The effect of different wrapping schemes on the shear capacity of rc beams using the finite element method

. Structural strength degradation was a highly important issue in the construction sector. In recent years, studies on the use of Natural Fiber Reinforced Polymer (NFRP) composites as external reinforcement have been started. The innovation of using abaca fibers as a mixture in NFRP composites provides a sufficiently high tensile strength. This innovation has the potential to be further developed to optimize the mechanical properties and applications of the composite. With the current technological advancements, numerical analysis carried out using various software based on finite element methods is one tool to solve the engineering problem. One of them was the ATENA software. This research aimed to strengthen the shear capacity of reinforced concrete beams using abaca FRP composites with various wrapping schemes (two sides wrap, U wrap, and complete wrap). The beams were modeled and analyzed by ATENA software. The solution of this problem was solved using the arc-length method. The numerical analysis results showed an increase in the maximum shear capacity by 11%, 14%, and 18% for two sides, U, and complete wraps, respectively. The crack angle on the complete wrap beam occurred at 37 degrees, and it was the largest among the other beams.


Introduction
A large number of structures that have been built are experiencing a decrease in structural strength and making them less safe.Damage to reinforced concrete (RC) structures has been one of the most significant issues in the construction sector for years.Replacing damaged or structurally unsafe structures will take a large amount of cost and time.Hence, methods for repairing and strengthening reinforced concrete elements become a solution due to their capability of increasing the load-carrying capacity of the structures and extending their service life.The horizontal elements that should take the first damage in the RC structures during the earthquake are RC beams [1].One of the common methods for repairing and strengthening elements is the use of Fiber Reinforced Polymer (FRP) composites, such as Carbon FRP, Basalt FRP, Glass FRP, Aramid FRP, and others.FRP composites exhibit properties like fatigue resistance, non-corrosion, low maintenance, and ease of application [2].
Although it has several advantages, FRP incurs a relatively high cost and lacks environmental friendliness due to recycling difficulties.This is an important obstacle that encouraged innovation in the form of Natural Fiber Reinforced Polymer (NFRP), which was produced using natural fibers [3].NFRP composites have different advantages like lightweight, renewable [4], biodegradable, less expensive, and exhibiting excellent mechanical properties [5].One example of fiber with high tensile strength is abaca fiber [6].
There are three types of FRP wrapping schemes used to increase the shear strength of rectangular beams.Completely wrapping around all four sides is the most efficient wrapping scheme [7].The other two types are by wrapping the FRP system around three sides of the component (U-wrap) or bonding to two opposite sides of the component [8].
Finite element analysis is one tool to solve the engineering problems.ATENA is one of the finite element software that has been used to study the behavior of various RC concrete structures [9 -12].In this study, numerical analysis was conducted using ATENA V5 and GID as the pre-processor.Problem-solving was performed using the Arc-Length method.The nonlinear solution of reinforced concrete structures, particularly in generating comprehensive load-deflection responses, requires an approach to tracking the equilibrium path and the proper treatment of boundary and branch points.The usual solution technique causes instability near the cutoff point and also has snap-through and snap-back problems.Hence, they fail to predict the comprehensive load-displacement response.The arc-length method serves its purpose effectively, is widely accepted in finite element analysis, and has been extensively used [13].This research aims to evaluate the effect of using different wrapping schemes with abaca FRP composites on the shear capacity of reinforced concrete beams using finite element analysis.

Specimen description and material properties
There were two specimens, namely BN (normal beam, without NFRP strengthening) and BS (beam strengthened with NFRP using two sides wrap) as shown in Figures 1 and 2, which are experimental specimens from a previous study [14] were used to validate and ensure the accuracy of the numerical model developed in this study.The difference in results between the experimental and numerical results was less than 10% indicating that the finite element model was valid.Therefore, it could be used as a finite element model development tool to predict the response of reinforced concrete beams [15].The beam specimen had a cross-section area of 150 x 300 mm and a length of 2200 mm.The steel reinforcements used in this study were 2-D13 rebars as compressive reinforcement and 2-D16+2-D19 rebars as tensile reinforcement.As for the shear reinforcements, Ø6-150 bars were used at the study span while Ø6-50 bars were used at the other span as shown in Figure 1.Table 1 shows the details about the parameters of the reinforced concrete beam specimens used in this study.These specimens were evaluated using the ATENA-GID software.The specimen was placed on two supports with a distance between the supports of 2000 mm.The loading was conducted by applying two equally concentrated loads with a distance of 600 mm between the loads.The representation of the reinforced concrete beam specimens based on each strengthening configuration can be seen in Figures 1 to 3.

Strain Gauge
Load Cell Concrete material was modeled using the CC3DNonLiCementitious2 concrete constitutive model with parameters as shown in Table 2. Steel reinforcement was discretely modeled using the CCReinforcement model and also a bilinear law as shown in Figure 4.The steel reinforcement material data is shown in Table 3. NFRP material was modeled using 2D Membrane elements with Plasticity Material employing the Von Mises plasticity model [16].Table 4 shows NFRP material data.The NFRP and concrete interface were modeled as Fixed Contact in their interaction.The reinforced concrete beam specimen was modeled as a simple beam with boundary conditions where one support restrained movement in the x and y directions while allowing movement in the z direction, and the other support restrained all three movements in the x, y, and z directions.Point monitors were used to observe the structural response, such as loads and deflections on the reinforced concrete beam, as well as stress and strain behavior in the steel reinforcement.This problem was resolved using the Arc-Length method.

Results and Discussion
Validation was carried out by comparing the maximum load results from experimental and numerical analyses.Table 5 and Figure 5 show the comparison of loads and deflections on specimens BN and BS based on the analysis results using ATENA V5 and experimental results in previous study [14].The good agreement between experimental results and numerical analysis results proved that the finite element model used in this study can be used to simulate the behavior of RC beams strengthened by NFRP composites.Comparison of the load-deflection relationships obtained from numerical analysis using ATENA-GID and experiment [14] for BN and BS The results in Table 6 and Figure 6 indicated that beams strengthened with NFRP exhibited higher maximum loads compared to those without reinforcement.Numerical analysis results using ATENA-GID showed an increase in maximum load of 11%, 14%, and 18% for BS, BU, and BC specimens, respectively.The highest increase in maximum load occurred in BC, where the use of NFRP was fully wrapped on each side of the beam.In contrast, the beam BS showed the lowest increase in maximum load.This was due to the fact that NFRP wrapped around all four sides of BC, increasing the load capacity that reinforced concrete could withstand, thus preventing shear failure more effectively.Beams with a completely wrapped scheme are the most efficient, followed by a U-wrap and two sides of the beam [8].7 show the crack angles of each reinforced concrete beam at maximum load based on ATENA-GID analysis results.An increase in the angle of the crack provided a greater opportunity for the beam to experience flexural failure.Thus, the use of NFRP was effective in preventing shear failure in reinforced concrete beams.

Conclusion
The maximum loads obtained by numerical analysis using ATENA-GID were 0.280 MN, 0.311 MN, 0.318 MN, and 0.330 MN for BN, BS, BU, and BC specimens, respectively.This signified a maximum load increase of 11%, 14%, and 18% for BS, BU, and BC, respectively, compared to BN.The increased maximum load results explained that the use of NFRP could hinder shear failure.The crack angles were 25°, 32°, 34°, and 37° for BS, BU, and BC specimens, respectively.An increase in the angle of the crack provided a greater opportunity for the beam to experience flexural failure.Thus, the use of NFRP was effective in preventing shear failure in reinforced concrete beams.

Fig. 5 .
Fig.5.Comparison of the load-deflection relationships obtained from numerical analysis using ATENA-GID and experiment[14] for BN and BS

Table 1 .
Parameters of the reinforced concrete beam specimens

Table 2 .
Parameters of the concrete constitutive model

Table 3 .
Steel reinforcement tensile strength and young's modulus

Table 5 .
Maximum load and deflection

Table 6 .
Maximum load and deflection Graph of load and deflection relationship based on the results of the analysis with ATENA-GID

Table 7 .
Crack angles of beam Fig. 7. Crack pattern of the beams after loading in ATENA-GID

Table 7 and
Figure