Improving Seismic Performance of RC Structures with Innovative TnT BRBs: A Shake Table and Finite Element Investigation

Abstract

Addressing the critical seismic vulnerabilities of reinforced concrete (RC) beam-column joints remains an imperative research priority in earthquake engineering. This study presents an experimental and analytical investigation into the seismic performance enhancement of non-ductile RC frames using an innovative all-steel Tube-in-Tube Buckling-Restrained Brace (TnT BRB) system. Shake table tests were performed on one-third scale RC frame specimens, including a baseline structure representing conventional substandard design and a counterpart retrofitted with the proposed TnT BRBs. Experimental results revealed that the unretrofitted specimen experienced pronounced brittle shear failures, excessive lateral deformations, and significant degradation of beam-column joints under cyclic seismic loading. In contrast, the TnT BRB-retrofitted specimen exhibited substantially improved seismic behavior, characterized by enhanced energy dissipation, controlled inter-story drifts, and preserved joint integrity. Advanced fiber-based finite element modeling complemented the experimental efforts, accurately capturing critical nonlinear phenomena such as hysteretic energy dissipation, stiffness degradation, and localized damage evolution within the structural components. Despite inherent modeling limitations regarding bond-slip effects and micro-level cracking, strong correlation between numerical and experimental results affirmed the efficacy of the TnT BRB retrofit solution. This integrated experimental-analytical approach offers a robust, cost-effective pathway for upgrading seismically deficient RC structures in earthquake-prone regions.

1. Introduction

One of the major threats to the safety of buildings is their vulnerability to natural disasters, which can lead to collapse or severe damage of structures, loss of human life, and socio-economic breakdown. Buildings that have been designed and constructed without considering the seismic lateral loads and in areas with high seismicity are considered unsafe, and retrofitting or rebuilding them is essential to reduce the effect of a strong seismic event.

Beam-column connections are vital for the seismic resilience of reinforced concrete (RC) frames. Modern earthquake-resistant design codes such as ACI 318 [1], Eurocode 8 [2], and NZS3101 [3] detail requirements to enhance the ductility and energy dissipation capacity of these joints. Structural failures often stem from poor seismic performance of RC beam-column joints lacking seismic design considerations. A range of substandard design strategies has been developed for these connections. The cyclic behavior of substandard designed connections during seismic events is heavily influenced by design methodology and the detailing of concrete frame components. Evaluating the seismic performance of these members and connections can be done through nonlinear simulations and experimental investigations post-failure.

Seismic vulnerability in RC structures remains a paramount concern, particularly in regions where legacy construction practices have prioritized compressive strength over ductility. While extensive experimental investigations have shed light on the behavior of RC beam-column joints and confirmed the efficacy of conventional BRBs under seismic excitations, a notable gap persists in the literature regarding the complementary role of computational models in elucidating these phenomena. Advanced fiber-based finite element (FE) models, for example, have emerged as indispensable tools that capture the intricate hysteretic responses, localized damage mechanisms, and evolving stiffness degradations observed in RC systems during cyclic loading. These models, by integrating nonlinear material behavior with complex bond interactions and discrete damage accumulation, offer a more granular insight into seismic performance than experimental observations alone. This dual approach not only refines the calibration of experimental data but also significantly enhances the predictability of seismic energy dissipation and the overall resilience of RC frames.

Recent advancements in computational modeling have considerably advanced our ability to simulate dynamic structural responses under seismic loads. Seminal works by Correia and Virtuoso [4] have demonstrated that incorporating total co-rotational formulations within FE frameworks enables the capture of large nodal displacements and rotations, a critical requirement for accurately modeling the behavior of RC structures during seismic events. Likewise, distributed plasticity models, as expounded by Filippou and Fenves [5], provide a robust methodology for discretizing RC cross-sections into multiple fibers, each governed by uniaxial stress-strain relationships. Such approaches are particularly effective in replicating the progressive degradation of bond strength and the localization of cracks, phenomena that are often inadequately captured by simpler lumped plasticity models.

In parallel with these computational developments, there has been a burgeoning interest in innovative retrofit technologies that not only dissipate seismic energy but also facilitate self-centering behavior, a feature that is critical for reducing residual deformations after seismic events. A notable example of this emerging technology is the self-centering energy-dissipative brace (SCED), which has recently garnered considerable attention in the literature. The SCED system, as rigorously investigated by Qin et al. [6], exhibits superior self-centering performance while maintaining high energy dissipation capacities. This advanced brace system is engineered to restore the pre-seismic configuration of a structure after a seismic event, thereby mitigating the accumulation of permanent deformations and enhancing post-earthquake functionality.

Integrating advanced computational models with emerging retrofit technologies such as the SCED system represents a promising pathway for advancing the seismic resilience of RC structures. The fiber-based FE approach, when combined with high-fidelity material models and refined discretization techniques, can accurately predict the behavior of RC frames retrofitted with innovative energy dissipation devices. For instance, the simulation frameworks discussed by Fragiadakis and Papadrakakis [7] have underscored the importance of capturing localized damage phenomena, such as bond-slip and cracking in beam-column joints, which are critical in determining the overall hysteretic performance of a structure. Moreover, experimental validations conducted by Sung et al. [8] have provided empirical evidence that reinforces the potential of advanced computational models to predict the complex interactions between traditional BRBs and novel systems such as SCED. Such studies highlight the synergies between simulation and experimentation, establishing a feedback loop that continuously refines our understanding of seismic performance.

The integration of these advanced computational techniques and innovative retrofit solutions is not merely an academic exercise but a pragmatic necessity in the face of escalating seismic hazards. Modern seismic design codes, while progressively incorporating computational insights, still leave significant room for improvement in their treatment of RC joints and energy dissipation mechanisms. In this context, the dual approach of employing robust numerical models alongside cutting-edge experimental research offers a holistic perspective that can inform the next generation of design standards. By bridging the gap between theoretical predictions and real-world behavior, these methodologies provide engineers with a more reliable basis for designing structures that can withstand severe seismic events with minimal damage.

Furthermore, the incorporation of self-centering mechanisms, as embodied by the SCED system, represents a paradigm shift in seismic retrofitting strategies. Unlike conventional BRBs that primarily focus on dissipating energy through plastic deformations, SCED systems are engineered to combine energy dissipation with an inherent capacity for self-recovery. This dual functionality not only curtails the propagation of damage during an earthquake but also expedites the restoration process post-event, thereby reducing the downtime and repair costs associated with seismic retrofits. The promising results reported by Qin et al. [6] provide compelling evidence that SCED systems could redefine the standards for seismic retrofitting in RC structures, particularly when integrated within a computational framework that rigorously assesses their performance. This study, therefore, seeks to extend the state-of-the-art by bridging these perspectives, ultimately contributing to the development of safer, more resilient structures in seismically active regions.

Joint failures can manifest as shear, flexural, or bond failures, each significantly undermining structural integrity. Analyzing these modes is critical for designing resilient RC frames, especially with enhancements such as buckling-restrained braces to improve performance under various loads. The primary failure mode in non-ductile reinforced concrete joints is brittle shear failure within the joint core. As shown in Figure 1a, seismic lateral loads generate significant diagonal tensile and compressive stress in the joint panel. If the joint lacks adequate transverse reinforcement diagonal cracking can quickly develop, leading to internal fracturing and crushing. Notably, shear cracks can appear even with modest story drifts, before the yielding of adjacent members, causing a rapid decrease in the connection’s load-carrying capacity. The appearance of diagonal shear cracks indicates a considerable reduction in the joint’s load-bearing ability. This initial failure may escalate, risking a mechanism that could cause a story collapse if multiple joints fail. Unlike the ductile flexural failures of beams or columns, joint shear failures are brittle and provide little warning, identified by X-shaped cracks, core concrete compaction, and compromised structural integrity at the node connecting frame members.

A common failure mechanism involves the deterioration of the bond between reinforcing bars and surrounding concrete in joints, leading to slipping or pull-out of the reinforcement. In older constructions, longitudinal bars of beams and columns often terminate or splice in joint regions without adequate development length or 90° hooks. Cyclic loading can cause these bars, particularly if they are smooth or surrounded by cracks, to gradually slip within the joint. Bond-slip is often seen in gravity-designed frames and has been identified as a key factor in damage and collapse of reinforced concrete buildings built before the 1970s. As illustrated in Figure 1b, the slipping of longitudinal bars into the joint reduces stiffness, shown by pinched hysteresis loops, and causes premature strength degradation under lateral loads. This results in a “loose” beam-column connection, compromising steel anchorage and decreasing moment transfer capacity. Joint shear cracking frequently accompanies anchorage failure; as slip and cracking initiate, the joint’s truss mechanism weakens, increasing the load on the concrete strut and potentially leading to failure. Notable indicators of bond-slip failure include bar movements, widening cracks along beam bar paths, and sometimes bar pull-out or hook opening after testing. Inadequate bond anchorage, from insufficient embedment or smooth bars, critically impacts the cyclic performance of beam-column joints.

An additional factor contributing to joint distress is an inadequate strength hierarchy within the structural frame. Engineering guidelines advocate for a configuration where columns and joints are robust while beams are weaker. This design ensures that the beam ends yield before the shear capacities of the joints are exceeded, or before column hinging occurs. Many legacy frames, however, overlooked this principle. During seismic events, beams can exert forces on joints surpassing their shear capacity, especially at joints with multiple beam connections. Weak-column scenarios may occur, where columns hinge at the joint, increasing shear demands. This can lead to joint failure even with nominal ties, as the joint may be insufficient for the imposed demand. A notable instance involves connections linking heavily reinforced beams to lightly reinforced columns, causing excessive shear in the joint panel. Experimental studies show that designs violating capacity principles, such as “weak column-strong beam”, result in joint failure in shear before beam yield, as shown in Figure 1c. Inadequate proportions in dimensions and strength, such as reduced column cross-sections or lack of supporting beams in exterior joints, can force joints to absorb excessive loads, leading to brittle failure. This underscores the need for careful joint geometry and member sizing consideration to avoid joint inadequacies, a common issue in older design practices that led to failures during seismic activities.

One effective retrofit technique developed in recent years is the use of buckling-restrained braces (BRBs) [9,10,11,12,13,14,15]. This method has been adopted widely for seismic retrofitting of existing structures and for new designs intended to withstand seismic action, applicable to both engineered and heritage buildings. BRBs are energy-dissipating components that restrain elastic and plastic deformation, effectively controlling buckling. They dissipate vibration energy and reduce the structure’s natural period via hysteretic behavior instead of relying on physical impacts. Key advantages of BRB systems over conventional bracing include (a) high energy dissipation, (b) superior ductility and symmetrical hysteretic responses, (c) adjustable energy dissipation through core tube modification, (d) resistance to residual buckling and minimal structural damage after severe loading, and (e) early warning of potential failure indicated by localized pinching in hysteresis loops [16,17].

Tube-in-Tube braces consist of two concentric tubes: a main brace and an outer tube. The main brace contracts the inner tube. During seismic events, the outer tube prevents buckling by providing support, ensuring stabilization [18]. It resists forces on the structure and enhances lateral stability. The main tube handles tension and compression, increasing the brace’s resistance. A key advantage of the Tube-in-Tube system is its compatibility with standard lateral frames and diagonal bracing, offering higher resistance values. The outer tubes can take various shapes for architectural design, providing benefits for diaphragm wall systems and accommodating significant construction variations.

A significant number of researchers have focused on experimental studies evaluating the efficacy of BRB systems [19,20,21,22,23,24,25] and their potential failure mechanisms. This emphasis on experimental methods stems from their reliability in substantiating research outcomes in structural engineering and guiding design standards. Accumulating experimental data is crucial for developing and maintaining these standards, forming the basis of performance-based engineering and validating nonlinear response history analysis models. While numerical models can be backed by various experimental data types, small-scale structural tests offer the clearest validation.

Recent investigations have provided significant insights in experimental studies. Sung et al. [8] executed shake table experiments on a portal reinforced concrete frame with rubber cylinders to improve load-bearing capabilities, revealing that these braces enhanced seismic performance. Rafi et al. [26] conducted shake table tests on a concrete frame retrofitted with a brace beam, finding that it markedly increased stiffness and reduced lateral story drift. Sadoon et al. [27] examined the seismic response of a poorly designed frame retrofitted with a novel brace system, concluding that it significantly lowered inter-story drift ratios and exhibited stable hysteretic behavior, thus improving older buildings’ seismic responses in prone regions. Wu et al. [28] performed quasi-static tests to investigate failure mechanisms of conventional braces, proposing a double-stage brace design that verified gradual failure instead of catastrophic. Xie et al. [29] tested two reinforced concrete column piers—one with braces and one without—demonstrating that braces curtailed displacement and curvature by effectively dissipating seismic energy. Cabrera and Bruneau’s [30] testing program with Bidirectional Ductile Diaphragms showed a reliable hysteretic response when using V-configuration braces. Lastly, Li et al. [31] analyzed composite frames, finding that those with braces enhanced lateral resistance by up to 142% and had an initial stiffness at least 8.4 times greater. Gong et al. [32] examined a replaceable coupling beam with hybrid energy dissipation devices, showing it effectively reduced inter-story drifts and mitigated damage to nearby elements.

2. Significance of Research

Many existing structures use RC frames that fail to meet quality standards. In regions with moderate to low seismic activity, these frames are built without necessary seismic detailing, compromising safety and integrity. Such constructions are prevalent in industrial, residential, and commercial areas. The past performance of these poorly designed frames during seismic events has been inadequate, leading to concerns about their reliability [33,34,35,36,37,38]. Thus, evaluating and improving these substandard buildings is crucial for mitigating risks and ensuring occupant safety.

This research examines the potential for collapse among deficient RC structures and evaluates the effectiveness of all-steel Tube-in-Tube BRBs in mitigating such risks. This innovative solution not only enhances seismic performance but also remains cost-effective. In light of the substantial ground motion event recorded in Kahramanmaraş in 2023, shake table experiments were conducted on two one-third-scale structural models: the first serves as a standard representation of a typical substandard RC building (reference frame), while the second features an advanced Tube-in-Tube system designed to improve structural integrity.

The experimental outcomes were subsequently aligned with the analytical framework. This calibration facilitated a more precise depiction of the joint’s seismic response, underscoring the significance of integrating both empirical and theoretical methodologies for evaluating the efficacy of structures engineered to withstand seismic activity. The findings from this comprehensive investigation are meticulously scrutinized and juxtaposed regarding essential global response indicators and the diverse damage manifestations recorded during the shake table assessments. This analysis seeks to elucidate the overall viability of the proposed alternative design strategy.

3. Tube-in-Tube Buckling-Restrained Braces

According to the post-earthquake reconnaissance reports [39,40,41,42,43,44], most of the RC buildings collapsed or heavily damaged during the 2023 Kahramanmaraş earthquakes mainly due to the global deficiencies, either stiffness or strength or both. Therefore, the RC frame included in the present study was designed to represent such stiffness and strength deficiencies simultaneously. Among all the external bracing systems in seismic retrofitting to overcome global deficiencies, BRBs are one of the most popular ones for their large stiffness, strength, and stable inelastic response [45]. Despite their large energy dissipation capacity, traditional concrete-encased BRBs are relatively heavy compared with their all-steel counterparts and costly, which prevents their use for ordinary buildings.

To address the aforementioned issues related to conventional buckling bracings and existing traditional BRBs, Shen et al. [46] proposed Tube-in-Tube (TnT) BRBs, which are a new type of all-steel BRB with no formal design standards. The outer tube (jacket) helps prevent local and overall buckling in the inner tube (core) while enhancing structural strength. With their high strength, stiffness, reliability, and energy dissipation capacity, TnT BRBs are seen as better alternatives to traditional concrete encased BRB designs. Shen et al. [35] initially presented all-steel TnT BRBs as a solution to the challenges of diminished strength and stiffness resulting from buckling, which is frequently encountered with conventional buckling braces. Also, TnT BRBs are less labor-intensive due to their simplicity in fabrication and much lighter because of the absence of concrete encasing. Furthermore, unlike concrete-encased BRBs, TnT BRBs impose smaller demands on the surrounding members because of their small compression overstrength and cyclic hardening tendency, as reported in Shen and Seker [47].

The TnT BRB configuration utilized for the retrofitting of the substandard RC frame being analyzed is depicted in Figure 2. The load-bearing inner tube, characterized by its anticipated substantial inelastic axial deformation, is constructed using widely utilized circular or square hollow structural sections (HSS). Surrounding this load-bearing tube is the buckling restrainer, which consists of a two-segment outer tube that is fillet welded to a central stopper located in the mid-section. To facilitate fabrication and enable the load-bearing tube to laterally deform without imposing significant compressive loads on the outer tube, a small gap is incorporated between the load-bearing and the buckling restrainer tubes. The stopper, represented as a ring-shaped plate in the mid-section, is fillet welded to both the load-bearing and buckling restrainer tubes. This component serves to stabilize the two-segment outer tube while allowing the load-bearing inner tube to deform in an axial manner unrestrictedly. The connector plates, located at each end, function to transfer the axial load exerted on the load-bearing tube to the end connection assembly. These plates are interconnected via pretensioned high-strength bolts, ensuring a secure transfer of forces. Meanwhile, the end connection assembly comprises a reinforced gusset plate that links with the connector plate, adeptly transferring the axial loads from the load-bearing tube to the adjacent structural members, such as girders or columns, at both ends. This assembly is meticulously designed to restrict both in-plane and out-of-plane end rotations, which could potentially introduce global stability challenges. It is critical to note that such end rotations can lead to significant flexural demands, negatively affecting the overall performance of TnT braces, as supported by references [18,48].

An important consideration is the potential application of a low-friction coating or lubricant to the exterior of the load-bearing tube, aimed at reducing the transfer of shear forces across contact surfaces. This modification could enhance cyclic symmetry. Nonetheless, recent experimental findings [18,48] suggest that TnT BRBs exhibit a relatively symmetrical hysteretic response even in the absence of such lubrication within anticipated demand parameters. Additionally, it is essential that the in-service longevity of any low-friction lubricant or coating applied to metal surfaces be validated through rigorous testing.

The energy dissipation capacity of TnT braces was examined through cyclic testing of large-scale specimens at Iowa State University. The experimental setup and the inelastic cyclic behavior of a 3.5-m TnT specimen with about 500 kN capacity are illustrated in Figure 3a. The loading protocol adhered to the AISC Seismic Provisions (AISC 341) [49]. The axial force-displacement analysis demonstrated ductile, nearly symmetrical responses, with maximum ductility around 10 and story drift exceeding 0.03 rad (Figure 3b). Total ductility approached 250, with peak compression overstrength near 10%, indicating minimal unbalanced brace forces in girders. As seen in Figure 3b, the development of inelastic deformations began by yielding of the load-bearing tube (inner tube) in both tension and compression. Following the initial inelastic cycles at yielding deformation, the displacement-controlled load amplitudes were gradually increased to 50 mm, which corresponds to a ductility of 10 (an equivalent story drift ratio of 0.035 rad.). Note that two cycles were applied at each deformation quantity to comply with the loading protocol given in AISC 341 [49]. After attaining the peak ductility of 10, two additional cycles were applied at an axial displacement of around 38 mm (ductility of 7.5) to satisfy the cumulative ductility requirement [49]. The specimen showed a stable and virtually symmetrical response until the last cycle, as seen in Figure 3b. During the last compression cycle at a ductility of 7.5, the load-bearing tube experienced local plastic deformations close to the loading end, which led to a strength deterioration (Figure 3b). Soon after the plastic local deformation took place, the load-bearing tube fractured in tension due to low-cycle fatigue. The lack of global buckling significantly enhanced energy dissipation capacity, shown by significant hysteresis loop areas. TnT braces effectively dissipate energy while maintaining stiffness, making them ideal for improving non-ductile reinforced concrete frames. Refer to Shen and Seker [48] for further details on the experimental program.

4. Configuration for Shake Table Testing

The experimental study utilizes a 3.0 m by 3.0 m shake table at the Allianz Teknik Earthquake and Fire Test and Training Center in Istanbul, Türkiye, with a maximum payload of 10 tons. Hydraulic actuators generate seismic forces, and the closed-loop controller includes three variables, adaptive control, and differential pressure stabilization. The shake table reaches a peak acceleration of 1 g, essential for accurately simulating realistic earthquake ground motions within a frequency range of 0 to 50 Hz.

4.1. Criteria for Similitude Requirements

Modeling theory outlines key parameters for linking geometric features, material properties, initial conditions, boundary limitations, and environmental effects of models and prototypes. This interaction is crucial for understanding how one entity behaves in relation to another. The main principle enabling the formation of correlation functions, which depict the model-prototype relationship, is known as similitude [50].

In this framework, developing and analyzing a structural model requires a careful approach that follows specific similitude criteria connecting the model to the original prototype. These criteria stem from modeling theory, clarified through dimensional analysis of physical phenomena affecting structural behavior. In dynamic model testing, this analysis helps identify principles governing scaling laws for force, time, and other variables, enhancing understanding of their interactions and relationships during testing [51].

The concept of similitude is based on scaling factors that maintain the proportional relationship between a model and its prototype. This framework can be divided into three main categories: geometric similitude, kinematic similitude, and dynamic similitude.

Geometric similitude guarantees that the scaled models faithfully represent the geometry of the actual prototype structures. As noted by Harris and Sabnis [52] and Li et al. [53], geometric similarity necessitates that all linear dimensions of the model be proportionately scaled from the prototype. In our investigation, geometric similarity was meticulously preserved by uniformly scaling the dimensions of structural components—such as beams, columns, joints, and reinforcing bars—by a factor of 1:3. This scaling factor was chosen after thorough consideration of practical limitations, encompassing laboratory space, instrumentation capabilities, and the ability to accurately capture intricate seismic responses. The geometric scaling upheld realistic reinforcement configurations, including bar diameters and spacing arrangements, thereby ensuring a faithful representation of actual RC structural layouts.

Kinematic similitude pertains to the proportionality of time-variable attributes, encompassing displacement, velocity, and acceleration. In accordance with the comprehensive protocols established by the National Earthquake Hazards Reduction Program (NEHRP, 2011) [54], the attainment of kinematic similarity is vital for the precise simulation of seismic phenomena observed in authentic contexts [55,56]. Within our shake table investigations, we maintained kinematic similitude by uniformly adjusting displacement and acceleration metrics in accordance with the principles of geometric and dynamic scaling. The resultant scaled seismic inputs effectively emulated typical earthquake motion, enabling us to accurately document critical structural response metrics, including peak accelerations, relative displacements, and deformation characteristics.

Dynamic similitude encompasses the proportional relationships among mass, stiffness, and damping attributes to guarantee that the dynamic responses of scaled models accurately mirror the behavior of prototypes under seismic loads [50]. To accomplish this objective, we rigorously adhered to the principles of dynamic similitude, which included preserving mass and stiffness ratios in alignment with the geometric scaling factor. Additional mass was judiciously incorporated into our specimens utilizing steel blocks to replicate the requisite scaled mass density while maintaining structural stiffness. To compensate, steel blocks were added to the roof, preserving overall stiffness. Each block was 1750 mm long, 570 mm wide, and 60 mm high, weighing 430 kg. Fourteen blocks were welded together, creating a total weight of 6 tons.

Moreover, stiffness similitude was attained through the meticulous selection and calibration of material properties in accordance with the established scaling principles, thereby ensuring a realistic depiction of the stiffness characteristics intrinsic to actual structures. Damping characteristics, which often present challenges in precise scaling, were also meticulously evaluated and modified through material selection and joint detailing to closely correspond with the prototypical damping ratios encountered in practical applications. The physical variables obtained from this setup are detailed in

Table 1. Calculated physical quantities for shake table tests.

Physical Quantity	Scale Factor
$\mathrm{Length}, l_r$	3
$\mathrm{Modulus} \mathrm{of} \mathrm{elasticity}, E_r$	1
$\mathrm{Time}, t_r$	1.732
$\mathrm{Gravitational} \mathrm{acceleration}, g_r$	1
$\mathrm{Strain}, {\epsilon }_r$	1
$\mathrm{Acceleration}, a_r$	1
$\mathrm{Frequency}, {\omega }_r$	0.577
$\mathrm{Velocity}, v_r$	1.732

.

The representativeness of the scaled specimens was additionally corroborated by the intentional reproduction of prevalent construction methodologies and standard shortcomings noted in non-ductile RC structures. This encompassed inadequate lateral reinforcement, deficient bar anchorage, and various typical detailing deficiencies that typify antiquated or inferior construction practices commonly found in regions susceptible to seismic activity.

It is imperative to acknowledge that there exist certain limitations intrinsically associated with scaled modeling methodologies. These limitations primarily encompass discrepancies in concrete compressive strengths, variations in steel yield strengths, and deviations attributable to the scaling of gravitational effects, all of which could potentially affect the fidelity of scaled model results. To mitigate these inherent discrepancies, meticulous attention was dedicated to the selection, preparation, and handling of construction materials, aligning their mechanical properties as closely as feasible with those observed in typical full-scale structures. Furthermore, rigorous experimental procedures were implemented to ensure minimal divergence from the expected prototypical responses.

It can be definitively posited that these meticulously controlled minor variances are inadequate to substantially compromise the legitimacy or diminish the relevance of the experimental results to practical applications. Therefore, while recognizing the inherent constraints of scaled modeling, the strength and precision of the research outcomes remain securely preserved.

4.2. Examination of the Test Specimen

The experimental setup included two identical single-bay, single-story reinforced concrete frames, as shown in Figure 4. One frame acts as the control specimen, while the other has a diagonal TnT brace for enhancement. The frames will be called Specimen 1 (Bare Frame) for the control and Specimen 2 (TnT-retrofitted Frame) for the reinforced variant. Both are scaled models, reduced to one-third of the original dimensions, following the similitude rule in Table 1.

The structural simulations involved columns with a rectangular cross-section of 100 mm width and 150 mm height, spaced 1350 mm apart. Each column had four longitudinal reinforcement bars of 8 mm diameter, the smallest available locally. The height of the columns was 950 mm from the foundation to the slab underside. As illustrated in Figure 5, transverse reinforcement included 8 mm diameter bars spaced 100 mm apart, with stirrups featuring 90-degree hooks, indicating suboptimal detailing. Additionally, 8 mm bars were used at 100 mm intervals in the slab’s upper and lower sections. The foundation’s longitudinal reinforcement consisted of 16 mm bars, with 10 mm stirrups spaced at 150 mm intervals. The top slab measured 1450 mm long, 450 mm wide, and 50 mm thick. A foundation beam, measuring 1950 mm long, 600 mm wide, and 400 mm deep, was anchored to the shake table with 50 mm diameter bolts.

Specimen 2 was created as a replica of the first specimen but included a TnT brace, as presented in Figure 4. The seismic retrofit aimed to enhance the strength and stiffness of the original RC frame, surpassing its initial load-bearing capacity. TnT bracing system features a Tube-in-Tube design with a circular hollow structural section (HSS) of 42 × 1.5 mm made of S235JRH steel, encased in a 48.4 × 2.0 mm outer tube. This structure incorporates an outer tube as a buckling restraint that is split into two segments, while a single load-bearing tube connects the end plates. The assembly begins with an 8 mm-thick ring-shaped stopper plate attached to a 1235 mm load-bearing tube via fillet welding. Two 595 mm outer tubes are then welded to this stopper plate. The load-bearing tube is connected to 8 mm-thick rectangular end plates at both ends through fillet welding, with an intentional 18 mm gap included between the outer tube and end plates for accommodating potential tube shortening under compression. This design ensures effective performance in both compression and tension, as the outer tube’s contribution to compressive strength is disregarded. The clearance dimensions were based on expected brace deformations. Finally, 75 × 75 mm end plates were connected to the pre-welded end plates on gusset assemblies using four M12 grade 8.8 bolts to prevent end rotations, thereby enhancing stability, reinforced by stiffeners at key locations as supported by scholarly references [47,48,57,58].

It should be mentioned that incorporating bracings, either buckling or non-buckling, in an existing RC frame in particular is a challenge for several reasons. One of the major difficulties was taking accurate measures to produce shop drawings required for the fabrication of the TnT bracing and its connections. To overcome the erection tolerance issues, small tolerances that existed in the bolted connections were accommodated by the repair mortar injected between the steel reinforcing plates and the existing frame. Likewise, the installation of the joint-reinforcing jacket made with steel plates requires careful rebar scanning to prevent potential damage to stirrups and longitudinal rebars while drilling anchorage holes. Therefore, all these drawbacks combined tend to increase the complexity of the seismic retrofitting process, not to mention the architectural and functionality constraints in an actual building.

The experiments aimed to achieve low uniaxial compressive strength in concrete. RC frames were constructed at Allianz Technical Laboratory, where various cubic samples were tested. The 28-day compressive cylinder strength for the frames was recorded at 9 MPa. To assess the steel’s stress-strain relationships, three samples were tested, along with transverse reinforcement of the same diameter, which revealed a yield stress of $F_{y,measured }=473 \mathrm{M}\mathrm{P}\mathrm{a}$ and an ultimate tensile stress of $F_{u, measured }=643 \mathrm{M}\mathrm{P}\mathrm{a}$. Tensile tests revealed the steel met the strength criteria of ASTMA615/A615M-05 [59].

To evaluate the load-bearing tube’s material properties made of HSS42 × 1.5, two dog bone-shaped coupons were extracted. Uniaxial tensile tests were conducted at the Turkish Standard Institution’s Material Testing Laboratory. It is important to note that yield stresses were assessed using the 0.2% proof stress standard. The yield stresses for the two examined coupons were 397 MPa and 431 MPa. Peak engineering stresses ranged from 494 MPa to 520 MPa, with ultimate strain at fracture around 0.30 or higher. Average yield and ultimate tensile stress values from both tests were approximately 414 MPa and 507 MPa, respectively.

The test specimens’ responses to seismic activity were meticulously documented using various instruments including accelerometers and linear voltage displacement transducers (LVDTs). Illustrated in Figure 6, all LVDTs were capable of measuring displacements at frequencies up to 200 Hz. In addition to the LVDT at the slab level (LVDT#1), two more were positioned at the ends of the TnT brace (LVDT#2 and #3) to capture axial displacements during excitations. Four accelerometers recorded accelerations in both the foundation and slab of the test frames, and on the shake table surface. Both acceleration and displacement responses were continuously logged by a computer-aided data acquisition system. Twelve strain gauges were also embedded within the reinforced concrete frame to monitor strain responses from various locations, as depicted in Figure 6.

4.3. Applied Ground Motion

On 6 February 2023, at 04:17 local time (+3 GMT), a major seismic event struck southeastern Turkey, registering a moment magnitude of 7.7. The Disaster and Emergency Management Presidency (AFAD) noted that the earthquake’s epicenter was in Kahramanmaraş Province, near Pazarcık [60]. The Turkish Building Earthquake Code (TBEC) classifies seismic risk into four categories: DD-1, DD-2, DD-3, and DD-4, with probabilities of events at 2%, 10%, 50%, and 68% over 50 years. Figure 7 shows the normalized response spectra at DD-2 level alongside a time-history record from the 2023 Maraş earthquake, with critical damping values of 2.5%, 5%, and 10%.

The experimental evaluations were executed in two sequential phases. Initially, both types of frames were exposed to ground motion that had been appropriately scaled in accordance with the similitude law outlined in the preceding section. Since the frames tested were designed in alignment with substandard principles, the application of the scaled ground motion was executed with precision. Notably, Specimen 1 exhibited signs of damage when subjected to 35% of the ground motion. Conversely, Specimen 2 demonstrated resilience by enduring the same ground motion without sustaining any damage. As a result, an assessment was conducted to analyze the overall seismic performance of TnT-enhanced Specimen 2 when exposed to 100% of the unscaled ground motion, characterized by a significant strength demand on short period structures. The primary objective was to evaluate the frame’s behavior under conditions of intense ground shaking.

5. Analytical Study and Model Calibration

This section outlines and examines the modeling strategies related to the analysis software, the methodologies implemented, and the specifics surrounding the material models.

5.1. Approaches to Modeling

FE models for the two tested RC were created utilizing Seismostruct V2025 [61], an advanced fiber-based platform capable of executing nonlinear static and dynamic analyses. Additionally, this software allows for the incorporation of both material and geometric nonlinearity effects in the modeling process. This is made possible through a total co-rotational formulation by Correia and Virtuoso [45], accurately representing kinematic transformations tied to large displacements and three-dimensional rotations of beam-column members. This method allows small deformations in relation to the chord without losing general applicability, even with large nodal displacements and rotations. In the local chord coordinate system, six fundamental displacement degrees of freedom are presented in Figure 8a,b.

On the other hand, distributed inelasticity elements are increasingly used in earthquake engineering for research and professional applications. Their advantages over simpler lumped-plasticity models, as well as their historical development and constraints, are documented by authors such as Filippou and Fenves [5] and Fragiadakis and Papadrakakis [7]. Notably, these elements do not require the complex calibration of empirical parameters against actual or ideal responses under simplified loading conditions, unlike concentrated-plasticity models. This fiber approach models cross-sectional behavior, linking each fiber to a uniaxial stress-strain relationship. The stress-strain state of beam-column elements is determined by integrating the nonlinear responses of typically 100 to 150 fibers in the section.

Figure 8c represents a schematic illustration of the Gaussian integration procedure employed in this fiber-based FE analysis. This figure is pivotal for understanding the discretization strategy that underpins the accurate computation of the nonlinear behavior of RC beam–column elements. In this schematic, the RC element is depicted with its endpoints (0 and L), its midpoint (L/2), and, crucially, an integration point positioned at a distance of 0.3 L from the midpoint. This specific placement is not arbitrary; rather, it arises from an extensive sensitivity analysis and is consistent with the optimal Gaussian integration schemes documented in the literature and is also recommended in the software manual employed in this study [4,5,61].

The rationale for selecting an integration point at 0.3 L from the midpoint is rooted in the need to accurately capture the spatial variability of stress and strain across the RC cross-section, particularly in regions where steep gradients may develop due to localized damage phenomena. By situating the integration point at this strategically determined location, the method ensures that the fiber-level responses, which collectively contribute to the global structural behavior, are computed with a high degree of precision. This is essential for modeling the complex nonlinearities inherent in seismic response, including material nonlinearity, bond degradation, and the evolution of damage under cyclic loading.

Figure 9 provides a comprehensive graphical representation of the stress-strain relationships for the primary materials utilized in the analysis—namely, concrete, reinforcing steel, and the TNT-BRB system. The concrete curve is derived from the seminal Mander model [62], which rigorously characterizes the quasi-brittle behavior of concrete—from the initial linear elastic range to the onset of cracking and eventual post-peak softening. This model is widely recognized for its ability to capture the degradation of stiffness and the evolution of damage under increasing strain, which are critical for predicting seismic performance. Similarly, the behavior of reinforcing steel is modeled using the Menegetto-Pinto formulation [63], a formulation that effectively delineates the yield plateau and subsequent strain-hardening phase, ensuring that the ductile properties of the steel are accurately represented under cyclic loads. For the TnT-BRB system, a buckling-restrained steel brace model from the literature [18] is employed to illustrate its distinctive energy dissipation characteristics. These constitutive models underpin the simulation of the intrinsic nonlinear material behavior and drive the emergence of hysteretic loops during cyclic loading—thereby providing a robust foundation for predicting the overall seismic response of the retrofitted RC frames.

Figure 10 eloquently depicts the intricate three-dimensional finite element models of the two RC structures, meticulously capturing the complex interrelations of the beam–column joints, reinforcement configurations, and overall structural geometries, thereby providing a robust foundation for the ensuing analytical comparisons and validation of the computational predictions against experimental data.

5.2. Calibration of the Analytical Model

This section presents a comparative analysis of the results obtained from the analytical model against the outcomes of the shake table tests. Initially, the eigenvalue results of the specimens subjected to testing are examined. This is subsequently followed by an assessment of the LVDT results in relation to the nonlinear time history analysis derived from the analytical models. After calibrating the analytical models with the empirical results from the shake table tests, the damped hysteretic energy values of these models are computed and discussed in relation to the established code threshold limits.

The natural vibration periods were computed by taking into account the rigidities of the cracked sections in both longitudinal and transverse directions, and these calculations for both specimens are juxtaposed with the experimental data, as shown in

Table 2. Comparison of the natural vibration periods.

Specimen No	Shake Table Test (s)	Analytic Model (s)	Error (%)
1	0.495	0.463	6.45
2	0.151	0.147	2.65

. The calculated eigen periods demonstrate concordance with the results obtained from the shake table tests for each specimen. An evaluation of the LVDT data obtained from the shake table test juxtaposed with the computed displacement trace derived from the analytical model is presented in

Table 3. Comparison of the top displacements.

Specimen No	Ground Motion	Shake Table Test (mm)	Analytic Model (mm)	Error (%)
1	0.35 g	53.14	53.57	0.43
2	0.35 g	1.87	2.06	9.22
2	1 g	19.86	18.97	4.48

. The data presented in the tables indicates a strong correlation between the outcomes of the analytical model analysis and the shake table experiments. This observation suggests that the analytical model has been effectively calibrated.

To further substantiate the coherence between the experimental shake table results and the numerical simulations, Figure 11 presents a direct time-history comparison of displacement responses obtained from both the physical tests and the calibrated FE model of the two specimens, considering 0.35 g and 1 g ground excitations. Each subplot illustrates overlaid displacement traces, with the red lines representing the measured response from the shake table tests and the blue lines corresponding to the simulated output from the FE model.

Across all intensity levels, the experimental and numerical results exhibit strong agreement not only in peak amplitudes but also in waveform shape, frequency content, and phase alignment. The fidelity of this match reinforces the robustness of the fiber-based FE modeling approach adopted in this study, particularly in capturing nonlinear dynamic response characteristics of the retrofitted RC frame. These results confirm that the numerical model is sufficiently accurate to reflect the global seismic behavior observed experimentally, thereby providing a validated basis for subsequent parametric studies and design-oriented evaluations.

5.3. Limitations of the Fiber-Based Finite Element Model

At the core of the fiber-based FE methodology lies the discretization of an RC cross-section into a finite number of fibers, each endowed with a uniaxial stress-strain relationship that approximates the behavior of either the reinforcing steel or the concrete. This discretization enables the efficient summation of fiber responses to yield an overall sectional response; however, it does so by assuming a perfect bond between the steel and the surrounding concrete. Such an assumption, while expedient for computational purposes, neglects the intricate interfacial phenomena such as bond-slip, localized debonding, and the onset of micro-cracking that are inherently present in RC systems under cyclic loading conditions.

The literature underscores that this assumption may lead to a systematic underestimation of stiffness degradation and strength loss during the post-yield phase. The phenomenon of bond deterioration, particularly under high-cycle fatigue conditions typical of seismic events, can precipitate significant deviations between the modeled and observed structural responses, especially in regions where bond failure governs the initiation of localized plastic hinges [64].

Furthermore, the inherent assumption of a uniform strain distribution across each fiber in the cross-sectional discretization tends to homogenize the actual material behavior. Concrete, characterized as a quasi-brittle material, exhibits highly localized cracking and crushing phenomena, particularly in zones of elevated stress concentration such as the vicinity of beam-column joints. In practice, these localized nonlinearities manifest as discrete regions of strain softening and damage accumulation, phenomena that are frequently averaged out in the distributed plasticity approach. It was shown that the distributed plasticity approach can mask the precise onset of inelastic behavior, thereby reducing the accuracy of the model in replicating critical localized damage mechanisms [65].

The limitations of the fiber-based approach are further accentuated by the discretization strategy itself. In an ideal scenario, the division of a cross-section into fibers would capture the true heterogeneity of material properties and the spatial variability of stress and strain fields. However, practical implementations often necessitate a compromise between computational efficiency and resolution. Coarser discretizations may lead to an oversimplification of the complex stress distribution, especially in regions where steep gradients exist. This is particularly problematic when modeling the progression of damage in areas subject to concentrated plastic strains, where phenomena such as diagonal cracking or localized crushing are critical [66].

An additional point of concern is the calibration process of the fiber-based FE model against experimental data. While the present study demonstrates a commendable correlation between the analytical predictions and the global response characteristics observed during shake table tests, the calibration predominantly focuses on overall displacement and eigenfrequency metrics. Such calibration procedures, though effective in establishing the global accuracy of the model, may not adequately account for the evolution of localized strain concentrations and damage mechanisms.

It is also important to consider the implications of the aforementioned limitations in the context of the intended application of the model. In seismic analysis, the accurate prediction of the energy dissipation capacity of RC structures is of paramount importance. The fiber-based approach, by averaging out localized phenomena, may overestimate the energy absorption capabilities of RC members, particularly in cases where local damage mechanisms such as bond-slip and localized cracking are predominant. This overestimation can have significant ramifications when the model is used to assess the performance of retrofitting strategies, such as the TnT BRB system examined in this study.

In light of these considerations, it is evident that while the fiber-based finite element model provides valuable insights into the global seismic behavior of RC structures, its limitations in capturing the intricate, localized phenomena must be transparently acknowledged. Future research endeavors should aim to integrate hybrid modeling strategies that combine the computational efficiency of the fiber-based approach with more refined localized damage mechanics models. For example, a multi-scale modeling framework could be developed wherein the global response is captured by the fiber model, while critical regions identified as prone to localized damage are modeled using detailed finite element methods that incorporate sophisticated constitutive models and high-resolution discretization. Such an approach would enable the capture of both global structural response and the critical local phenomena that govern failure mechanisms.

5.4. Validation Against Shear-Critical Experimental Data

In order to rigorously assess the predictive capability of the fiber-based FE model, an extensive validation exercise against four independent experimental datasets have conducted that specifically address shear-critical phenomena in RC beam-column joints.

Table 4. Critical shear stress at joint Comparison of Experimental Data with Model Predictions.

Reference	Experimental Value (MPa)
Kalogeropoulos et al. [67]	5.0
Sung et al. [8]	~5.0
Cabrera and Bruneau [30]	5.1
Lopez et al. [10]	~5.1

below encapsulates the experimental values reported in the literature. Studies such as Kalogeropoulos et al. [67], Lopez et al. [10], Sung et al. [8], and Cabrera and Bruneau [30] have consistently measured critical shear stresses in the range of 5.0–5.2 MPa. Conversely, the analytical model presented in Section 5.1 revealed a critical shear stress value of 5.16 MPa.

In conclusion, the advanced calibration of this fiber-based model against these six experimental datasets significantly bolsters its predictive accuracy. This comprehensive validation not only corroborates the simulation results but also reinforces the study’s claims regarding the superior seismic performance achieved via the TnT BRB retrofit strategy. The detailed comparison with experimental data thus serves as a critical benchmark, ensuring that the fiber-based model reliably captures both the global dynamic behavior and the localized shear-critical phenomena that dictate the seismic resilience of RC structures.

6. Discussion on the Results

Hysteretic behavior encompasses various forms of structural damage, such as slip or shear cracks in joints, bond failure in reinforcing materials, and shear failure in beams. This behavior is characterized by the fact that the restoring forces rely solely on the relative displacement. The force-displacement curve exhibits a steeper incline during tension compared to compression, with distinct and well-defined corner and yield points. Additionally, this behavior is marked by a degradation of stiffness following a sudden decrease in strength.

Substandard RC structures usually feature a number of defects such as inadequate detailing of reinforcement, poor material qualities, poor quality control in construction and emphasis on strength rather than ductility of structures. These deficiencies lead to formation of a complex mode of failure with yield plateau, energy dissipation capability, and large deformation demands of the system. Elucidation of behavior of such structures requires some understanding of their energy dissipation capability and their deformation demands.

Hysteretic behavior has long been recognized as a confusing aspect of structural performance because it might lead to nonlinear and unexpected response of structural systems subjected to severe cyclic loads, such as earthquakes [68]. Hysteresis in force–deformation response represents energy dissipation during loading and unloading cycles. This phenomenon is of vital importance to seismic behavior and response of structures and should be validated with experimental tests. Over the years, numerous experimental studies have been conducted to investigate how substandard RC components behave under cyclic and seismic loading. These tests—ranging from individual element tests (beams, columns, joints) to full-scale frame tests—have provided invaluable insights and data on hysteretic degradation in non-ductile RC structures.

A notable illustration of the deficiencies in seismic design is presented by the research conducted by Hakuto, Park, and Tanaka [69]. They executed simulated seismic loading assessments on both interior and exterior beam-column joint configurations that featured inadequate reinforcing details characteristic of older construction practices, such as the absence of transverse reinforcement within the joint core and insufficient anchorage of beam bars. When subjected to cyclic lateral loads, these joints displayed limited strength and ductility, with the external joints particularly prone to joint shear failures and substantial loss of strength after only a few drift cycles. This groundbreaking study highlighted the susceptibility of inadequately detailed joints and emphasized the necessity for retrofitting interventions, noting improvements in performance when some joints were retrofitted with fiber-reinforced polymer (FRP) wraps.

More contemporaneous research has continued to underscore these vulnerabilities. Kalogeropoulos et al. [67] performed tests on four exterior beam-column joint subassemblies designed to replicate the detailing prevalent in reinforced concrete structures built prior to the 1970s. The specimens, examined in their original (unretrofitted) condition, displayed inadequate hysteresis behavior, indicative of brittle failure mechanisms. Among them, two joints were subject to joint shear failures, while the other two experienced anchorage pullout of beam bars, aligning with the expected deficiencies of their designs. The authors noted that “all specimens exhibited poor hysteresis behavior dominated by catastrophic damages of brittle nature”. The hysteresis loops produced during these experiments were particularly tight and non-symmetric, reflecting a critically diminished capacity for energy dissipation. Notably, one specimen featuring a deficient column lap splice exhibited an anomalously asymmetric response, wherein the splice failure in a unidirectional loading scenario triggered a significant reduction in strength during that half-cycle.

These experimental findings are relatively uncommon and serve to underline how the interplay of multiple detailing inadequacies, such as deficient lap splices combined with inadequate joint ties, can result in complex hysteretic degradation. Collectively, the joint testing results consistently indicate that insufficient joint and core detailing contributes to rapid degradation of stiffness and poor energy dissipation, positioning these joints as a critical weakness in older structural frameworks.

Elnashai and Di Sarno [70] emphasized that significant structural damage results from a high capacity for energy absorption. This leads to the inference that a substantial area under the story shear-inter-story drift curves—representing total absorbed energy—inevitably results in excessive damage and permanent deformation. Furthermore, hysteretic energy is defined as that part of the mechanical energy absorbed by a structure during a cycle of loading which is not recovered during the cycle of unloading. It is the area inside a plot of load versus displacement that depicts the loading and unloading cycle of a system. Hysteretic energy is known to be dissipated in a material when it is subjected to loading and unloading conditions. While many models have been developed to portray the complex behavior of materials and structures under cyclic loading, few are capable of describing adequately the deterioration of mechanical properties of materials subjected to low cycle (frequency) fatigue [71].

The analysis presented in Figure 11, which vividly illustrates the hysteretic response of the tested specimens, provides an invaluable qualitative insight into the energy dissipation mechanisms and stiffness degradation phenomena that underpin the seismic behavior of the RC frames. This figure graphically depicts the progressive evolution of hysteresis loops, thereby capturing the cyclic deterioration of structural performance, as manifested in the gradual degradation of the restoring forces. However, while Figure 12 effectively conveys the visual narrative of damage through the widening and pinching of hysteresis loops, it stops short of offering a direct, quantitative measure of damage.

To bridge this gap, we have employed the Park–Ang damage index [72] (D), which is a seminal quantitative measure in seismic engineering that synthesizes both the displacement demand and the energy dissipation capacity of a structure under cyclic loading. This integration of displacement and energy parameters facilitates a more nuanced and objective quantification of structural damage, thereby complementing the qualitative assessments derived from Figure 12. The Park–Ang damage index values for the three specific scenarios, specifically Specimen 1 subjected to 0.35 g, Specimen 2 also subjected to 0.35 g, and Specimen 2 under 1 g, were determined to be 0.89, 0.03, and 0.34, respectively.

When these quantitative indices are compared with the qualitative observations derived from Figure 11, a coherent correlation emerges. Specimen 1 under 0.35 g excitation exhibits a pronounced hysteretic response with extensive energy dissipation and significant displacement, which is consistent with its high damage index (D ≈ 0.89). In stark contrast, the retrofitted frame, Specimen 2, displays negligible hysteretic activity and minimal displacement at low seismic levels (0.35 g), as reflected in an exceptionally low damage index (D ≈ 0.03). Under full-scale seismic excitation (1 g), Specimen 2 exhibits a moderate increase in hysteretic response and displacement, resulting in a damage index of approximately 0.34, a value that remains substantially lower than that of the bare frame under similar conditions.

These findings not only underscore the superior performance of the retrofitting strategy but also highlight the robustness of the Park–Ang damage index as a composite metric that integrates both deformation and energy-based degradation mechanisms. The ability of this index to reconcile the visual evidence from hysteretic curves with quantitative damage assessments provides a powerful tool for benchmarking and comparing different structural configurations and retrofitting interventions. In essence, by incorporating both indices—displacement and energy—the Park–Ang model offers a comprehensive and nuanced framework for evaluating seismic damage, thus reinforcing our overall conclusions drawn from both experimental observations and numerical simulations.

Figure 13 presents photographs of the shake table tests conducted on the selected RC specimens. An analysis of the figure indicates that the initial specimen has experienced considerable damage, in contrast to the second specimen, which appears to be unscathed. The prominent cracking in the upper corners of the first specimen, along with the observed concrete crushing, indicates a significant joint shear failure. Further, significant areas of the concrete overlay have separated, especially in the regions near the base and the junctions between beams and columns. The damage at the joints may have compromised the bond between the reinforcement and the surrounding concrete, leading to further weakening. In contrast, the second specimen exhibited no signs of damage, such as cracks or spalling, suggesting that the TnT BRB performed its function of dissipating seismic energy effectively. The inclusion of the diagonal brace enhanced resistance to lateral forces, which in turn minimized deformation and safeguarded against early failure of the beam-column joints. Thus, it can be deduced that the TnT BRB system played a crucial role in absorbing and redistributing seismic forces, thereby averting significant stress accumulation in the joints.

7. Conclusions

This research emphasizes the substantial efficacy of the innovative TnT BRB system as a seismic retrofitting method specifically designed to enhance the resilience of RC beam-column joints. Comprehensive experimental investigations conducted via shake table testing clearly highlighted critical shortcomings inherent in conventionally designed non-ductile RC structures. Such structural systems exhibited pronounced brittle shear failures, substantial lateral displacements, and significant joint degradation under cyclic seismic excitations. These observed vulnerabilities underscore the pressing need for robust and effective seismic retrofitting strategies for existing infrastructure.

Conversely, the integration of TnT BRBs resulted in considerable enhancements in seismic performance. The retrofitted RC frames demonstrated notable reductions in lateral drift, improved capacity for energy dissipation, and sustained integrity of key structural joints. The substantial mitigation of structural damage progression and enhanced global stability under seismic loading clearly illustrates the transformative potential of the proposed retrofitting solution.

The value of this investigation is amplified through the integration of advanced analytical techniques, particularly sophisticated fiber-based FE modeling. This analytical approach effectively captured complex structural responses, such as hysteretic behaviors, localized damage phenomena, stiffness deterioration, and energy dissipation. Although the fiber-based FE element model provides key insights into the seismic performance of RC structures, its limitations in capturing complex localized behaviors must be acknowledged. Future research should prioritize hybrid modeling techniques that combine the strengths of fiber-based frameworks with detailed models of localized damage.

As a conclusion, this study effectively bridges empirical and analytical methodologies, providing critical insights and validated tools for seismic rehabilitation of vulnerable RC structures. This integrated framework represents a significant contribution to both theoretical knowledge and practical application, offering valuable guidance for ongoing and future research efforts, as well as enhancing seismic design standards and resilience strategies within earthquake engineering. Future research should focus on optimizing the design parameters of TnT BRBs, exploring their long-term durability, and assessing their applicability across a broader range of structural configurations.