Nonlinear Time History Research Articles

Effect of Subsequent Subgrade on Seismic Response of the High-Speed Railway Track–Bridge System

As an important part of the boundary conditions on both sides of the high-speed railway track–bridge system, the seismic response of the subgrade structure is different from that of the bridge structure. This difference has become increasingly significant with the widespread adoption of continuous welded rail technology in bridge construction. Therefore, investigating the seismic response of the bridge system, with a specific focus on the longitudinal constraint effects of the subsequent subgrade track structure, is of paramount importance. Utilizing finite element software, two distinct bridge models are developed: one incorporating the subsequent subgrade track structure and another excluding it. Through nonlinear time history analysis under varying seismic intensities, it is demonstrated that the longitudinal constraint of the subsequent subgrade track structure mitigates the longitudinal displacements and internal forces in critical components of the high-speed railway track–bridge system. Concurrently, acknowledging the heightened complexity and cost associated with post-earthquake repairs of the bridge structure compared to subgrade structure, this study uses a risk transfer connecting beam device. This device can redirect seismic damage from bridge structure to subgrade structure, thereby potentially reducing post-seismic repair expenses for the bridge.

Surrogate models for seismic and pushover response prediction of steel special moment resisting frames

For structural engineers, existing surrogate models of buildings present challenges due to inadequate datasets, exclusion of significant input variables impacting nonlinear building response, and failure to consider uncertainties associated with input parameters. Moreover, there are no surrogate models for the prediction of both pushover and nonlinear time history analysis (NLTHA) outputs. To overcome these challenges, the present study proposes a novel framework for surrogate modelling of steel structures, considering crucial structural factors impacting engineering demand parameters (EDPs). The first phase involves the development of a process by which 30,000 random steel special moment resisting frames (SMRFs) for low to high-rise buildings are generated, considering the material and geometrical uncertainties embedded in the design of structures. In the second phase, a surrogate model is developed to predict the seismic EDPs of SMRFs when exposed to various earthquake levels. This is accomplished by leveraging the results obtained from phase one. Moreover, separate surrogate models are developed for the prediction of SMRFs’ essential pushover parameters. Various machine learning (ML) methods are examined, and the outcomes are presented as user-friendly GUI tools. The findings highlighted the substantial influence of pushover parameters as well as beams and columns’ plastic hinges properties on the prediction of NLTHA, factors that have been overlooked in prior studies. Moreover, CatBoost has been acknowledged as the superior ML technique for predicting both pushover and NLTHA parameters for all buildings. This framework offers engineers the ability to estimate building responses without the necessity of conducting NLTHA, pushover, or even modal analysis which is computationally intensive.

Design and Nonlinear Dynamic Response of a Steel Stack

AbstractIndustrial stacks are built in order to reduce atmospheric pollution and release gases to the higher level of the atmosphere. Since they are high and slender structures, they are significantly affected by lateral forces, in particular, induced by winds and earthquakes. This paper aims to summarize the design principles for steel stacks given in the international standards, codes and specifications considering the evaluation of the results from the investigation on nonlinear dynamic response of a typical steel stack subjected to the earthquake. For this purpose, a typical self-supporting steel stack has been designed and its performance under earthquake and wind forces has been investigated in terms of the applied design principles, such as the displacement limit and the potential plastic deformations. The study is accomplished by using finite element models employing nonlinear time history and pushover analyses. The numerical results are presented particularly by considering the design principles used for the model. The results show that wind loads considered are more pronounced in the design of industrial steel stacks than earthquake especially in terms of limiting top displacement. The flue openings which reduce strength and lateral stiffness of the stack web is significantly effective in the lateral behavior of the stack. Moreover, the principles considered are found applicable for the design of such steel stacks. Based on the results from nonlinear time history analyses, no yielding and plastic deformation are detected along the stack.

Probabilistic seismic demand of typical highway bridges in moderate-intensity zones

The probabilistic seismic demand for typical highway bridges in moderate-intensity zones is investigated. The seismic demands and infrastructure destructions are severe on critical bridge components during and after seismic activity in moderate-intensity zones. This article aims to determine seismic demand, predict the probabilistic seismic demand model (PSDM), and identify the interdependence of bridge components. Based on bin-ground motion, 154 analytical bridge-ground motion samples are prepared to record output data using nonlinear time history analysis (NLTHA). High-level ground motion duration and peak ground acceleration are used to measure the seismic demand and intensity of the bridge. The best-fitting lognormal distribution and correlation coefficient between demand in the transformation states are analysed to indicate the interaction between the two at dissimilar levels of interdependence. As a result, bearing pads on all abutments, the bearing pad on pier-1, and the shear key on pier-2 are best fitted with a high level of interdependence to design the seismic performance of highway bridges. Therefore, the ground motion characteristics play a vital role in the infrastructure collapse of the highway bridges in the moderate-intensity zone and should be held in high regard.

Method to identify if torsional mode of a building is its first mode

Torsionally flexible buildings (that have torsional mode as fundamental mode) twist during earthquake shaking, and may collapse partially or completely depending upon the direction and level of shaking. The problem is aggravated when the building is torsionally unsymmetrical. Some design codes (like Eurocode, Indian Code) explicitly prohibit the design of such buildings. This paper presents a simple approximate method to identify torsionally flexible RC Moment Frame and RC Structural Wall buildings at the initial proportioning stage itself without carrying out a detailed structural analysis. It is possible to identify whether or not the first mode is torsional mode of a building (i.e., torsionally flexible building) if Natural Period Ratio τ>1 by modelling the building with rigid diaphragm and distribution of mass & stiffness along the height of building, and estimating: (1) radius of gyration of rotational mass rm of each floor plan geometry by lumping the masses of slabs, beams and all vertical elements at each nodes, (2) radius of gyration of twisting stiffness rKθ of all vertical elements using their translational and torsional stiffnesses (considering flexibility of adjoining beams and vertical elements accounting for both flexural and shear deformations), and (iv) τ (=rm/rKθ). The method is validated with 3D Modal Analysis (using τ =Tθ/T, where Tθ is Uncoupled Torsional Natural Period and T Uncoupled Translational Natural Period) of hypothetical buildings using a commercial structural analysis software. Also, parameters are identified that lead to τ>1, and solutions suggested to avoid torsional flexibility in buildings. Further, the method helps identify vertical stiffness irregularity in buildings. Draft provisions are suggested for inclusion in seismic codes. Also, poor performance of multi-storey building (with τ>1) is demonstrated using nonlinear static and nonlinear time history analyses.

Effects of Soft Story Locations on the Nonlinear Time History Analysis of Multistory Reinforced Concrete Buildings

Abstract The current paper included studying the effects of soft storey locations on dynamic response of reinforced concrete (RC) buildings under the impacts of earthquakes. Soft storey is essential to provide the building with a functional space such as vehicle garages or open meeting rooms. Further analytical investigation was necessary to understand the impact of these flexible floors on the building's response during earthquakes, as conducting experimental research to address this issue is highly difficult. The research encompassed the effects of soft storey location in two types of buildings, one with equal spans and the other with unequal spans, on the nonlinear time history response. Each building consists of a 10-stories (G+9) RC residential structure subjected to earthquake effects. The analysis was carried out using program sap2000 v23. An analogous diagonal strut was used to illustrate the infill panels. The study included the effect of soft storeys on the natural period, the change in base shear with time, and the change of displacement and acceleration along time for each building. The obtained results showed that including a soft storey in the analysis for buildings having either equal or unequal spans increased the time period, displacement, and storey drift, causing a decrease in the acceleration and base shear forces. Building with the soft storey on the fifth floor (at the mid-height of the building) showed a better dynamic response compared with that using the soft storey on the ground and last floors.

The cumulative plastic deformation demand for buckling restrained braces imposed by the strong motions in the 2023 Türkiye earthquake sequence

The Türkiye earthquake sequence on February 6, 2023, was featured by the closely located earthquake doublet of Mw 7.8 and Mw 7.5. The consequent strong ground motions are supposed to be able to impose high demands on the ultra-low-cycle fatigue performance of metallic dampers in buildings, including the widely used buckling restrained braces. This study evaluates the cumulative plastic deformation (CPD) demands on buckling-restrained braces (BRBs) in multi-story buildings imposed by the strong ground motions in the 2023 Türkiye earthquake doublet. Thirty-two records of the highest peak ground accelerations were selected from the strong motion database. Among them, eight captured the ground motions during both events, and the rest only captured the shaking of either of the events. The CPD demands on the BRBs in reinforced concrete frames with various fundamental periods, brace-to-frame stiffness ratios, and BRB ductility ratio are calculated by nonlinear time history analyses and are summarized in the form of enveloped spectra of CPD ratios at constant ductility. The results show that the CPD demands on BRBs increase with smaller brace-to-frame stiffness ratios and larger BRB ductility ratios. The enveloped CPD demands are several hundreds of times the nominal yield deformation of the BRB, which are much higher than the CPD demands for the calibration tests of BRBs stipulated by AISC 341 in the US.

Strong ground motion characteristics observed in the February 6, 2023 MW7.7 Türkiye earthquake

Türkiye is located in a seismically active region, where the Anatolian, African, and Arabian tectonic plates converge. High seismic hazards cause the region to be struck repeatedly by major earthquakes. On February 06, 2023, a devastating MW7.7 earthquake struck Türkiye at 01:17 am local time (01:17 UTC). In this regard, near and far-field ground motion data within the distance of 120 km are compiled and later characterized to identify the key ground motion intensity measures. Additionally, the vertical components of ground motions were examined to capture the complete three-dimensional nature of the seismic event. Moreover, the effect of Pulse-Like (PL) and Non-Pulse-Like (NPL) ground motion on a representative RC frame structure built as per the Türkiye code was investigated. The results indicate that PL behavior was observed in both horizontal and vertical components of ground motions and PL behavior were noted both near the epicenter and at higher distances from the epicenter. Moreover, the ratio of the peak vertical acceleration to peak horizontal acceleration at certain stations was found to be close to 1. Finally, the non-linear time history analysis of the representative reinforced concrete frame structure for ground motions recorded at stations located equidistant from the epicenter, indicated that PL ground motions led to more significant damage compared to NPL ground motions.

Comparative Analysis of Concentrically Braced Frames with FeSMA and Steel BRBs Under Long-Duration Earthquakes

ABSTRACT Owing to high fatigue life, the iron-based shape memory alloy (FeSMA) buckling-restrained braces (BRBs) are emerging as a promising candidate against long-duration earthquakes. However, the corresponding analysis cannot be found. Current emphasis is paid on unveiling the seismic response differences between concentrically braced frames (CBFs) with FeSMA and steel BRBs when they are attacked by long-duration earthquakes. To directly assess the effect of earthquake duration, this paper selects a total of 90 pairs of short- and long-duration earthquake records, which are record-to-record spectrally equivalent over a wide range of fundamental periods, for nonlinear time history analysis. A benchmark six-story CBF is selected for demonstration purposes. In the numerical simulation process, the fatigue-induced damage is particularly considered. A preliminary examination is first conducted in the case study, in which a representative pair of short- and long-duration records is selected. In what followed, the statistical results from the ground motion suites are analyzed. This work not only highlights the higher failure risk of steel BRBs than FeSMA BRBs under long-duration earthquakes associated with maximum considered earthquake hazard level, but also confirms the advantages of FeSMA BRBs over steel BRBs in controlling residual deformations.

Seismic evaluation and retrofit of a typical reinforced concrete hospital building in Indonesia with DCFP isolation system

In this paper, a study on seismic evaluation and retrofit of a typical reinforced concrete (RC) hospital building in Indonesia is presented. Seismic evaluation is performed against basic structural performance objectives outlined in the current code for structural seismic evaluation. The target building is a typical 5-story RC building designed by the 1970s Indonesia seismic and building codes, which imposed lower seismic demand and were not as strict as the current codes in the requirements for strength and ductility. The first part of the paper describes a seismic evaluation procedure against specific target performance levels. Nonlinear time history analysis (NLTHA) is conducted and structural performances were evaluated against structural responses (base shear force and inter-story drift ratio) and acceptance of seismic performance level for local (element rotational limit) and global (roof drift ratio) performance criteria under 225, 975, and 2475-year return period earthquake scenarios. Results reveal that seismic performances of some structural elements are unsatisfactory and under the acceptable performance level, especially for 2475-year return period (BSE-2 N/MCER) earthquake scenario. Seismic retrofit is thus recommended and the use of double-concave friction pendulum (DCFP) base-isolation system as a retrofit strategy is explored. The seismic performance of DCFP-retrofitted building is examined by NLTHA, where effectiveness of DCFP base-isolation system in improving seismic performance is confirmed by comparing structural responses, local and global structural performance of the existing building and the DCFP-retrofitted building under 2475-year return period earthquake scenario. Results of NLTHA demonstrate that local structural performance level has improved from Collapse Prevention to Immediate Occupancy level, whereas the global structural performance has improved from Limited Safety level to Operational level.

Seismic retrofit of framed structures using a steel frame with springs and friction dampers

In this research, a seismic retrofit device was proposed and its performance was tested under cyclic loading. The developed damper is composed of a steel frame with friction hinges and springs at corners to provide stiffness and restoring force. Theoretical formulas for its mechanical behavior and its analytical model were developed and verified by comparing them with the results of an experimental test. To further evaluate the applicability of this retrofit system, it was applied to the seismic retrofit of a case study structure designed without considering seismic load. The structure was retrofitted to satisfy a given performance objective and its seismic behavior was compared using nonlinear time history analysis before and after retrofit. The seismic performance of the structure was assessed in terms of maximum interstory drift ratio, residual displacement, and energy dissipation. It was observed that the installed retrofit frames could properly dissipate the seismic energy and reduce both inter-story drifts and residual displacements of the case study structure.

Seismic performance of BRBF with SMA core using incremental dynamic analysis

ABSTRACT In this paper, a new model for Buckling Restrained Braced Frames (BRBF) is proposed that Shape Memory Alloy (SMA) is used for the yielding core instead of steel. The seismic behaviour of a framed structure with chevron type buckling restrained braces is investigated and their seismic performance factors, such as permanent displacements, inter story drifts and response modification factors are evaluated. Nonlinear time history analysis and Incremental Dynamic Analysis (IDA) of two models subjected to 11 ground motion records is performed using OpenSees software. In order to evaluate the efficiency of the proposed model, it is compared to a BRB model with a steel core that the length of yielding core is 1 m for each model. Comparing the proposed bracing systems with conventional BRBFs indicates that buckling restrained braced frames equipped with SMA are better in terms of permanent roof displacement and maximum inter-story drift. However, the response modification factor of BRB models with steel core is higher.

Seismic response of structures with friction pendulum inerter system (FPIS) under near-fault earthquakes

Near-fault ground motions with high acceleration peaks and long-period velocity pulses pose a serious threat to the reliability of engineering structures. To reduce the displacement of isolation layer and improve the seismic performance of superstructure under the near-fault ground motions, a composite isolation system, which is composed of friction pendulum system (FPS) and inerter system, namely FPIS, was used in this paper. Based on D’Alembert’s principle, the nonlinear motion equations of a base-isolated structure with FPIS were established. The damping effect of two different mechanical layouts of FPIS subsystems, i.e, series-parallel inerter system-I-FPS(SPIS-I-FPS) or series-parallel inerter system-II-FPS(SPIS-II-FPS), were investigated in this study. The strong nonlinearity of FPIS was considered, and the inerter system parameters were designed based on the principle of maximum damping enhancement. The fourth-order Runge-Kutta approach was used to solve the dynamic response of a multi-degree-of-freedom system under seismic excitations. The effectiveness of FPIS was verified by comparing the isolation layer displacement and the acceleration of superstructure calculated by MATLAB with the friction pendulum system and viscous damper (FPS-VD). The nonlinear time history analysis results indicate that within a certain additional damping range, the SPIS-I-FPS subsystem performs effectively than SPIS-II-FPS in reducing the superstructure acceleration and isolation layer displacement. To increase the energy dissipation efficiency of structures, it is recommended to increase the design parameters of the inerter system and control the friction coefficient of FPS within the range of 0.05∼0.10.

Feasibility of using superelastic shape memory alloy in plastic hinge regions of steel bridge columns for seismic applications

AbstractThis paper contributes to the further development of seismic resilient infrastructure by introducing a novel prototype bridge which integrates tubular steel piers with superelastic shape memory alloy (SMA). The proposed bridge pier is composed of a circular steel tube which is bonded to a superelastic SMA tube in regions of high stress. The pier is distinguished by its ability to minimize residual drifts following inelastic deformations induced by cyclic loading. Three‐dimensional continuum finite element (FE) models are utilized to examine its lateral behavior. Experimental data is used to demonstrate the effectiveness of the continuum FE procedure in replicating the cyclic response and capturing both global and localized behaviors. A novel composite material model is proposed to represent the degradation of strength and accumulation of irreversible strains in the cyclic response of superelastic SMAs. An iterative procedure for the calibration of this material is presented. Investigations, employing the calibrated FE procedure, focus on the quasi‐static cyclic response of steel piers with superelastic SMA in the plastic hinge zone, aiming to identify the optimal length of the SMA tube for achieving a self‐centering response with reduced residual deformation. The study is then further expanded to examine the seismic response of a bridge structure incorporating such piers. Development of the FE model for the prototype bridge includes the modelling of the piers using continuum elements, while the superstructure, bearing units, abutment walls, and backfill material are modelled using discrete elements. Nonlinear time history analyses are undertaken to investigate the effects of column wall thickness and materials used in the plastic hinge zones of the piers. Dynamic FE study results indicate that bridges employing such piers are capable of returning to their original position, provided the SMA tube is of adequate length.

Advanced tree-based machine learning methods for predicting the seismic response of regular and irregular RC frames

In this study, predicting the maximum drift ratio (MDR) for two types of structures: 8-story regular (R8) and vertically irregular (IR8) reinforced concrete (RC) frames are focused. To accomplish this, advanced tree-based machine learning (ML) methods, namely Random Forest (RF), eXtreme Gradient Boosting (XGBoost), and Stochastic Gradient Boosting (SGB) are utilized. 2300 ground motion (GM) records, includes twenty-one input parameters and their nonlinear time history analyses results are considered as a dataset. The performance of the RF, XGBoost, and SGB models was examined considering the impact of the data pre-processing issue to test whether the use of data pre-processing approaches in model development could improve the prediction performance of the advanced ML models. Various data pre-processing techniques, including outlier detection using boxplot, missing data imputation using RF, data transformation using log transformation, and feature selection using Hill Climbing are employed as part of ML pipeline. The models' performance is evaluated using six different well-established statistical evaluation metrics. Subsequently, the results are systematically compared to identify the most effective prediction model. Our findings highlight the substantial impact of data pre-processing on the performance of ML models when predicting seismic responses, specifically the MDR of RC frames. Notably, RF consistently outperformed other ML models for both R8 and IR8 structures in the case of the simple ML pipeline strategy and data pre-processing approach. The RF model achieved R2 scores of R2 = 0.87 and R2 = 0.91 on the test data before implementing data pre-processing for R8 and IR8, respectively. After data pre-processing, R2 scores showed an improvement of 12% and 6.22% in the cases of R8 and IR8. In contrast, the performance scores of SGB consistently fell behind those of RF and XGBoost models.

Effect of U-Shaped Metallic Dampers on the Seismic Performance of Steel Structures based on Endurance-Time Analysis

Seismic performance of steel moment-resisting frames is investigated through the incorporation of U-shaped metallic dampers. The primary objective is to assess the effectiveness of these dampers in mitigating seismic responses by utilizing various analysis techniques. Two representative structural configurations (5 and 10-story) are studied in both damped and undamped states to reveal the impact of dampers on seismic response reduction. The study utilizes the endurance time analysis (ETA) method, known for its efficiency in evaluating structural seismic performance. To validate the analysis results, a benchmark comparison is made through nonlinear time history analysis (NTHA). Incremental dynamic analysis (IDA) is also conducted to assess structures’ intensity measures with respect to their damage intensity index. The findings demonstrate that U-shaped metallic dampers substantially reduce inter-story drift and story shear forces. Importantly, a close alignment between the results obtained from ETA and NTHA underscores the reliability of the former in assessing seismic performance with supplemental damping devices.

Seismic performance assessment of RC bridge piers with variable hysteresis performance dampers

A novel variable hysteresis performance damper (VHD)—multi-stage slip friction damper is developed and applied to implement multi-level seismic resistance of structures. Different from the conventional slip friction dampers, which feature only a single type of slip friction surface, this innovative damper incorporates two types: a flat slip surface and a wedge slip surface. The quasi-static cyclic loading tests of the VHD were carried out to investigate its variable hysteresis performance. The test results revealed that the developed damper presented excellent adaptive performance, and its hysteresis behavior changed from a complete rectangle with efficient energy dissipation to a flag-shaped curve with exceptional self-centering capacity as deformation increases. Subsequently, the developed VHD with unique adaptive performance was applied in RC bridge piers (BP) to improve the seismic performance. Nonlinear time history and fragility analysis methods were employed to assess the seismic performance of the RC bridge piers with VHDs (BP-VHD) in deterministic and probabilistic manners, considering maximum and residual deformations as performance indicators. For comparison, seismic responses of RC bridge piers with traditional buckling restrained braces (BRBs) and self-centering energy dissipation braces (SCEBs) were also presented. The analysis and comparison results demonstrate that the developed VHD is as effective as BRB in reducing maximum deformation at small PGAs, meanwhile, it can effectively reduce the residual deformation of the structure to allowable values when the PGA is large. Furthermore, the failure probability of BP-VHDs is lower compared to piers with BRBs and SCEBs, particularly concerning maximum and residual drift ratios as performance indicators. The application of the VHD can effectively achieve the goal of multi-level seismic resistance for RC bridge piers.

Seismic response modification factors of single-layer diamatic dome structures

In this research, the seismic behavior of single-layer diamatic dome (SLDD) structures was analyzed under earthquake loads, and then the seismic response modification factors (SRMFs) of these structures were extracted. For this purpose, 16 models with different span lengths (SLs) and rise-to-span ratios (RSRs) were designed, and the effects of SL and RSR on the SRMFs of these structures were evaluated. Also, the effect of member density on the SRMFs was studied. The models were first designed under the applied loads based on relevant design codes. Then, by performing the nonlinear time history analyses using the three translational components of ground motion records, the control point and target displacement in the horizontal and vertical directions were obtained to implement the pushover analyses. Thereafter, the pushover analyses were implemented by using the target displacements derived from the nonlinear time history analyses, and the SRMFs of SLDD structures in both horizontal and vertical directions were obtained. The results indicate that models with RSRs of 1/7 to 1/3 remained in the elastic range in the horizontal direction. For the models with an RSR greater than 1/3, if the RSR increases, the ductility and behavior factor increases in the horizontal direction. However, there is a downward trend in the vertical direction due to the increase in the vertical stiffness. The horizontal and vertical behavior factor was obtained in the range of 1.155–2.459 and 1.155–2.893, respectively. Finally, by using the results obtained and through the nonlinear regression analysis, equations were proposed for the period, target displacement, displacement amplification factor, and behavior factor for SLDD structures in terms of the SL and RSR in the horizontal and vertical directions.

Open Ground Story Mid-Rise Buildings Represented by Simplified Systems

An improved methodology for the condensation of Multi-Degree-Of-Freedom (MDOF) systems to equivalent Two-Degree-Of-Freedom (2EDOF) systems is presented. The methodology is applied to mid-rise buildings with Open Ground-Story and verified by means of Nonlinear Time History Analyses. The buildings studied are divided into two main segments: (a) ground story, whose stiffness and lateral strength are both provided only by reinforced concrete moment-resisting frames; and (b) from the second story to the roof, whose stiffness and lateral strength are provided by confined masonry walls. The proposed methodology allows us to do the following: (a) get the closest approximation to the real behavior of the MDOF system through the use of hysteresis rules with strength and stiffness degradation in the simplified system; (b) analyze the behavior of an OGS whose lateral stiffness is lower than the stiffness of the stories above; and (c) identify in which of the two subsystems (either the ground story with reinforced concrete frames or the second story with masonry) the maximum seismic demand of non-linear behavior occurs. For most of the cases studied and different scenarios of non-linear behavior, the 2EDOF simplified system reasonably approximates the MDOF system’s response; however, when a local failure in an upper story causes the collapse mechanism, the 2EDOF system does not adequately approximate the response of the MDOF system.

Study on the mechanical properties of a viscoelastic self-centering brace with rotational displacement amplification and its application in RC frames

This paper introduces a novel viscoelastic self-centering brace with a rotational displacement amplification function (VSB-RA), developed to address the issue of limited energy dissipation in traditional self-centering braces. The basic structure and working mechanism of the VSB-RA are detailed. Low-cycle reciprocating loading tests were performed on two types of VSB-RA specimens with different initial amplification angles, and a comprehensive analysis was conducted on their bearing capacity, energy dissipation performance, self-centering capability, and frequency correlation. A refined finite element model was developed in ABAQUS software to simulate the complete test loading process. Nonlinear dynamic time history analysis is then performed on an 8-story reinforced concrete (RC) frame structure with the VSB-RAs using different initial amplification angles. The results demonstrate that the hysteresis curves of the VSB-RA exhibit distinct flag-shaped characteristics and excellent self-centering performance, and its energy dissipation capacity increases exponentially with the decrease of the initial amplification angle. The numerical simulation results of the hysteresis curves align well with experimental findings. The inter-story drift, residual inter-story drift, floor acceleration, and base shear force are effectively controlled in the VSB-RA frame structures compared to the uncontrolled structure. Under rare earthquake actions, the base shear forces of the structure are reduced by 27.2 %, 27.9 %, and 30.7 % at initial amplification angles of 45°, 37.5°, and 30°, respectively.