Finite element modeling of flexural behavior of reinforced concrete beams externally strengthened with CFRP sheets

In this research, the finite element method is used to develop a numerical model to analyse the effect of the external strengthening of reinforced concrete beams by using carbon Fiber Reinforced Polymer (CFRP) sheets. A finite element model has been developed to investigate the behavior of RC beams strengthened with CFRP sheets by testing nineteen externally simple R.C. beams, tested under a four-point load setup until failure. Various CFRP systems were used to strengthen the specimens.  The numerical results using the (ANSYS workbench v.19.1) were calibrated and validated with the experimental results.  The research results indicate a significant improvement in the structural behavior of the specimens strengthened using CFRP sheet systems. Then the validated model investigated the effect of the width of CFRP sheets, no of layers, and CFRP size on the behavior of strengthened R.C. beams. Results of this numerical investigation show the effectiveness of increase CFRP width to improve the flexural capacity of R.C. beams. An increase in the flexural capacity up to 100 % compared to the control beam.


INTRODUCTION
ver the past decades, (FRP) has been commonly used to repair and rehabilitate civil structures, showing signs of aging degradation and distress. (CFRP) is a brittle material that typically fails at a lower load level (i.e., horizontal crack propagation or debonding). As a result, the ultimate capacity of the reinforced concrete structural elements is challenging to achieve., Kang et al., [1]. In the past, various researchers conducted studies on reinforced concrete beams with CFRP retrofitted in flexure, and the failure patterns were observed [2][3][4]. Recent research has focused on the impact of geometric factors such as length and the FRP-concrete width ratio. It has been shown that the ultimate stress for debonding increases with bonded length up to a critical bond length. Although numerous researchers have presented results demonstrating the influence of FRP laminate width on ultimate load, these results are frequently inconsistent [5][6][7]. The available results in the literature are frequently contradictory. While some O studies have indicated that average bond strength decreases with FRP width [5], others have found that bond strength increases with FRP width [8]. Travassos et al [9] suggested adding more CFRP composite at the ends of the CFRP plate to prevent premature debonding. Two approaches were offered in particular: (i) addition of more layers of rectangular CFRP sheets; and (ii) addition of more layers of CFRP sheets across the main CFRP plate. Hasnat et al. [10] studied reinforced concrete beams strengthened by carbon-fiber-reinforced polymer sheets. A CFRP wrap (u-shape) had prevented the premature cover from debonding, increasing the final moment's efficiency. The study on reinforced concrete beams, consisting of a T-section, was carried out by Mostafa et al. [11]. Lusis et al. [12] investigated the influence of insertion of short fibers on reinforced concrete's mechanical characteristics using a series of experiments and numerical analysis. They had a significant effect on the tensile strength of the structure. Abid et al. [13] performed a systematic analysis of previous scientific studies based on the strength and durability of concrete beams externally covered by FRP reinforcement. The research study focused on bond behavior, testing techniques, and models used to determine bond performance. Bennegadi et al. [14] developed a numerical model for optimization of reinforced concrete beams by external (HFRP) plate, and they found that the ultimate load of the reinforced concrete beam was increased when compared to the reference beam, the geometrical and mechanical properties of the HFRP plate must be optimized. El-Ghandour [15] carried out three-point load checks on seven half-scale reinforced concrete beams, strengthened with longitudinal CFRP sheets and U-wraps. Kara and Ashour [16] developed a numerical system for predicting curvature, deflection, and the moment capacity of reinforced concrete beams strengthened by FRP. Narmashiri et al. [17] conducted more experimental and numerical research on CFRP-reinforced steel I-beams in terms of failure analysis and structural behavior. They concluded that the geometric and mechanical characteristics control the loadbearing capacity of CFRP plates. Kermiche and Redjel [18] provided experimental research and an analytical model to simulate the mechanical behavior of concrete and reinforced concrete. Osman et al., [19]. Performed experimental studies on seven reinforced concrete beams under four-point loads with specific span-to-depth shear ratios. A comparative analysis of 27 reinforced concrete beams with and without CFRP sheets was also carried out. The findings obtained using ANSYS have been similar to the experimental outcomes of the studies. Considering the previous literature review, it is clear that only few researchers have studied the effect of different CFRP strengthening schemes and locations on bending moment and RC beam failure behaviour. A total of nineteen FE models were developed to study the flexural behavior of RC beams externally bonded with CFRP sheets. ten specimens were used to validate the accuracy of the numerical model by comparing it with experimental results by Madqour et al. [20] and nine models were developed to investigate the effect of increasing CFRP sheets size.

DESCRIPTION OF THE EXPERIMENTAL PROGRAM
he FE model was created to investigate the flexural behavior of RC beams reinforced with CFRP sheets [20] by Madqour et al. Information on the RC beams is omitted and briefly summarized in the following.

Geometric features of the beams
A total of ten RC beam specimens strengthened with various schemes were tested by Madqour et al. [20]. The specimens examined included a control beam (B01) reinforced with two steel bars with a diameter of 10 mm. The tested beam has a rectangular cross-section with a nominal width, depth, length of 150 mm, 200 mm, and 2000 mm and spanned over 1800 mm. The compression reinforcing of the specimens tested consisted of two steel bars of 8 mm diameter Fig. 1 Also, the 6 mm diameter stirrups spaced at interval 125 mm. Table 1 provides the characteristics of the examined beams. The deflection of the beams was measured at mid-span using a displacement transducer (LVDT) placed on the beams Fig. 2. T Figure. 1. Details of the tested beams (in mm) [18].  The most recent version of ANSYS 19.1 [21] was selected for use in this research work. It can model non-metal materials and successfully model reinforced concrete as non-homogeneous material with nonlinear response. It also can predict and display the cracking and crushing patterns of the material. ANSYS 19.0 FE software is used to develop 3D FE specimen models tested by madqour et al. [20]. The geometry, constituent material characteristics, loading, and boundary conditions of the FE models are similar to those of the tested beams previously described in Table 1.

Numerical modeling
The concrete is modeled by using 8-noded SOLID65 Fig 3(a) element, which has three degrees of freedom at each node and can crack in tension and crushing in compression. Fig. 3(a) shows the geometry of the SOLID65 element. Due to the fact that concrete is highly nonlinear in compression, a proper uniaxial stress-strain relationship is used to describe this nonlinearity more precisely, the compressive behavior of concrete is modeled by using the nonlinear stress-strain relation proposed by Popovics, [28] and later modified by Thorenfeldt et al. [29]. Figure (2) shows the curve, which is defined using these Equations. The use of Thorenfeldt et al., [29]'s stress-strain model for concrete in compression was found to be effective for FRP reinforced RC beams by El-Tawil et al., [30]. εcu is the ultimate strain, and ε0 is the strain at maximum stress.
The steel reinforcement modeled with a 3-D spar LINK 180 element having three degrees of freedom at each node (translation in x, y, z directions), as shown in Fig. 3(b). The reinforcement element is assumed to be a bilinear isotropic elastic-perfectly plastic material identical in tension and compression. SHELL 181 element is used to model the FRP sheet. The thickness of a shell element is relatively small compared to other dimensions of the element. This element is a four-node element with six degrees of freedom at each node: x, y, z-direction translations, and x, y, and z-axis rotations Fig.2 (c). To exclude the debonding of FRP sheets, the effective FRP strain should be as recommended by ACI 440.2R-08 [31]. Therefore, such a recommendation is used to modify the debonding FRP strain equation originally proposed by Teng et al. [23]. The effective FRP strain to consider debonding failure in modified form is given by where,  SOLID 185 element is used to model the loading supports. Eight nodes represent this element Fig.2(d), each having three degrees of freedom in the nodal directions x, y, and z. Plasticity, stress stiffening, creeping, large deflection, and high strain power are all capabilities of the element. The adhesive is modeled using the element SOLID45 Fig. 2(d). It is an eight-node three-dimensional structure with three degrees of freedom at each node, i.e., translations in directions nodal x, y, and z. The element has the capacity for plasticity, creeping, swelling, stress stiffening, large deflection, and significant strain. Hawileh et al. [24] used the SOLID45 element to model adhesive and obtained satisfactory results in the study of RC beams reinforced by FRP. This system consists of two nodes, one set of nodes with the concrete element used in this analysis and another with FRP elements. The material properties of the concrete, steel reinforcement, CFRP, steel plate, and epoxy used in the developed FE models are summarized in Table 2.

FE MODEL VALIDATION
he flexural behavior of RC beams externally strengthening with CFRP sheets is studied using a total of nineteen FE models. The accuracy of the numerical model is validated by comparing experimental results with the ten beams reported in Table 1, and the remaining models are developed to study the effect of CFRP width and sheet size on the flexural behavior of the beams. Fig. 4 shows the developed FE models for a RC beam, externally strengthening with CFRP sheets. The four beams detailed in the previous section are modeled and to evaluate the accuracy of the numerical models. the predicted and obtained experimental data are compared for all beams. For four beams, in Fig. 5 are plotted the experimental and predicted results in terms of load versus mid-span deflection.     To investigate the behavior of the beam when the size (width) of CFRP sheets is changed, nine FE models were developed. One of the beams was modeled as an un-strengthened control, while the other eight were strengthened using CFRP sheets strengthening models One layer S01 (one layer) S01U (one layer + 6U shape) S01S (one layer + on sides) two layers S02 (two layers) S02 U (two-layers + 6U shape) S02 S (two layers + on sides) three layers S03 (three layers) S03U (three-layers + 8U shape) S03 S (three layers + on sides) of varying width of 150 mm. Table 3 lists the designations for each studied model. Figure 6 shows the predicted load versus mid-span displacement response curves. Table 3 further summarizes the predicted ultimate achieved load (Pu) and its corresponding mid-span deflection (u).

Effect of CFRP sheet size for the case one layer
As expected, the beams with a width of 150 mm bonded FRP sheets obtained a larger load-carrying capacity (flexural strength) than the beams with a width of 100 mm, as shown in Fig. 8 and Table 4. The load-carrying capacity (Pu) of beam S01, which has a 150 mm wide CFRP sheet, is 8% greater than the control specimen. Fig.8 further shows that the increase in Pu for beams S01U with 150 mm wide CFRP sheets and S01S with 150 mm wide CFRP sheets was 7.98% and 12.95%, respectively. As a result, the increase in the load-carrying capacity of a beam is inversely proportional to the increase in CFRP laminates' size (width).

Effect of CFRP sheet size for case of two-layers
The load versus mid-span deflection curves for the two layers are provided in Fig. 9. The load capacity (Pu) of beam S02, which has a 150 mm wide CFRP sheet, is 12.8 % greater than that of the control specimen. Table 4 further shows that the increase in Pu for beams S02U with 150 mm wide CFRP sheets and S02S with 150 mm wide CFRP sheets was 9.58 % and 10.47%, respectively, as a result, the increase in the load capacity of a beam is inversely proportional to the increase in the width of CFRP sheets. Figure 9: Numerical load-deflection curve for S02, S02S, and S02U beams.

Effect of CFRP sheet size for in case of three-layers
The predicted load versus mid-span deflection curves for the three layers are provided in Fig. 10. The ultimate load of beam S03 with a 150 mm wide CFRP sheet is 22.50 % greater than that of the control specimen. Table 4 shows that the increase in Pu for beams S03U with 150 mm wide CFRP sheets and S03S with 150 mm wide CFRP sheets was 14.10 % and 14.32 %, respectively.
The theoretical bending moment values are calculated by incorporating the additional strength reduction factor,  f . Table   5 shows the final results of the theoretical method.

CONCLUSION
he main aim of the research is to investigate the influence of increasing CFRP sheet size and width, the models have been validated by comparing the behaviour and response of nine beam specimens. At all levels of loading until failure, the numerical and experimental data demonstrated a high correlation, and it can conclude that.  The FE models accurately predicted the flexural behaviour of the tested reinforced concrete beam specimens with and without CFRP sheet reinforcement.  Increasing the number of layers of FRP sheets increases the ultimate strength of RC beams up to 100% compared to the control beam. However, the mid-span deflections are less than those of the control specimen.
 By increasing the width of CFRP sheets increases beam load capacity.