Shear behavior of CFRP - reinforced concrete beams using FEM con CFRP utilizando el MEF

In the current study, the finite element method using the ABAQUS program is employed to investigate the shear behavior of reinforced concrete (RC) beams strengthened by carbon fiber reinforced polymer CFRP. Load-deflection curves, modes of failure and the pattern of the cracks are studied. Also, the influence of compression strength of concrete, the configuration of CFRP (U shape and 2 side bond shape) and shear span to depth ratio (a/h ratio). The results show that the shear capacity of RC beams strengthened by CFRP increased by a maximum percentage of up to 111.7% compared to the unstrengthened beam. Also, it is found that by increasing the compressive strength of concrete from 40 MPa to 65 MPa the load-carrying capacity increases by 28% and the stiffness also increased, while the decrease of shear span to depth ratio from 1.66 to 2.33 leads to increasing the shear capacity by 23%. The maximum load of beam strengthened with U shape increased by up to11.5% when compared with the same beam strengthened with two side bond shapes of CFRP. However, the gain in the strength was reached to 22.7% for beams strengthened with CFRP laminate compare to unstrengthened beams. The strengthening of RC beams by CFRP laminates using the near surface mounted (NSM) technique is more efficient than the externally bonded reinforcement ( EBR) technique for all beams in the shear behavior. The finite element models provide a good level of accuracy compared to experimental results and ACI-440. el 111,7% en comparación con la viga no reforzada. Además, se observa que al aumentar la resistencia a la compresión del hormigón de 40 MPa a 65 MPa, la capacidad de carga se incrementa en un 28% y la rigidez también aumenta, mientras que la disminución de la relación entre la luz de corte y la profundidad de 1,66 a 2,33 conduce a aumentar la capacidad de corte en un 23%. La carga máxima de la viga reforzada con forma de U aumentó hasta un 11,5% en comparación con la misma viga reforzada con dos formas de unión lateral de CFRP. Sin embargo, la ganancia en la resistencia fue del 22,7% para las vigas reforzadas con laminado de CFRP en comparación con las vigas no reforzadas. El refuerzo de las vigas de hormigón armado con laminados de CFRP mediante la técnica de montaje en superficie (NSM), es más eficaz que la técnica de refuerzo de unión externa (EBR), para todas las vigas en el comportamiento cortante. Los modelos de elementos finitos proporcionan un buen nivel de precisión en comparación con los resultados experimentales y la norma ACI-440. comportamiento, cortante, viga


Introduction
Reinforced concrete (RC) structural elements such as beams may be subjected to significant shear stresses. Upgrading or strengthening becomes necessary when these structural elements are not able to provide satisfactory strength and serviceability. Shear failure of RC beams could occur without any warning. Many existing RC members are found to be deficient in shear strength and need to be repaired. Shear deficiencies in reinforced concrete beams may occur due to many factors such as inadequate shear reinforcement, reduction in steel area due to corrosion.
In general, shear resistance of RC beams has been increased when strengthed by CFRP against shear failure using NSM and EBR techniques. FRP composites are lightweight, non-corrosive, and easily constructed which exhibit strength and high specific stiffness. FRP composites have been used in rehabilitation and new construction structures, and external reinforcement for seismic upgrade and strengthening.
Maney experimental researches have investigated the effect of strengthening RC beams by CFRP laminate or sheet on the shear strengrth. However, some of the numerical studies were used to represent RC beams strengthed by CFRP as in. Accordingly, most of the previous works related to the strengthening of concrete beams by CFRP to enhance the shear behavior of RC beams were experimental studies. It is very essential to understand the behavior of CFRP-RC beams by presenting more theoretical and numerical studies. The theoretical works related to the behavior of RC beams with CFRP in shear using program ABAQUS are still limited.
In this study, finite element analysis using ABAQUS program was presented to investigate the efficiency of using CFRP with NSM or EBR technique to enhance the shear strength of RC beams. The FEM model was build based on the experimental results concluded by (Barros et al, 2007). A parametric study was presented to investigate the impact of different parameters on the shear strength of RC beams strengthened by CFRP.

Materials
The same properties of steel reinforcement and concrete proposed by (Barros et al., 2007) have been used in the current study. (Table 1) shows the properties of steel and concrete materials.
Two types of CFRP were used in this paper: the first type is CFRP sheets with 80 mm in width used for the flexural strengthening. The second type is CFRP-laminates with 1.4 x 9.6 mm2 as a cross-sectional area in the flexural strengthening. The properties of the CFRP used in this study are listed in (Table 2).

Finite element analysis
The finite element method (FEM) was performed to model the nonlinear behavior of RC beams strengthened by CFRP.

Concrete
The plastic damage was performed to model the concrete behavior. This model assumes that the major two failure modes of concrete are tensile cracking and compression failure as shown in (Figure 1)

Steel reinforcement
The steel reinforcement was used as an elastic-plastic material. (Figure 2) shows the stress-strain relationship of steel in compression and tension behavior. The elastic modulus and the yield stress were obtained from the experimental work conducted by Barros et al, 2007. A Poisson's ratio used in this study equal to 0.3 for the steel reinforcement. A perfect bond between concrete and steel was assumed.

CFRP
Generaly two models were used to represent CFRP. Firstly, CFRP was assumed as a linear elastic isotropic until failure. While in another model, CFRP was assumed as a linear elastic orthotropic material. The first model has been used in this study. The CFRP properties were specified by the manufacturer. A Poisson's ratio of 0.3 was used for CFRP. The stress-strain of CFRP is shown in (Figure 3).

CFRP-concrete interface
Two models were utilized to model the interface between CFRP concrete surfaces A perfect bond was assumed in the first model and a cohesive model was assumed in the second one. (Figure 4) shows the relationship between maximum shear stress ( :;< ) and effective opening displacement( ) in the interface zone between concrete and CFRP by using simple bilinear traction-separation law. The interface is modeled with a small thickness and the initial stiffness = is defined as (Guo et al., 2005)   The value of fracture energy (Gcr) was ranged between 300 J/m2 and 1500 J/m 2 as assumed in other researches. The value of 900 J/m 2 was used in current research.
The damage was assumed to occur firstly when the nominal stress ratios reached value one, this criterion can be represented by (Equation 13) (Hibbitt and Sorensen, 2000):

Shear strengthening
Numerical modeling to study the behavior of beam strengthened for shear by CFRP under four-point loading using the ABAQUS program using the experimental work conducted by (Barros et al., 2007) to build the model. The numerical study has been adopted based on the experimental study of four series of tested beams presented by (Barros et al., 2007). ( Figure 5) and (Table 3)

Load-deflection curve
This section discusses the ultimate load and the relationship between load and mid-span deflection of all tested beams. A summary of the experimental loads and predicted loads by finite element method at the ultimate level as well as the increase in the ultimate loads based on numerical results are presented in (Table 4).
The highest deformation capacity was registered in the beam strengthened with inclined laminates (A10_IL). The relationship between the applied load and the deflection at mid span of the beams for FEM and experimental results are shown in (Figure 6)

Mode failure
Shear failure was the failure modes of the control beams for all series (beams without shear reinforcement) and no yielding of tensile reinforcement was observed. Yielding of main steel reinforcement was observed firstly in beams A12_S and A10_S followed by shear cracks, while, shear cracks firstly occurred in beams (B10-S and B12-S) and the yielding of the longitudinal steel reinforcement was observed. Shear failure was the failure modes of beams A10-M, A12-M, B10-M, and B12-M. The shear cracks were started from compression to tension due to the U configuration of the CFRP sheets. Experimentally, the rupture of CFRP sheets was clearly observed. Conversely, no rupture was observed in the numerical results. Also, yielding of main steel reinforcement was observed firstly in beams A10_VL, and then a shear failure crack was formed. While beam A12_VL failed by shear cracks and no yielding of tensile steel was noted. The failure mode of beams B10_VL and B12_VL was forming shear cracks from load to support without yielding of longitudinal tensile reinforcement. Beams (A12_IL and A10_IL) failed by the formation of the flexural failure cracks. The mid-span deflection drops gradually after longitudinal tensile reinforcement yielded. Mode of failure of B10_IL, B12_IL beams is forming shear cracks from load to support without yielding of the longitudinal tensile reinforcement. (Figure 11)

Effect of Shear span to depth ratio (a/h)
The a/h ratio has an essential effect on the shear behavior of RC beams. change in a/h ratio may lead to a significant change in the shear resistance. The influence of (a/h) ratio was investigated by building an FE model. Three values of a/h ratios; 1.66, 2 and 2.33 were considered. (Figure 33) and (Figure 34) show that the increase of

Effect of shape of CFRP on shear strength
Generally, three types of CFRP wrapping schemes had been used to improve the shear strength of RC members such as beams and columns which one ( completely wrapping, U-wrap shape and two side bond shape). In this study, we used two types of strength: U shape and two side bond shapes. (Figure 35) shows that the retrofitting with U shape is slightly improves the strength of more than two sides boned. The maximum load in A10-M, A12-M, B10-M, and B12-M beams strengthened with U shape CFRP increased by 6. 2%, 5.9%, 11.5%, and 9.5% respectively compared with beams retrofitted with two sides shape (figure 35).

Effect of addition CFRP laminate to beams with stirrups
Four RC beams with traditional stirrups were strengthened by CFRP laminate to assess the effect of CFRP laminate on the strength of RC beams with stirrups (A10-S, A12-S, B10-S, and B12-S). Fig (36) shows that the capacity of beams was increased by 8. 74%, 12.13%, 15.87%, and 22.73% compared with beams (A10-S, A12-S, B10-S, and B12-S) without strengthening