Numerical Simulation of the Behaviour of RC T-Beams Strengthened by EB-CFRP Composites Under Bending and Shear Effects

T his article presents the results of numerical simulations performed using ABAQUS/CAE version 2019 . The study aims to evaluate the structural integrity of reinforced concrete (RC) T-beams strengthened with externally bonded carbon fiber reinforcements polymer composite materials (EB) (CFRP), especially their response to bending and shear forces . The numerical model was validated by comparing the numerical and experimental results of eight RC T-beams . The numerical analysis was then extended to include various factors, including the impact of the tilt angle of the U-CFRP shell on the shear strength . The goal of this numerical extension is to implement a numerical model capable of simulating the nonlinear behavior of these beams accurately . A comparative analysis is also performed on the experimental and computational models, focusing on the damage modes and their load-induced deformation characteristics . The results showed a satisfactory level of agreement between the two sides . The average ratio of ultimate load to deflection in the numerical model simulation and experimental beam test is 1 . 004 and 1 . 046 , respectively . The main finding is that inclined U-CFRP deformed at a 45° angle exhibits greater shear stiffness than beams embedded with vertical CFRP panels at a 90° angle, maintaining a constant CFRP


INTRODUCTION
In the last 30 years, carbon fibre-reinforced polymer (CFRP) products have been used to strengthen reinforced concrete (RC) parts.It was a captivating technique for rehabilitating infrastructure.CFRP strengthening has versatile applications, such as constructing new buildings and restoring existing ones (Abdulhameed and Said, 2019; Abbas and Al-Zuhairi, 2023).In addition to examining the overall failure criteria of (CFRP)-RC beams, some scholars investigated the localized behavior occurring close to the bond area.Considerable efforts were undertaken to fully understand the behavior of bonds at the interface, particularly in relation to early failures (Mhanna et al., 2019; Daraj and Al-Zuhairi, 2023).Strengthening using FRP composite materials is versatile because it may be employed on various structural elements, such as beams, columns, slabs, and walls.The enhancement may include one or many objectives depending on the individual's classification.Many objectives focus on enhancing the load capacities of a structure, including axial, flexural, and shear loads.Another goal is to improve stiffness to minimize deflections when subjected to service and design loads.Additionally, efforts were made to extend the fatigue life of the structure and enhance its durability against environmental factors (Buyukozturk et al., 2004;Hernoune et al., 2020;Ibrahim and Al-Zuhairi, 2022).The contact bond is of utmost importance in most cases.It is crucial in transmitting stresses from pre-existing concrete structures to externally attached CFRP materials.The requirement of an ideal bond length is another factor that limits the attainment of maximum tensile strength activation in CFRP materials.The primary cause of early debonding is the localized concentration of shear strain.However, determining the effective bond lengths might exhibit significant variability due to the divergent criteria and materials used by various researchers in their experimental investigations.For example, in CFRP-to-concrete joints with widths of 25 mm, the bond lengths for 1-ply and 2-ply configurations are The results show that when the quantity of sheets and installation distance are maintained constant, FRP sheets at a 45° installation angle reduce displacement more than those at 60°.This effect is greater when the installation angle is 60° instead of 90°.Plates lower the middle beam span's greatest lateral strain by 12.5%.Prestressed (FRP) sheets strengthen specimens.The load grows until compressive concrete smashing breaks the beam .This effort created a numerical model that correctly simulates the experiment.T-reinforced concrete beams strengthened for flexural and shear resistance were studied.The main objective was to determine how two parameters affected final bearing capacity and deflection.The influence of CFRP laminate width in the flexural group and U-CFRP sheet spacing in the shear group was evaluated.The experimental data confirmed the theoretical conclusions, which were used to conduct parametric studies on the U-CFRP sheet inclination angle's effect on shear strength.

TESTED SPECIMENS
Numerical simulation was conducted on the experimental results of (Alobaidi and Al-Zuhairi, 2023) on eight RC T beams, including two reference beams that are not subjected to any form of strengthening and six strengthened beams.These beams are categorized into two primary groups based on the type of strengthening applied: flexural and shear strengthening.The primary variable selected for the flexural group was CFRP laminate width, and that for the shear group was U-CFRP sheet spacing.Figs. 1 and 2 show the details of the flexural and shear group beams, respectively.Table 1.shows the details of the tested beams.The physical characteristics of concrete, such as its modulus of elasticity (24.405GPa), compressive strength (f'c=26.96MPa), and splitting tensile strength (2.9 MPa) were measured.Table 2 provides the reinforcement steel properties employed in this study.For the carbon fibre fabrics, the manufacturer/supplier provided their properties (mechanical and physical), including the nominal thickness of 0.012 and 0.166 mm, a tensile strength of 3100 and 4900 MPa, and an ultimate elongation value of 0.018% and 2.1% for the laminate and CFRP sheet, respectively.The modulus of elasticity was equal to 170000 MPa for the laminate and 230000 MPa for the CFRP sheet.

MODELLING AND ANALYSIS OF TESTED BEAMS
The FE method in the standard model implemented by the ABAQUS 2019 PC program was used to analyze the T-beams.The structure of all beams was studied using a single-step approach, specifically, static analysis.The concrete material properties were accurately represented by simulating the T-beams using the isoperimetric eight-node brick element (C3D8R).The truss element (T3D2), a two-node bar element that can undergo 3D displacement in the x, y, and z axes, was utilized for the reinforced steel bars.2D shell elements (specifically, the S4R element) represented the CFRP laminates or sheets.This element type is characterised by its ability to accurately model doubly curved thin or thick shells using decreased integration and hourglass control and to account for finite membrane stresses.Many components were generated to thoroughly analyze all the specimens inside the ABAQUS environmental framework, as shown in Figs. 3 and 4.  The simple support at one edge of the beam was simulated as a hinge by restricting the nodes along one line of supporting plate in tandem with the beam soffit's breadth in the local x and y directions (Ux=Uy=0).By contrast, the other support was treated as a roller by restricting the y-direction (Uy=0) and permitting longitudinal motions and rotations around the x-axis.Fig. 5 shows the boundary conditions and load definitions.The reinforcement was considered entirely embedded in concrete to evaluate complete interaction.The tie constraint option was employed to connect two distinct surfaces, the master concrete surface, and the slave CFRP surface, to ensure the absence of any relative motion between them.The concrete compressive and tensile strength were illustrated in Tables 3 and 4 based on the studies of (Elwi and Murray, 1979; Hordijk and Reinhardt, 1991), respectively.Table 5 presents the input data material for concrete plasticity properties.Mesh sensitivity, shown in Fig. 6, indicated that as long as the components were more significant than the aggregate size and showed reasonable agreement with the test results.
No considerable sensitivity to the mesh size was observed.Therefore, for efficient computation, the mesh size of 25.0 mm with an aspect ratio of ( 1), as shown in Fig. 7 Figure 6.Mesh sensitivity study.This study compared experimental and FE model peak load stage ultimate load and deflection.All static-tested beams were analyzed.Experimental and computer models' ultimate load and deflection were strongly correlated.The average value and coefficient of variation for ultimate load ratio (Pu)FE/(Pu)Exp were 1.004 and 2.216%, respectively.The average and coefficient of variation for the deflection ratio (δ FE/δ Exp) were 1.046 and 3.584%, respectively.As explained in Table 6.Therefore, FE analysis is a superior and dependable approach for modelling the nonlinear characteristics of RC T beams using CFRP.

Crack Patterns
According to the principles of continuum damage mechanics, a damage model must be used in conjunction with a plasticity model.accurate methodologies and techniques must be employed to accurately predict and simulate the behaviour of concrete  The correct simulation of concrete behaviour in a damaged-plasticity model may be achieved by defining damage parameters, such as compressive and tensile damage.Based on concrete damage plasticity (CDP) theory, cracks in RC members are generally formed in regions where the tensile strain exceeds the specified tensile strain of concrete, i.e. the concrete would crack when the plastic strain exceeds zero.In the current investigation, the plastic strain was employed as a representative of crack expansion

Numerical Parametric Study
After being verified as suitable for the experimental data, the FEM was used for a comprehensive parametric study of the inclination angle shown by U-CFRP sheets inside the shear group.The impact of the inclination angle of U-CFRP sheets on the beam's structural behaviour was studied using three previous models, BS.S1, BS.S2 and BS.S3, in addition to three new models, BS.DS1, BS.DS2 and BDS.S3, as listed in Table 7. Fig. 12 shows the creation of parts and assembly in ABAQUS for inclined CFRP models.The effect of the inclination angle of U-CFRP sheets from 90° to 45° on the load-deflection behavior at midspan is illustrated in Fig. 13.Each figure contains a beam with the same spacing as CFRP sheets.According to the load-deflection curves, the beams exhibited equivalent stiffness throughout the elastic range.However, the stiffness characteristics differed after cracking.
The beams with inclined CFRP sheets at (45°) had higher shear stiffness than those with vertical CFRP sheets at a similar spacing to CFRP sheets.Table 8 shows that the beam with inclined CFRP sheets (45°) had an ultimate load higher than the beam with vertical CFRP sheets (90°) with similar spacings of 7.5%, 5.4%, and 2.3%, to the CFRP sheet spacing of 166, 125 and 100 mm, respectively.The ultimate load (Pu) of the beams with vertical CFRP spacing of 166, 125, and 100 mm increased by 13.2%, 17.7%, and 23.5%, respectively, relative to that of the reference beam.
The beams with inclined CFRP spacing of 166, 125 and 100 mm exhibited an increase in ultimate load by 21.6%, 24.7%, and 26.2%, respectively, in comparison with the reference beam.
80 and 220 mm, respectively (Bizindavyi and Neale, 1999), 100 mm (Ueda et al., 1999), 80 mm (Lorenzis et al., 2001), and 64-135 mm ( Nakaba et al., 2001).(Deniaud and Roger Cheng, 2003) conducted a comprehensive investigation on the interplay among concrete, steel ties, and fiber-reinforced polymer (FRP) sheets to determine the structural soundness of RC beams under shear stresses.The empirical findings indicate that incorporating FRP reinforcement significantly enhances the maximum shear strength from 15.4% to 42.2% compared with the beams without FRP reinforcement.The increased shear capacity depends on the type of FRP material and the amount of internal shear reinforcement.(Benzeguir et al., 2019) reports experimental results from 18 RC T-beam samples of different sizes .They examined how the dimensions affect the shear strength of concrete when RC beams reinforced with externally bonded CFRP (EB) panels fail.There is a relationship between the size of concrete, CFRP panels, and shear capacity.(Zaki et al., 2020) conducted a series of studies, including the production and testing of five full-scale Tbeams, to determine the extent to which CFRP improves the beam's bending strength .Experimental results show that CFRP bending plates connected to CFRP anchors can increase the bending capacity of RC T beams .Performance improves proportionally to the quantity and quality of CFRP anchors until the section reaches its maximum bearing capacity.The ultimate load increases when the anchors are close together.(Al Shboul et al., 2021) thoroughly studied the behavior of reinforced lightweight and standard-weight concrete beams reinforced with EB high-modulus carbon fibre.A methodological framework included experimental techniques and analytical and computational assessments.The results indicate that more layers enhance the flexural capacity of conventional concrete beams.Even with more than two layers, lightweight beam use has a consistent pattern, according to empirical findings.(Abbasi et al., 2022) performed a numerical investigation to evaluate the impact of dimensions on the shear capacity of RC beams reinforced using EB-CFRP.Due to the limited experimental research, only a few finite element (FE) studies consider the size impact.The findings demonstrate that numerical simulations can accurately forecast experimental outcomes.Additionally, the shear strength of concrete and the contribution of CFRP to shear resistance decrease when the size of beams increases.(Najaf et al., 2022) simulated a concrete beam using the FE software ABAQUS and examined the effects of FRP type, amount, and installation angle.

Figure 1 .
Figure 1.Details of beams for the flexural group.

Figure 2 .
Figure 2. Details of beams for the shear group.

Figure 4 .
Figure 4. Creating parts and assembly in ABAQUS (shear group).

Figure 5 .
Figure 5. Boundary and loading circumstances were utilized in the study.

Figure 7 .Figure 8 .
Figure 7. Numerical meshed model.4. RESULTS AND DISCUSSION 4.1 Calibration of the Fabricated FE model Figs. 8 and 9 depict the comparison of load-deflection relationship between the experimental and numerical findings for the flexural and shear groups, respectively.

(
Mahmud et al., 2013; Tysmans et al., 2015; Feng et al., 2018; Faron and Rombach, 2020; Daneshvar et al., 2022).The cracks appeared orthogonal to the plastic strain.Contour plots in Figs. 10 and 11 depict the plastic strain distribution in the analyzed beams and the fracture patterns in the experimental beams at the ultimate stage.The influence of strengthening measures on the strain levels and fracture patterns of the flexural and shear groups is adequately shown by these graphic representations.The flexural failure mode was observed in the beams of the flexural group, and the shear failure mode was observed in the beams of the shear group.Additionally, a coincidence fracture pattern was found between the numerical and experimental findings.

Figure 13 .
Figure 13.Load-deflection behaviour for the numerical parametric study, a) beams with U-CFRP sheet spacing of 166 mm, b) beams with U-CFRP sheet spacing of 125 mm, c) beams with U-CFRP sheet spacing of 100 mm

Table 1 .
Details of the tested beams.

Table 2 .
Tensile characteristics of the steel reinforcement bars.

Table 5 .
Input data for concrete.

Table 6 .
Ultimate load and deflection at ultimate load: Experimental vs. FEA.

Table 7 .
Details of beams for numerical parametric study.

Table 8 .
Ultimate load of beams for numerical parametric study.