results of the experimental testing.( 5) Using the verified model in a parametric study to determine the effect of various parameters on the behavior of strengthened GFRC beams.

Element types
The elements used are classified into three types: SOLID65, LINK180, and SOLID185.
SOLID65 element was used to simulate the concrete, GFRC, and epoxy model of GFRP sheets due to its ability to present the compression stressestrain curve for concrete, as shown in Fig. 1a.The element has eight nodes with three degrees of freedom at each node.Plastic deformation, cracking in three orthogonal directions in tension, and crushing in compression are all incorporated into this element.Because the concrete used in this numerical study is fibrous, the model's rebar (discrete glass fiber) capability is considered.To represent the actual fiber volumes used in each beam specimen, the discrete glass fiber reinforcements were simulated as smeared reinforcements in SOLID65 elements by calculating their volumetric ratio in concrete elements (Said et al., 2020).
LINK180 element is a one-dimensional element that was used for idealized longitudinal steel and GFRP reinforcement bars and stirrups.This element requires two nodes to function.Six degrees of freedom are available for each node.Plastic deformation is also possible with this element, as shown in Fig. 1c.
SOLID185 element was used for both the steel plates in the beam at the supports and loading locations to prevent stress concentration issues and was used for the FRP sheets.The element is described by eight nodes each with six degrees of freedom as shown in Fig. 1b.

Glass fiber-reinforced concrete and ordinary concrete
Concrete was described by Ansys in models using linear isotropic and multilinear isotropic properties for GFRC and ordinary concrete elements in the SOLID65 element.When defining concrete beams in the program, the modulus of elasticity is selected to be 20,000 MPa and the Poisson's ratio is assumed to be 0.2.Other material properties were taken into Fig. 1.Geometry and node locations of element types for modeling the beams (Tahenni et al., 2021).
consideration such as two shear transfer coefficients (open crack bt and a closed crack bc).These coefficients have values between 0 and 1, with 0 denoting smooth crack and 1 denoting rough crack (Bouziadi et al., 2018a(Bouziadi et al., , 2018b;;Bouziadi et al., 2019;Hamrat et al., 2020;Lahmar et al., 2020;Ansys Release 21.0. Mechanical User's Guide, 2021).In this investigation, bt and bc were assigned the values 0.2 and 0.8, respectively.Moreover, the ultimate uniaxial tensile strength (modulus of rupture) (fctr ¼ 2.5 MPa) and ultimate uniaxial compressive strength (f'c ¼ 25 MPa) were used.In this numerical study, the distribution of glass fibers needs to be simulated.Thus, the linear elastic-perfectly plastic constitutive material was used to model the nonlinear mechanical properties of glass fibers.
Material properties for the discrete glass fiber added to the concrete mix are Poisson's ratio taken as 0.3, modulus of elasticity (E ¼ 200 GPa), and yield stress for glass fiber (fyf ¼ 2000 MPa).The tangent modulus for FRP elements was set to 2000 MPa.
The smeared model was used to simulate the geometry of steel fibers in concrete, which assumes steel fibers are uniformly distributed throughout the concrete elements in a defined region of the FE mesh.The following equations were used to calculate the multilinear isotropic stressestrain curve for the concrete as illustrated in Fig. 2 to derive the compressive uniaxial stressestrain relationship for the concrete model (Ibrahim and Wissam, 2009).In each beam model, the simplified stressestrain curve was made up of six points joined by straight lines.The stressestrain relationship of the concrete is determined at point 1 at 0.3 f'c (must satisfy Hooke's law).Points 2 and 3 were calculated using Equation (2), where 3o is computed using Equation (4).Point 5 is at strain at ultimate strength (3o) and ultimate compressive strength (f'c).After point 5, it was assumed that the behavior is completely plastic (Ibrahim and Wissam, 2009).

Steel and fiber-reinforced polymer bars
The steel and GFRP bars for longitudinal reinforcement, stirrups, and strengthening (links/bars/ bent bars) were modeled using the LINK180 element.The element is a linear elastic perfectplastic material model and exhibits an identical stressestrain curve in compression and tension (Ibrahim and Wissam, 2009).Fig. 3 shows the modified stressestrain relationship for steel and FRP bars.
Properties of the steel reinforcement were Poisson's ratio of 0.3, modulus of elasticity Es ¼ 200 GPa, yield stress for longitudinal reinforcement and strengthening links fy ¼ 360 MPa, and yield stress for stirrups (fyst ¼ 240 MPa).Steel elements will have a tangent modulus of 2000 MPa.
Material properties for the GFRP reinforcement are Poisson's ratio taken as 0.3, elastic modulus of elasticity (Es ¼ 70 GPa), and yield stress for longitudinal reinforcement and strengthening (linksbars-bent bars) (fyf ¼ 1400 MPa).FRP elements will have a tangent modulus of 2000 MPa.Material properties for the carbon fiber-reinforced polymer (CFRP) reinforcement are Poisson's ratio taken as  m, concrete fiber ratio; AS, longitudinal main reinforcement; S.S, strengthening systems on the beam's outer surface.B0, B1, and B2 denote GF ratios of 0.0, 0.6, and 1.2%, respectively.S1 and F1 are the main reinforcement materials steel and fiber, respectively.
V and D denote the vertical and diagonal with 45 strengthening links.20 and 14 refer to the distance in centimeters between strengthening links, bars, and strips.S and F refer to steel and fiber, two materials used for strengthening.U, Ps, and E represent the near-surface mounted double-C, near-surface mounted full warp, and EBR strengthening techniques, respectively.
Observing that PsF: GFRP strip was rounded to create a bar (strips with 100 mm width).The number of GFRP bent-up bars on each side is denoted by Sb1 and Sb2.

Supporting and loading steel plates
SOLID185 element was used to model the loading and supporting steel plates as elastic linear isotropic material to avoid stress concentration problems.Plasticity, hyperelasticity, constraint stiffness, creep, significant deflection, and extensive strain capabilities are all characteristics of SOLID185.The applied load and support were considered as rigid elements to create a surface-tosurface contact (Barour et al., 2022).The properties for steel plates (SOLID185) were the modulus of elasticity and Poisson's ratio, which were 2 Â 1010 MPa and 0.3, respectively.

GFRP sheets
The SOLID185 element was used to model the GFRP sheets, and the SOLID65 element was used to model the epoxy adhesive for GFRP sheets with the surface of the beam.
Ansys describes the GFRP sheets as an elastic linear orthotropic material.The properties used in the GFRP wraps were the elasticity modulus for GFRP sheets, elasticity modulus for epoxy adhesive, Poisson's ratio, and shear modulus, with values of 70, 4.5, 0.28, and 4.5 GPa, respectively.The layer thickness of GFRP sheets was 0.17 mm.Fiber works in one direction only, so local Cartesian must be created for each size of GFRP sheets so that the Xdirection is always the direction of the sheet.The epoxy adhesive was described using linear isotropic and multilinear isotropic.The modulus of elasticity was 4500 MPa and the Poisson's ratio was 0.3.Two points connected by straight lines made up the multilinear stressestrain curve.The curve starts at point 1 where there is no stress or strain.Point 2 is at strain at ultimate strength (3o ¼ 0.009) and ultimate compressive strength (f'c ¼ 40.5 MPa).Previous research had suggested that a perfect bond should be used to model the interaction between the concrete surface (SOLID65) and GFRP (LINK180).Because no debonding was observed between the two during the experimental part of the study, the perfect bond approach was used for this numerical analysis.To model the interface between the GFRP and the adhesive material, the perfect bond was assumed.The concreteeepoxy adhesive interface was also assumed to be perfectly bonded (Barour et al., 2022).

Models description
Four groups of 18 GFRC beams were modeled and analyzed.The same concrete dimensions (120 Â 300 mm) and top reinforcement (2 bars, dia.10 mm) were used in all beams.There were no internal stirrups between the two supports, but there    were two stirrups spaced 40 mm apart outside the supports.All specimens, except three, were reinforced with four high tensile steel bars of 16-mm diameter (4Ø16 steel) as the main reinforcement.Further boundary conditions were given to the model to constrain the beam to any translational displacements (dof 123) (hinge support) from one end and allow movement in one direction (roller support) from another end to behave simple beam and to have a displacement between two supports.A two-point load was applied at 550 mm from each support.Fig. 8 shows the loading and boundary conditions of the FE models for specimens.The remaining three beams (B0GF-F1, B1GF-F1, and B2GF-F1) were reinforced with four GFRP bars of diameter 16 mm as the main reinforcement.The total/loaded spans were 2200/2000 mm, respectively.Longitudinal and cross-section detailing for unstrengthened beams in group 1 together with control beams for strengthened GFRC beams in groups 2, 3, and 4, is shown in Fig. 4. Table 1 and Figs.5e7 provide a summary of the nomenclature and characteristics of the shear-strengthening methods for GFRC beams investigated in the current study (Hany et al., 2022).The beam models were subjected to six concentrated loads, three at each loading plate, as shown in Fig. 8.The control beam geometrical and reinforcing details as well as typical details for strengthened models created with Ansys are shown in Fig. 9.

Meshing
In the models, a perfect bond between the steel reinforcing and the concrete was assumed.The steel reinforcement element (LINK180) was connected to the concrete element adjacent nodes (SOLID65), enabling both materials to use the same mesh size and nodes.It is understood that the numerical outcomes depend on the mesh size (Kesteloot et al., 2018).
The specimen is divided into a number of small elements (20, 40, and 60 mm), and after loading, stress and strain are calculated at the integration points of these small elements.An important step in FE modeling is the selection of the mesh density.A convergence of results is obtained when an adequate number of elements are used in the analysis.Mesh sizes of 40 Â 40 mm and 20 mm in thickness were used in his study for concrete elements and 40 mm for reinforcements elements.This size was chosen to minimize the number of elements and computational time needed for analysis while maintaining the investigation's accuracy.GFRC beams with SNSM GFRP bars and EB GFRP strips were assumed to have a mesh size of 80 mm.Fig. 10 illustrates the mesh solid for some models of GFRC beams.

Solution procedure
The total load was applied incrementally, and the model stiffness matrix was updated at the end of each load increment to account for the nonlinear structural and material behavior.The stiffness   matrix was updated using NewtoneRaphson equilibrium iterations.The difference in forces caused by internal stresses and the external load applied was calculated as the out-of-balance load vector.If the difference was within the tolerance limit, convergence was achieved, and the load was incrementally increased further (Figiel and Kaminski, 2009).

Numerical analysis and discussion of the results
The experimentally tested specimen (Hany et al., 2022) was used to verify the reliability and accuracy of the FE model by Ansys with a variety of parameters.According to the theoretical results, the loadedeflection curves and crack patterns obtained from Ansys models were in high agreement with those measured in the experiments.

Loadedeflection curves
Deflections at the mid-point of the bottom face of the beams from both the FE analyses and the experimentally tested beam were compared.Table 2 lists the analytical and experimental ultimate loads and corresponding deflections.The loadedeflection curves for all beams in group 1 and shear-strengthened beams in groups 2, 3, and 4 for experimental and analytical results are shown in Fig. 11.In general, the loadedeflection curves for the beams from the FE analyses show good agreement with the experimental work.In general, the loadedeflection curves for the beams from the FE analyses show good agreement with the experimental work.However, when the beams were loaded, there were differences in the responses for some beams.The following points provide an outline of the possible causes for the difference in response between FE models and experimentally tested beams: (1) The shear transfer coefficients (open crack bt and a closed crack bc) are not a good representation of the concrete's actual behavior.(2) Loading the beams in load control rather than displacement control might contribute to the difference in responses.
(3) The adopted equally spaced amplitude loading might also contributed to the difference in responses.(4) The possibility of some errors in the laboratory during casting or loading or measurements also contributed to the difference in responses.
The results showed that the method had been successful in predicting the test specimen's final strength.The average deviation between the experimental ultimate loads and their numerical values was less than 4%.Additionally, there was an acceptable similarity between experimental ultimate loads/deflection and their numerical simulated values.
According to the theoretical results, the effect of the volume of glass fiber, main reinforcement materials (steel-GFRP bars), and variable parameters strengthening for GFRC beams was fully compatible with the experimental results executed by the authors, as shown in Figs.12e21.
The load-span deflection relationship for group 1 is shown in Figs. 12 and 13 for various glass fiber ratios (0, 0.6, and 1.2%).The first three beams reinforced with steel bars are shown in Fig. 12, and the second set of three beams reinforced with glass fiber bars are shown in Fig. 13.Fig. 14 shows the relation between fiber content and failure load for group 1.
When comparing the shear behavior of specimens B0GF-F1, B1GF-F1, and B2GF-F1 in group 1 with specimens B0GF-S1, B1GF-S1, and B2GF-S1 in the same group, as shown in Fig. 15, it is possible to observe the effect of using GFRP bars as

Crack pattern
Ansys program records a crack pattern at each load interval.The program shows circles where concrete elements are crushing or cracking.A circle outline on the plane of the crack indicates cracking, a red circle indicates the first crack at an integration point, a green circle at the second crack, and a blue circle at the third crack.Fig. 22 illustrates the crack patterns for experimental beams in pictures (Hany et al., 2022) and FE beams for each beam at the final loading step below each picture.
The diagonal shear cracking in the region of maximum shear led all the beams to fail during testing.In all specimens, shear cracks generally started in the shear zone near the supports of the beam.As the load increased, one or two major cracks and a few smaller secondary cracks appeared on both sides of the beam along the line from the support to the point of loading until failure.All the specimens failed in shear.The shear failure was produced by the concrete cracking in the line from the support to the concentrated point of loading.The GFRC beams in the first group failed when the splitting cracks began to appear.Increasing the glass fiber ratio in the first group reduced the number and width of cracks as fibers transfer tensile stresses across diagonal cracks and thus control the widening of diagonal cracks.
When compared with the control beam (B2GF-S1), the strengthened beam diagonal crack appeared at a considerably higher load owing to improvement in the contribution of the dowel action and limiting the widening of inclined shear cracks.Increasing the number of shear reinforcements by comparing beam models B2GF-V14S and beam B2GF-V20S showed a clear effect in controlling the crack width and contributing to the behavior of the shear mechanism and enhancing shear transfer by aggregate interlock.The diagonal tension caused partial premature debonding (delamination between GFRP and concrete) or separation of the sheets at the shear zone of the beams strengthened with sheets, which resulted in the ripping off some strengthening elements as illustrated in Fig. 23.
When examining data from the experimental GFRC beams (Hany et al., 2022), the FE model failure modes were proven to exhibit good consistency.The cracks in tested beams were similar to those estimated by Ansys.When the beam in the model was loaded gradually, cracks began to spread in the shear zone at higher loads.The model predicts that cracks will have inclined orientations in the shear span region and vertical orientations in the constant moment zone.Experimental results supported the crack patterns and cracking order expected by the model.At the maximum load applied during the test, the inclined crack in the shear span grew wider and the concrete under the load point was crushed.The model indicated a significant deformation of element nodes, which predicted the crushing of concrete at the ultimate limit.All beams have exhibited shear failure, according to the FE model crack patterns.

Loads and deflection values at failure
Table 2 compares the ultimate loads and deflections at the model midspan to those from the experimental results (Hany et al., 2022).In group 1, the ultimate load for beams B1GF-S1 and B2GF-S1 compared with the beam B0GF-S1 and for beams B1GF-F1 and B2GF-F1 compared with the beam B0GF-F1 is shown in Table 2.In groups 2, 3, and 4, the ultimate load for all strengthened beams compared with the control beam (B2GF-S1) is shown in Table 2. Owing to multiple cracks and significant deflections, the loads from the FE models diverge at the last applied load stages.The ultimate loads of 18 beams from experimental testing divided by numerical studies were in the range of 0.96e1.04,as shown in Table 2. FEM was successful in forecasting the test specimen strength with an average difference between the experimental ultimate loads and their numerically predicted values of less than 4%.Fig. 24 illustrates the deflections for all beams along the model length at the maximum load.

Ductility factor
A member's ductility is defined as its capacity to withstand inelastic deformations exceeding yield without significantly losing load energy.The ductility factor (DF) of the specimen was calculated using the loadedeflection curves of the tested models.Based on the deflection of the beam, the DF can be defined as the ratio [Du/Dy] (Said et al., 2020), where Du denotes the deflection at the ultimate level and Dy denotes the deflection at the yield level.The ductility value for each tested beam is shown in Table 2.The ductility ratio in the first group increased as the fiber ratio in the concrete mix increased.

Parametric study
Using Ansys 21.0 software, a parametric study was carried out on beams B2GF-S1, B2GF-EV20F, B2GF-Sb1, B2GF-Sb2, B2GF-Sb1-EV20F, and B2GF-Sb2-EV20F to further illustrate the viability of the FE model and numerical analysis.The influence of GFRC compressive strength on the shear strength behavior of the GFRC beam was investigated and reported in this work.The GFRC that was employed had characteristic compressive strengths of 29, 35, and 40 MPa.The results are summarized in the following paragraphs.

Effect of compressive strength on the shear strength of GFRC beams
The three different values of compressive strength considered in this study are 29, 35, and 40 MPa.The influence of compressive strength on load-carrying capacity and the shear strength of the GFRC beam was predicted using Ansys 21.0 software.When the concrete's strength grades are increased, the predicted shear strength of the concrete beam also increases.The loadedeflection curves at the midspan for GFRC beams reinforced with longitudinal steel bars for concrete strengths 29, 35, and 40 MPa are shown in Fig. 25.According to the results, increasing concrete strength improved the ultimate shear strength, load-carrying capacity, and ductility of the beam, as shown in Fig. 25 and Table 3.
In general, all beam models' behavior passed through two phases.The first phase where the tensile stresses were within the concrete's tensile strength limit consisted of linearly elastic behavior.This phase was identified from other phases by its high stiffness and low deflection.The second phase experienced postcracking of the concrete because the tensile stresses were greater than the concrete's ability to withstand them, causing a crack and decreasing the stiffness.
The crack and crush plots for the beam B2GF-S1, which had varying concrete strength at the point of failure, are shown in Fig. 26.Therefore, increasing the concrete's compressive strength increased the beam specimens' ability to withstand cracking loads.

Effect of type of strengthening material
Three different materials (steel-GFRP-CFRP) of shear-strengthening bent-up bars were used in this study for beams B2GF-Sb1, B2GF-Sb2, B2GF-Sb1-EV20F, and B2GF-Sb2-EV20F.The influence of materials on the shear strength of the GFRC beam and load-carrying capacity was predicted using Ansys.The predicted shear strength of the concrete beam increases when GFRP and CFRP bars are used due to the high tensile strength of FRP compared with steel bars with lower tensile strength.Moreover, the predicted deflection of the beams at the same load decreases when steel and CFRP bars are used owing to their high modulus of elasticity compared with GFRP bars with a lower modulus of elasticity.Fig. 27 illustrates the loadedeflection curves at the midspan of beams that strengthened with steel, GFRP, and CFRP bent-up bars.Tables 4 and 5 shows the effect of shear-strengthening material; CFRP bentup bars gave the highest shear strength.Steel bentup bars gave the lowest shear strength.By using CFRP bent-up bars, the obtained results indicated improvement in the ultimate shear strength, the load-carrying capacity, and ductility of the beam when compared with GFRP bent-up bars and decrease in mid-span deflection at failure, as shown in Fig. 27 and Table 4.The CFRP material increased ultimate shear capacity by 8.1, 7.1, 7.3, and 6% for beams B2GF-Sb1, B2GF-Sb2, B2GF-Sb1-EV20F, and B2GF-Sb2-EV20F, respectively, compared with GFRP bent-up bars.By using steel bent-up bars, the ultimate shear strength, load-carrying capacity, and deflection decreased when compared with GFRP bent-up bars, as shown in Fig. 27 and Table 4.The steel material decreased ultimate shear capacity by 3, 2.2, 2, and 2.6% for beams B2GF-Sb1, B2GF-Sb2, B2GF-Sb1-EV20F, and B2GF-Sb2-EV20F, respectively, compared with GFRP bent-up bars.

Effect of strengthening reinforcement ratio (variation in the value of the bar diameter).
In this parametric study, three different diameters (8, 10, and 16 mm) of shear-strengthening bent-up bars are used for beams B2GF-Sb1, B2GF-Sb2, B2GF-Sb1-EV20F, and B2GF-Sb2-EV20F.Using Ansys, it was possible to estimate how the bar diameter value would affect the GFRC beam's shear strength and load-carrying capacity.The parametric study has proved that the shear strength and the stiffness of the GFRC beams increase with the increase in strengthening GFRP reinforcement ratio by increasing the bar's diameter and increased midspan deflection of the beams at failure.Fig. 28 shows an approximately linear increase in ultimate shear capacity and the loadedeflection curves of beams with an increase in the diameter of the bent-up bars.Table 4 shows the effect of strengthening the reinforcement ratio with variation in the value of the bar diameter on shear strength.The strengthening of beams by 16 mm GFRP added 22, 28, 28, and 34% increase in ultimate shear compared with 10-mm GFRP for beams (B2GF-Sb1, B2GF-Sb2, B2GF-Sb1-EV20F, and B2GF-Sb2-EV20F, respectively).The ultimate shear capacity of beams B2GF-Sb1, B2GF-Sb2, B2GF-Sb1-EV20F, and B2GF-Sb2-EV20F decreased by 17, 17, 17, and 19%, respectively, when the bar diameter was reduced from 10 to 8 mm.

Conclusions
In this study, GFRC beams reinforced with steel and GFRP are subjected to FE analysis using the Ansys program.The following conclusions can be drawn considering the numerical results: (1) Ansys is capable of simulating and analyzing GFRC as a nonhomogenous material with a nonlinear response by the loadedeflection relationship at midspan and produces satisfactory results.(2) All tested models failed in shear.
(3) The final loads from the FE analyses are very close to the ultimate loads from the experimental results.However, the average deviation between the experimental ultimate loads and their numerically simulated values was less than 4%.(4) The observed failure modes of the experimental beams match up well with the FE model's crack patterns at the final loads.(5) According to the FE model results, adding more fiber to the concrete mix increased shear stress at the ultimate and cracking loads and ductility compared with the control beam.(6) When using GFRP longitudinal reinforcement instead of steel longitudinal reinforcement, the FE model results showed improvements in the shear strength of the beam models.(7) In comparison with beams with longitudinal steel reinforcement, longitudinal GFRP reinforcement enhanced the ultimate shear strength of beams without stirrups by 22.6, 18, and 19% for glass fiber ratios of 0, 0.6, and 1.2%, respectively.It also improved the ductility and loadcarrying capacity of the beams.(8) The use of various strengthening systems by the FE analysis enhanced the load-carrying shear capacity by a significant improvement compared with the control beam by a ratio of 26e115%.(9) The FE model results showed that using inclined links performs better than using vertical links in shear strengthening with the same spacing between links by increasing the cracking and ultimate shear load.(10) The FE model results show that the EBR strips technique and NSM bars twisted from the same strips significantly increase the shear resistance of GFRC beam models.In comparison with the control beam (B2GF-S1), the ultimate load of the two beams, B2GF-EV20F (EBR strips) and B2GF-20PsF (NSM bars), increased by 88.5 and 75.3%, respectively.(11) According to the FE model results, the combination of GFRP strips and two layers of bent bars was determined to be the best strengthening technique.When compared with the control beam, ultimate load and ductility increased by 115 and 153%, respectively. (12) The ratio between the FEA (Ansys) and experimental results for ultimate shear capacity ranged between 0.96 and 1.04 for all beams.(13) When compared with an actual experimental test method, the rapid development of computer capabilities and progress in designing proposed constitutive models such as the Ansys program provide a suitable approach that would save time and money.Experimenting with GFRC beams is expensive and time consuming.

Research recommendations
More analysis methods for shear strengthening of GFRC beams with GFRP bars and strips can be employed with more parameters such as follows: (1) Size of the beam.
(3) Discrete glass fiber ratio.(4) The ratio of main reinforcement in beams.
(5) Fiber type.As a potential future research topic, the authors will investigate this.

Fig. 11 .
Fig. 11.Comparison between loadedeflection curves between analytical and experimental for all tested specimens.

Fig. 14 .
Fig. 14.The relation between fiber content and failure load for group 1.

Fig. 15 .
Fig. 15.The loadedeflection curve for the steel and GFRP-reinforced beams in group 1.

Fig. 22 .
Fig. 22. Cracks patterns from experimental tests (Hany et al., 2022) in comparison to finite element models for all beams.
reinforcement.The behaviors of beams (B2GF-V20S and B2GF-V20F) having vertical links and beams (B2GF-D20S and B2GF-D20F) having inclined links, as SNSM stirrups technique allowed somebody to observe the influence of strengthening materials (steel links-GFRP links), are shown in Fig. 16.The behaviors of beams (B2GF-V20S and B2GF-D20S) with steel strengthening and beam (B2GF-V20F and B2GF-D20F) with GFRP strengthening, as SNSM stirrups technique can show the effect of links inclination (90 vertical links, 45 inclined links), are shown in Fig. 16.The effect of spacing between steel links shown in Fig. 17 beam model B2GF-V20S had spacing between the links of 200 mm and beam model B2GF-V14S had 140 mm.Fig. 18 shows the loadedeflection relationships for strengthened beam models (B2GF-V20F) with SNSM links, (B2GF-U20F) with NSM FRP double-C stirrups, (B2GF-20PsF) with NSM GFRP transverse stirrups around cross-section (box shape or full wrap), and (B2GF-S1) as control beam to identify the effect of SNSM links technique and NSM FRP stirrups shape.The behavior of the beams B2GF-EV20F and B2GF-20PsF, respectively, illustrates how well EBR and NSM techniques work to increase the shear resistance of GFRC beams, as shown in Fig. 19.Fig. 20 exhibits the loadedeflection behavior of beams B2GF-Sb1 and B2GF-Sb2, which had one or two bent GFRP bars on either side, respectively, to discuss the effect of NSM GFRP bent bars technique.The behavior of five specimens (B2GF-EV20F, B2GF-Sb1, B2GF-Sb2, B2GF-Sb1-EV20F, and B2GF-Sb2-EV20F) in comparison with the control beam (B2GF-S1) is shown in Fig. 21 to discuss the effect of GFRP strips, GFRP bent-up bars, and GFRP bent bars with GFRP strips together.
(6) The number of GFRP layers and bent-up bars.(7) Type and orientation of fiber sheet.(8) Shear span to depth ratio.(9) Strips by NSM.(10) Strip width.(11) Spacing between strips and links.(12) Type of internal shear reinforcement.(13) Use of anchored to prevent brittle debonding, which eliminates ultimate failure and enables full utilization of the GFRP bars.

Table 2 .
Experimental and analytical, ultimate load capacity, and ultimate deflection for all models.

Table 3 .
The ultimate shear strength for different values of compressive strength.

Table 4 .
The ultimate shear strength for different materials of shear-strengthening bent-up bars.

Table 5 .
The ultimate shear strength for different ratio of strengthening reinforcement.