Numerical Assessment of RC beam Flexural behaviour using Different Arrangement of EB-FRP laminates

Numerical Assessment of RC beam Flexural behaviour using Different Arrangement of EB-FRP laminates

Declaration
This is to affirm that the thesis titled: “Numerical Assessment of RC beam Flexural behaviour using Different Arrangement of EB-FRP laminates” is an original work and that it has not been submitted either in part or fully to any institution for the award of degree or diploma.

Name.: Nawaf Alqahtani

Date

Signature

Acknowledgement

Executive Summary
Studies and research on ways to improve the performance of reinforcement has been an ongoing activity ever since the invention of concrete. One such way of improving the performance of concrete is through strengthening the reinforced concrete using externally bonded fibre reinforced polymers. Existing studies have shown the potential of externally bonded fibre reinforced polymer to significantly increase the strength capacity of concrete elements such as beams, slabs and columns. In this paper a numeral assessment has been done using ABAQUS, finite element analysis software, to investigate the flexural behaviour of concrete beams that have been strengthened using externally bonded fibre reinforced polymers bonded in different arrangements. Five beams were modelled and analysed and the different arrangements included fully wrapping the four sides of concrete beam; U-shape wrapping of only three sides of the concrete beam; wrapping of only sides of the beam and the final arrangement was an arrangement where only the bottom face of the beam was wrapped with the FRP laminate. A two-point loading test was simulated with software and the displacement response to loading results observed. The results of the finite element analysis compared so well with the experimental analytical methods. It was also observed that using the FRP laminates to strengthen concrete beam increased the beam flexural strength by 15.6%. Thus, conclusion was made that that ABAQUS can be used to accurately predict the flexural behaviour of EB-FRP strengthened RC beam. However, a recommendation was proposed that further research should be done to assess the results of the flexural behaviour when different numbers of laminate layers and different thicknesses of laminate were to be used.

Table of Contents
Declaration ii
Acknowledgement iii
Executive Summary iv
Table of Contents iv
List of Figures vii
List of Tables viii
1. INTRODUCTION 10
1.1. Background 10
1.2. Problem Statement and Justification of the Research 10
1.3. Research Objectives 11
1.3.1. Specific Objectives 11
1.4. Scope of the Research 12
1.5. Outline of the Thesis 12
2. LITERATURE REVIEW 13
2.1. Background and Historical Development of EB-FRP in Construction Industry 14
2.1.1. Fibre Reinforced Polymer (FRP) 14
2.2. Flexural Strength of Concrete 17
2.3. Structural Application of FRP in Construction Industry 19
2.3.1. Flexural Strengthening Application of FRP 19
2.3.2. Shear Strengthening Application of FRP 22
2.4. Use of 3D Finite Element (FE) Modelling to Study EB-FRP Strengthened Concrete Members 24
3. METHODOLOGY 25
3.1. General 26
3.2. Description of the Experimental Procedure Based on Chellapandian et al (2019) Study 28
3.3. Finite Element Model Details Using ABAQUS (2018) 28
3.3.1. Creating the Models 31
3.3.2. Material Model Details 31
4. RESULTS AND DISCUSSION 38
4.1. Overview 38
4.2. Validation Analysis 38
4.3. Mesh Sensitive Analysis 41
4.4. ABAQUS Results 41
4.4.1. ABAQUS Results for Beam without FRB Laminates 43
4.4.2. ABAQUS Results for Beam with all the 4-sides Bonded with FRP Laminates 43
4.4.3. ABAQUS Results for Beam with U-shaped FRP Bonding Set-up 43
4.4.4. ABAQUS Results for Beam with Only 2-sides Bonded with FRP 44
4.4.5. ABAQUS Results for Beam with the FRP Laminate Bonded Only at the Bottom 44
4.5. Parametric Studies Analysis 44
4.6. Overall Effect of EB-FRP on the Flexural Behaviour of Reinforced Beams 45
5. CONCLUSION AND FUTURE WORKS 46
5.1. Conclusion 46
5.2. Future Works 47
References 48
APPENDIX 51
5.3. Appendix A: ABAQUS Results for Beam without FRP Laminates 52
5.4. Appendix B: ABAQUS Result for the Beam with all the Four Sides Bonded 53
5.5. Appendix C: ABAQUS Result for Beam with U-shaped FRP Bonding 56
5.6. Appendix D: ABAQUS Results for Beam that is Bonded on Only 2-Sides 57
5.7. Appendix E: ABAQUS Results for Beam with only 1-Side (Bottom) Bonded with FRP 60

List of Figures
Figure 1: Examples of components of a typical composite 6
Figure 2: Categories of application of FRP in building Industry 7
Figure 3: Different orientation schemes used in strengthening concrete beams with EB-FRP laminates 8
Figure 4: Three-point load test (ASTM C78) 9
Figure 5: Centre point load test 9
Figure 6: Different schemes of attaching FRP to concrete for flexural strengthening 11
Figure 7: Different failure of concrete member under flexural strengthening 12
Figure 8: Typical 3D model in a FE software 16
Figure 9: The cross section and dimensions details of the RC beam used in this study (after Chellapandian et al., 2019) 17
Figure 10: The EB-FRP confinement conditions investigated in this study. 18
Figure 11: Methodology flow chart implemented in this thesis 18
Figure 12: Test setup and instrumentation details for flexural load test of the RC beams (Chellapandian et al., 2019) 19
Figure 13: the different RC beams FEM used in this study, namely, (a) RC beam without strengthen, (b) full four sides (box) EB-FRP strengthen RC beam, (c) bottom EB-FRP strengthen RC beam, (d) two side EB-FRP strengthen RC beam, and (e) U-shape EB-FRP strengthen 21
Figure 14: The details of the part used in this study. 22
Figure 15: stress-strain behaviour of concrete to uniaxial loading in (a) tension and (b) compression (ABAQUS, 2018) 24
Figure 16: Uniaxial stress-strain curves of concrete and the damage variables with the strain for concrete C40 (a) compression (b) tension. 25
Figure 17: Failure mode comparison between experimental result and FEM 30
Figure 18: Failure mode comparison between experimental result and FEM 30
Figure 19: Displacement against Load trend 31
Figure 20: Mesh sensitive analysis graph 32

List of Tables
Table 1: Reinforcing bar parameters adopted in this study to simulate steel Grade 60. 23
Table 2: Adopted parameters for simulation of concrete C40 in this study (Sharari, Fatahi and Hokmabadi) 26
Table 3: Hashin material properties for CFRP sheets (Kadhim, Jawdhari and Altaee) 27
Table 4: Summary of principle stresses and strains as obtained from numerical FEA 33
Table 5:Summary of parametric studies results 35

INTRODUCTION
Background
The use of reinforced concrete has been very pivotal in the construction industry. In fact, its use can be dated back in the second half of the 19th century (Moussard, et al., 2017). Ever since its invention, it has been used in making different structural elements, such as beams, columns and slabs among others. There exist myriads of literature materials and fully published researches about reinforced concrete. However, even with all the available literature/published materials; studies are still ongoing to further improve the performance of reinforced concrete. One such important is the use of fibre reinforced polymers (FRP) to strengthen reinforced concrete elements such as beams, columns and slabs. As a result, this paper presents a study that is aimed to research the flexural behaviour of reinforced concrete beams that are strengthened with externally bonded fibre reinforced polymers (EB-FRP).
Several experimental testes have been carried out on this subject and are still ongoing. Although, in the paper the approach is to use numerical method that entails finite element analysis using ABAQUS software. The resent past has seen the rise in use of computer analysis software in modelling real time problems to predict the expected result (Anıl, et al., 2017). This paper, therefore, attempts to explore the comparison between the results obtained from numerical analysis using FE software and results from experimental tests.

Problem Statement and Justification of the Research
Laboratory and experimental tests are very expensive to perform and time consuming. Besides, they are prone to human error among other limitations. Experimental tests have been very useful in the past and still continue to address serious areas of knowledge gaps by offering answers through research. But since the global demand for engineering products and solutions keeps on rising, relying on real experimental data alone may drag the process of timely meeting human demands for engineering solutions and products (Juuti, et al., 2019). Also, engineering products and solutions are built around well set out standards, information and knowledge (Juuti, et al., 2019). For instance, in order to achieve the right design concrete class, it is important that an engineer has the right information about the design mix required to achieve the required strength class of the concrete.
Also, besides the use of FRP being used in engineering for several decades, they only found use in automotive, marine and aerospace industries. However, now that their application is receiving remarkable attention in the construction industry; understanding their structural performance in conjunction with other construction material is key (Naser, et al., 2019). One of the areas that FRP has been used, within the construction industry, is in strengthening concrete elements. Its application in strengthening reinforced concrete elements has generated several interests among scholars with many research now being carried out.
Using computer and appropriate software is a sure way to solve the time problem as well as cut down on the cost of performing experiments. However, until computers simulations can be fully relied upon, there has to be tests done to compare them with the existing experimental data. These tests help in validating the software and the modelling approach used as well as adding to the pull of knowledge required in providing engineering solutions. Thus, this research project is crucial in addressing the aforementioned issues. The research will potentially address the issues of validity of using numerical assessment with ABAQUS to study the flexural behaviour of reinforced concrete that is strengthened with EB-FRP. At the end of it, its findings and results are expected to contribute to the academia world.

Research Objectives
The main objective of this research is to use numerical assessment method to study the flexural behaviour of reinforced concrete beam that is strengthened with EB-FRP laminates using different arrangements of the laminates on the RC beam surface. In order to achieve the main objective of the research, the work is divided in specific objectives that has to be competed in order to complete the research.

Specific Objectives
To use ABAQUS FE software to foretell the flexural behaviour with load displacement response for RC beams that are externally bonded with FRP laminates in different arrangements
To compare the output of FEA software with the existing experimental analytical results
To observe the effect of various arrangement pattern of the FRP laminates on the flexural behaviour of the strengthened RC beams.

Scope of the Research
The research covers three broad areas which can further be subdivided into smaller sub-tasks. The research entails an extensive review of relevant literature material that are related to the research objectives. The literature materials reviewed or referenced are credible and answers the key issues of the research problem. The research also covers finite element modelling of 5 RC beams using ABQUS. Conclusion is also drawn based on the analysis of the results obtained from the finite element modelling and data from the literature materials.

Outline of the Thesis
This thesis is divided into 5 main chapter as described below

Chapter 1 – Introduction:
This chapter highlights the background of the research as well as stating the problem statement and presenting the justification for the research. Additionally, it contains the research objectives, research scope and the outline of the research.

Chapter 2 – Literature Review
This chapter captures an extensive review of all the relevant literature materials that have been used to build the knowledge around the research topic. It briefly describes the historical background and development of EB-FRP in the construction industry. The chapter also delves into the various studies about the properties of FRP, its structural applications and the gaps that present an opportunity for this research study to be relevant. Chapter 2 also presents the concepts of 3D finite element analysis method software and their relevance.

Chapter 3 – Methodology
This chapter present the various methods used in the research, for example; it highlights the finite element modelling method using ABAQUS, meshing of the elements, and validations of the process This chapter also present the various methods and calculations used in arriving at different material properties that have used in the FEA method.

Chapter 4 – Results and Discussions
This is the section where all the output from the FE modelling have been presented. Chapter 4 also presents the analysis and interpretations of the results obtained from the study. Relevant diagrams, graphs and tables that are the results of the studies have been presented in this section.

Chapter 5 – Conclusion and Future Works
This is the final chapter of the research. It presents a summary of the findings and facts obtained from the research. It is also the section the states some of the future works that should be carried following the outcome of this study.

LITERATURE REVIEW
Background and Historical Development of EB-FRP in Construction Industry
The application of fibre reinforced polymers (FRP) in the construction industry has existed for several decades and engineers have continued to use the material in solving concrete problems that occur under service. The application of FRP has been in existence for over 50 years (Naser, et al., 2019). In fact, according to Czaderski and Meier (2017), the introduction of externally bonded reinforcement advent into the construction industry was in the late 1960s whereas that of FRP was in the 1990s. The initial applications of strengthening concrete with externally bonded reinforcement utilized an epoxy bonded steel plates where an adhesive was used in to attach a steel plate to the concrete beam (L’Hermite & Bresson, 1967). The first usage of this technology was on a highway bridge and subsequently used a building between the year 1966 and 1967 (Ruggli, et al., 1980). Subsequently, more studies and investigation on the application of externally bonded reinforcement began. One notable study was conducted in the year 1981 where 16 tests were conducted on plated reinforced concrete element that was put under different types of loading: bending, shear, and axial tension (Johnson & Tait, 1981).

Fibre Reinforced Polymer (FRP)
Fibre reinforced polymers (FRP) are low-weight to high modulus and high strength materials used in various engineering applications. They are composite material, meaning it is made using two or more materials combined together to augment the performance of the final product. For example, the final properties of the FRP are more superior than the properties of individual constituent materials (Teng, et al., 2001; Hollaway, 2010; Rasheed, 2014). Basically, a FRP material is made up of high strength reinforcements and a polymer acting as the matrix that binds the reinforcement.
In the construction industry, the main types of fibres that are normally used are the carbon fibres, E-, S-, and Z-glass fibres and the aramid fibres (Naser, et al., 2019). Aramid fibre exist as either the aromatic polyamides or the Kevlar 49. Also, the polymer matrices used in the construction industry also come in two broad categories; either the thermoplastics or the thermosetting. Figure 1 below shows the categorisation of the different components of typical FRP. Given the variations in the types of fibres or the matrices that can be used, the final properties of the FRP used in the construction industry also vary (Dai, et al., 2011; Hollaway, 2010).

Figure 1: Examples of components of a typical composite
In the initial stages of the development of FRP, they were only used in the marine, automotive and aerospace industries and not in the construction industries because their cost were very high and unjustifiable (Hollaway, 2010; Teng, et al., 2001; Rasheed, 2014). Although, this problem has been solved by the advanced technology which has enabled cheaper means of production. Currently, FRP in construction industries are used in retrofitting and strengthening of concrete members and they have proven to have more benefits over the traditional steel reinforced concrete (Naser, et al., 2019; Hollaway, 2010). For example, FRP have greater resistance to chemical attack, they are more environmentally durable as well as being easy to tailor to fit different structural requirements.
Although FRP was initially used in rehabilitating buildings, its application has presently advanced strengthening of large infrastructures as well as building of new structures (Naser, et al., 2019; Czarnecki, et al., 2013). As such, the application of FRP in civil engineering can be broadly categorized into two, application in rehabilitation and application in new constructions as illustrated in figure 2 below. In rehabilitation applications they are used for repair of corroded concrete members, strengthening of weakening elements as well as seismic retrofitting. In new construction the FRP are essentially used in strengthening and sometimes as construction elements.

Figure 2: Categories of application of FRP in building Industry
The application of FRP in strengthening concretes is mostly achieved through external bonding. Through external bonding onto concrete members, FRP has been used to enhance the flexural behaviour of concrete members, and shear and torsional capacities of reinforced concrete (RC) (Naser, et al., 2019; Stefano & Gianmarco, 2015; Nayak, et al., 2018). Also, the bonding system is achieved through two main ways that include FRP laminates or sheets while the second method is known as the near surface mounted (NSM) method (Darain, et al., 2016). The FRP sheets or plates are bonded on the external surface of a concrete that has been well prepared. The preparation procedures entail grooving the surface of the concrete member, attaching the laminates and then filling them up using an epoxy adhesive (Darain, et al., 2016; Naser, et al., 2019). However, the method of using externally bonded laminates is prone to debonding; especially, under the conditions when the axial strains are low (Lorenzis & Teng, 2007). This makes the use of externally bonded laminate application undesirable as they do take the full potential of the tensile strengths. In order to solve the debonding problem, NSM approach is used. NSM method produces a better surface bonding as well as high level of strength efficiency as it is less susceptible to debonding failure and mechanical wear (Stone, et al., 2002; Darain, et al., 2016).
There a number of schemes in which the FRP laminates can be bonded to the concrete members. For instance, the FRP laminates can be wrapped around the whole member (also known as full wrap). There is also U-jacket bonding whereby the tension side and the two opposite sides while leaving out the compression side. The different schemes and orientation are as depicted in figure 3 below.

Figure 3: Different orientation schemes used in strengthening concrete beams with EB-FRP laminates

Flexural Strength of Concrete
Flexural strength can be described as the capacity of a material to withstand bending forces applied to that material vertically to its longitudinal axis. In concrete materials, flexural strength is a measure of the tensile capacity of the concrete (Hamakareem, 2021; Walker & Bloem, 1997). The flexural strength of concrete is sometimes denoted as Modulus of Rapture (MR). There two standard test procedures for testing the flexural strength of concrete as provided in ASTM: three-point load test (ASTM C78) and centre point load test (ASTM C293). The flexural test set up for the two methods are as shown in figure 4 and 5 below.
Using the two standard methods in determining the value of modulus of rapture, the value obtained by the centre point load test set up is always lower than that obtained from a three-point load test set up. Studies have shown that the difference is by 15% (Hamakareem, 2021). Additionally, testing concrete specimen with large size yields low values of modulus of rapture. The modulus of rapture, f_r, is determined using the following equation
f_r=7.5√(f_c^’ )
Where: f_c^’is the concrete compressive strength

Figure 4: Three-point load test (ASTM C78)

Figure 5: Centre point load test
Concrete materials are good in compression and poor in resisting tensile forces. For example, the tensile strength of concrete is in the range of about 10% to 15% of the concrete compression strength (Hamakareem, 2021). Concrete materials are, therefore, reinforced with fibres in order to improve the overall tensile strength. The fibres used in reinforcing concrete must have excellent tensile strength. For example, steel reinforcement fibres are often used to improve the flexural properties of concrete.

Structural Application of FRP in Construction Industry
The recent decade has been coupled with a number of research on FRP in the construction industry following the capabilities of the FRP materials to be used in strengthening concrete members. A number of literature materials are also available to prove the ongoing studies on several areas of the application of the FRP in as a strengthening component of concrete. Specific studies have focused on the flexural, axial, seismic, torsional as well as the shear strengthening power of the FRP. The focus of this literature review will however focus on the flexural behaviour studies as that is the basis of this research.
Flexural Strengthening Application of FRP
In practise, FRP has been used to enhance the flexural capacity of both plain concrete and RC members. This has been achieved by externally bonding the FRP laminates to the soffit of simply supported beams as illustrated in figure 6 below. Studies have shown that using a number of failure modes are encountered when FRP sheets are externally bonded to either beams or slabs for the purposes of flexural capacity improvements. For instance, yielding of steel bars and then rapture of FRP sheets, debonding of the sheets from the adjacent concrete surface and separation of concrete cover are some of the notably failure modes often encountered in concrete members that are strengthened with FRP in flexure (ACI 440.2R-08, 2008).

Figure 6: Different schemes of attaching FRP to concrete for flexural strengthening

The first failure mode occurs whenever the externally attached FRP sheets is already under the conditions of its ultimate strain ahead of the top part or the compression region of the concrete crushing strain. On the other hand, the second failure mode, debonding, often happens when the axial force in the FRP reinforcement is greater than that of the concrete substrate. This process of debonding is a result of flexural-shear cracks within the areas of highest moment sections which afterwards proceed to the length of the FRP along the bonding/adhesive material. The separation of concrete cover on the other hand is as a result of the formation of cracks within the areas of high stress concentration just near the curtailment regions of the FRP sheets. These cracks further move to the sections of steel reinforcement making the concrete cover to separate. The different failure modes for a concrete member that is under flexural loads are as illustrated in figure 7 below.

Figure 7: Different failure of concrete member under flexural strengthening

Despite the existence of the three failure modes illustrated above, the use of externally bonded FRP laminates significantly increases the flexural strength of the strengthened concrete member. For example, research was carried out that tested 60 RC beam specimens using a simulated four-point bending test (Meier, 1992). In that study, CFRP laminates of o.3mm thickness and width of 200mm were externally bonded to the beam specimens. The finding of the study showed that the beams with externally bonded CFRP had strength improvements of up to 100% as compared to the ones that had no the CFRP. On different research, CFRP sheets were used to strengthen reinforced concrete beams that already had cracks (Arduini & Nanni, 1997). The findings of this research indicated that that the direction of the fibres, the number of the laminates as well as the stiffness of the carbon fibre substantially influences the strength of the bonded beams. For example, it was shown that attaching FRP laminates vertical to the boundaries of the bonded beam would easily delay debonding on the FRP strengthened members.

Still under the flexural behaviour and strength capacity of the externally bonded FRP on concrete another study was carried out to observe the performance of RC flexural member that are externally bonded with glass fibre reinforced polymers (GFRP) (Nayak, et al., 2018). In this study, ten beams were subjected to a two-point loading test. Using varied bonding patterns and varied number of GFRP laminates (1 up to 4 laminates), nine beams were wrapped with the GFRP while one beam was used for control experiment. Two important findings were concluded in this study. It was found out that the flexural capacity increases with the number of GFRP laminates used and that the failure mode shifts from ductile to brittle when the number of GFRP laminates are increased. Stefano and Gianmarco also presented their findings on a study that investigated the tensile behaviour of a mortar-based composite for externally bonded reinforced system (Stefano & Gianmarco, 2015). In this study, the aim was to assess the behaviour of the strengthened system under the condition of different matrices and textile materials. The two researchers found out that different textile materials and different matrices affect the ultimate strength, the tensile modulus of elasticity as well as the failure mode of the strengthened systems.
Whereas the above studies have focused on the flexural behaviour of the observed member under the influence of FRP used, other researchers have investigated the flexural behaviour based on the type of approach used in bonding the FRP and the concrete member. In one of the studies, the performance of RC beams strengthened with externally bonded with a combined system of different FRP systems were investigated (Hawileh, et al., 2014). In this study, it was shown that the achieved strength varied depending on the percentage variation of the FRP systems used. Carbon fibre reinforced polymer and glass fibre reinforced polymers were used. The study also showed that higher level of strength and ductility were realized when a combination of CFRP and GFRP system were used rather than a single system of CFRP. In order to further highlight the concept of using hybrid FRP systems in strengthening concrete members a different study was conducted to evaluate the outcome hybrid FRP systems by employing the use of two different continuous systems of CFRP however with different properties (Wu, et al., 2007). One system was high strength system while the other CFRP was high modulus. The finding of this research indicated that there exists an optimum combination that yields optimum performance. For example, the results showed that the optimum combination was that having a ratio of 2:1 for high strength to high modulus.

Shear Strengthening Application of FRP
Besides the application of improving flexural properties, FRP materials have also find use as shear capacity enhancing agents in reinforced concrete beams. One of the most notable early research to investigate the shear enhancement using externally bonded FRP was done published in 1995 (Chajes, et al., 1995). Twelve under reinforced beams were tested in this study to evaluate the efficiency of FRP in enhancing shear behaviour. The study showed an improvement of the shear capacity of the investigated materials up to a 150% compared to the materials were not externally bonded with FRP. This finding inspired several other studies such as that of U-wrapping (Carolin & Täljsten, 2005; El-Maaddawy & Chekfeh, 2012) which showed how the shear capacity of a worn-out reinforced concrete beam could be restored using FRP laminates. Additionally, it was also established that alongside using the EB-FRP to enhance shear capacity together with appropriate end anchors, occurrences of debonding failure could be prolonged (Ali, et al., 2014; Smith, et al., 2011). According to Chennareddy and Taha, (2017), using a hybrid of a NSM and U-wrapping would substantially augment both the shear and flexural potential of a concrete member. Although, this type of combination presents another problem of altering the failure mode where instead debonding of NSM bars, there is a sudden failure resulting from the rapture of NSM-FRP bars.
However, in the research and academia field, the study of performances of deep solid reinforced concrete beams strengthened with EB-FRP laminates has not been thoroughly explored and there is very little literature materials as well (Islam, et al., 2005; Maaddawy & Sherif, 2009). Islam et al, (2005) established an improvement of approximately 40%. Though the study establishes some significant improvements, in reality the sides of the beam might not be reachable for strengthening based on several factors of design such as geometry.
The aforementioned literature publications depict the unending prospect for EB-FRP incorporation in the building industry. Each depict the superior qualities possessed by the application of FRP in strengthening concrete members. However, FRP also have some properties that creates a challenge when it comes to its application to a maximum potential (Shi, et al., 2012; Naser, et al., 2015; Silva, et al., 2014). For example, FRP performs undesirably in extreme conditions such as in freeze cycle conditions, in saline surroundings and in high temperature environments. Also, durability of FRP is still a subject of concern that continues to present a challenge in its application (Naser, et al., 2019). These challenges can be solved through an extensive research and tests. However, given the expensive nature of carrying real laboratory tests that ranges from procurements of material, laboratory equipment as well as trained personnel; such limitations can be solved using computer modelling/simulation that equally yield better results. Use of computer simulation to assess the properties of FRP also forms the basis of this research and is potentially to provide a basis to solve this limitation.

Use of 3D Finite Element (FE) Modelling to Study EB-FRP Strengthened Concrete Members
Alongside experimental researches that entail laboratory tests, some scholars have opted to pursue the investigations using computer simulations that do finite element analysis (FEA) to study the flexural behaviour of strengthened reinforced concrete members with externally bonded FRP laminates (Kodur & Bhatt, 2018; Anıl, et al., 2017; El-Zohairy, et al., 2017; Zhang & Teng, 2014). The first study on strengthened concrete member with externally bonded FRP was first done in the year 2001 (Kachlakev, et al., 2001). This study only focused modelling and analysis. No attention was given to the nature of the bond between the concrete and the laminate and as such was insufficient in its findings. However, it did lay the foundation for modelling and FEA of FRP strengthened systems using 3D FE computer applications.
Presently the FE modelling computer software have been at the centre of the analysis. They are fast, accurate and therefore achieve a significant saving on the computational time (Chen, et al., 2012). The process is generally the same regardless of the software used. It entails discretization of a 3D model into finite elements, application of loads and boundary conditions and then performing the analysis. An example of a 3D model highlighting a typical beam and EB-FRP laminates is shown in figure 8 below.

Figure 8: Typical 3D model in a FE software

METHODOLOGY
General
As mentioned previously, ABAQUS 2018 used in this study to conducted the numerical assessment of the RC beam strengthen under flexural load, by addressing the effect of different arrangement of the external bounded (EB) FRP sheet. Firstly, the numerical model validated with literature experimental work proposed by (Chellapandian et al., 2019), where the implemented RC beam presented in Figure 9, as evidence, the RC beam used in the experiment was a square cross section with 230 mm width and 2000 mm total length. For this controlled RC beam (CB) used in this study, eight longitudinal reinforcing bars with 12 mm diameter, and 10 mm diameter for stirrups reinforcing with 100 mm spacing were used. The details of the reinforcement and the RC beam dimensions explained in Figure 9 where displacement controlled four-point bending moment tests were conducted to study the effect of EB-FRP different arrangements.

Figure 9: The cross section and dimensions details of the RC beam used in this study (after Chellapandian et al., 2019)
Two validation analyses conducted for the RC and EB-FRP RC beams numerical models, and a mesh sensitive analysis performed as well to ensure the accuracy of the mesh size selection. When the numerical models showed their capability to capture the bending behaviour for EB-FRP confined and unconfined RC beams, parametric study for different arrangement of the EB-FRP beams were performed. Indeed, Figure 10 represents the confinement/EB-FRP analysis conditions performed in this study.

Figure 10: The EB-FRP confinement conditions investigated in this study.
The methodology of this study is explained in Figure 11, the finite element model created using ABAQUS 2018 and the analysis procedure are explained in details in the following section.

Figure 11: Methodology flow chart implemented in this thesis
Description of the Experimental Procedure Based on Chellapandian et al (2019) Study
In the study by Chellapandian et al. (2019), four set of RC beams were tested using four bending tests method to assess their flexural capacity with and without FRP strengthening method. Where the RC beams were designed per IS 10262-2008, the concrete mixed to have 40.0 MPa compressive strength, the reinforced steel rebars of grade Fe500 were used. For the Fe500 rebars grade, the yield strength was 512 MPa, the ultimate strength and rupture strain were 620 MPa, and 7.8% respectively. In addition, for external bounded of RC beam with FRP laminates, the CFRP fabric implemented per ACI 440.2 R (2017), where the CFRP sheets were covered the beams using a two-component based epoxy resin. The experimental setup using 2000 kN testing capacity machine to perform the four-bending flexural beam test. The test performed using displacement-controlled technique with quasi-static loading rate 0.03 mm/s. Figure 12 represent the experiment setup.

Figure 12: Test setup and instrumentation details for flexural load test of the RC beams (Chellapandian et al., 2019)

Finite Element Model Details Using ABAQUS (2018)
To create the Finite Element Model (FEM) ABAQUS (2018) used in this study, as this multi-purpose software consider as a powerful tool can capture the structure behaviour accurately under different load conditions, such as four bending flexure tests for RC beams. Running the analysis using this engineering software can help in reducing the experimental work cost and time, therefore, in this study five different models were tested and tested to assess the efficiency of different arrangement of EB-FRP laminates on the flexural behaviour of the RC beams. Firstly, validation models created and the best mesh size was selected, after that the parametric study conducted. In general, same materials were assigned for all the different numerical models, but different parts and interaction properties were assigned, Figure 13 represent the different numerical model created for this study. Where Figure 13a, represent the control RC beam for unconfined/strengthen RC beam case, and this model used twice for validation process and for parametric study where the grade of the concrete used in each running analysis was different. Same for Figure 13b which represent the finite element model for fully/box strengthen EB-FRP RC beam. In addition, Figures 13c, 13d, and 13c represent the different arrangement of the EB-FRP sheet used, namely, bottom sheet, two sides and U-shape EB-FRP strengthen beams. The details for creating these models are explained in the next section.

Figure 13: the different RC beams FEM used in this study, namely, (a) RC beam without strengthen, (b) full four sides (box) EB-FRP strengthen RC beam, (c) bottom EB-FRP strengthen RC beam, (d) two side EB-FRP strengthen RC beam, and (e) U-shape EB-FRP strengthen.

Creating the Models
For creating FEM in ABAQUS, several steps need to be done, first creating parts using the suitable features for each part, then assign the properties for each part, meshing the parts, assemble the parts and defined how these parts should interact with each other. Finally, the analysis steps with the applied load should be defined. Figure 14 explains the different parts used in this study. Where for the rebar, beam element was used, and for the FRP laminate shell element, finally for the RC beam the solid element was used the details of these element mesh will be explained later in this chapter. It should be mentioned, the load part and support part are rigid analytical surfaces, therefore these parts will not affect the beam response but will transfer the load, and generate the reaction forces.

Figure 14: The details of the part used in this study.
Material Model Details
Different materials model used in this study for each part, for example, for the steel rebars the Isotropic hardening material model used to capture the nonlinear response of steel Grade 60, in this material model the linear elastic behaviour is capture till the yielding point (i.e., yield stress), after that the plasticity nonlinear response is defined using the ultimate stress point (i.e. ultimate strength) and the corresponding plastic strain. Through these parameters ABAQUS can defined the Isotropic hardening modulus and capture the stress strain behaviour of the steel in both the linear elastic region, the yielding and the nonlinear hardening response till ultimate response. Indeed, the parameters used for steel reinforcement are 512 MPa and 620 MPa corresponding to yield strength f_y, and ultimate strength f_ult , respectively. the other parameters obtained from ASTM A615 / A615M-18e1 (2018) and Hawileh et al. (2009) to represent the steel reinforcement used in the experimental part. The details of the material parameters are summarized in table 1.
Table 1: Reinforcing bar parameters adopted in this study to simulate steel Grade 60.
Parameter Symbol Value
Tensile strength (MPa) f_ult 620
Tensile yield stress (MPa) f_y 512
Elongation (%) δ 20
Young’s Modulus (GPa) E_r 206.56
Density (kg/m3) ρ_r 7850
Poisson’s Ratio v 0.3
For the concrete the Concrete Damage Plasticity (CDP) used in this study, this model adopts plasticity-based damage for the concrete, assuming two failure mechanisms, compression crushing and tensile cracking. The yield function for this material model is controlled by two hardening parameters as explained by ABAQUS 2018 (see Figure 15), tensile plastic strain (ε ̅_t^pl), and the compressive plastic strain (ε ̅_c^pl) to control the failure under tension and compression, respectively.

Figure 15: stress-strain behaviour of concrete to uniaxial loading in (a) tension and (b) compression (ABAQUS, 2018)
However, the failure in the concrete generated gradually by losing the concrete strength under tension and compression loading, where ABAQUS need to defined a scalar parameter for this stiffness degradation by using tension and compression damage parameters (d_(t ),d_c), these parameters represent the reduction of concrete initial stiffness (i.e., E_0). Though, the uniaxial stress strain in compression and in tension are defined separately as shown in figure 15. The following equations used for defining tensile stress-strain σ_t,ε_t and compressive stress-strain σ_(c,) ε_t for CDP model under uniaxial load in ABAQUS:
σ_t=(1-d_t ) E_0 (ε_t- ε ̅_t^pl) (3.1)
σ_c=(1-d_c ) E_0 (ε_c- ε ̅_c^pl) (3.2)
where, the subscripts t and c refer to tension and compression. The tension and compression damage parameters (d_(t ),d_c) can have the value from 0 (no stiffness losing) to 1 (total damage happened). The cracking strain and crashing strain (the plastic strain values) need to be defined according to following relations:
(ε ) ̅_t^cr=ε_t-σ_t/E_0 (3.3)
ε ̅_t^pl= (ε ) ̅_t^cr-d_t/((1-d_t ) ) σ_t/E_0 (3.4)
To defined the compressive stress with crushing strain curve, and the tensile stress with cracking strain curve Saenz (1964) and Nayal and Rasheed (2006) models were used for the compression and tension stress-strain values, respectively. For the concrete C40 grade (i.e., 〖f`〗_c = 40 MPa) adopted in this case study to meet the material properties of the concrete used in the experiment, the modulus of elasticity of concrete (MPa) was determined based on ACI 318-08 (2014) as E_c=0.043*〖 W_c〗^1.5 √(〖f`〗_c ) , where W_c is concrete density (kg/m3) taken as 2400 kg/m3 in this study. In addition, referring to ACI 318 (2014), the tensile strength of concrete (σ_t0) was taken to be 0.62√(〖f`〗_c ), while the strain corresponding to 〖f`〗_c was considered to be 0.0025 as reported by Hu and Schnobrich (1989). The parameters used for CDP model in this study for concrete C40 are explained below in Figure 16 and Table 2:

Figure 16: Uniaxial stress-strain curves of concrete and the damage variables with the strain for concrete C40 (a) compression (b) tension.

Table 2: Adopted parameters for simulation of concrete C40 in this study (Sharari, et al., 2020)
Parameter name Symbol Value
Dilation angle ψ 36˚
Eccentricity ϵ 0.1
Biaxial/uniaxial compressive yield strength ratio F_B0/F_C0 1.16
The tensile and compressive hydrostatic effective stress ratio K 0.667
Compressive stiffness recovery parameter WC 1
Compressive stiffness recovery parameter Wt 0
For the FRP unidirectional laminate/ sheet, this two-dimensional part placed as each direction defined by a local coordinate system; therefore, it can be considered with two different moduli of elasticity in each direction, namely, the parallel direction to the fibres and the perpendicular direction. The material behaviour captures the linear elastic response and the plastic response, which mainly represented by brittle failure, Hashin damage model used to capture the failure mode for the EB-FRP sheets according to Kadhim et al. (2020) CFRP material parameters, same used for the CFRP laminates in this study and summarized in Table 3
Table 3: Hashin material properties for CFRP sheets (Kadhim, et al., 202)
Parameter Symbol Value
Longitudinal elasticity modulus, (GPa) E1 130000
Transversal elasticity modulus, E2 (GPa) E2 800
Longitudinal–transversal Poisson’s ratio, v12 0.28
Shear moduli, (MPa) G12 4500
G13 4500
G23 3600
Tensile strength in the fiber direction, (MPa) XT 2200
Compressive strength in the fiber direction, (MPa) XC 2200
Tensile strength in the transverse direction, (MPa) YT 61
Compressive strength in the transverse direction, (MPa) YC 130
Longitudinal shear strength, SL (MPa) SL 85
Transverse shear strength, (MPa) ST 40

Interaction, Interfaces and Meshing
To define how each part will interact with the others, interaction properties need to be defined between them, for example, the rebars were totally bonded with the RC beam using Embedment constraints. Between the FRP laminate and the RC beam cohesive interaction properties using adhesive was used with epoxy elastic modulus of 2.83 GPa, in addition, using tie constraint can ignore the FRP sheet instability rather than affect the final results, in case of investigation of the failure mode this option can be used (Chellapandian, et al., 2019).
For mesh size several sizes were investigated for the RC beam, namely, 50 mm, 30 mm, 25 mm and 20 mm. The 25 mm mesh size used based on the accuracy and the time of the analysis. Solid element mesh with 8 node linear brick, reduced integration, hourglass control technique type (C3D8R) used for the RC beam, shell laminated element 4 node doubly curved thin or thick shell with reduce integration, hourglass control, finite membrane strains element (S4R) used for FRP sheets, and beam meshed using 2-node linear beam element (B31) for the rebars.

Boundary Conditions and Loads
Two hinge supports used for the simple beam in this study, the applied load assigned as controlled displacement test for the four bending moment tests. Total of 200 mm applied at each applied load unit as Figure 12 shows. The analysis run using Dynamic Explicit solver while the load applied using smooth amplitude to control the loading rate for the beams. Each analysis takes 8- 15 hours based on the generated plasticity in the tested model.

RESULTS AND DISCUSSION
Overview
This section presents the results as well as the interpretations and an in-depth analysis of the results obtained in the research. Besides, it also incorporates relevant literature materials in explaining the outcomes of the research. The discussions presented in this chapter includes the analysis of the global results which compares the experimental findings with the ones obtained from the finite element analysis using ABAQUS. The section also discusses the results of the mesh-sensitive analysis, parametric studies and the overall effect of external bonded FRP on the flexural behaviour of reinforced concrete beams.

Validation Analysis
To validate the numerical model, the outcomes of the finite element analysis and that from experimental tests in the literature compared, the results show a similar trend. For example, the failure pattern of both the experimental and the simulated models showed a similar trend of cracking beginning from the bottom section where the initial cracking start from the tensioned regions in the beam as shown in Figures 17 and 18 below, which represent that the reinforcement rebars were yield first and then the crack start (i.e. brittle failure). The experimental results for RC beam without reinforcement (Figure 17) show cracks appearing on the tested beam at the bottom when the failure occurs. Moreover, in ABAQUS results the tension stiffness degradation parameter (dt), which indicates the decreasing of RC elastic stiffness reported with the corresponding plastic strain. It can be seen, when the crack region generated and reported in the elements dt was around 0.8, that mean only 20% of tension elastic stiffness remined in that element and definitely the cracking will be appeared. Also, the results from ABAQUS show the plastic strain generated in the RC beam, where the maximum plastic strain reach to 0.25% and these strains concentrated at the maximum deflection region in the beam (i.e. at bottom side of the mid-span of the RC beam). indeed, comparing ABAQUS reported results with the experimental observations, both results show an agreement which mean the ABAQUS numerical model is capable to capture the RC beam flexural behavior under bending test (Buyle-Bodin, et al., 2002; Chellapandian, et al., 2019). For RC beam without strengthen the cracks developed and the 45º cracks appeared, compared with EB-FRP strengthen beam the dt was 0.7 and the plastic strain was 0.22%, the crack remains in the middle and were not developed to 45º, indeed, the deflection significantly reduced when the peak load response was observed (Figure 18). This indicates the strengthen impact of EB-FRP on the RC beam, as the cracks pattern range decreased, the maximum strain decreased as well. It seems the EB-FRP increase the bending stiffness of the RC beam by improve the tension stiffness.
Additionally, the trend of displacement response of the EB-FRP strengthened RC beams to loads is similar in both cases – the experimental trend and finite element method. This outcome also points out at the validity of the finite element method in numerical analysis of the flexural behaviour of an EB-FRP strengthened reinforced concrete beam (Buyle-Bodin, et al., 2002). The trend is summarised by the graph shown in Figure 19 below. It shows a difference of 5% and 7% for RC beam and EB-FRP beam, respectively. Which is within the acceptable range, thus, the FE numerical method can be accurately used to foretell the flexural behaviours of an RC and EB-FRP strengthened beams.

Figure 17: Failure mode comparison between experimental result and FEM

Figure 18: Failure mode comparison between experimental result and FEM
Comparing the RC beam with and without EB-FRP sheets (Figure 19), show significant improvement in the ductility (i.e., displacement at failure) and minor improvement in the RC strength (peak load). These observations highlight the significant strengthen of RC beam having depth sight on the cracks pattern for both beams. RC beam without EB-FRP strengthening developed second stage cracking, where the 45º cracks developed in the beam showing the high values of losing tension stiffness for the beam. This means the rebars were yielded earlier for tension zone in RC beam.

Figure 19: load deflection graph for experiment and numerical analysis for (a) RC beam and (b)EB-FRP beam
Mesh Sensitive Analysis
The numerical analysis in the finite element analysis software is always performed by dividing the model into meshes. The size of the meshes determines the level of accuracy that can be obtained in a FEA method. For example, the smaller the size of meshes the higher the level of accuracy obtained. However, small-sized meshes implies an increased computational time due to the increased number of analyes elements and nodes. Nonetheless, mesh sensitive analyses are still important in determining convergence. The numerical analysis begins with an arbitrary size of mesh and the sizes are further refined while observing the results until there is convergence. In this research, mesh sensitive analysis results have been obtained for four different sizes of meshes: 50 mm, 30 mm, 25 mm and 20 mm. The mesh convergence was at mesh size 20 mm as the results were closer to the experimental results. The results of the graph in Figure 20 below shows the trend with mesh size 20 mm being comparing more closely with the experimental results. In addition, increase mesh size lead to overestimation of the hardening part for load-defliction graph and under estimation the load at failure, refine the mesh make the results closer to the experimental one.

Figure 20: Mesh sensitive analysis graph

ABAQUS Results for different EB-FRP arrangements
Five beams were modelled in ABAQUS software and the load deflection results are obtained and compared in Figure 21, the RC beam without any strengthen show the highest level of brittle failure, where the displacement at peak load observed at 21 mm, the failure displacement observed at 29 mm, which represent very brittle failure mode, the lowest ductility response. This mean the reinforcement is less than the required ratio for sustain the applied load. This indicated the need for further improvement/ strengthen of RC beam. The effect of the different arrangement of EB-FRP sheet can be explained from the represented curves.

Figure 21: the load deflection curve for different arrangement of EB-FRP sheet compared with the RC beam.
The peak load for the beam that is fully wrapped (EB-RC box) has the highest peak load followed by the U-wrapped beam. The results of the peak loads are summarized in Table 4 below. The beam without the FRP strengthening has the least peak load. These results imply that using EB-FRP to strengthen reinforced beams leads to a significant increase in strength of the beam.
Table 4: Summary of parametric studies results
Parameter RC Beam EB-RC (box) EB-RC (U-shape) EB-RC (sides) EB-RC (bottom)
Peak load (kN) 175.5 203 199 187 176.5
Displacement at peck load ∆peak load (mm) 21 85.5 89 88.5 30
Increasing of peak load (%) – 15.6 13.4 6.5 0.57
Failure mode Flexural failure mode

The displacement values for the peak load are least for the case of non-strengthened beams. For all the strengthened beams, the one with the FRP sheets at the bottom has the least displacement at peak load. The results of peak load displacement point out at the fact that using FRP sheet to strengthen the beam changes their failure mode from brittle to ductile. Although, it would be anticipated the fully wrapped beam to have the highest value of the displacement at peak value; the case is different from the result obtained from FEA with U-wrapped beam being the most ductile. This can be related to the effect of the fully confinement of the RC beam, which prevent the deflection of the beam and thus increasing the displacement (Naser, et al., 2019).
The percentage increase in peak load is higher for the fully wrapped beam followed by the U-wrapped beam and least in the beam externally bonded at the bottom. The result of the percentage increase in peak load is summarized in Table 4 above. This again represent the confinement effect of the box/full wrapped beam.
Following the results of the parametric studies, using FRP laminates as strengthening agents has the effect of increasing the load bearing capacity of the reinforced concrete beam. The results show an increase in strength by 15.6% (with regards to size of peak load) for the fully wrapped beam and 13.4% for the U-wrapped beam. These values are significant in terms of strength enhancement. However, it is important to note that this study only used one layer of FRP laminate and exploring the results with different numbers of layers, and various layer orientation will potentially yield different results. Based on experimental tests, increasing number of FRP laminates has the effect of increasing the strength capacity of the strengthened beam (Naser, et al., 2019). Exploring the effect of different number of laminates using ABAQUS FE software presents an opportunity to further research.

Stress strain response for the RC Beam with different EB- FRP arrangement
Figure 22 represent the Von Mises stresses contours along the RC beam when the peak load observed and the coresponding plastic strain of the RC beam, for the full sides and U-shape sides of EB-FRP beams. The results for the maximum principle stress and strain give indication of how much load can the RC withstand before it raptures. Normally, Von Misses stress are used to investigated ductility properties of materials.as represented below (see Figure 22 and Table 5), the beam without FRP laminates has the least principal stresses and strain, implying it fails at very low value of stresses and strain as compared other tested beams. Also, the principal stresses and strain for the beam without the FRP laminates are experienced at the top just near the point where loads are applied.

RC Beam without strengthen

Full sides EB-FRP

U-shape EB-FRP

Figure 22: stress stain contours for RC beams with different confinement conditions.

From figure 22 above, the results of the stresses contours show principle maximum stresses to occur at the lower sections. The cases of the box and U-shaped EB-FRP bonding, the stresses at taken by the FRP laminates. Failure is, thus, prolonged because the sheet has to experience failure before the cracking of the concrete and subsequent rapture of the steel reinforcement bars. It is worth noting that the points of maximum stresses are acting within the FRP shell. Also, the plastic strain for the box FRP sheet arrangement is significantly small indicating a reduced extent of permanent deformation of the system at the point of failure.

Table 5: Summary of principle stresses and strains as obtained from numerical FEA
Type of EB-FRP Bonding Stress (Principle/Mises Stress) MPa Plastic Strain (Principle Strain)
Without FRP Bonding 29.1 1.423e.-01
Steel bars for beam without bonding 531.5 5.284e.-02
Box/Fully FRP Bonding 5310. 1.063e.-01
Steel bar for box FRP bonding 528.8 4.632e.-02
U-shaped FRP2 Bonding 4883 1.413e.-01
Steel bars for U-shaped bonding 527.0 4.423e.-02
2-side FRP Bonding 27.95 1.280e.-01
Steel bars for 2-sides FRP bonding 529.4 4.724e.-02
1-side/Bottom side FRP bonding 27.12 1.468e.-01
Steel bars for 1-side bonding 530.6 6.249e.-02

From table 5 above, for all the set-ups it can be seen that the maximum stress values for all the steel bars are virtually the same. The difference is in the plastic strain where the set-up with only bottom side strengthened with the FRP laminate has the steel reinforcement bars having the highest plastic strain values followed by the RC beam with no FRP. This is an indication of high permanent deformation of the steel bars under the aforementioned set-ups. The plastic strain for the U-shaped set-up shows the least value explaining that it undergoes the least permanent deformation. This is followed by the RC beam that is fully wrapped in both sides; an indication of a low level of permanent deformation of the steel reinforcement bars. The RC beam with two sides bonded with FRP laminates also has a significantly low plastic strain values that closely compares with that of the box and U-shaped FRP laminate arrangement. The strengthening provided by the FRP laminates protects the RC beams and specifically the steel reinforcement bars from undergoing large permanent deformations.

ABAQUS Results for Beam without FRB Laminates
The principles stresses for the beam with now FRP laminates exhibited the stresses and strain behaviour as indicated in appendix A. Principal stresses and strain for the beam alone have been observed at the upper part, the compressions regions, just near the point of loads whereas for the reinforcement bars principal stresses and strain occurs at the tension region. Also, the principal stresses and strain for the beam without the FRP laminates are experienced at the top just near the point where loads are applied. However, the principles stresses and strain for the steel reinforcement bars of the beam without the FRP laminates are the highest as shown in table 4. This shows that the greatest load within the beam for will be taken by compression while the maximum tension forces are taken by the reinforcement bars.

ABAQUS Results for Beam with all the 4-sides Bonded with FRP Laminates
The results are in appendix B and shows the area of great principal stresses to occur at the bottom region. The principal maximum strains are also within the bottom region, although the least for all the modelled beams. This implies an improvement showing that the beam with all the four sides bonded can withstand high stresses before it raptures. This is explained by the fact that FRP sheets help in providing additional strength. The stress is now resisted by the FRP layers. Thus, instead of the RC beam to crack and then rapturing of the steel reinforcements, the FRP laminates prevents or delays that abrupt failure.
The reinforcement steel bars for box FRP laminate set up also withstands the highest stresses before rapturing for all the beams that have been bonded with the laminates. However, the value is less than that of the beam that has no FRP laminates. This is because the bonded beam has a high stress resistance capacity caused by the FRP sheet and being that the principal stresses are acting within the tension region, the steel bars whose function is to provide tensional stresses resistance only gets affected once the FRP sheets rapture and then after the subsequent cracking of concrete section. Thus, the rapture process is in the order of FRP sheet, then concrete surface at the interface and finally the steel reinforcement bars.

ABAQUS Results for Beam with U-shaped FRP Bonding Set-up
The results are in appendix C. This beam has the second highest value of Mises’s stress among the beams with EB-FRP strengthened beams. However, it also has a high strain value, the second highest value after the beam that is only bonded with FRP laminate on the bottom side only. Also, the principal strains for this beam are at the top within the compression region. This can be explained by the fact that the top part is not strengthened by the laminates, thus, a higher value of strain. Unlike the fully wrapped beam where maximum strain is at the point of maximum stresses; the U-wrapped beam maximum strains are exhibited at the top section that has no laminate. Strengthening of the top part has been reduced and maximum strains have been shifted to this region.
However, its high stress resisting capacity has been augmented by the presence of the FRP sheets that helps in taking high tensional forces. The stress points are shifted to the FRP sheets first. Therefore, in order for the system to fail, the FRP sheets has to experience the distortion first before the concrete cracking can begin. It is only after these FRP shell and then concrete materials experience failure that the steel reinforcement bars get affected and raptures as well.

ABAQUS Results for Beam with Only 2-sides Bonded with FRP
The results for this beam are shown in appendix D. Both the principal stresses and strain for this beam are exhibited at the top region. In fact, the principles stresses are just near the point of application of the loads. In reinforced concrete beams or slabs, the areas of principle stresses are within the top and bottom section where the maximum compressive stresses and maximum tensions respectively are resisted. Thus, strengthening only the two sides and leaving the bottom and top sides unstrengthen reverts the system to normal flexural behaviour. This, now compares with the beam with no FRP where the principles maximum stresses and strain are exhibited at the top section of the beam.

ABAQUS Results for Beam with the FRP Laminate Bonded Only at the Bottom
The results for the bottom side only externally bonded with FRP are shown appendix E. This set up exhibits maximum stresses and strain at the top of the beam, especially near the point of load application. This beam has the highest strain value of all the modelled beams. It also has the lowest principal maximum stress, implying rapture at very low stress level comparing to the other beams. Performance-wise, it has the least desirable flexural properties compared to all the 5 modelled beams.
Strengthening only one side of the beam and leaving the other sections has the impact compromising the strength of the three sections as only one sections appears to be robust. This leaves the other sides unbalanced to handle the other.

Parametric Studies Analysis
The peak load for the beam that is fully wrapped (EB-RC box) has the highest peak load followed by the U-wrapped beam. The results of the peak loads are summarized in table 5 below. The beam without the FRP strengthening has the least peak load. These results imply that using EB-FRP to strengthen reinforced beams leads to a significant increase in strength of the beam.

Table 5:Summary of parametric studies results
Parameter RC Beam EB-RC (box) EB-RC (U-shape) EB-RC (sides) EB-RC (bottom)
Peak load (kN) 175.5 203 199 187 176.5
Displacement at peck load ∆peak load (mm) 21 85.5 89 88.5 30
Increasing of peak load (%) – 15.6 13.4 6.5 0.57
Failure mode Flexural failure mode

The displacement values for the peak load are least for the case of non-strengthened beams. For all the strengthened beams, the one with the FRP sheets at the bottom has the least displacement at peak load. The results of peak load displacement point out at the fact that using FRP sheet to strengthen the beam changes their failure mode from brittle to ductile. Although, it would be anticipated the fully wrapped beam to have the highest value of the displacement at peak value (Naser, Hawileh and Abdalla); the case is different from the result obtained from FEA with U-wrapped beam being the most ductile.
The percentage increase in peak load is higher for the fully wrapped beam followed by the U-wrapped beam and least in the beam externally bonded at the bottom. The result of the percentage increase in peak load is summarized in table 5 above.

Overall Effect of EB-FRP on the Flexural Behaviour of Reinforced Beams
Using FRP laminates as strengthening agents has the effect of increasing the load bearing and stress resistance capacity of the reinforced concrete beam. The results show an increase in strength by 15.6% (with regards to size of peak load) for the fully wrapped beam and 13.4% for the U-wrapped beam. These values are significant in terms of strength enhancement. Also, using the FRP, especially, in the box and the U-shaped FRP arrangement reduces the extent of perfect deformation of the steel reinforcement bars for the RC beam. This is exhibited by the low reduced plastic strain in those two system set-ups. Strengthening the RC beam with the FRP laminates also affects the failure pattern assumed by the beam by shifting it from an abrupt brittle failure to a ductile failure. FRP laminates delay cracking of the beam during failure. By the stress points shifting to the FRP shells, the cracking in the beam is lessened.
However, it is important to note that this study only used one layer of FRP laminate and exploring the results with different numbers of layers, and various layer orientation will potentially yield different results. Based on experimental tests, increasing number of FRP laminates has the effect of increasing the strength capacity of the strengthened beam (Naser, Hawileh and Abdalla). Exploring the effect of different number of laminates using ABAQUS FE software presents an opportunity to further research.

CONCLUSION AND FUTURE WORKS
Conclusion
From the foregone, the evaluation of the flexural behaviour of strengthened reinforced concrete with externally bonded FRP has been done using ABAQUS finite element analysis software. From the research the following conclusions are made:
ABAQUS can be used to accurately to predict the flexural behaviour of reinforced concrete beam strengthened with EB-FRP.
Using ABAQUS in the numerical analysis of the flexural properties of EB-FRP strengthened RC beam is cost efficient solution than the experimental method.
High accuracy level using ABAQUS is dependents on the mesh sizes used in the analysis; more refined meshes yield accurate results, and better convergence to accurate results in ABAQUS is achieved through mesh sensitive analysis
The use of EB-FRP in strengthening reinforced concrete beams significantly improves the flexural strength of the by 15.6%
Using EB-FRP to strengthen concrete shifts the failure from a brittle failure to a ductile failure
Variation in the arrangement of the FRP laminates on the surface of the concrete beam or the area of concrete beam bonded with FRP laminate affect the amount of strength enhancement realized in the system
A U-wrapped/bonded beam exhibited the highest ductility and can offer reasonable solution in case of there is a limit access for the four sides of the RC beam.
Reinforced concrete beam with all the four sides bonded with laminates performs better in flexure and the performances reduces as the number of sides bonded with FRP laminate reduces.
The flexural performance of EB-FRP strengthened reinforced beams reduces with the reduction in the number of faces that are bonded with the laminates.
The beam that has only one sides strengthened shows the least improvement in terms of the strength enhancement; from ABAQUS analysis, its performance is the least among the 5 modelled beams. The advantage it has over the unbonded beam is the delayed rapture
The failure mode of the EB-FRP is through cracking/rapturing within the tension section of the beam for a fully bonded and U-shape bonded beams
At failure, the reinforcement bars for the RC beams strengthened with FRP laminates in the box and U-shaped arrangement experiences the least plastic strain which consequently means the least permanent deformation

Future Works
This research has presented key opportunities that lay ground for future research studies. As such recommendation is made for the following future works
It is recommended that further finite element analysis studies should be carried out to study the flexural behaviour when different layers of laminates are used instead two layer as was the case with this research.
Recommendation is also made to carry out numerical analysis with FRP laminates with different thickness and orientation and evaluate the effect on the flexural behaviour of reinforced concrete beam.
Investigation the effect of reinforcement ratios and concrete grades on the EB-FRP strengthen efficiency.

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