Cyclic Behavior of FRP Strengthened Beam-Column Joints under Various Concrete Damage Levels

This paper is intended to examine the efficiency of utilizing the FRP composite material with an externally bonded technique in enhancing the behavior of the damaged B-C joints and controlling their failure mode using the NLFEA approach. At first, the modeled Beam-Column joint was validated as per the previously-attained experimentally-attained results. Later, the model was widened to experiment with the impact of axial-column load and the concrete compressive strength on the reinforced and un-reinforced models with FRP. To run the experiment, there were three cases of applying the axial column load: no load applied (0%), applying 25%, applying 50%, and applying 75%, while the concrete compressive strength degradation level was (0% damage), (25% damage), and (50% damage). All models were evaluated for structural performance, considering: the failure mode, stresses distribution, and the ultimate capacities in pulling and pushing with its corresponding displacements. However, the horizontal load-displacement hysteretic loops and envelopes, stiffness degradation, displacement ductility, and energy dissipation were reported. The experimental results revealed that using FRP to externally-reinforce B-C joints improved overall cyclic performance, as the FRP caused a rise in the ultimate load capacity, horizontal displacement, ductility of displacement, and displacement energy dissipation, while it slowed down the stiffness degradation. In addition, the FRP material converted the failure mode of the region between the joint and column from brittle to ductile due to the formation of a plastic hinge only on the side of the beam when the axial column load exceeded 25%. It must be noticed that when the column’s axial load is less than 25%, the ultimate capacity of axial load and resultant deflection is solely improved. However, it has been stated that increasing the column’s axial loading by 25% increases the resulting stiffness degradation by 3% for undamaged joints, which further increases by 16% for each increased damage level. In contrast, the absorbed energy is increased by 170% under axial loading, increasing by 25%, which is reduced to only one-fourth under the various damage levels. Generally, the resulting observations help specialized engineers retrofit appropriate B-C joints in already-standing buildings due to their accuracy.


Introduction
Reinforced concrete (RC) constructions are subjected to deterioration due to many reasons, such as environmental reasons (weathering, reinforcement corrosion, environmental conditions, and chemical attacks) or putting more loads on the construction beyond the normal capacity of the construction, such as increasing the number of floors [1]. As a result, it has been imperative to run retrofitting and maintenance for structural elements, for example, beam elements (or girders), column elements (or piers), beam joints (B-C) joints, or slabs [2][3][4][5]. Many countries have issued obligatory instructions and regulations to tion, which was not ductile in the first place. Lately, Antonopoulos and Triantafillou [41] broadly investigated, experimentally, (18) B-C joint specimens in an already-standing framed structure, having no essential details. Moreover, the study concentrated on: the axial load level in columns; the existence of the joint panel's steel reinforcement, transversally and longitudinally; the FRP composite's type, shape, and quantity that existed in beams and columns, in addition to the existence of shear reinforcement for confinement purposes. Lastly, the influence of FRP laminates with the impact of textile-reinforced mortar (TRM) has been examined by Al-Salloum et al. [42], where TRM was a reinforcing material used to strengthen the B-C joints that were deficient seismically. The outcomes indicated that sufficient layers of TRM might considerably increase the deformation capacity and shear strength of joints with TRM more than those with CFRP/GFRP composites.
However, the behavior of externally beam-column joints under the effect of strengthening by different CFRP composites schemes has been evaluated using the ABAQUS program by Sinaei et al. [43]. In contrast, a combined analytical and numerical study has been carried out by Mosallam et al. [44] for the behavior of internal joints under the effect of gravity and low cyclic loading retrofitted with different types of fiber-reinforced-polymeric (FRP) composite laminates and hybrid connectors. Moreover, due to the difficulties in modeling such problems, the Vector2 program has been utilized to assess the shear behavior of joints under seismic behavior in a real structure [45]. Not many researchers adopted the FE method to experiment with the behavior of reinforced and repaired B-C joints using FRP materials [45][46][47][48][49][50][51][52]. This is because it is rather complicated to simulate the concrete's shear cracks in the externally-strengthened elements, particularly in the joint region and the damaged concrete-FRP composite bond area. Since the concrete cracking mainly causes the slippage of FRP-concrete bond, it is essential to precisely model such cracks, using FEM, to describe the strengthened/repaired joints' behavior. Most studies omitted the bond-slip behavior of the bond between concrete and FRP, especially when debonding failure was simulated. There has been a good agreement between experimental and theoretically-obtained ones regarding the patterns of cracking; or distribution of strains in fiber laminates [45][46][47][48][49][50][51][52][53].
Reinforced concrete B-C joints risk deterioration due to external environmental attacks. That is because this type of attack degrades the joints' structural capacity. As a result, the B-C joints must be externally strengthened with high-quality composite composites, such as FRP. This strengthening method consists of confining (or wrapping) the B-C joints from the outer side by wraps of FRP. This method restores the joint's structural capacity and prevents brittle failure, which is abrupt. The NLFEA method has been used in this numerical investigation to create comprehended guidelines regarding internally strengthening concrete compressive strength degradation damaged B-C joints with FRP since the available design codes suffer a severe shortage. This is achieved considering the effectiveness of both the axial column load and the level of damage by concrete compressive strength degradation. As a result, the study has adopted the Non-Linear Finite Element Analysis (NLFEA) modeling to predict patterns of cracks and seismic behavior and the type of failure of the environmentally-damaged models that were reinforced, from the external side, with FRP. Relationships representing the concrete's mechanical characteristics were used in simulating the beam-column joint's response. Further, adequate models were devised to investigate damaged/un-damaged concrete, the reinforcing bars of steel, the bond between concrete and steel, and experimental conditions. The present experiment started with validating the model with respect to Shannag and Alhassan's outcomes [33]. After that, the validated models were expanded to investigate the behavior of unstrengthened and strengthened joints under the following sensitive parameters: the axial load of the column (0%, 25%, 50%, and 75%), and the concrete compressive strength degradation level was of (0% damage), (25% damage), and (50% damage).

Experimental Program Overview
In a study presented by Shannag and Alhassan [33], RC B-C joints were prepared and cured, as shown in Figure 1. The specimen's geometry represented the inflection points between the columns and the ones between beams (i.e., null-moment points) at the column-beam mid-span location, under cyclic loading. However, steel-plate supports were fixed at the bottom side of the column, where the top side was left free to permit the column of relative drift, while the beam's two-end were simply supported by rollers ( Figure 1). In addition, the concrete of 27 MPa compressive strength was used, whereas the yielding strength of steel bars-in deformation-was 310 MPa. The column's loads were added utilizing two hydraulic actuators with a compression capacity of 160 kN and tensile capacity of 90 kN ( Figure 1). An adequate cyclic loading history was applied to simulate earthquake activity (Figure 1). Constr. Mater. 2023, 4, FOR PEER REVIEW 4 load of the column (0%, 25%, 50%, and 75%), and the concrete compressive strength degradation level was of (0% damage), (25% damage), and (50% damage).

Experimental Program Overview
In a study presented by Shannag and Alhassan [33], RC B-C joints were prepared and cured, as shown in Figure 1. The specimen's geometry represented the inflection points between the columns and the ones between beams (i.e., null-moment points) at the column-beam mid-span location, under cyclic loading. However, steel-plate supports were fixed at the bottom side of the column, where the top side was left free to permit the column of relative drift, while the beam's two-end were simply supported by rollers ( Figure  1). In addition, the concrete of 27 MPa compressive strength was used, whereas the yielding strength of steel bars-in deformation-was 310 MPa. The column's loads were added utilizing two hydraulic actuators with a compression capacity of 160 kN and tensile capacity of 90 kN ( Figure 1). An adequate cyclic loading history was applied to simulate earthquake activity (Figure 1).

NLFEA Description
NLFEA method is highly efficient in the simulation of RC structures, regardless of their complexity, as it saves costs, time, materials, and labor. Through highly precise simulation, the designer can reveal any design mistakes and correct them before the actual execution. Moreover, the design can be modified by adjusting any variable (loads, displacements, stresses, strains, etc.) to monitor its effect at any location and under various situations. For more accurate simulations, the ANSYS program package (a high-fidelity, 3D FEA software) [54] has been employed to predict the specimen's seismic performance, as elaborated in Table 1. Afterward, the models were enlarged to monitor the performance of the models, with/without FRP reinforcement, was impacted by: the axial load level in the column (0%, 25%, 50%, and 75%), and the concrete compressive strength degradation level was of (0% damage), (25% damage), and (50% damage), as shown in Table 1. As per the code ACI 318-08 [55], the column's axial load level of 0% corresponds to 0.0 kN; 25% corresponds to 63.5 kN, 50% corresponds to127.0 kN, and 75% corresponds to190.5 kN.

NLFEA Description
NLFEA method is highly efficient in the simulation of RC structures, regardless of their complexity, as it saves costs, time, materials, and labor. Through highly precise simulation, the designer can reveal any design mistakes and correct them before the actual execution. Moreover, the design can be modified by adjusting any variable (loads, displacements, stresses, strains, etc.) to monitor its effect at any location and under various situations. For more accurate simulations, the ANSYS program package (a high-fidelity, 3D FEA software) [54] has been employed to predict the specimen's seismic performance, as elaborated in Table 1. Afterward, the models were enlarged to monitor the performance of the models, with/without FRP reinforcement, was impacted by: the axial load level in the column (0%, 25%, 50%, and 75%), and the concrete compressive strength degradation level was of (0% damage), (25% damage), and (50% damage), as shown in Table 1. As per the code ACI 318-08 [55], the column's axial load level of 0% corresponds to 0.0 kN; 25% corresponds to 63.5 kN, 50% corresponds to 127.0 kN, and 75% corresponds to 190.5 kN.

Modelling of B-C Joint Using NLFEA
Upon constructing the modeled joints using NLFEA, the following factors have been considered: the concrete material nonlinearity (Figure 2), the elastoplastic behavior of steel reinforcement (Figure 2), added to the elastic response of FRP composites, as shown in Figure 2). Besides utilizing the ANSYS program package with elements of higher orders [54]. The procedures began with validating the simulated FE B-C joint with respect to the experimentally-achieved results of Shannag and Alhassan [28]. Next, the models were enlarged to study the effect of other variables: the axial load level and the damage extent. When preparing the models, the values of the concrete's compressive strength were: 40, 30, and 20 MPa, while the concrete's tensile strength was at values of: 2.6, 1.9, and 1.4 MPa, which were set at levels of (0% damage), (25% damage), and (50% damage), respectively, as illustrated in Figure 3. The models' detailed geometry and reinforcement are demonstrated in Figure 1. The best suitable dimensions of the mesh were employed in the modeling process post carrying out the convergence test with a satisfactorily-accurate numerical solution. It was affirmed by the results obtained in a reasonable processing time [33].  For a more realistic simulation of B-C models, boundary conditions were set. The first boundary was to apply a hinge on the column's bottom end and free movement at their end; the beams were also equipped with roller constraints, at the center point of supporting steel plates, on the right and the left ( Figure 1). The second boundary was applying an axial load, as a first loading stage, on the column's free edge where the cyclic loading was applied to simulate the earthquake load ( Figure 1).

Material Modeling
Concrete: the concrete mix was prepared to utilize SOLID65, an eight-node solid element that can move at every node in all directions. Furthermore, Solid65 can mimic the state of crushing, the development of cracks, and plastic deformation in all directions. However, the Solid65 element can capture the crushing failure in the concrete material but has been ignored since this case has not been monitored experimentally when applying the load [45][46][47][48][49][50][51][52]. Therefore, the joint models' tensile strains are governed by the resulting cracks and the ultimate structural element capacity [45][46][47][48][49][50][51][52]. The value of 0.2 has been selected for Poisson's ratio for this experiment, as the usually-used value ranges between 0.15 and 0.22 [58]. The concrete elastic modulus, compressive and tensile strength have been determined to capture the resulted failure in the concrete material as depicted in (Figure 3) [59]. The shear transfer coefficient (βt) defines the condition of the side of Constr. Mater. 2023, 4, FOR PEER REVIEW 6 Strain (e c ), me . (a) Concrete compressive strength [56] (b) Concrete tensile strength [33] (c) CFRP [57]  For a more realistic simulation of B-C models, boundary conditions were set. The first boundary was to apply a hinge on the column's bottom end and free movement at their end; the beams were also equipped with roller constraints, at the center point of supporting steel plates, on the right and the left (Figure 1). The second boundary was applying an axial load, as a first loading stage, on the column's free edge where the cyclic loading was applied to simulate the earthquake load ( Figure 1).

Material Modeling
Concrete: the concrete mix was prepared to utilize SOLID65, an eight-node solid element that can move at every node in all directions. Furthermore, Solid65 can mimic the state of crushing, the development of cracks, and plastic deformation in all directions. However, the Solid65 element can capture the crushing failure in the concrete material but has been ignored since this case has not been monitored experimentally when applying the load [45][46][47][48][49][50][51][52]. Therefore, the joint models' tensile strains are governed by the resulting cracks and the ultimate structural element capacity [45][46][47][48][49][50][51][52]. The value of 0.2 has been selected for Poisson's ratio for this experiment, as the usually-used value ranges between 0.15 and 0.22 [58]. The concrete elastic modulus, compressive and tensile strength have been determined to capture the resulted failure in the concrete material as depicted in (Figure 3) [59]. The shear transfer coefficient (βt) defines the condition of the side of For a more realistic simulation of B-C models, boundary conditions were set. The first boundary was to apply a hinge on the column's bottom end and free movement at their end; the beams were also equipped with roller constraints, at the center point of supporting steel plates, on the right and the left ( Figure 1). The second boundary was applying an axial load, as a first loading stage, on the column's free edge where the cyclic loading was applied to simulate the earthquake load ( Figure 1).

Material Modeling
Concrete: the concrete mix was prepared to utilize SOLID65, an eight-node solid element that can move at every node in all directions. Furthermore, Solid65 can mimic the state of crushing, the development of cracks, and plastic deformation in all directions. However, the Solid65 element can capture the crushing failure in the concrete material but has been ignored since this case has not been monitored experimentally when applying the load [45][46][47][48][49][50][51][52]. Therefore, the joint models' tensile strains are governed by the resulting cracks and the ultimate structural element capacity [45][46][47][48][49][50][51][52]. The value of 0.2 has been selected for Poisson's ratio for this experiment, as the usually-used value ranges between 0.15 and 0.22 [58]. The concrete elastic modulus, compressive and tensile strength have been determined to capture the resulted failure in the concrete material as depicted in (Figure 3) [59]. The shear transfer coefficient (βt) defines the condition of the side of cracking with 0.2 [60,61]. For more precise FEM models, the stress-strain behavior of concrete has been modeled by Kent and Park [56], who presented a descriptive model to describe the stress-strain relationship for concrete ( Figure 2).
Steel: The Link180 element has been utilized to model the steel reinforcement, which can plastically deform and move freely on all sides at all nodes. The bond at the concretesteel interface has been assumed to be perfect since the loss in the damaged concrete's strength was negligible [62]. The reinforcing steel bars had similar tensions and compressions, with an elastic-plastic property of 200 GPa and 0.3 for the elastic modulus and Poisson's ratio, respectively, as in Figure 2.
Steel plates: plates were modeled using SOLID45, a brick element with eight nodes capable of moving freely in every orientation. A linear elastic behavior with 200 GPa modulus of elasticity and 0.3 Poisson's ratio has been selected for modeling the element's behavior.
FRP composites: internal FRP laminates were modeled utilizing SOLID186, which handled up to 250 layers of FRP in many orientations. In Figure 2, the FRP laminates' mechanical properties are illustrated. The FRP laminates were presumably elastic, linear, and orthotropic, with a 0.35 value for Poisson's ratio [63]. The perpendicular-direction modulus of elasticity was neglected, i.e., considered a unidirectional fiber. However, the interface bond between the FRP and concrete materials was assumed to be perfect.

Data Entry and Failure Criteria
The SOLID65 element was used to capture the resulting degradation in the concrete and steel material. However, three sets of real constants were introduced that could capture the real behavior of the studied joints under various cases. Lastly, the fourth constant set included the direction and thickness of the FRP composites. However, a mesh size of 25 mm was utilized for all models, including control models, damaged models, and those strengthened with FRP. It was specified by adopting a convergence approach. In Figure 1, the joint models that have been discretized are illustrated. Hinge supports were assumed at both column ends (Ux and Uy equal to 0), while roller supports were the beams' boundary conditions (Uy equal to 0) at the two ends of the beam. The first step of the process was to add the axial column load. Later, the horizontally-applied load was simulated as a displacement control to capture the descending part of the load-displacement curve. However, loading has been applied in substeps to avoid abrupt failure, which might cause the solution to diverge, stabilizing the analyzing procedure. As stipulated, the ANSYS software [54] discretized the applied load automatically into steps that could be entered manually, where the stiffness matrix is recalculated at the end of each step. However, the iterative Newton-Raphson equilibrium procedure with 0.001 tolerance. As the tensile and compressive stresses govern the failure criterion of concrete, the multi-linear isotropic (MISO) plasticity has been used along with Kent and Park model [56]. As stipulated, failure usually occurs if the prime compressive or tensile stresses, in all orientations, emerge out of the failure surface.

Control B-C Connection
Results of the horizontal load versus the net drift hysteresis loops have been plotted along with NLFEA results and compared as illustrated in Figure 4, where a significant agreement has been reached with the experimentally-obtained loops in terms of the ultimate capacity and net drift values. So, the experimental B-C joint models' capability of reducing seismic behavior and evaluating their mechanical response is validated. However, it is observed that S8 specimens have asymmetrical hysteretic loop behavior due to the higher induced strain rate, where it undergoes a high drift value under a lower loading stage compared to other validated specimens, and this lower rate resulted in a software divergent within one cycle causing the unusual behavior appeared in S8 specimen. In detail, the following sections discuss the predictions of the damaged, strengthened-with-FRP joint model's cyclic behavior. The generated-by-NLFEA failure modes were in big agreement with the achieved experimentally-obtained results ( Figure 5). It has been shown that the strength of the modeled joint area degraded. In contrast, the beam model showed inelasticity, with little hairline-shaped cracking. This identified mechanism is governed based on the strong column weak beam concept, which produced a pre-mature joint failure. divergent within one cycle causing the unusual behavior appeared in S8 specimen. In detail, the following sections discuss the predictions of the damaged, strengthened-with-FRP joint model's cyclic behavior. The generated-by-NLFEA failure modes were in big agreement with the achieved experimentally-obtained results ( Figure 5). It has been shown that the strength of the modeled joint area degraded. In contrast, the beam model showed inelasticity, with little hairline-shaped cracking. This identified mechanism is governed based on the strong column weak beam concept, which produced a pre-mature joint failure.

FRP Strengthened B-C Connection
Eight full-scaled samples of interior joints between the beam and column have been tested by Khaled et al. [57] that were designed in compliance with the code (ACI 318-14) [59]. Low-frequency full-cyclic and gravity loads were applied to a sub-assembly of the samples. The beams were dimensioned as 254 mm × 406 mm. The beams were reinforced, in a longitudinal orientation, along with installing four 19 mm bars on both of the beam's ends, at the top and bottom, and transversely strengthened with (13) mm-stirrups of steel that were evenly put at 102 mm spacing between them on the face's center of the column located at a 381 mm distance from the edge of the beam. In contrast, the remaining were placed at a 76 mm spacing. The column has a 254 × 406 mm 2 cross-section and is reinforced at the top and bottom ends with four 19 mm steel, resulting in approximately 2% reinforcement ratio with a total height that is fully confined stirrups of 13 mm length, having a 76 mm spacing center-to-center. To elaborate more on the precision of NLFEA modeling of reinforced B-C joint where the load versus the drift were compared as per Figure 4b, where a good agreement was captured to an extent, with the results achieved by Khaled et al. [57] besides comparing the stress contours in Figure 6 where the resulting differences were less than 15% that could be considered an acceptable value. However, results were compared as illustrated in Table 2. In addition, Figures 4b and 6 show that NLFEA predicted, with high accuracy, the ultimate load and load-drift hysteresis response until failure. However, in this study, only the effect of utilizing one FRP layer was presented since the literature performed for validation does not examine the multi-layer FRP effect besides the resulting enhancement being good and feasible. Meanwhile, the effect of multi-layers could be further investigated after ensuring that no FRP debonding will occur between the layers.

FRP Strengthened B-C Connection
Eight full-scaled samples of interior joints between the beam and column have been tested by Khaled et al. [57] that were designed in compliance with the code (ACI 318-14) [59]. Low-frequency full-cyclic and gravity loads were applied to a sub-assembly of the samples. The beams were dimensioned as 254 mm × 406 mm. The beams were reinforced, in a longitudinal orientation, along with installing four 19 mm bars on both of the beam's ends, at the top and bottom, and transversely strengthened with (13) mm-stirrups of steel that were evenly put at 102 mm spacing between them on the face's center of the column located at a 381 mm distance from the edge of the beam. In contrast, the remaining were placed at a 76 mm spacing. The column has a 254 × 406 mm 2 cross-section and is reinforced at the top and bottom ends with four 19 mm steel, resulting in approximately 2% reinforcement ratio with a total height that is fully confined stirrups of 13 mm length, having a 76 mm spacing center-to-center. To elaborate more on the precision of NLFEA modeling of reinforced B-C joint where the load versus the drift were compared as per Figure 4b, where a good agreement was captured to an extent, with the results achieved by Khaled et al. [57] besides comparing the stress contours in Figure 6 where the resulting differences were less than 15% that could be considered an acceptable value. However, results were compared as illustrated in Table 2. In addition, Figures 4b and 6 show that NLFEA predicted, with high accuracy, the ultimate load and load-drift hysteresis response until failure. However, in this study, only the effect of utilizing one FRP layer was presented since the literature performed for validation does not examine the multi-layer FRP effect besides the resulting enhancement being good and feasible. Meanwhile, the effect of multi-layers could be further investigated after ensuring that no FRP debonding will occur between the layers.

Stress Contours
The theoretically-obtained stress contours of the expanded joint models are illus- Figure 6. Stress contours validation.

Stress Contours
The theoretically-obtained stress contours of the expanded joint models are illustrated in Figure 7; specimen J25FRP1D0 is equipped with one layer of FRP as reinforcement, with an axial loading level of 25%. The control specimen had the initial diagonal cracks at the joint's corners, at the top and bottom, in the pulling phase of loading. Generally, flexural cracks are initiated at the tension zone of the joint's furthest fibers, around the column's ends; later, the cracks expand flexural cracks sideways. Further, evenly-shaped cracks emerged in the pushing and pulling loading directions, along with an increment in the displacement values. Inspecting Figure 6 shows that the joint area encountered a degradation in strength, whereas the beam stayed inelastic with the emergence of some tiny cracks. This failure is called the (weak-column strong-beam) failure, which results in an abrupt failure of the joint model. Flexural cracks extend up to 650 mm from the edge of the column along the beam. Conversely, the un-reinforced (control) B-C joint witnessed flexural cracks extending across the beam to 300 mm from the column's edge. During the pushing phase, cracks emerged in the same model but in the opposite diagonal direction. So, the control model exhibited a significant vulnerability of the joint panel zone and failed in shear. However, the joint model's behavior maintained its elasticity without plastic hinging. Figure 7 reveals that the steel's stress at failure was 310 MPa (matching the point of yielding). Lastly, Figure 7 shows that the stress failure of the FRP was 3086 MPa (almost 81% of stress at rupture of FRP). This indicates the effectiveness of FRP jacketing in availing better protection to the joint panel and externally strengthening the joint model. However, the presence of FRP composite in the most-critical location resulted in eliminating the resulting flexural crack and suppressing the brittle type of failure by forming a plastic hinge at the side face of the beam ending up with a ductile type of failure. So, the behavior of a strengthened-with-FRP-jacketing joint model showed improved cyclic performance as the joint panel's failure took place in the beam. In this case, the load-carrying capacity of the joint is mainly controlled by its flexural capacity.

The Load Versus Displacement Hysteretic Loops
The load versus the horizontal displacement is plotted in Figure 8 Figure 10 indicates that the unstrengthened joint with zero axial loadings modeled joint, tested at 50% damage level J0FRP0D50, experiences lower load and displacement values. In contrast, the model J0FRP0D0 (unreinforced, no axial load, and 0% damage) (Figure 8) had the most significant strength and correspondent displacement, compared to joints J0FRP0D25 ( Figure 8) and J0FRP0D50, despite the inadequately-imposed lateral reinforcement in turning the failure to occur within the beam. Horizontal load-displacement loops of the reinforced joints showed a significantly improved performance in horizontal load and correspondent displacements (Figures 8-10) because the region was confined with FRP, as it availed internal arresting mechanism of cracks besides increasing the ductility capability after cracking occurs. Moreover, the loops are also affected by the axial loading level, where the column's compressive stress is improved under increasing the loading level (Figure 8 through Figure  10), which resulted in initiating cracking in the joint tensile concrete, causing a strength

The Load Versus Displacement Hysteretic Loops
The load versus the horizontal displacement is plotted in Figure 8 (0% damage), Figure 9 (28% damage), and Figure 10 (50% damage). Figure 10 indicates that the unstrengthened joint with zero axial loadings modeled joint, tested at 50% damage level J0FRP0D50, experiences lower load and displacement values. In contrast, the model J0FRP0D0 (un-reinforced, no axial load, and 0% damage) (Figure 8) had the most significant strength and correspondent displacement, compared to joints J0FRP0D25 ( Figure 8) and J0FRP0D50, despite the inadequately-imposed lateral reinforcement in turning the failure to occur within the beam. Horizontal load-displacement loops of the reinforced joints showed a significantly improved performance in horizontal load and correspondent displacements (Figures 8-10) because the region was confined with FRP, as it availed internal arresting mechanism of cracks besides increasing the ductility capability after cracking occurs. Moreover, the loops are also affected by the axial loading level, where the column's compressive stress is improved under increasing the loading level (Figure 8 through Figure 10), which resulted in initiating cracking in the joint tensile concrete, causing a strength degradation. Furthermore, Figure 11 exhibits the modeled joint's load-displacement envelopes, where the highest load and correspondent displacement values are obtained in every half-cycle of loading (push-pull). Figure 11 revealed a proportional relationship between the axial loading level and the load displacement, but the displacement lessened when the level of damage was increased.
Constr. Mater. 2023, 4, FOR PEER REVIEW 12 degradation. Furthermore, Figure 11 exhibits the modeled joint's load-displacement envelopes, where the highest load and correspondent displacement values are obtained in every half-cycle of loading (push-pull). Figure 11 revealed a proportional relationship between the axial loading level and the load displacement, but the displacement lessened when the level of damage was increased.

Horizontal Displacement Versus Steel and FRP Strain Envelopes
The obtained strain data of the steel reinforcement were utilized for the modeled joints near the interface between the joint and the beam. The strain-displacement envelopes of steel rebar are graphed in Figure 12. All of the joint specimens without reinforcement (excluding J50FRP0D0, J75FRP0D0, and J75FRP0D25) fail before steel yielding occurs (Table 2), as per the B-C joint's design criteria. It has been observed that the whole reinforced-with-FRP joints failed at the beam's highest capacity, where the steel rebar's tensile strain was significantly higher than the threshold of the yielding strain. Moreover, the displacement versus the strain envelopes for FRP-strengthened joints are illustrated in Figure 13. By inspecting Figure 13, it is observed that the FRP composite proved efficient as the joint's horizontal displacement was: 8.0 mm, 6.5 mm, and 5.9 mm when the joint was exposed to damage levels of 0%, 25%, and 50%, respectively. This indicates that the concrete was negatively affected because the damage level made the FRP carry the applied load at the early stages. Furthermore, Table 2 shows that the FRP has good effectiveness by increasing the axial load by 52%, 73%, 92%, and 97% of the maximum FRP strain of 15,000 µε corresponds to axial loading levels of 0%, 25%, 50%, and 75%, respectively. The damage level decreased the strain of FRP by 11% at a 25% damage level and 22% at a 50% damage level. damage decreased the load by 14.6% and displacement by 13.7%, at 25% damage, while 50% damage decreased the load by 30.2% and displacement by 22.9%. Further, FRPstrengthened joints have enhanced loading and displacement capacities (compared to the un-damaged joint sample): 104%, 83% at 0% damage level; 82%, 34% at 25% damage; and 52%, 23% at 50% damage.

Horizontal Displacement Versus Steel and FRP Strain Envelopes
The obtained strain data of the steel reinforcement were utilized for the modeled joints near the interface between the joint and the beam. The strain-displacement envelopes of steel rebar are graphed in Figure 12. All of the joint specimens without reinforcement (excluding J50FRP0D0, J75FRP0D0, and J75FRP0D25) fail before steel yielding occurs (Table 2), as per the B-C joint's design criteria. It has been observed that the whole reinforced-with-FRP joints failed at the beam's highest capacity, where the steel rebar's tensile strain was significantly higher than the threshold of the yielding strain. Moreover, the displacement versus the strain envelopes for FRP-strengthened joints are illustrated in Figure 13. By inspecting Figure 13, it is observed that the FRP composite proved efficient as the joint's horizontal displacement was: 8.0 mm, 6.5 mm, and 5.9 mm when the joint was exposed to damage levels of 0%, 25%, and 50%, respectively. This indicates that the concrete was negatively affected because the damage level made the FRP carry the applied load at the early stages. Furthermore, Table 2 shows that the FRP has good effectiveness by increasing the axial load by 52%, 73%, 92%, and 97% of the maximum FRP strain of 15,000 με corresponds to axial loading levels of 0%, 25%, 50%, and 75%, respectively. The damage level decreased the strain of FRP by 11% at a 25% damage level and 22% at a 50% damage level.

Displacement Ductility and Energy Dissipation
The ratio between the ultimate and yield displacements ( ) is known as the displacement ductility index. Strengthened NLFEA models' values of displacement ductility are shown in Table 3, from which it can be seen that the displacement ductility of the models was 0, indicating a fragile seismic behavior. This does include the models: J50FRP0D0, J75FRP0D0, and J75FRP0D25. The reason behind this bad behavior is that failures occur before steel yielding is reached. However, the strengthened-with-FRP joint models showed higher values of displacement ductility (twice as much) than the unstrengthened models (i.e., J50FRP0D0, J75FRP0D0, and J75FRP0D25). This was because the strengthened models were perfectly confined with FRP wraps, which made the joints' failure ductile where a plastic hinge is initiated within the beam element. Moreover, Table  3 shows that there was an enhancement in the displacement ductility due to applying axial load (in comparison with a strengthened joint specimen with 0% axial load) by; 95%, 185%, and 340% corresponding to axial loading levels of 25%, 50%, and 75%, respectively. Further, the ductility is reduced by 45% at 25% and 60% at 50% under the different damage levels.

Displacement Ductility and Energy Dissipation
The ratio between the ultimate and yield displacements ( dm dy ) is known as the displacement ductility index. Strengthened NLFEA models' values of displacement ductility are shown in Table 3, from which it can be seen that the displacement ductility of the models was 0, indicating a fragile seismic behavior. This does include the models: J50FRP0D0, J75FRP0D0, and J75FRP0D25. The reason behind this bad behavior is that failures occur before steel yielding is reached. However, the strengthened-with-FRP joint models showed higher values of displacement ductility (twice as much) than the un-strengthened models (i.e., J50FRP0D0, J75FRP0D0, and J75FRP0D25). This was because the strengthened models were perfectly confined with FRP wraps, which made the joints' failure ductile where a plastic hinge is initiated within the beam element. Moreover, Table 3 shows that there was an enhancement in the displacement ductility due to applying axial load (in comparison with a strengthened joint specimen with 0% axial load) by; 95%, 185%, and 340% corresponding to axial loading levels of 25%, 50%, and 75%, respectively. Further, the ductility is reduced by 45% at 25% and 60% at 50% under the different damage levels.
Energy dissipation is an essential criterion to evaluate a B-C joint's performance. This criterion measures the energy lost by the joint before the system de-stabilizes. B-C joints lose considerable energy due to inelastic deformation, which minimizes the amount of dissipated energy, and ensures structural safety. Energy dissipation is determined by computing the constrained area under the total load-displacement envelopes. Table 3 exhibits the energy dissipated by the joint models. The un-reinforced joint models had a fairly-low energy dissipation, as indicated by the little constrained areas under the horizontal load-displacement hysteretic loops (Figures 8-10). The amounts of energy dissipated by all the joint models are shown in Figure 14. It must be mentioned that, in the early loading stage, the joints' cumulative values of energy dissipation were so close to each other. However, when the loading exceeded five cycles, the values of energy dissipation increased considerably. Meanwhile, energy dissipation increased under increasing the loading level (compared to joint under an axial load of 0%) by 200%, 442%, and 583% when exposed to axial load: 25%, 50%, and 75%, respectively. Further, the level of damage reduced the energy dissipation by 13.7% at a 25% damage level and 22.2% at a 50% damage level. On the other hand, FRP composites substantially upgraded the load and displacement by 81% at 0% damage level, 35% at 25% damage level, and 22% at 50% damage level. These values were much better than those of the un-reinforced models, reflecting an improvement in energy dissipation and seismic behavior. Further, FRP composites absorb energy in an effective manner, decreasing load transfer to other members. The strengthened models' energy dissipation was nearly 4.7 times more than the un-reinforced one, as illustrated in Table 3. The optimum energy dissipation capacity was reached for the strengthened joints with 75% axial load since they had larger displacement and loading capacities. Moreover, Table 3 shows that increasing the loading level increases the energy dissipation capacity; when the axial load was: 25%, 50%, and 75%, the energy dissipation raised by: 185%, 322%, and 413%, respectively. In addition, the damage level decreased the energy dissipation, whereas 25% reduced the dissipated energy by 33%, while 50% reduced dissipation by 51%. Further, FRP composites absorb energy in an effective manner, decreasing load transfer to other members. The strengthened models' energy dissipation was nearly 4.7 times more than the un-reinforced one, as illustrated in Table 3. The optimum energy dissipation capacity was reached for the strengthened joints with 75% axial load since they had larger displacement and loading capacities. Moreover, Table 3 shows that increasing the loading level increases the energy dissipation capacity; when the axial load was: 25%, 50%, and 75%, the energy dissipation raised by: 185%, 322%, and 413%, respectively. In addition, the damage level decreased the energy dissipation, whereas 25% reduced the dissipated energy by 33%, while 50% reduced dissipation by 51%.

Secant Stiffness Degradation and Damping Factor
The resulting degradation in the secant stiffness has been qualitatively measured for the B-C joints in every cycle by plotting every load-displacement loop envelope. The sum

Secant Stiffness Degradation and Damping Factor
The resulting degradation in the secant stiffness has been qualitatively measured for the B-C joints in every cycle by plotting every load-displacement loop envelope. The sum of the maximum reached load in pushing-pulling is divided by the resulting displacements representing the slope of the initial line at each cycle. Therefore, the joint's cyclic stiffness is calculated as per Equation (1) as follows: where: F + i and F − i are the maximum reached loads in positive and negative directions for each cycle and the corresponding displacements at each cycle i. Figure 15 shows that un-reinforced joints had a drastic degradation in secant stiffness due to the newly initiated cracks at each cycle; that is referred to as the joints' critical reinforcement details, which reduced the concrete strength, leading to softening. The secant stiffness values' consistent decrease is pronounced in the strengthened joints because of the perfect confinement with FRP, as this strengthening method eliminated the emergence of major cracks in the joint area and increased the initial stiffness value. The resulting stiffness degradation is stabilized under the increased loading at each. That is referred to as increasing the axial load, enhancing the column's compressive stress, and decreasing the diagonal tensile stresses. Moreover, it could be revealed in Figure 15 that stiffness degradation increased minorly under increasing the axial loading level (compared to strengthened joint under 0% of axial load) by 3%, 6%, and 9%, corresponding to an axial loading level of 25%, 50%, and 75%, respectively. In addition, the degradation is reduced by 19% and 38% at 25% and 50% under the various damage levels.
under the various damage levels.
Meanwhile, dividing the energy dissipation value at the end of each cycle by 2π times the elastic strain energy is generally known as the equivalent damping factor for the hysteresis loops, which is stored within a linear elastic system as per Equation (2) where Ei denotes the energy dissipated, Fmi is the load value, and Dmi is the peak displacements for each loading cycle i. The calculated damping factor for each cycle is plotted in Figure 16 for all simulated joints. Observing Figure 16 revealed that strengthening the B-C joints with FRP material increases the damping factor significantly compared to the unstrengthened ones. That is interpreted by the fact that the strengthened specimens have enhanced deformability. Meanwhile, the rising damping factor enhanced seismic performance when five loading cycles were reached. However, strengthening the B-C joint with FRP composites has been found to improve the overall performance, including all of its aspects. Consequently, such joints were the best because they were able to convey the failure pattern to the connected area.   Meanwhile, dividing the energy dissipation value at the end of each cycle by 2π times the elastic strain energy is generally known as the equivalent damping factor for the hysteresis loops, which is stored within a linear elastic system as per Equation (2) [64]: where E i denotes the energy dissipated, F mi is the load value, and D mi is the peak displacements for each loading cycle i.
The calculated damping factor for each cycle is plotted in Figure 16 for all simulated joints. Observing Figure 16 revealed that strengthening the B-C joints with FRP material increases the damping factor significantly compared to the unstrengthened ones. That is interpreted by the fact that the strengthened specimens have enhanced deformability. Meanwhile, the rising damping factor enhanced seismic performance when five loading cycles were reached. However, strengthening the B-C joint with FRP composites has been found to improve the overall performance, including all of its aspects. Consequently, such joints were the best because they were able to convey the failure pattern to the connected area.

Conclusions
The efficiency of utilizing FRP composites in strengthening damaged B-C joints under cyclic loading has been experimentally tested by Shannag and Alhassan [33] and simulated using the NLFEA modeling approach by ANSYS package. Further investigation has been carried out on the effect of the resulting damage level on the concrete compressive strength (0%, 25%, and 50%) and the column's axial loading (0%, 25%, 50%, and 75%) on the overall performance of the B-C joints and based on the presented results, the following was concluded: 1. Both the column's axial loading and the concrete damage level considerably affect the joint's behavior besides the utilized reinforcement scheme's role in suppressing their effect. However, Stiffness degradation was slightly affected when the axial load was changed but considerably affected the other sensitive performance parameters. 2. Using FRP to reinforce B-C joints externally allows the restoration of strength, and

Conclusions
The efficiency of utilizing FRP composites in strengthening damaged B-C joints under cyclic loading has been experimentally tested by Shannag and Alhassan [33] and simulated using the NLFEA modeling approach by ANSYS package. Further investigation has been carried out on the effect of the resulting damage level on the concrete compressive strength (0%, 25%, and 50%) and the column's axial loading (0%, 25%, 50%, and 75%) on the overall performance of the B-C joints and based on the presented results, the following was concluded:

1.
Both the column's axial loading and the concrete damage level considerably affect the joint's behavior besides the utilized reinforcement scheme's role in suppressing their effect. However, Stiffness degradation was slightly affected when the axial load was changed but considerably affected the other sensitive performance parameters. 2.
Using FRP to reinforce B-C joints externally allows the restoration of strength, and the failure mode of the joint-column area became ductile instead of brittle, making a plastic hinge in the beam only at column axial load levels higher than 25%. Applying axial column loads below 25% enhanced the ultimate axial load and deflection capacities.

3.
For FRP-strengthened joints, the energy dissipation is done through the joint before the system de-stabilizes. This is an indicator of the joint's ultimate stress capacity till failure. In contrast, strengthened joint models encountered an overall failure when the beam's maximum capacity was reached, where only 50% of the FRP ultimate strain was reached. 4.
Due to the resulting accurate simulation, the behavior of the unstrengthened and FRPstrengthened B-C joints could be effectively predicted using the NLFEA modeling approach. However, the resulting observations help specialized engineers retrofit appropriate B-C joints in already-standing buildings with deficient seismic regions, sparing lives, time, and money.