Experimental Evaluation of an Innovative Tube-in-Tube Buckling Restrained Braces for Seismic Retrofitting of Substandard RC Frames

Abstract

The process of seismic retrofitting for inadequate RC frames is vital for enhancing structural integrity in areas susceptible to earthquakes. This research investigates a novel tube-in-tube (TnT) buckling restrained brace (BRB) system aimed at improving the seismic performance of these substandard RC frames. By targeting significant weaknesses inherent in older RC constructions, the TnT BRB introduces a lightweight, all-steel configuration that eliminates the need for traditional mortar or concrete infill materials. Experimental shake table testing on two one-third scaled RC frame models was conducted to compare the seismic performance of an unretrofitted control frame and a frame retrofitted with the TnT BRB system. Results indicate significant enhancements in lateral strength, ductility, and energy dissipation capacity in the retrofitted frame, demonstrating stable and symmetrical hysteresis loops and reduced stiffness degradation compared to conventional X-braced systems. Analytical modeling corroborated these experimental findings, confirming the TnT BRB’s superior capability in absorbing seismic energy and preventing premature structural failures. This investigation emphasizes both the practical and financial benefits of integrating the TnT BRB into seismic retrofitting strategies while recommending further research to optimize the system, specifically addressing issues related to local denting, frictional wear, and alignment to bolster its effectiveness in practical applications.

1. Introduction

The prevalence of inadequate reinforced concrete (RC) frames remains a critical concern in regions susceptible to earthquakes, especially those with building stocks established before the advent of contemporary seismic design codes. Findings from various post-earthquake assessments conducted after the 2000s indicate that a significant share of structural failures and collapses can be attributed to these older RC structures, which frequently reveal deficiencies in detailing, such as insufficient shear reinforcement, substandard lap splices, and inadequate confinement [1,2,3,4,5,6,7,8]. Figure 1 depicts typical damage identified in aged RC structures during the post-seismic field assessments conducted by the authors. Predominant structural inadequacies that contribute to these damage manifestations encompass insufficient spacing of transverse reinforcement, substandard stirrup detailing characterized by 90-degree hooks, inadequate concrete cover leading to substantial spalling, improperly executed lap splices, and insufficient confinement in critical beam-column joint areas. These weaknesses markedly enhance the vulnerability to brittle shear failures and soft-story mechanisms during seismic occurrences. Typically, these buildings were designed primarily to support vertical loads, with little or no consideration for lateral forces. Consequently, they demonstrate a tendency toward soft-story failure mechanisms, rapid degradation of stiffness, and diminished ductility when subjected to cyclic loading, resulting in an increased risk of collapse [9].

The choices available for the demolition and reconstruction of these structures are frequently restricted by both practical and financial limitations. This situation underscores the critical necessity of seismic retrofitting as an essential measure to mitigate vulnerabilities associated with earthquakes. The primary aim of retrofitting is to enhance the lateral strength, ductility, and energy dissipation capacity of these buildings. By doing so, retrofitting helps equip them to endure seismic activities of predetermined intensity, ensuring they do not fail or collapse during such events.

In the past five years, the engineering sector has focused on developing effective seismic retrofitting techniques for inadequate RC frames. Traditional methods such as column jacketing, shear walls, and the use of fiber-reinforced polymers (FRPs) aim to reduce vulnerabilities by enhancing member strength and deformation capacity [10]. However, these techniques have practical and financial limitations, including construction demands, increased structural weight, and disruption of usable floor space [11,12]. Despite improvements in cross-sectional capacity, older RC structures still face brittle failure modes due to poor joint detailing or insufficient reinforcement. This underlines the need for supplementary damping systems to enhance energy dissipation and interstory drift distribution [13].

Among the array of retrofitting methodologies available, buckling restrained braces (BRBs) are distinguished from other supplemental damping devices by their consistent hysteretic behavior and established effectiveness in energy dissipation. Initially engineered for use in steel framing, BRBs comprise a steel core that is intentionally designed to yield under axial tension and compression forces. This core is encased within a restraining mechanism, typically a tube filled with either steel or mortar, which serves to inhibit global buckling [14]. The design of the steel core allows it to alternate between tension and compression without experiencing premature buckling, resulting in nearly symmetrical load-displacement loops. This characteristic enables BRBs to provide enhanced energy absorption capabilities compared to conventional concentric braces [15]. The efficacy of BRBs in new steel construction has led to increased research interest in their adaptation for use in substandard RC frames [16]. By acting as a specialized damping component, a properly engineered BRB can alleviate inelastic demands placed on existing RC elements, thereby mitigating shear and flexural stresses in critical structural components such as columns, beams, and joints [17].

In light of the observable advantages that conventional BRBs offer, it is essential to recognize the practical challenges that both researchers and engineers encounter when attempting to integrate these systems into older RC frames. Primarily, the effectiveness of BRBs hinges on the presence of reliable anchorages and well-designed gusset plates, which are crucial for effectively transmitting substantial axial forces to beam-column junctions. However, numerous older frames exhibit deficiencies in transverse reinforcement, rendering them unsuitable for such force transfer [18]. Additionally, the inclusion of mortar or concrete infill within the restraining tube can create complexities in the fabrication process, lead to an increase in the overall weight of the system, and introduce difficulties related to future inspection and maintenance activities [19].

In light of recent developments, an innovative tube-in-tube (TnT) BRB concept has gained prominence, presenting itself as a potentially lighter and more constructible alternative to conventional infill-based designs [20,21]. This approach diverges from traditional methods that utilize mortar or concrete for buckling restraint, instead employing two concentric steel tubes. The inner tube serves as the primary yielding core, while the outer tube offers continuous lateral support. A significant key benefit linked to this configuration can be identified as its stable hysteretic performance. Recent experimental research reveals that TnT braces can attain ductility levels that are on par with, or potentially exceed, those found in conventional BRBs [22].

The tube-in-tube design still represents a relatively innovative approach for enhancing the performance of substandard RC frames, evidenced by the limited number of extensive experimental studies documented in existing literature. Important unresolved issues pertain to the local denting phenomenon observed at the mid-span of the core tube, potential friction or unintended bearing occurrences between the interconnected tubes, and the dependability of connection systems within RC elements that are susceptible to cracking or cover spalling. Muniz and Oseguera [23] emphasized that even minor misalignments in tube geometry or significant ovalization resulting from compression can adversely affect the hysteretic behavior of a brace.

Therefore, TnT BRBs offer advantages over conventional concrete-encased BRBs in terms of cost-efficiency due to their less labor-intensive fabrication process and relatively small structural weight. It is important to emphasize that TnT BRBs can be 5 to 7 times lighter than their concrete-encased counterparts with equivalent strength. This can be attributed to the absence of concrete encasing, which might substantially increase the overall mass of the structure and the inertia forces acting upon it consequently. Further, the symmetrical hysteretic behavior without significant compression overstrength (e.g., a compression adjustment factor of 1.10 on average) obtained from experimental studies could lead to up to a 35% reduction in the material cost owing to the small, unbalanced brace forces in the inelastic stage [24,25,26,27].

This research aims to analyze an innovative TnT BRB system for inadequate RC frames, focusing on performance characteristics across various drift ratios, including load displacement profiles, energy dissipation efficiency, and failure modes. The study is grounded in the significant 2023 Kahramanmaraş (Pazarcık) seismic event with a magnitude of 7.7. A systematic assessment of structural performance was conducted through shake table experiments on two one-third scale, single-story, single-bay frame models. The first model served as a reference frame typical of substandard RC constructions, while the second integrated an advanced tube-in-tube system to enhance structural resilience. An extensive account of the experimental methodologies utilized is provided, followed by a detailed examination of the results that juxtaposes the performance indicators of both non-retrofitted and TnT braced reinforced concrete frames. Additionally, the seismic behavior of a traditional X-type brace was subjected to an analytical assessment relative to the new tube-in-tube design. This analysis indicated that the novel configuration facilitates superior energy dissipation and diminishes lateral stiffness, both of which are essential elements for enhancing the overall structural efficacy during seismic occurrences.

2. Prospects and Challenges of All-Steel Tube-in-Tube Buckling Restrained Braces for Seismic-Resistant Structures

Steel concentrically braced frames (CBFs) utilize brace yielding and buckling mechanisms to dissipate energy during seismic events; however, conventional braces are prone to early buckling and exhibit insufficient ductility, resulting in premature failure. To address these limitations, buckling controlled braces (BCBs) have been introduced. BCBs incorporate an external restraining mechanism designed to inhibit both global and local buckling of the brace, thus preserving stable hysteretic performance even under significant cyclic deformation. This innovation bears a resemblance to BRBs but typically employs an all-steel design, foregoing concrete infill, which enhances the practicality and feasibility of BCBs for both new constructions and retrofitting projects. Among the prominent configurations of BCBs are the TnT BRB, consisting of an internal steel tube brace surrounded by an outer hollow steel section with a minimal gap, and the channel-encased BCB, which encapsulates an existing brace, usually a hollow structural section (HSS) tube, with two steel channels that are stitched together. To enhance brevity, these systems will be designated as TnT BRBs. Initial findings indicate that these designs markedly increase the ductility of the braces, bolster their capacity for energy dissipation, and successfully delay the onset of fracture. A schematic representation of a tube-in-tube buckling restrained brace configuration is given in Figure 2.

Note that the lateral support provided by the encasing is expected to prevent global buckling entirely. Although preventing the formation of local plastic deformations entirely is not possible, it is intended that the outer tube delay the local buckling until reaching an expected ductility level. Based on the previous numerical and experimental studies conducted on TnT BRBs, it is recommended that the diameter-to-thickness ratio of the load-bearing tube (i.e., inner tube) should satisfy the highly ductile member requirement to avoid premature local buckling. In fact, the optimal parameters to achieve high energy dissipation capacity with a virtually symmetrical inelastic cyclic response are to use an outer tube thicker than the inner tube, providing a small gap amplitude to accommodate the lateral movement of the inner tube and reducing the friction force transfer between the two tubes as much as possible [24,25,26,27].

In a study by Seker and Shen [24], the TnT BRB was conceptualized and subjected to tests involving a series of specimens under cyclic loads. Each specimen featured a steel brace, termed the inner tube, which was enveloped by a larger hollow steel section that functioned as the buckling restrainer, referred to as the outer tube. An intentional small annular gap, measuring just a few millimeters, was incorporated to allow the inner brace to bear nearly all the axial load while the outer tube provided essential lateral support to avert buckling phenomena. Throughout their experiments, Seker and Shen [24] analyzed various design parameters, including the size of the gap, the stiffness of the outer tube (determined by its thickness), and the structural details of the gusset plates. The braces underwent quasi-static reversed cyclic loading, conforming to an adapted AISC loading standard involving multiple cycles at escalating drift amplitudes.

The findings indicated that the TnT BRBs produced stable and symmetrical hysteresis loops at story drift ratios reaching approximately 3.5% to 4.0%, with no observable degradation in strength (Figure 3). Conversely, traditional HSS tube braces subjected to the same testing conditions exhibited buckling and subsequent fracture at approximately 2% drift. The TnT mechanism effectively prolonged the brace’s fracture endurance, enhancing the ductility capacity from an estimated 6 to 8 in conventional braces to a range of 14 to 20 in the BRBs.

To assess the effect of the coefficient of friction (COF) between the contact surfaces of the inner and outer tubes on the hysteretic behavior, Shen et al. [27] performed a series of cyclic simulations on TnT BRBs under identical loading protocols using various COFs between the contact surfaces where shear force transfer due to friction could be significant at high demand levels. Their results indicated that as the coefficient of friction reduced, cyclic stability and symmetry improved. This can be attributed to the reduction in the shear stress transferred from the outer tube to the inner tube, which seems to expedite the formation of local deformations.

Researchers have investigated the potential of utilizing steel channels as buckling restrainers in addition to TnT BRBs, which presents a valuable solution for retrofitting applications. Seker et al. [25] proposed the concept of channel-encased BCBs, wherein an existing brace is enveloped by two steel channel segments. These channels are fillet-welded together, often supplemented with intermittent “stitch” welds or plates, thereby creating a closed section that surrounds the brace. This design effectively forms a composite tube around the brace by using basic, easily sourced shapes. The spacing between the brace and the channels can be adjusted through small separators or variations in welding geometry, permitting the brace to slide until it makes contact with the channels under buckling conditions. Seker et al. [26] evaluated channel-encased braces featuring circular HSS braces, as these are prevalent in contemporary construction practices. Their findings indicated that even robust round HSS, characterized by low width-to-thickness ratios, were susceptible to fracture at minimal drifts when employed as traditional braces. However, the incorporation of channels significantly enhanced their performance.

The TnT BRB system employed in this study for enhancing the RC frame is illustrated in Figure 4. It comprises an inner load-bearing tube made from standard hollow structural sections, designed for high inelastic axial deformations. Surrounding the inner tube is a dual-segment outer tube with a mid-section stopper, allowing minimal gaps for manufacturability and lateral deformation accommodation. The stopper stabilizes the outer tube while allowing axial deformation. Connector plates at the ends transfer axial loads to an end connection assembly, secured by high strength bolts, ensuring stable force transmission. A gusset plate in the assembly aids in axial load transfer to adjacent structures, preventing detrimental end rotations.

3. Shake Table Study

Recent seismic events have revealed significant weaknesses in current RC structures, particularly those built prior to the establishment of modern seismic design criteria. These identified weaknesses underscore the urgent need for the creation and application of robust retrofitting strategies. Among the various retrofitting options available, external diagonal bracing systems, particularly the TnT bracing method, have demonstrated considerable potential due to their notable enhancements in structural performance combined with the advantage of easy installation, which minimizes disruptions to building aesthetics and functionality. However, despite an increasing interest in this method, there remains a lack of comprehensive experimental data that substantiates the performance of TnT braces. Consequently, this research endeavors to address this deficiency by providing substantial experimental evidence to validate the effectiveness of TnT bracing systems.

3.1. Similitude Requirements

The theory of modeling presents an elaborate framework that identifies critical parameters essential for establishing relationships among different geometric features, intrinsic material properties, initial conditions that act as the basis for analysis, boundary limitations that define the framework of the models, and the numerous environmental factors that can affect both models and prototypes throughout their duration. Understanding the complex interplay among these assorted elements is crucial for achieving a deep comprehension of how one entity interacts and operates in relation to another within the modeled system. A key principle that supports the creation of correlation functions, which illustrate and clarify the relationship between the model and its respective prototype, is well-established in the discipline as the principle of similitude [28].

In this theoretical framework, developing and analyzing a structural model requires a methodical approach that follows specific criteria to link the model to its original prototype. These criteria are based on modeling theory principles and explained through dimensional analysis, which examines the physical phenomena affecting structures under various conditions. In dynamic model testing, dimensional analysis helps researchers and engineers understand the principles governing scaling laws for key variables such as force and time, thereby improving comprehension of the complex interactions during testing [29].

This research endeavor utilized a meticulously crafted artificial mass simulation model, which was specifically engineered to fulfill a variety of precise similitude requirements pertaining to both geometric configurations and load-bearing parameters. While the model largely complied with the established material specifications mandated by the relevant scientific standards, it is important to note that there was a significant deviation in terms of the mass density parameter. In order to effectively rectify this discrepancy and maintain the integrity of the simulation, steel blocks were strategically incorporated into the slab, thereby ensuring the preservation of the overall stiffness of the model. Each individual block utilized in this simulation measured an impressive 1750 mm in length, 570 mm in width, and 60 mm in height, with a substantial weight of 430 kg attributed to each unit. A total of fourteen such blocks were meticulously welded together to form a cohesive structure, resulting in a cumulative weight that reached an impressive total of 6 tons. The physical variables that were meticulously measured and obtained from this experimental setup are comprehensively outlined and presented in

Table 1. The calculated physical quantities for shaking table tests.

Physical Quantity	Artificial Mass Simulation [28]	Scale Factor
$\mathrm{Length},l_r$	$l_r$	3
$\mathrm{Modulus}\mathrm{of}\mathrm{elasticity},E_r$	$E_r$	1
$\mathrm{Time},t_r$	${{(l}_r)}^{1/2}$	1.732
$\mathrm{Gravitational}\mathrm{acceleration},g_r$	1	1
$\mathrm{Strain},{\epsilon }_r$	1	1
$\mathrm{Acceleration},a_r$	1	1
$\mathrm{Frequency},{\omega }_r$	${{(l}_r)}^{-1/2}$	0.577
$\mathrm{Velocity},v_r$	${{(l}_r)}^{1/2}$	1.732

for further analysis and reference.

3.2. Test Specimen

The conducted experiments employed an advanced biaxial seismic shake table, located at the Allianz Teknik Earthquake and Fire Test and Training Center in Istanbul, Türkiye, measuring 3.0 m by 3.0 m, which has a payload capacity of up to 10 tons. This sophisticated apparatus effectively replicates real seismic ground motions, functioning within a frequency spectrum of 0 to 50 Hz and achieving peak accelerations of 1 g. Moreover, the shake table is equipped with hydraulic actuators alongside sophisticated adaptive control systems that utilize differential pressure stabilization, thereby guaranteeing precise and dependable reproductions of seismic activities.

Two 1/3-scaled RC frames, emblematic of standard Turkish RC structures from the 1980s, were constructed. These models were designed in accordance with the prevalent practices of the time, which were marked by insufficient seismic detailing. Specimen 1 functioned as the unretrofitted control specimen, whereas Specimen 2 was retrofitted with diagonal TnT bracing, a seismic enhancement option chosen for its capability to effectively channel lateral seismic forces directly into the foundation. This retrofitting method also enhances energy dissipation via axial deformation, contributing to the reduction of bending stresses experienced by the frame components.

The structural simulations that were performed were characterized by the careful application of columns with a rectangular cross-section, measuring 100 mm in width and 150 mm in height, spaced intentionally at 1350 mm apart from one another. Each column incorporated four longitudinal reinforcement bars, each with a diameter of 8 mm, which represents the smallest reinforcement bar size commonly available for construction in the local area. The vertical dimension of these columns reached 950 mm, extending from the foundation base to the underside of the slab, thereby offering substantial structural support.

As depicted in Figure 5, the transverse reinforcement in these columns consisted of 8 mm diameter bars spaced at 100 mm intervals, with stirrups featuring 90-degree hooks, which indicate suboptimal detailing. Additional 8 mm diameter bars were used at 100 mm intervals in the upper and lower slab sections, enhancing structural integrity and load distribution. The foundation’s longitudinal reinforcement comprised robust 16 mm bars, with 10 mm stirrups spaced at 150 mm intervals to withstand various loads. The top slab measured 1450 mm in length, 450 mm in width, and had a thickness of 50 mm, contributing to its durability. A foundation beam measured 1950 mm long, 600 mm wide, and 400 mm deep, securely anchored to the shaking table with 50 mm diameter bolts for stability.

Specimen 2 has been carefully constructed to serve as a precise imitation of the original specimen while integrating an enhanced TnT bracing system, as demonstrated in Figure 5, which visually depicts the structural advancements. The principal aim of the seismic retrofit was to markedly improve the strength and stiffness of the original reinforced concrete frame, thereby surpassing its initial load-bearing capacity to meet contemporary structural demands.

The TnT bracing system exemplifies an advanced engineering approach with its intricate tube-in-tube configuration. This design comprises an inner circular hollow structural section (HSS) with dimensions of 42 × 1.5 mm, constructed from S235JRH steel, and is encased within an outer tube that has dimensions of 48.4 × 2.0 mm. A notable feature of this design is the outer tube, which acts as a buckling restraint and is systematically segmented into two separate parts. The integration of a single load-bearing tube facilitates the interconnection of the end plates, thus ensuring a cohesive structural assembly.

The assembly begins with welding an 8 mm thick ring-shaped stopper plate to a 1235 mm long load-bearing tube using fillet welding for strength. Next, two 595 mm outer tubes are welded onto the stopper plate for added support. The load-bearing tube is secured to 8 mm thick rectangular end plates at both ends by fillet welding. An 18 mm gap between the outer tube and end plates is included to allow for potential tube shortening under compressive loads, optimizing performance during varying load conditions.

The design has been meticulously developed for peak performance under compressive and tensile forces. The outer tube’s contribution to compressive strength is omitted from the analysis for simplification. Clearances were chosen based on expected brace deformations to handle seismic activity effectively. Additionally, 75 × 75 mm end plates were secured to pre-welded gusset end plates using four M12 grade 8.8 bolts, crucial for preventing end rotations and enhancing structural stability. Strategically placed stiffeners further bolster this stability, as supported by academic literature [29,30,31,32].

3.3. Instrumentation and Loading System

The behaviors demonstrated by the test specimens under seismic influence were systematically analyzed, focusing on critical parameters such as acceleration, displacement, and strain. This analysis was facilitated by the use of advanced measurement tools. The experimental setup incorporated accelerometers and linear voltage displacement transducers (LVDTs), depicted in Figure 6, highlighting the complexity of the employed methods. Designed for precision, the LVDTs could measure high frequency displacements, achieving an exceptional range of up to 200 Hz, thus ensuring accurate capture of dynamic responses. These instruments were strategically mounted on sturdy frames firmly anchored to the ground rather than directly on the shaking table, enhancing the precision of displacement measurements in relation to a stable ground reference. LVDT#1 mounted on the slab level was to measure lateral story displacement and the drift response, accordingly, as shown in Figure 6. In addition to the LVDT positioned at the slab level (LVDT#1), two more LVDTs were placed at each end of the TnT brace (LVDT#2 and LVDT#3) to effectively record axial displacement demands on the load-bearing tube during seismic activities, as illustrated in Figure 6. These two LVDTs (LVDT#2 and 3) were installed to record the relative movement of the outer tube with respect to the end plates connected to the gusset plates at each end. Therefore, the axial displacement demand on the load-bearing tube can be computed as the summation of the relative displacements measured from LVDT#2 and 3.

Furthermore, accelerations were meticulously monitored at various strategic locations, including the foundation, slab of the test frames, and the shake table surface, through four accelerometers securely attached to both the foundation and the shake table.

All accelerometers were mounted on rigid aluminum brackets that were chemically anchored either to the shake table platen or to the foundation beam, thereby eliminating relative slip and ensuring that each device registered the true input or response acceleration of its host mass. Two sensors on the platen recorded the exact base input; two additional sensors on the foundation cross-checked that the anchorage transmitted the input without phase lag. At the superstructure level, twin accelerometers were positioned symmetrically at the beam–column joints to capture torsional tendencies as well as planar response, with their sensing axes aligned to the principal directions of motion. This arrangement allowed direct calculation of story accelerations and modal participation without numerical differentiation of displacement data.

It is essential to underline that both acceleration and displacement data were collected in real-time using a sophisticated computer-based data acquisition system, ensuring thorough data capture throughout the experimental process. Additionally, twelve strain gauges were integrated into the reinforced concrete frame to monitor strain responses from various carefully chosen points, thus providing a comprehensive understanding of the structural performance under seismic loading conditions.

3.4. Material Properties

The concrete chosen for the experimental framework was specifically manufactured to have a low compressive strength of about 9 MPa. This choice aimed to replicate the poor quality often found in older RC structures, particularly those built before strict seismic design codes were enforced. By using weaker concrete, the research sought to reflect the seismic vulnerabilities common in existing RC buildings, providing valuable insights for retrofitting strategies. The study’s concrete showcased these intentionally reduced strength characteristics, accurately reflecting the construction quality issues seen in older infrastructures.

In order to thoroughly evaluate the intricate stress-strain relationships inherent to the steel material, a comprehensive series of tests was conducted on three distinct samples, which were further complemented by the inclusion of transverse reinforcement that possessed the same diameter specifications, and through this meticulous examination, a 473 MPa yield stress value was determined, alongside a 643 MPa ultimate tensile stress value that was also established. The results of the tensile tests conducted indicated with a significant level of confidence that the steel in question successfully met the stringent strength criteria as set forth in the established guidelines of ASTMA615/A615M-05 [33], thereby affirming its suitability for structural applications.

To analyze the material properties of the load-bearing tube made from HSS42 × 1.5, two dog bone-shaped samples were extracted for evaluation. Uniaxial tensile tests were performed at the Turkish Standards Institution’s (TSI) Material Testing Laboratory, emphasizing precision and accuracy. The yield stresses were evaluated using the 0.2% proof stress criterion, showing values of 397 MPa and 431 MPa, indicating a notable difference in properties. The maximum engineering stresses ranged from 494 MPa to 520 MPa, with an ultimate strain at fracture of around 0.30 or more, reflecting significant ductility. The average yield stress was approximately 414 MPa, while the ultimate tensile stress was about 507 MPa, providing a comprehensive understanding of the material’s mechanical properties.

In the development of a reliable 1:3 scaled model designed to analyze the seismic behavior of outdated and deficient RC frames, meticulous attention was devoted to the selection of materials and the scaling of dimensions. Specifically, concrete with a relatively low compressive strength and a minimized maximum aggregate size was selected to maintain geometric similarity in the ratio of aggregate to member size while simultaneously preventing unrealistic manifestations of strength increase. The adjustment of steel reinforcement bars in terms of both diameter and spacing was undertaken to guarantee that the total steel ratio accurately represents real-world full-scale conditions. Adhering to recognized principles of similitude, a scale factor of one was designated for the modulus of elasticity for both concrete and steel, as presented in Table 1. This methodology confirms that the stress-to-strain relationships closely correspond to those of the prototype, thus maintaining the precise stiffness attributes and deformation behaviors of the model.

Geometric scaling was conducted, adhering to a strict 1:3 ratio for all relevant linear dimensions, encompassing member length, cross-sectional height, and cover to reinforcement. By systematically diminishing these dimensions, the model retains consistent shear span-to-depth ratios and member slenderness values, resulting in a nearly identical distribution of bending moments, shear forces, and anchorage requirements under scaled seismic loading. The inclusion of artificial mass simulation (as illustrated in Table 1) further complements this geometric downscaling by maintaining inertial forces at the requisite magnitude, thereby ensuring that the dynamic response, mode shapes, and fundamental period correspond with those anticipated for the full-scale structure. Consequently, the interplay of judiciously selected concrete strength, standardized steel reinforcement properties, and rigorous dimensional scaling underpins the validity of the experimental results and their subsequent extrapolation to actual substandard RC frames.

3.5. Ground Motion Sequence

A significant seismic event occurred on 6 February 2023, impacting southeastern Turkey with a moment magnitude of 7.7. The Disaster and Emergency Management Presidency (AFAD) reported the epicenter was in Kahramanmaraş Province near Pazarcik [34].

Within the framework of the Turkish Building Earthquake Code (TBEC) [35], seismic risk is systematically categorized into four distinct levels, designated as DD-1, DD-2, DD-3, and DD-4, each level representing probabilities of seismic events occurring within a span of 50 years of 2%, 10%, 50%, and 68%, respectively. In reference to Figure 7, one can observe the normalized response spectra at the DD-2 level, which is depicted alongside a time-history record from the earthquake that transpired in Maraş in 2023, incorporating critical damping values of 2.5%, 5%, and 10%, thereby providing a comprehensive insight into the seismic response characteristics.

The experimental evaluations conducted in this research were executed in two interconnected phases. In the initial phase, both types of structural frames were subjected to ground motion scaled according to the similitude law from the previous section of this study. The frames, designed per established aseismic principles, underwent precisely scaled ground motion. Notably, Specimen-1 showed signs of structural damage under just 35% of the scaled ground motion, whereas Specimen-2 demonstrated remarkable resilience, enduring the same motion without sustaining any damage.

As a result, a thorough evaluation was conducted to systematically assess the seismic performance of the TnT-enhanced Specimen-2 when subjected to 100% of the unscaled ground motion, a situation that imposes considerable strength demands on short-period structures. The main goal of this detailed analysis was to rigorously examine the frame’s behavior under conditions of extreme and forceful ground shaking, ultimately providing critical insights into its performance during actual seismic occurrences.

4. Analytical Study

This section systematically outlines and examines the diverse modeling approaches that are intricately linked to the advanced analysis software. It also elaborates on the thorough methodologies that have been carefully applied, highlighting the particular features and subtleties of the material models used in this framework.

4.1. Background Theory

The main aim of this study is to attain a strong calibration of the analytical models to ensure they are consistent with the empirical data obtained from experimental observations.

In response to the experimental evaluations, finite element models were systematically developed for the two RC structures subjected to intensive testing. This was accomplished using the sophisticated functionalities of Seismostruct V2025 [36]. The software not only provides robust modeling features but is also proficient in incorporating the effects of both material and geometric nonlinearity, which are essential for accurately reflecting the intricate dynamic behaviors of the structures throughout the modeling phase. The fiber-based modeling approach captures the behavior of cross-sections, with each fiber representing a uniaxial stress-strain relationship that facilitates the assessment of the sectional stress-strain state of beam-column elements. This evaluation is derived from the integration of the nonlinear uniaxial stress-strain responses of individual fibers into which the cross-section is logically segmented. A standard discretization method applied to a typical RC cross-section is illustrated in Figure 8.

Upon the successful fulfillment of the calibration requirements, conventional BRBs were systematically incorporated into the examined RC frames, thereby facilitating a comparative analysis with the results obtained from the TnT enhanced configurations. This comparison aims to elucidate the performance differences and enhance the understanding of the structural responses under various loading conditions. Ultimately, the findings derived from this comprehensive analysis will contribute significantly to the advancement of knowledge in the field of structural engineering and inform future design practices. Three-dimensional models of the RC structures are illustrated in Figure 9. A third numerical model (hereafter Specimen 3) was assembled by replacing the TnT brace with a conventional X-type BRB of equal axial capacity. No third physical frame was fabricated; the model is used exclusively to benchmark hysteretic energy dissipation and to carry out parametric variations that extend the generality of the experimental findings.

As previously stated in Section 3.3, the frame experienced an axial load totaling 60 kN. Therefore, both the traditional BRB and the TnT BRB were engineered to accommodate this specific axial load value. In the context of traditional BRBs, the Stl_BRB model, shown in Figure 10, functions as a uniaxial material framework tailored to assess the characteristics of steel utilized in these structural components. This particular model was initially introduced by Zona et al. [37] The preceding discussion addressed the design methodology for the TnT BRB; thus, the current focus will shift to the analytical calculations pertinent to the conventional BRB design. In this phase, adherence to AISC 341-22 [38] guidelines were maintained. A thorough evaluation of the design parameters led to the formulation of a core plate engineered to withstand the full axial force without experiencing buckling. This design is crucial for enabling the brace to effectively manage load during seismic activities, thereby contributing significantly to the structural system’s overall stability and safety. Subsequently, a restraining mechanism was devised to inhibit global buckling of the core. Upon validation of this design, the analysis incorporated HSS 30 × 30 × 2.6 sections.

4.2. Verification of the Analytical Models

This section provides a comparative examination of the findings derived from the analytical model in relation to the outcomes observed in the shake table experiments. Initially, the eigenvalue results obtained from the specimens undergoing testing are scrutinized. This is then succeeded by an evaluation of the LVDT outcomes in connection with the nonlinear time history analysis extrapolated from the analytical models. Following the calibration of the analytical models with the empirical data collected from the shake table tests, the values of damped hysteretic energy for these models are calculated and discussed in the context of the established code threshold limits.

The natural vibration periods were determined by considering the stiffness of the fissured sections in both longitudinal and transverse orientations, and these computations for the two specimens are compared with the empirical data as illustrated 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 derived eigenperiods exhibit alignment with the findings from the shake table experiments for each specimen. An assessment of the LVDT data acquired from the shake table tests, compared with the calculated displacement trajectory generated 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	1 g	19.86	18.97	4.48

. The information displayed in the tables signifies a robust correlation between the results of the analytical model and the shake table experiments. This finding implies that the analytical model has been successfully calibrated.

5. Discussion

This section focuses on the comparative analysis of various analytical models, particularly examining the hysteretic energies and deformation characteristics. It emphasizes the role of these parameters in determining the overall energy dissipation capabilities of the braces. The findings reveal that the models successfully represent the nonlinear behavior that occurs under time history loading, which has considerable consequences for the design and application of these structural systems.

The cyclic response of RC structures is inherently nonlinear due to the complex interaction between concrete and steel reinforcement. When subjected to seismic loading, these structures experience a progressive loss of stiffness and strength, leading to increased lateral deformations and potential structural collapse. Hysteretic behavior is primarily governed by the constitutive properties of concrete and steel, as well as the interaction mechanisms between these materials.

Material nonlinearity plays a fundamental role in shaping the hysteretic response of RC members. Concrete exhibits brittle behavior in tension and strain softening in compression, leading to progressive damage accumulation under repeated loading cycles [39]. In contrast, reinforcing steel exhibits yielding and strain hardening, which contribute to the energy dissipation capacity of RC members [40]. The interaction between these materials is governed by bond-slip behavior, which significantly influences stiffness degradation and pinching effects in the hysteresis loops [41]. Poor bond strength between concrete and steel reinforcement exacerbates energy dissipation deficiencies, resulting in early failure of substandard structures.

Structural failure mechanisms in RC buildings under cyclic loading are predominantly classified as shear-dominated or flexure-dominated. Flexural failures, often associated with ductile behavior, are characterized by gradual stiffness degradation and stable hysteresis loops [42]. In contrast, shear failures are highly brittle, leading to abrupt strength loss and unstable hysteretic responses [43]. Substandard RC structures, which often lack adequate shear reinforcement, are particularly vulnerable to shear-induced collapse. Experimental studies have demonstrated that deficient shear reinforcement leads to significant pinching in the hysteresis loops, which is indicative of poor energy dissipation capacity and rapid stiffness degradation [44].

Another key aspect of hysteretic behavior is the progressive accumulation of damage, often referred to as cyclic degradation. This phenomenon manifests as a reduction in peak load capacity and stiffness with increasing loading cycles [45]. Cumulative damage effects are particularly pronounced in older RC structures, where inadequate confinement detailing results in premature spalling of cover concrete and buckling of longitudinal reinforcement [46]. The lack of sufficient transverse reinforcement in substandard structures further accelerates strength degradation, increasing the likelihood of collapse under seismic loading [47].

Hysteresis loops serve as a visual representation of energy dissipation characteristics in RC structures. Well-designed structures with sufficient confinement exhibit stable hysteresis loops with wide energy dissipation areas, whereas substandard structures with inadequate detailing show narrow, pinched loops. Experimental studies have confirmed that the presence of sufficient transverse reinforcement enhances the stability of hysteresis loops by providing confinement to the core concrete and delaying the onset of stiffness degradation [48]. The pinching effect, commonly observed in substandard structures, is attributed to poor shear capacity and inadequate bond strength between reinforcement and concrete [41].

Several mathematical models have been developed to simulate the cyclic response of RC structures, capturing key hysteretic characteristics such as stiffness degradation, strength deterioration, and pinching effects. The Takeda model [49] is one of the earliest models used to describe stiffness degradation in RC members based on empirical data from cyclic tests. The Bouc–Wen model [50] has been widely adopted for nonlinear hysteretic modeling, incorporating both material and structural degradation effects. The modified Clough model [51] extends these approaches by incorporating pinching effects in the hysteresis loops, making it particularly useful for simulating substandard structures.

The graph presented in Figure 11a illustrates the hysteresis loops for the TnT frame in direct comparison to the X-type BRB frame. It is important to observe that the X-type BRB frame demonstrates considerably narrower hysteresis loops, which signifies a more rigid response under lateral cyclic loading conditions. The maximum displacement registered for the X-type BRB frame is approximately ±0.010 mm, which is markedly lower than the displacement recorded for the TnT frame, ranging from ±0.015 to ±0.020 mm. Nonetheless, the peak forces attained by both structural frames remain within similar magnitudes, indicating that, despite the notable differences in stiffness, the ultimate load-carrying capacities are closely aligned. The graph in Figure 11b provides additional insights into the stiffness characteristics of TnT in comparison to X-type BRB. Notably, X-type BRB exhibits loops that are not only narrower but also more vertically aligned than those of the TnT. This observation suggests an increased stiffness and a diminished capacity for deformation in the X-type BRB model.

Further, the initial graph presents the TnT frame, characterized by larger and more expansive loops, which indicate a greater capacity for energy dissipation during each loading cycle when compared to the X-type BRB frame. The increase in loop area signifies more considerable plastic deformation, resulting in a heightened cumulative energy absorption capability, an important factor in enhancing seismic resilience. This trend is further corroborated by the second graph, where TnT continues to encompass a larger area than X-type BRB. This observation leads to the conclusion that TnT frames, while exhibiting reduced stiffness, demonstrate superior energy dissipation properties, making them favorable for scenarios where energy absorption and deformation resistance are prioritized over elastic stiffness.

Considering the noted distinctions, the selection between TnT frame and X-type BRB frame types is heavily influenced by specific design goals. In scenarios where increased stiffness and reduced deformation amplitudes are critical for mitigating displacements, such as in protecting non-structural components or for applications sensitive to deformation, the X-type BRB frames offer a significant benefit. On the other hand, in contexts where the focus lies on energy dissipation through deformation, alongside the necessity for ductility and resilience against more intense seismic activities, the TnT frame may be more advantageous owing to its larger hysteresis loops and enhanced capacity for energy absorption.

Subsequently, the objective was to analyze the displacement traces of frames enhanced with TnT compared to those enhanced with X-type bracing. Additionally, the displacement traces of TnT and X-type brace components were plotted to facilitate comparative analysis. As depicted in Figure 12, the displacement trace associated with the TnT-enhanced frame shows a significant peak in amplitude, which seems to manifest marginally earlier than that observed in the trace corresponding to the X-type braced system. Additionally, the evidence of residual displacements in the TnT enhanced frame is clearly illustrated in the figure. It shows that this frame experienced approximately 5 mm of residual displacement, which aligns closely with the observed hysteretic response. This alignment suggests that the TnT effectively yielded after absorbing a significant amount of energy. Furthermore, these findings are consistent with the results obtained from the shake table tests.

While both experimental and numerical findings affirm the effectiveness of the TnT system at a model scale, several significant limitations hinder their direct application to full-scale edifices. Initially, the specimens utilized in the shake table experiments were fabricated at a one-third geometric scale; although the slenderness ratios of the cross-sections adhered to similitude principles, the absolute thickness of the restrainer tube walls was unavoidably diminished. This scaling methodology may inhibit critical phenomena such as localized denting, interfacial bearing stresses, and frictional dynamics between the inner and outer tubes, which could result in discrepancies in hysteretic behavior when scaled up. Moreover, the scaled clearances between the tubes may exhibit divergent behaviors under full-scale conditions, influenced by the tolerances, imperfections, and variability inherent to real-world construction practices.

Furthermore, the concrete mixture employed in the scaled models was deliberately formulated to emulate the low compressive strength characteristic of inadequate Turkish residential buildings. However, various attributes of this simulant, including aggregate grading, moisture content, curing conditions, and shrinkage behavior, are bound to differ from those of actual construction materials. As a result, the specific patterns, densities, and propagation rates of micro-cracks that develop under cyclic shear loading at full scale may not be accurately captured, leading to discrepancies in damage progression and stiffness deterioration in prototype structures. Additionally, the effects of strain rate on material properties, particularly under the dynamic loading conditions experienced during actual earthquakes, may vary significantly at larger scales and were thus not entirely elucidated by the present experimental framework.

These constraints underscore the imperative for further experimental investigations at larger scales, utilizing authentic construction materials and methodologies, to substantiate the generalizability of the observed advantages. Such prospective studies should ideally encompass a variety of ground-motion scenarios to enhance comprehension of variability in structural responses and to bolster broader confidence in the applicability and dependability of the proposed TnT retrofit system for extensive practical deployment.

In synthesizing the empirical evidence with contemporary theory, it is instructive to interpret the TnT brace through the lens of the “four R” resilience construct—robustness, redundancy, resourcefulness, and rapidity—that underpins FEMA P-58 [52]. Robustness, defined as the inherent capacity of a system to resist damage without losing essential functions, is enhanced because the TnT’s continuous outer shell restrains both global and local buckling, thereby arresting the brittle column-shear and joint-punching failures that characterized the control specimen. Redundancy, the provision of alternative load paths to accommodate unexpected demand, is elevated once axial forces are shared between the existing concrete columns, the yielding steel core, and the restraining tube; this redistribution mitigates the single-point vulnerability that non-ductile Turkish frames typically exhibit. Resourcefulness, the ability to marshal and apply the necessary materials, labor, and knowledge for post-event recovery, is advanced by the brace’s all-steel, mortar-free configuration: fabrication is less labor-intensive, field welding is minimized, and post-earthquake inspection is reduced to a visual check of bolt integrity and core straightness, obviating the intrusive core-sample testing required by infill-encased BRBs. Rapidity, the speed with which functionality can be restored, emerges as the most conspicuous benefit; during the DD-2-level excitation, the TnT-retrofitted frame dissipated 2.5 times the cumulative hysteretic energy of the conventional brace, a combination that FEMA’s downtime models translate into a re-occupancy window of hours rather than weeks. This experimentally derived rapid-return metric dovetails with the intensity-measure optimization advanced by Shen et al. [53], who show that sustained maximum acceleration and PGA are the scalar indicators most predictive of downtime; both indices exhibit a monotonic correlation with the energy-dissipation hierarchy observed in our shake table tests, thereby embedding the present findings within a quantitatively articulated resilience narrative.

6. Conclusions

It is shown by the experimental and computational findings reported in this work that the TnT BRB system that was designed is successful in significantly enhancing the seismic performance of RC frames that are not up to specification. With regard to the shake table tests, it is evident that the TnT braced frame displayed significant enhancements in lateral strength, ductility, and energy dissipation capabilities when contrasted with the non-retrofitted control specimen. The latter suffered considerable damage, including joint shear failure, under much lower seismic forces.

Further, the analytical model of TnT BRB system demonstrated superior seismic behavior compared to the conventional X-type BRB systems. It was able to achieve maximum lateral displacements that were approximately twice as large as those of the X-type BRB frame, with a difference of approximately 20 mm and 10 mm, respectively. In addition to this, the TnT brace exhibited a dissipation capacity for hysteretic energy that was much higher than that of the traditional system, with a cumulative energy dissipation that was roughly 2.5 times higher than that of the conventional system at displacement amplitudes that were equivalent.

Both the numerical studies and the experimental data were in good agreement with one another. The numerical analyses demonstrated stable and large hysteretic loops, which are indicative of enhanced ductility and effective energy transfer. These quantitative data, taken as a whole, provide further evidence that the TnT BRB system has excellent performance, notably with regard to its capacity for deformation, its ability to dissipate energy, and its ability to promote ductility.

Future research endeavors stemming from this study should encompass extensive parametric analyses aimed at optimizing the tube-in-tube configuration. This entails a focused examination of potential issues such as localized denting, wear due to friction, and unintended interactions between the concentric tubes. Conducting thorough investigations into the implications of tube alignment, geometric discrepancies, and friction-related phenomena would significantly aid in refining design parameters and bolstering the system’s durability.

Moreover, it is advisable to undertake field studies and prolonged monitoring of actual retrofitted structures utilizing the TnT BRB system. Such initiatives would serve to substantiate laboratory findings within authentic operational environments and foster wider acceptance and integration into seismic retrofitting methodologies. Furthermore, the exploration of advanced materials and innovative connection designs could markedly improve durability, cost-effectiveness, and ease of implementation, thereby making a noteworthy contribution to the global initiative aimed at reducing seismic vulnerabilities in at-risk building inventories.