Application of pre-stressed CFRP rods in self-centring buckling-restrained brace for enhanced seismic resilience

Abstract

The self-centring brace is recognized as one of the practical solutions for mitigating catastrophic consequences caused by earthquakes and improving structural resilience. Compared to the current methods where self-centring capacity is typically provided by pre-stressed steel rods or disc springs, carbon fiber-reinforced polymer (CFRP) material of higher tensile strength and deformation capacity is emerging as a preferred alternative to traditional materials. Based on that, this study mainly aims to propose a novel self-centring buckling-restrained brace (SC-BRB) by using pre-stressed CFRP rods as self-centring components, named the CFRP-SC-BRB. First, component-level analysis was conducted by experimental and numerical methods, to verify the feasibility of the designed configuration. Cyclic and ultra-low-cycle fatigue tests on the specimen demonstrated the excellent performance of the CFRP-SC-BRB, with the peak force of the brace at the drift ratio of 1/120 over 2900 kN and a residual drift ratio controlled below 0.5%. Finite element models in refined and simplified methods were validated by the experimental results and theoretical prediction. Then, a series of system-level analyses are carried out on a prototype frame incorporating the proposed CFRP-SC-BRBs. Compared to the original design with conventional BRBs, seismic responses of the frame fully or partially replaced by the SC-BRBs show a competitive advantage in seismic performance. Especially for the SC-BRB frame with full replacement, the median residual inter-storey drift ratios are reduced by 29.3% and 50.5% under design basis and maximum considered earthquakes, respectively, compared to the conventional BRB frame. In conclusion, it is demonstrated that the proposed CFRP-SC-BRB is effective in improving seismic resilience both at component and system levels. Practical suggestions are also provided to address potential challenges in promoting the novel product in actual application.

Graphical abstract

Keywords

carbon fibre reinforced polymer / self-centring / buckling-restrained brace / seismic analysis / resilience

1 Introduction

To prevent the catastrophic consequences to the safety of life and property caused by earthquake hazards, the self-centring structure is regarded as one of the solutions with high seismic resilience [1]. The minor residual deformation of the self-centring structure under ground excitations can significantly reduce the difficulty of post-earthquake repair, saving both time and economic costs [2]. In recent two decades, this kind of system has been investigated in different parts of the structure in various configurations, such as self-centring beam-column joints [3–5], column bases [6–8], and structural braces [9–11]. Among them, the self-centring brace is an effective solution to enhance the seismic resilience of structures, providing a stable energy-dissipation capacity and a re-storing force [12]. The self-centring brace can be implemented without significantly altering the conventional design, making its application acceptable and practical not only in new construction but also in retrofitting projects.

The self-centring braces consist of two major components, i.e., the energy-dissipation component and the self-centring component, the combination in various configurations has been continuously investigated in different systems. As to the energy-dissipation component, there has been research on different forms, such as yielding steel bars [13], friction devices [14,15], and hybrid dampers [16–18]. Among different configurations, the buckling-restrained steel core is a kind of widely-used energy-dissipation component, and the brace incorporating the core is known as the buckling-restrained brace (BRB). There have been lots of variations of the buckling-restrained core, e.g., Zhao et al. [19] conducted experimental investigations into BRBs with low-yield-point steel core, and discussed the responses between three different grades. Wang and Tong [20] proposed another BRB with a low-yield-point steel core in an assembled all-steel configuration. Furthermore, the core designed with multi-stage yielding forces also gains increasing attention recently. For instance, Zhang et al. [21,22] proposed assembled BRBs with different configurations to achieve multi-stage stiffness and yielding force to phased control structural response in different intensities of the earthquake. Azizi and Ahmadi [23,24] proposed a dual-core BRB with both low-yield-point and ultra-high-strength steels, achieving two-stage yielding and self-centring behavior by fully utilizing the steels with contrasting strength properties. Shi et al. [25] investigated the performance of bridge bents with multi-stage BRBs, where one high-yield-point core is sandwiched between two low-yield-point steel cores. He et al. [26] investigated another novel BRB with two weakened segments in the bracing core, exhibiting a distinct three-stage yielding characteristic. It should be noted that the buckling-restrained core (usually used in conventional BRBs) can be easily combined with self-centring components to convert it into a self-centring BRB (SC-BRB).

Regarding the self-centring component, it is typically designed as the pre-pressed rods or springs, with the re-storing force adjusted by varying the pre-stress and number of sets. With the application of advanced materials in civil engineering field [27–29], a few emerging studies are exploring their performance in the self-centring component to further improve the self-centring capacity. For example, Erochko et al. [30] used pre-tensioned aramid tendons in an enhanced-elongation telescoping self-centring brace, and the prototype frame incorporating the brace was capable of withstanding a drift of 3.9%, enough for resisting extreme earthquakes. Chen et al. [31] proposed a variable-friction self-centring brace with pre-tensioned NiTi shape memory alloy cables, of which the super-elastic property contributes to the self-centring and energy-dissipation capacity. Results showed that the frame with the novel product can more effectively reduce peak structural deformation compared to other types of self-centring braces. Xie et al. [32] applied pre-stressed basalt fiber-reinforced polymer tendon in a self-centring buckling-restrained brace, to utilize the elastic property and the high ultimate strain of the material. The designed mechanism was proven effective, and both the post-activation stiffness and potential ductility rate were improved by increasing the tendon area. Inspired by the promising outcomes of previous studies, it is meaningful to investigate higher-performance material to further enhance seismic resilience.

Carbon fiber-reinforced polymer (CFRP) is regarded as one of the advanced materials, primarily owing to its excellent strength-to-weight ratio which is superior to conventional materials [33]. CFRP material has been increasingly applied in civil engineering these years, including the field of structural strengthening and retrofitting (e.g., [34,35]), as well as new construction in bridge and building engineering (e.g., [36,37]). Based on that, it is suitable to apply this advanced material in the self-centring brace discussed in this study. The CFRP rods can achieve the same or greater bearing force as steel ones with fewer sets and smaller cross-sections, benefitting from the higher tensile strength. Meanwhile, its relatively lower elastic modulus compared to steel enables a better deformation capacity. Specifically, taking the steel rod with a tensile strength of 1860 MPa (highest among the common) and elastic modulus of 200 GPa and the CFRP rod with a strength of 2400 MPa (after reduction considering anchorage efficiency) and modulus of 160 GPa for comparison, the ultimate strains are 0.9% and 1.5%, respectively. Clearly, it highlights the superior performance of CFRP rods in such applications. Besides, CFRP rods also have the advantages of excellent corrosion and fatigue resistance, leading to superior life-cycle performance compared to steel ones.

Accordingly, this study mainly aims to apply pre-stressed CFRP rods in the self-centring brace to improve seismic resilience. The configuration is modified based on a conventional BRB which is commonly used in engineering projects, to realize the mechanism that the self-centring and energy-dissipation capacity are provided by pre-stressed CFRP rods and the steel core, respectively. Note that the main focus of this study is to demonstrate the feasibility of CFRP rods as self-centring components. Consequently, the standard buckling-restrained steel core serves solely as the energy-dissipation component, and other configurations like multi-stage or hybrid energy dissipation methods are not discussed herein. The proposed CFRP self-centring buckling-restrained brace (CFRP-SC-BRB) is going to be first validated by the experimental and numerical investigation at the component level, and then the structural response of a prototype frame incorporating the novel braces will be analyzed by system-level seismic analysis. The structural responses of the SC-BRB frame will also be compared with the conventional BRB frame, to provide a comparative assessment and reveal the difference between them. Moreover, potential challenges and possible solutions will be further discussed to promote the proposed SC-BRB in practical application.

2 Proposed configuration

2.1 Basic characteristics

The configuration of the proposed CFRP-SC-BRB and its deformation mechanism are illustrated in Fig. 1. The CFRP-SC-BRB mainly consists of the steel core, concrete restraint, CFRP rods and the anchorage, inner and outer tubes, and endplates. The steel core serves as the energy-dissipation component by yielding in tension and compression, of which the buckling in compression is restrained by the concrete around it. The group of CFRP rods performs as the self-centring component with the pre-stress applied during the assembly, to reduce or eliminate the residual deformation of the brace after seismic loadings. The inner and outer tubes are connected with the steel core on two different sides, with earplates of tubes perpendicular to the width of the core. The endplates are pressed against the ends of the tubes by tensioning the CFRP rods, without any other rigid connection methods. Note that while both the core and the sheath (inner and outer tubes) are made of steel, the material selection criteria are different. Since the core is used to dissipate energy by yielding in both tension and compression, a steel material with relatively low yield stress and excellent ductility is recommended. In opposite, the steel sheath is used to restrain the concrete and also bear the reaction force of the pre-stressed CFRP rods, so it should be made of steel with relatively high strength to remain elastic throughout the working life of the brace.

The deformation mechanism of the proposed self-centring brace lies in the relative motion between inner and outer tubes, with the gap opening at the tube-endplate interface. Specifically, assuming the outer tube is relatively stationary, and when pulling out the inner tube, the steel core is in tension, with the endplate close to the loading point moving away from the other that is hindered by the outer tube, stretching the CFRP rods simultaneously. On the contrary, when pushing in the inner tube, the steel core is in compression, with the endplate far from the loading point moving away from the other, also stretching the CFRP rods. That is, regardless of whether the steel core is in tension or compression, the CFRP rods are always stretched, and the increasing tension force will help recover the deformation after unloading. It is evident that to realize the designed mechanism, pre-formed openings on the endplate are required to allow the steel core and the earplate to pass through. Besides, the inner tube should be slotted on the section close to the earplate of the outer tube to not hinder the relative motion between them.

As designed, each end of the CFRP rods deforms simultaneously with the endplate on the same side. It is straightforward to anchor the CFRP rods directly on the endplates, but in practice, due to the anchorage of CFRP rods usually in a relatively large size, it is better to embed the rod anchor inside the double tubes. Specifically, an adapter can be used to connect the rod anchor (inside the tubes) and the extended screw (outside the tubes), of which the cross-section of the latter should be smaller than the former. On the one hand, it can help mitigate the cross-sectional reduction of the endplate, so that to control its thickness and opening. On the other side, embedding both the CFRP rods and the anchorage can protect them from environmental threats including fire and corrosion, to ensure safety and durability. The extended screw can also be used to tension the CFRP rods with a through-type jack, after which the screw can be anchored with nuts on the endplate, and the extra length can be truncated directly.

Compared to the conventional BRB, though the configuration of the proposed SC-BRB is indeed more complicated, the design is relatively straightforward, and the manufacturing feasibility has been proved through standardised production processes. As to the construction, the process for the proposed SC-BRB is identical to the conventional, both through processes of lifting, positioning, and welding the ends of the steel core to the gussets. It should be noted that, since the CFRP rods are anchored on the endplates of the tubes, not directly connected to the gussets, it does not influence the installation of the overall brace. For the post-earthquake replacement in practical application, the de-construction of the self-centring BRB is also similar to that of the conventional one. Besides, due to the CFRP rods remaining elastic in common scenarios, they can be reused after replacing the steel core, thereby improving sustainable performance.

2.2 Theoretical behavior

Based on the conceptual design, a bilinear theoretical model can be used to predict the envelope response of the self-centring brace in axial loading. The yielding of the steel core can be regarded as the transition point of the two stages, before which the brace performs as a whole, while after which the stiffness is contributed mainly by the CFRP rods and the post-yield steel core. Correspondingly, the primary and secondary stiffness before and after the transition, i.e., k₁ and k₂, can be calculated as Eq. (1)–(4).

(1)F_0={\sigma }_0{A}_{\mathrm{r}\mathrm{o}\mathrm{d}},

(2)F_{\mathrm{y}}=F_{\mathrm{c}}+F_{\mathrm{s},\mathrm{y}}=\left(F_0+\frac{{\sigma }_{\mathrm{s},\mathrm{y}}}{E_{\mathrm{s}}}{E}_{\mathrm{c}}{A}_{\mathrm{r}\mathrm{o}\mathrm{d}}\right)+{\sigma }_{\mathrm{s},\mathrm{y}}{A}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}},

(3)k_1=\frac{F_{\mathrm{y}}{E}_{\mathrm{s}}}{{\sigma }_{\mathrm{s},\mathrm{y}}L}=\frac{F_0{E}_{\mathrm{s}}}{{\sigma }_{\mathrm{s},\mathrm{y}}L}+\frac{E_{\mathrm{c}}{A}_{\mathrm{r}\mathrm{o}\mathrm{d}}+E_{\mathrm{s}}{A}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}}{L},

(4)k_2=\frac{E_{\mathrm{c}}{A}_{\mathrm{r}\mathrm{o}\mathrm{d}}+\alpha E_{\mathrm{s}}{A}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}}{L},

where F₀ and σ₀ are the pre-load and pre-stress of the CFRP rods, F_y is the yield load of the brace at the transition point, contributed by the yield load of the steel core F_s,y and the corresponding force of CFRP rods F_c (remaining elastic but in the same deformation of the core), E_c and E_s are the elastic modulus of CFRP and steel, A_rod and A_core represent the cross-sectional area of CFRP rods and steel core, σ_s,y is the yield stress of steel, α is the hardening ratio after yielding, and L indicates the length of the brace.

It should be noted that the bilinear model is used for simplification, assuming that the gap opening at the endplate-tube interface and the yielding of the steel core occur nearly simultaneously. A tri-linear model can offer higher accuracy in predicting the monotonic behavior of the brace, to distinguish the points of gap opening and core yielding. Since the cyclic behavior of this kind of seismic brace is the primary focus of this study, and the steel core yields in the loading cycle at the very beginning, the bilinear model is sufficiently accurate to capture the envelope response, as will be validated by experimental investigation later in this paper.

3 Component-level analysis

To realize the conceptual design of the proposed CFRP-SC-BRB, a full-scale component specimen was produced and assembled for experimental investigation, including both cyclic and ultra-low-cycle fatigue tests. Numerical models were established in both refined and simplified methods, and the simulated behavior was compared with test results to validate modeling accuracy, prepared for the system-level analysis in the next section.

3.1 Specimen details

The designed yielding force of the specimen was 1800 kN, of which the total length is 5 m. The width × thickness of the steel core was 145 mm × 35 mm made of Q235 (nominal yield stress = 235 MPa), and the CFRP rods were 4Φ16 with the pre-stress of 600 MPa (25% of the nominal ultimate stress, i.e., 2400 MPa). With the elastic modulus of CFRP and steel being 160 GPa and 206 GPa, the yielding force of the specimen can be calculated by Eq. (2) as 1822 kN, meeting the design requirement. The outer and inner tubes were made of Q355 (nominal yield stress = 355 MPa), in square tube sections of 250 mm × 250 mm × 5 mm and 240 mm × 240 mm × 5 mm (height × width × wall thickness), respectively. The earplates of the inner and outer tubes were also made of Q355 and in a thickness of 40 mm. The cross-section of the endplate was 280 mm × 280 mm × 50 mm (height × width × thickness), in the material of SM570 (nominal yield stress = 570 MPa). A cross-shaped opening was milled in the middle of the section for the steel core and earplates of the tubes, with CFRP rods symmetrically arranged at the four corners of each endplate. Due to the complex stress state caused by the openings, the material and thickness of the endplate were determined by finite element simulation to ensure its elasticity throughout the entire loading process (before the failure of CFRP rods). The extended screw was in a diameter of 27 mm and an initial length of 1 m (considering the additional length required for tensioning), made of Grade 10.9 high-strength steel (nominal ultimate stress = 1000 MPa and yield stress = 900 MPa, respectively). The adapter had a total length of 130 mm, with 60 mm connecting to the rod anchor via the external thread and 70 mm engaged with the extended screw via the internal thread.

Regarding the actual material properties, coupon tests of the steel core and CFRP rod were conducted. As a result, the average yield and ultimate stress of steel were 240.4 and 428.6 MPa, respectively, and the average fracture elongation was 36.2%. For CFRP, the average elastic modulus and ultimate stress were 158 GPa and 2530 MPa, respectively.

3.2 Assembly process

The photograph of the specimen and detailed configuration is presented in Fig. 2. The whole assembly process was divided into three steps.

1) Assemble the steel core and the two tubes with earplates. Considering the convenience of the manufacturing process, the outer and inner tubes were fabricated by welding four steel plates, rather than using the seamless tube. It allowed the earplates to be first welded to the upper and lower plates of the tube as well as the end of the core plate, followed by welding the two side plates of the tube. Besides, grease was applied on the interface between the inner and outer tubes, to reduce friction and ensure smooth relative motion.

2) Connect the CFRP rods and extended screws with adapters. As explained before, it is better to embed the CFRP rods and the anchorage inside the tubes for protection, so an extended screw was connected to the rod anchor with an adapter. The adapter was designed with an external thread on one end and an internal thread on the other, connecting to the rod anchor and the screw, respectively. To further protect the CFRP rods and the anchorage from shear force and friction, pre-buried pipes can be employed, with the pipe sections divided into two parts to match the size of the rod and anchor, respectively.

3) Apply pre-tension of CFRP rods and anchor them on the endplates. After locating the screw-rod assembly and the endplates, the through-type jack was installed to apply pre-tension of the CFRP rods. A pressure sensor and digital display were used to provide real-time monitoring of the tensile force of the rods. In addition, bench-shaped support was used to transfer the reaction force to the endplate and provide sufficient space for tightening the nut of the screw for anchorage. After removing the tensioning equipment, the extra length of the screw could be easily cut off by an angle grinder. The concrete restraint could be filled either before or after tensioning the CFRP rods, while the latter was preferred for more accurate positioning of the rods.

3.3 Component tests

Cyclic and fatigue tests were conducted on the CFRP-SC-BRB specimen, the test set-up, loading protocol, and response are given in Fig. 3. The test specimen was fixed at one end and allowed to slide at the other end, where the actuator was used to apply axial loadings. The loading protocol was displacement-controlled, and the target drift ratios (the ratio of axial deformation Δ to the length of the brace L) were set as 1/300, 1/200, 1/150, and 1/120 in the test. The drift ratio of 1/150 was the design level of the target specimen under seismic loadings, while 1/120 was the considered maximum response in this context. In detail, the test specimen was first subjected to the drift ratio of 1/300 and 1/200 for 3 cycles each, and then excited by 30 cycles at 1/150 to simulate the ultra-low-cycle fatigue, followed by 3 cycles at 1/120 in the end.

3.3.1 Cyclic test results

The results of the cyclic test are shown in Fig. 4(a), where only the first 3 cycles at the drift ratio of 1/150 are presented. It is evident that the hysteresis performs as a flag-shaped response with two-stage stiffness as expected, demonstrating the feasibility of the designed mechanism. The key parameters of the cyclic response are extracted, and the reduction factors of maximum force F, secant stiffness K, dissipated energy E, equivalent damping ratio ξ, and residual drift ratio θ of each loading level are also shown in the figure and tabulated as Table 1. At the considered loading levels, all the variables exhibit a linear relationship with the target peak drift ratio. Except for the secant stiffness, which decreases with deformation, all other metrics are increasing. The peak force of the brace at the drift ratio of 1/120 is over 2900 kN, with a residual drift ratio controlled below 0.5%.

It should be noted that, though the hysteresis of the target specimen is indeed flag-shaped, it performs a partially self-centring response rather than a completely self-centring hysteresis (i.e., zero residual deformation). Under the design principle of equal brace yielding force, the allocation of the energy-dissipation capacity and self-centring capacity is designable. It means that if complete self-centring is required, the cross-section steel core can be reduced and the pre-tension of the CFRP rods can be increased, which is technically feasible. However, in the context of this study, the CFRP-SC-BRB is used to replace the conventional BRB in an engineering project, and out of the conservative considerations, it is required that the energy-dissipation capacity should not be reduced dramatically from the original design. Thus, a partially self-centring design is adopted to balance the self-centring and energy-dissipation capacity, which is more practical in actual application.

3.3.2 Fatigue test results

The results of the fatigue test are presented in Fig. 4(b), where all 30 cycles at the drift ratio of 1/150 are presented. The reduction factors of all the key parameters are also illustrated with increasing cycles in the figure. It indicates that only minor degradation can be observed after 30 cycles of fatigue loading. Specifically, the reduction factors of F, K, E, ξ, θ at the 30th cycle are 0.982, 0.984, 0.969, 0.989, and 0.988 of the 1st cycle, respectively, demonstrating the excellent ultra-low-cycle fatigue performance of the proposed CFRP-SC-BRB. It is worth noting that conducting cyclic and fatigue tests separately would yield more accurate results compared to the alternating protocol used in this study. However, given the negligible degradation after 30 cycles of fatigue, the cyclic response at the drift ratio of 1/120 is sufficiently reliable to replace the results obtained by regular incremental amplitude loaading.

3.4 Numerical modeling

Finite element analysis (FEA) was conducted with the software ABAQUS [38] by both refined and simplified methods. The former was mainly used for component analysis, reflecting all the details of the target specimen, while the latter mainly served large-scale simulations such as system analysis with higher computational efficiency. These two simulation methods can offer cross-validation and allow for flexible selection based on the required analysis scenarios. The numerical methods were validated by the comparison with experimental results and theoretical prediction, so that to be extended for system-level analysis.

3.4.1 Refined model

The refined model consisted of all solid elements with identical geometry to the test specimen, as shown in Fig. 5. Reference points were coupled with the ends of the CFRP-SC-BRB, with boundary conditions consistent with test set-ups, i.e., one end fixed and the other allowed for axial translation. The welding connections, e.g., tube-earplate and earplate-core connections, were modeled as tie constraints for simplicity. Besides, the connections between the CFRP rods and hollow cylindrical anchors were also set as tie constraints. The contact between components, such as the endplate-tube interface, was defined as hard contact in the normal direction and friction in the tangential. Especially, the interface between the inner and outer tubes, as well as the concrete restraint and steel core, was considered frictionless due to the low-friction material placed between them.

Regarding material definition, the steel was defined with elastoplastic properties, with the elastic modulus and Poisson’s ratio of 206 GPa and 0.3, and its plasticity was defined in a bilinear model with kinematic hardening, with the yield strength as the nominal value and a hardening ratio of 0.01. Linear elasticity was defined for the CFRP material, with the elastic modulus and Poisson’s ratio of 160 GPa and 0.1, respectively. All the types of elements were C3D8R, i.e., eight-node linear brick with reduced integration, meshed in reasonable sizes to a total number of 39015 elements.

Two static general steps were defined for the loading process, where the tension force of each CFRP rod was applied as bolt loads in the first step, followed by the displacement-controlled protocol at the loading end in the second step.

3.4.2 Simplified model

The simplified model was proposed based on the configuration of the target CFRP-SC-BRB, which can also be referred to by other similar configurations. It was built with one damper element as the metallic energy dissipator and one spring element to model the nonlinear elasticity, so named the Damper-Spring model, as Fig. 6. The damper represents the steel core, modeled as a single truss element (T2D2, a 2-node linear 2-D truss) to only consider the axial deformation and exhibit identical responses in both tension or compression. That is, the core buckling was excluded in the simplified modeling because it is designed not to occur with the restraint of the concrete. The material was defined as the same as the elastoplastic properties introduced before, with the elastic and post-yield stiffness of the damper element being k_d1 = E_sA_core/L and k_d2 = αE_sA_core/L. The spring with bi-linear elasticity refers to the contribution of the inner and outer tubes before the gap opening at the first stiffness, followed by the contribution of the CFRP rods, corresponding to the stiffness of k_s1 = E_sA_tube/L and k_s2 = E_cA_rod/L. It should be noted that the CFRP rods also contribute to part of the stiffness before the gap opening. However, since the contribution is significantly smaller compared to that of the tubes, it is excluded herein for simplification. The Damper-Spring model provides a straightforward method to simulate the behavior of the SC-BRB, effectively capturing the designed mechanism only with the energy-dissipation and self-centring components.

3.4.3 Modeling results

Both the cyclic responses obtained by refined and simplified FEA models are compared with experimental and theoretical results, as shown in Fig. 7. The comparison of selected parameters derived by different methods is given in Table 2, including primary and secondary stiffness (k₁,k₂), maximum force at the drift ratio of 1/300 and 1/120 (F_1/300,F_1/120) and the corresponding residual drift ratio after un-loading (θ_1/300,θ_1/120). Generally, the numerical responses exhibit high consistency in a flag-shaped hysteresis, demonstrating the reliability of the modeling methods. Compared to the solid-element model, the Damper-Spring model shows sufficient good fitness with much higher computational efficiency, which is recommended to be used in more complicated analyses at the system level.

Despite the good fitness in the overall hysteresis and other indicators, it can be found that the primary stiffness k₁ derived from test results is lower than theoretical and numerical values, with a reduction factor around 0.7. It is because the gap opening in the practice is a gradual process, i.e., the stiffness of the SC-BRB decreases gradually rather than suddenly, while the experimental value of k₁ is taken as the secant stiffness at the yielding force F_y. The difference between the primary stiffness obtained from theoretical the experimental methods is considered a common phenomenon in other self-centring configurations (e.g., [4,39]). Furthermore, the idealised bi-linear transition not only aligns with the straightforward theoretical prediction but also maintains high accuracy in fitting other key parameters despite its simplicity, making it a practical and effective approach for simulation.

4 System-level analysis

Serving for an actual engineering project, the proposed CFRP-SC-BRB is intended to be applied in a designed structure, to replace conventional BRBs in the original design. To investigate the seismic resilient performance of the SC-BRB frame compared with the conventional BRB frame, a series of system-level analyses are conducted in ABAQUS [38], considering both geometric and material nonlinearity. It should be noted that though various novel configurations of BRBs are proposed continuously, the conventional BRBs are still absolutely dominant in the market, making the comparison between them straightforward and meaningful, thus serving as the major concern of this study.

4.1 Prototype frame and scenarios

The prototype frame is an office building designed as a core tube structure, with a total height of 98.2 m in 18 floors. A selected 2d-frame of core tube is used for seismic analysis, illustrated as Fig. 8(a), in a total of 4 bays in 7.80, 3.82, 3.25, and 5.27 m, respectively. The BRBs are designed in a single diagonal configuration to meet the requirements of mechanical performance, spatial arrangement, construction simplicity, and economic benefits in the considered contexts. The seismic precautionary intensity is 7 degree, with the design basic acceleration value of ground motion of 0.10g and the characteristic period T_g is 0.90 s. The structural response in precautionary earthquakes and rare earthquakes are analyzed, according to Chinese standard GB 50011-2010 [40], similar to the design basis earthquake (DBE) and maximum considered earthquake (MCE), respectively. A total of 7 ground motions are selected and scaled following the requirements in GB 50011-2010 [40], making the median spectrum a good fit with the design spectrum, as shown in Fig. 8(b).

The BRBs are designed in the 2nd and 4th bay, 1st–14th floor of the frame, with the floor height and designed yielding force of the brace listed in Table 3. The conventional BRB frame and SC-BRB frame are designed with the identical brace yielding force, the design parameters of the two frames are given in Table 4. The A_core0 and A_core represent the cross-sectional area of the steel core for conventional and self-centring BRB, A_rod and σ₀/σ_u are the section of CFRP rods of the SC-BRB and the ratio of pre-stress to the nominal ultimate stress, respectively. It is evident that to replace the conventional BRBs with self-centring ones, the steel core area can be reduced by 39.4% and 34.3% for the brace with F_y of 2880 and 8000 kN. This is because the pre-tension applied on the CFRP rods contributes to a portion of the yield force of the entire brace, reducing the demand on the steel core.

It should be reiterated that since this study aims to directly serve an actual engineering project, the geometry and loading of the prototype frame are identical to that of the designed structure. Besides, the consideration of the two earthquake levels can fulfil the requirements in this study and the engineering application. In future research, the structural system in different heights (low-, medium-, and high-rise buildings) in more seismic hazard levels (with incremental dynamic analysis) can be further extended for compassion, to reflect more details of structural response and failure process under seismic loads.

4.2 Structural modeling

Regarding the modeling method, the SC-BRB is defined with the Damper-Spring model introduced in Section 3.4.2, while conventional BRB is simulated by a single truss element (T2D2) with elastoplastic steel properties (i.e., the single damper model). As mentioned before, the simplified model offers a practical approach to simulate brace behavior with good accuracy and high computational efficiency. All the beam and column components are established with the beam elements B21, each is a 2-node linear beam in a plane. Besides, the lateral displacements of all nodes on the same floor are coupled to simulate the restraining effect of the rigid diaphragm. The leaning column with hinged ends and lumped seismic mass are incorporated to consider the P-Delta effects, with the equivalent concentrated loads applied on each floor in a static general step. Afterwards, each ground motion is applied by releasing the translational restraints of the base and imposing the time history of acceleration in a dynamic implicit step.

4.3 Seismic responses

Seismic responses of the prototype frame are analyzed, comparing the results of the frame with all conventional BRBs replaced by the proposed CFRP-SC-BRBs against the original design. Furthermore, to address practical application scenarios, the frame with SC-BRBs replaced on only a single selected floor is also analyzed, to evaluate the impact of the single-floor brace replacement on the overall structural response.

In short, the terms ‘BRB fame’ and ‘SC-BRB frame’ refer to the frames with all conventional BRBs and all self-centring BRBs, respectively, in the following analysis and discussion. Natural periods of the two frames are obtained by eigenvalue analysis, with the natural periods listed in Table 5, and the first three mode shapes of the BRB and SC-BRB frames shown in Fig. 9, where Δ_i/Δ₁ refers to the ratio of the lateral displacement at the ith floor to the 1st floor. It indicates that the two frames, designed with the same brace yielding forces, are of nearly identical periods and mode shapes, ensuring the comparability of the results. Based on that, the comparison of seismic responses is given as follows.

4.3.1 SC-BRB frame with full replacement

The peak inter-storey drift ratio (PIDR) and residual inter-storey drift ratio (RIDR) of the SC-BRB frame in DBE and MCE are shown in Fig. 10, with all the responses under each ground motion and also the median response. In general, the distribution of the inter-storey drift ratios is relatively uniform, especially under the design basis earthquake, with slightly larger deformations observed in the middle floors of the frame. In all considered ground motions, the maximum PIDR and RIDR of the SC-BRB frame in MCE are below 2.0% and 0.5%, respectively, showing a resilient response of the designed frame.

Since the median response to all considered excitations is the primary focus for statistical significance, the comparison between the median responses of the BRB and SC-BRB frames is further discussed, which is illustrated in Fig. 11. It can be seen that the PIDR of the SC-BRB frame is smaller than that of the BRB frame in DBE, while the response in the middle floors is slightly larger in MCE. It can be explained that the structural response is influenced by both stiffness and damping. Compared to the conventional BRB, the SC-BRB has higher post-yield stiffness contributed by the CFRP rods, but lower energy-dissipation capacity due to the reduced section of the steel core. The obtained results indicate that the stiffness appears to contribute more in DBE, while the damping shows a greater impact on structural behavior in MCE, leading to the observed difference in peak response of the two frames.

Despite this, it shows that the SC-BRB frame performs better in residual response than the BRB frame in both DBE and MCE scenarios, with a particularly higher reduction ratio under MCE. Specifically, the median RIDR responses of BRB and SC-BRB frames are given in Tables 6 and 7, along with the relative errors of the latter compared to the former. In DBE, the mean and median RIDR reduction of all the floors are 22.1% and 29.3%, respectively. The maximum reduction of RIDR is observed on the 9th floor with a value of 37.2%. In MCE, the reduction of RIDR is further amplified, with the mean and median reduction of 50.0% and 50.5%, and the maximum reduction is as high as 58.3% found on the roof. It is widely recognized that the residual deformation significantly affects the difficulty of post-earthquake repairs and associated time and economic costs. From this perspective, the frame equipped with CFRP-SC-BRBs performs the advantage of higher seismic resilience over the frame with conventional BRBs.

4.3.2 SC-BRB frame with partial replacement

Due to the challenges in promoting the new braces for full replacement in the structure, replacing part of the braces as a trial is more acceptable in actual practice. To ensure the self-centring effects, all braces on the selected floor should be replaced at the same time, and the floor with a relatively larger response is prioritised for replacement. Based on that, the replacement of braces on the 9th and 12th floor of the original frame is selected as two scenarios for comparison.

Results indicate that replacing BRBs on the 9th or 12th floor has a minor impact on the PIDR response, with the average and maximum reduction of 2.0% and 12.5% in MCE, respectively. Similarly, there is also a negligible difference between the RIDR response of the BRB frame and the frame with SC-BRB only replaced on a single floor. However, in MCE, it shows a noticeable reduction in the RIDR response, not only on the floors adjacent to the replaced floor but the lower floors with larger deformation, as shown in Fig. 12. Specifically, the median RIDR responses of the frame where SC-BRB only replace on a selected floor in MCE are listed in Table 8, along with the ratio to the conventional BRB frame. It indicates that the RIDR responses of almost all the floors are reduced by replacing conventional BRBs with SC-BRBs, and the reduction in MCE can be up to approximately 20% on the 7th floor.

Comparing the structural response when replacing braces with SC-BRBs on the 9th and 12th floors, the former performs slightly better than the latter, with average reductions of 8.7% and 7.9%, respectively. The major difference concentrated on the responses of the 8th–13th floors, as magnified also in Fig. 12. It can be observed that replacing the braces on the selected floor directly reduces the responses of itself and the adjacent floors, making the RIDR on the 12th floor being the only one among all floors that is smaller when replacing the 12th-floor BRBs, compared to the 9th-floor replacement. Based on the above analysis, it indicates that applying the self-centring brace only on the floor with the largest inter-storey drift ratio can still contribute to limiting the overall structural response to some extent.

5 Further discussion

From the experimental and numerical investigation introduced above, it is demonstrated that the proposed CFRP-SC-BRB is effective in the designed self-centring mechanism, thereby enhancing seismic resilience. In addition to the detailed analyses on both component and system levels in previous sections, further discussion is presented herein to address potential limitations and challenges so that to provide possible optimisation methods for practical application.

5.1 Applicable scenarios

In actual projects, BRBs are typically required to be designed within specified dimensions to allow for embedding into the walls, ensuring both structural performance and architectural aesthetics. Although the self-centring and energy-dissipation capacity can be flexibly designed by adjusting the proportion between the steel core and CFRP rods, the spatial arrangement of rods within the limited section becomes a critical design constraint. Unlike regular steel rods, expanded anchors are required at the ends of the CFRP rods, which limits the available space for arrangement. For instance, a typical Φ20 CFRP rod currently requires an anchorage diameter of up to 54 mm due to manufacturing constraints. To address this, it is recommended to adapt the rod anchor by using the extended screw with a reduced cross-section, as proposed in this study. Besides, using the anchor-screw adapter can help reduce the openings on the endplates, thereby enhancing their resistance to the reaction forces from the CFRP rods. However, the sections of inner and outer tubes are still affected by the size of the rod anchor embedded within them. Consequently, careful design of the size and number of CFRP rods is necessary considering these spatial constraints. The proposed configuration is thus most suitable for applications in braces with relatively moderate yielding force. Further optimisation of rod anchor manufacturing is also required to facilitate greater design flexibility.

5.2 Structural optimisation

Deformation capacity is a basic requirement for braces mainly subjected to axial loads. Though the CFRP rod has an advantage over the steel rod in the self-centring BRB (with its ultimate strain being 1.67 times that of steel), the ductility of the entire SC-BRB in extreme cases is still much lower than the conventional BRB, which depends only on the steel core with the ultimate strain over 15%. To increase safety redundancy in extreme conditions, the configuration of the SC-BRB can be optimised to improve the deformation capacity. Some methods can be referenced and adapted from related studies (e.g., [30,41]), such as containing one or more intermediate steel tubes for cross-anchoring the rods, or connecting additional devices with the CFRP rods to allocate part of the deformation. That is, the deformation of the CFRP rods can be partly de-coupled from that of the steel core to postpone its failure. In addition to changing the configuration, using more advanced materials can further improve the deformation capacity. It could be considered to develop high-strength, relatively low-modulus CFRP products for special applications controlled by axial deformation. It is worth noting that, although the CFRP rods typically fail before the steel core, the system can still behave as a conventional BRB, preventing sudden brittle failure and maintaining safety redundancy.

5.3 Economic benefits

Although the SC-BRB can offer excellent seismic resilience and low post-earthquake repair costs, the large-scale promotion also needs to consider the economic benefits in the initial investment. Designed by the same brace yielding force as the conventional BRB, the cost of the steel core in the SC-BRB can be reduced due to the contribution of the pre-tension in the CFRP rods. However, a key economic challenge is that the price of a single CFRP rod-anchor system is comparable to that of the steel core itself, meaning the total SC-BRB cost significantly increases with each additional rod set. This high cost is primarily attributed to the raw CFRP material and customised anchorage machining, making the price of SC-BRB about twice that of the conventional BRB. Thus, controlling the economic costs is essential, which involves exploring more economical raw CFRP or alternative materials, and optimising processing or anchoring methods. Furthermore, a careful cost-effectiveness analysis is needed, comparing high-strength fiber (higher unit price, fewer sets) and ordinary-strength material (lower unit price, more sets) to determine the optimal design. Moreover, the welding connection between the inner or outer tube and the earplates can be replaced by integrated molding to improve manufacturing efficiency so that to enable large-scale production.

6 Conclusions

This study investigated the seismic behavior of a novel self-centring buckling-restrained brace with pre-stressed CFRP rods providing the self-centring capacity. For component-level analysis, cyclic and ultra-low-cycle fatigue tests were conducted on the CFRP-SC-BRB specimen, followed by numerical modeling in both refined and simplified methods, validated with the test results and theoretical prediction. For system-level analysis, a prototype frame applied with proposed CFRP-SC-BRBs is subjected to seismic excitations, and the overall responses are compared with a conventional BRB frame designed by identical yielding forces, considering the full and partial replacement scenarios of the braces. The analysis results throughout the whole process can be summarized with the main conclusions addressed below.

1) The CFRP-SC-BRB specimen in cyclic test performs a peak force over 2900 kN at the maximum drift ratio of 1/120 with a residual drift ratio controlled below 0.5%, and in fatigue tests, it appears negligible deterioration in any mechanical metrics after 30 cycles at the drift ratio of 1/150. Both the component tests demonstrate the excellent cyclic and fatigue performance of the proposed configuration.

2) Finite element analysis shows high consistency with experimental and theoretical results in a flag-shaped hysteresis by both refined and simplified models. The Damper-Spring model aligns with the straightforward theoretical prediction and performs a sufficient good fitness with much higher computational efficiency, recommended to be used in system-level analysis.

3) The structural response of the frame fully or partially replaced by the SC-BRBs shows a competitive advantage over the conventional BRB frame. With full replacement, the median residual inter-storey drift ratios are reduced by 29.3% and 50.5% under design basis and maximum considered earthquakes, respectively. Besides, partial replacement with SC-BRBs on the floor with the largest response can still contribute to limiting the overall structural response.

The findings reveal that the proposed CFRP-SC-BRB is effective in improving seismic resilience both at component and system levels. Future research should focus on optimising the configuration, including but not limited to: 1) arrange the CFRP rods within a limited cross-section ensuring both structural performance and architectural aesthetics; 2) apply deformation amplification mechanism to postpone the failure of the CFRP rods; 3) explore cost-effective solutions with alternative materials and advanced manufacturing methods for optimal design. By pursuing these directions can the novel product be enhanced in structural response and rendered more suitable for promotion in practical projects.

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