Absolute Acceleration Research Articles

H∞ closed-form solution of tuned mass damper enhanced with negative stiffness element (TMD-NS) for structural vibration control

Negative stiffness element has been applied to improve the control performance of tuned mass dampers (TMDs) recently, and two tuned mass dampers enhanced with negative stiffness (TMD-NS) element, namely KDamper (Without loss of generality, it is referred to as TMD-NS I in the present study) and Extended KDamper (EKD, TMD-NS II), have been developed. Previous studies have demonstrated the control effectiveness of TMD-NS I and II. However, there still exist some issues to be addressed: (1) previous studies normally optimize TMD-NS via the intricate and time-consuming numerical methods, the analytical solutions for the optimal design parameters of TMD-NS II remain unknown; (2) a comprehensive and exhaustive evaluation that compares the control effectiveness of TMD-NS I and II is absent from existing literature. To fill these research gaps, this study derives closed-form optimum solutions for TMD-NS II using the H∞ approach. The control effectiveness of TMD-NS I and II in suppressing the seismic responses of structures is investigated systematically. Specifically, the analytical model of an undamped SDOF system equipped with TMD-NS I or II is first developed within a unified framework, and corresponding dynamic equations of motion are formulated. Subsequently, the optimal parameters of TMD-NS I and II are derived based on the classical “fixed-point” theory. Based on the derived optimal parameters, the control effectiveness of TMD-NS I and II are examined by using a damped SDOF system subjected to harmonic excitations and real earthquake ground motions. Finally, a 5-storey isolated benchmark building model is adopted to further investigate the effectiveness of TMD-NS in the seismic protection of engineering structures. The results reveal that the derived closed-form solutions are accurate in capturing the optimal parameters of TMD-NS. In addition, both the optimized TMD-NS I and II outperform the conventional TMD in reducing the seismic responses of structures. Furthermore, TMD-NS I proves more effective in reducing the absolute acceleration of the isolated building, whereas TMD-NS II demonstrates better performance in mitigating the isolating deformation. In a nutshell, both the TMD-NS I and II are highly effective alternatives to conventional TMDs, showcasing superior performance in vibration reduction and robustness.

Development of Seismic Fragility Functions for Reinforced Concrete Buildings Using Damage-Sensitive Features Based on Wavelet Theory

In this study, wavelet-based damage-sensitive features are employed to derive the seismic fragility functions/curves for reinforced concrete moment-resisting frames. Two different wavelet transform functions, namely, Bior3.3 and Morlet mother wavelet families, were applied to absolute acceleration time histories of building frames to extract the wavelet-based and refined wavelet-based damage-sensitive features (i.e., DSF and rDSF). The accuracy of seismic assessments and certainty in predicting structural behavior strongly depend on the specific optimal intensity measures selected, reliability of wavelet-based damage-sensitive features, and some such intensity measures as PGA, PGV, PGD, Sa, and Sdi as the conventionally utilized measures to detect the damage state of a structure. These measures were examined against their statistical properties of efficiency, practicality, proficiency, coefficient of determination, and sufficiency to select the appropriate optimal intensity measures, which were then used to drive the fragility curves disclosing the failure or other damage states of interest. For the purposes of this study, three different concrete moment-resisting frames with four-, eight-, and twelve-story building frames were adopted for implementing the proposed approach. The findings demonstrate that the wavelet-based damage-sensitive features (DSFs/rDSF) simultaneously satisfy all the statistical properties cited above. This is evidenced by the low variance and dispersions observed in the frame damage state predictions by the fragility functions derived from the wavelet-based DSF when compared with those derived from the classical fragility analyses such as spectral acceleration at the first mode period of the structure. A final aspect of the study concerns the superior performance and efficiency of the fragility curves derived by the Bior3.3 wavelet-based DSF over those derived from Morlet wavelet-based DSF.

Shaking table tests on seismic performance of a five-story reinforced concrete frame structure with MoS2 sliding bearings and steel dampers

The seismic performance of friction isolated structure is greatly affected by the friction coefficient, and the combination of low friction material and limit device is an available option. Via the Motion State module simulating the friction conditions and the Bouc Wen model describing the restoring characteristic of the steel dampers, a single-degree-of-freedom model was established to investigate the influence of the friction coefficient and limit stiffness on the isolation effect. Then, for the evaluation of the seismic performance of the proposed isolation system with molybdenum disulfide (MoS2) sliding bearings and steel dampers, the shaking table tests of a 1/5 scaled five-story reinforced concrete frame structure model, subjected to three ground motions with different peak ground acceleration, were implemented to obtain the isolation layer drift, absolute acceleration, inter-story shear and damage energy of the structure under the testing conditions of free sliding, limited sliding, multi-dimensional seismic excitation, and top additional layer sliding. It is found that the ideal friction coefficient for sliding isolated structure is 0.03–0.07, and the corresponding reasonable elastic stiffness of steel dampers is (0.2–0.5) Ks that is the stiffness of the structural standard story, and the proposed MoS2 sliding bearing presents remarkable low-friction characteristic with a friction coefficient of 0.04–0.05. The appropriate steel dampers can reduce the isolation layer drift without obviously increasing the acceleration. The low-frequency components in the ground motion significantly increase the isolation layer drift, while the high-frequency components cause the superstructure acceleration to show a K-shaped distribution along the height. Moreover, the proposed isolated system can be effectively used for structural protection under multi-dimensional earthquakes, the sliding additional layer on the roof can be considered as the second defense line in the structural seismic design, and the seismic energy the superstructure bears can directly estimate the seismic isolation effect that is consistent with the analysis result of dynamic response.

Comparative seismic performance evaluation of friction, self-centering and hybrid self-centering dampers

This study explores comparative seismic performance of a shape memory alloy (SMA)-only device, a friction damper, and a hybrid self-centering device. The self-centering device considered in this study, named as superelastic friction dampers (SFDs), is a hybrid damper operating on a mechanism where SMA cables and frictional components are arranged in parallel. A detailed description of the device and an experimental characterization of mechanical behavior are presented first. Then, an 8-story archetype steel frame building is designed and modeled with each seismic protection device (SMA-only, hybrid self-centering, and friction only). To enable comparative performance assessment, each device is designed to have similar initial stiffness and the same maximum force at design displacement. Nonlinear time history analyses are conducted using a total of 44 ground motion records. The results are evaluated to compare performance of each frame design at design-basis and maximum considered earthquake hazard levels. Next, a risk-based seismic hazard demand analysis framework that involves comprehensive incremental dynamic analyses is employed for further assessing the performance of each system. The experimental results validate the parallel working mechanism of SMA cables and frictional components in the SFD, with 90% of the damper deformations recovered. Comparative analysis of seismic responses demonstrates the excellent performance of the SFDs in reducing interstory drift ratio, residual interstory drift ratio, and absolute acceleration responses. Furthermore, fragility analysis and risk-based seismic hazard assessment further reveal that the SFDs provide a well-balanced combination of energy dissipation capability and self-centering ability, thereby enhancing the seismic resilience of structures.

Investigating the effect of ballast contamination in vertical and shear interlocking stiffness: Experimental and numerical study

The maintenance of railway tracks faces a significant challenge due to ballast contamination. This issue arises from the inevitable ingress of fine particles into the track structure through various means, such as fine sands, coal infiltration, aggregate breakage, and substructure pumping. Climate change exacerbates these conditions, leading to increased external debris contamination and the accelerated degradation of ballast aggregates. This contamination has major consequences, impacting track quality in terms of drainage capacity and dynamic behavior. As a response to this, the study focuses on assessing ballast contamination from sand infiltration, specifically evaluating vertical and shear interlocking stiffness through a dedicated experimental setup for ballast behavior analysis. Using materials from an actual track, contamination levels from clean to 30 % were simulated, and an empirical formulation of contaminated ballast stiffness was derived based on laboratory tests. Moreover, numerical sensitivity analyses were conducted to explore the impacts of ballast contamination on the dynamic behavior of track components. The findings indicate a significant increase in dynamic track responses up to a 30 % contamination level, based on gravimetric measurements, leading to substantial increases in maximum absolute accelerations of sleeper and ballast layer as well as exerted forces on the ballast layer by about 28 %, 21 %, and 46 %, respectively.

Hybrid self-centering braces with NiTi-SMA U-shaped and frequency-dependent viscoelastic dampers for structural and nonstructural damage control

This study proposes a novel hybrid self-centering brace (HSB) with structural and nonstructural damage-control capabilities for the seismic resilience of building structures. NiTi-based shape memory alloy (SMA) U-shaped dampers and frequency-dependent viscoelastic dampers are included in HSBs to provide self-centering capacity for avoiding structural damage and velocity-proportional damping for nonstructural damage control, respectively. This study includes two major parts, i.e. component-level mechanical behaviour and system-level dynamic response evaluation of HSBs. The working principle and desired nonlinear behaviour of the HSB were first presented. Then, the preliminary design procedures were developed. After validating the efficiency of the modelling of SMA U-shaped and viscoelastic dampers using prior test results, comprehensive 3D finite element model simulations were performed to study the hysteretic responses of HSBs under cyclic loadings, where the influences of loading frequency, loading amplitude and viscoelastic damper’s contribution were considered. Analysis results demonstrated that the designed HSB can attain the desired deformation mechanism and nonlinear hysteretic behaviour during dynamic cyclic loadings. Higher loading frequency and amplitude and more contributions of the viscoelastic damper can introduce higher loading and energy-dissipation capacity. Subsequent dynamic analyses of the single-degree-of-freedom systems were conducted to assess the dynamic performance and advantages of HSBs. Results showed that compared with traditional self-centering systems without velocity-proportional damping, the systems with HSBs can achieve zero residual deformations, lower base shear demands and smaller absolute acceleration responses, confirming the promising potential of HSBs in developing seismic resilient building structures by reducing structural and nonstructural damage.

An analytical approach for shock response of fractional viscoelastic beams with tip mass

This paper specifically analyzes the behavior of a beam with fractional viscoelastic properties and a tip mass under shock. The shock is applied longitudinally to the beam, and a fractional Kelvin–Voigt model is employed to describe the viscoelastic properties. Additionally, the paper examines the fractional viscoelastic power as a function of time during the shock. The equation of motion for the fractional viscoelastic beam with a tip mass is derived using Hamilton’s principle. In order to ensure accurate analysis of the results, the graphs are carefully analyzed in both the time and frequency domains. To solve the equations, the special technique provided for differential equations of variable order (VO) is used. Two distinct methods, namely, absolute method and square root of the sum of squares method, are thoroughly examined to calculate the absolute acceleration. Subsequently, the most suitable method is selected based on the evaluation results. The study’s results demonstrate that the damping parameters of the viscoelastic beam have a significant impact on shock transmissibility. Additionally, the findings demonstrate that the ability to transfer shocks can be manipulated by modifying the system’s geometry and mass.

Multi-scene mobile absolute gravity surveying by developing a vehicle-mounted static-base atom interferometry gravimeter

Land-based absolute gravity measurement are of interest to various fields, including geodesy, geophysics, seismic observations, and military. Currently, indoor static, outdoor transportable or vehicle-mounted base-less absolute gravimeters are either lacking in mobility or precision, thus reducing practicality. Here, we propose and report a novel vehicle-mounted static-base atom interferometry absolute gravimeter, where the sensing section can be decoupled from the vehicle and rigidly coupled to the ground during gravity measurements by employing a liftable structure attached to the static-base platform. The measurement performances have been evaluated under on-board static conditions, illustrating sensitivity of 570 μGal/Hz, long-term stability of about 10 μGal, and precision of about 20 μGal. The system can determine the local absolute gravitational acceleration within mere minutes of parking, which has been demonstrated in different conditions with bias of 10 to 100 μGal, such as urban and mountain as well as highway spanning nearly 1000 kilometers. This gravimeter proves particularly suitable for point-to-point absolute gravity surveys in vehicle-mobile form during broad-area or long-travel missions.

Phản ứng động đất của các hệ nhị tuyến tính đàn - dẻo và tự tâm định dưới tác dụng của các chuyển động nền do động đất xa và gần

This study presents seismic response of single degree of freedom (SDOF) elasto-plastic and self-centering systems under far and near-fault ground motions. These parameters was conducted to determine the influence on SDOF structure response in term of ductility, absolute acceleration, absorbed energy, strength ratio and strength reduction factor. It was found that maximum ductility for bilinear elasto-plastic systems was qualitatively similar to self-centering hysteretic systems, by adjusting the value of α and β, a self-centering hysteretic systems could be made qualitatively better than bilinear elasto-plastic systems in term of ductility. With respect to the absorbed energy, the self-centering hysteretic systems always less than comparable bilinear elasto-plastic systems. A three 3-story steel frame Self-Centering Brace Frame (SCBF) was designed according AISC seismic provison to validate of response of single degree of freedom self centering systems. 20 far field earthquake groundmotion are used for analysing of three 3-story steel frame SCBF under DBE (Design Based Earthquake) and MCE (Maximum Considerded Earthquake) level by using computer program PISA3D. The maxmimun value of interstory drift are under 1% and 2%, while residual drift are small.

Investigations on seismic performance of nuclear power plants equipped with an optimal BIS-TMDI considering FSI effects

This paper introduces a base isolation system-tuned mass damper inerter (BIS-TMDI) hybrid system to the AP1000 nuclear power plant (NPP), which reduces seismic damage potential of the NPP structure. The effects of fluid-structure interaction (FSI) caused by the passive containment cooling system water storage tank (PCCWST) on NPP's seismic performance are investigated. The FSI of water tank theoretical model is considered based on the Housner's model, and a series of time history analyses are performed to prove the rationality of the proposed model. Three single-objective optimization strategies are employed to minimize the relative displacement variance and absolute acceleration variance of the upper structure, as well as the filtered energy index (FEI). Furthermore, a multi-objective optimization strategy considering all these three indexes is proposed to obtain optimal parameters of vibration control. The influence of vibration control strategies on the relative deformation and acceleration of the upper structure is explored with various water level ratios. The analytical results indicate that the proposed BIS-TMDI strategy has significantly reduced the NPP structure's seismic response. The effectiveness of the vibration control strategy is influenced by the water level ratio, emphasizing the significance of designing an appropriate water level ratio to reduce NPP structure's seismic response.

Performance-based seismic design method for disc spring-based self-centering viscous dissipative braced steel frame

Disc spring-based self-centering viscous damper (SCVD) has emerged as a novel technology, offering velocity-dependent energy dissipation and exceptional self-centering capabilities. Integrating this damper in structural bracing systems can effectively enhance passive control over critical structural demands such as peak deformation, residual displacement, and floor acceleration. Nevertheless, a seismic design method specifically tailored for self-centering viscous dissipative braced steel frames (SCVDFs) needs further refinement. This study proposes a performance-based seismic design (PBSD) method for SCVDFs, which is grounded in the performance-based plastic design (PBPD) approach. The proposed procedure primarily considers the effects of two critical hysteresis parameters: the post-activation stiffness ratio and the viscous damping ratio. To verify the effectiveness of the design method, a set of SCVDFs was designed, each utilizing different combinations of design parameters. Nonlinear static and dynamic analyses were performed on these archetypes to evaluate their seismic performance. The evaluation findings demonstrated that the properly designed SCVDFs can achieve the expected design performance and effectively suppress the peak inter-story drift, residual inter-story drift, and peak absolute floor acceleration of the structure, thereby achieving a favorable trade-off in the design outcome and maximizing the advantages of the SCVDF in seismic resilience.

Distinguishing Passive and Active Standing Behaviors From Accelerometry

Purpose: To investigate whether active standing can be identified separately from passive standing via accelerometry data and to develop and test the accuracy of a machine-learning model to classify active and passive standing. Methods: Ten participants wore a thigh-mounted activPAL monitor and stood for three 5-min periods in the following order: (a) PASSIVE: standing with no movement; (b) ACTIVE: five structured weight-shifting micromovements in the medial–lateral, superior–inferior, and anterior–poster planes while standing; and (c) FREE: participant’s choice of active standing. Averages of absolute resultant acceleration values in 15-s epochs were compared via analysis of variance (Bonferroni adjustment for pairwise comparisons) to confirm the dichotomization ability of the standing behaviors. Absolute resultant acceleration values and SDs in 2- and 5-s epochs were used to develop a machine-learning model using leave-one-subject-out cross validation. The final accuracy of the model was assessed using the area under the curve from a receiver operating characteristic curve. Results: Comparison of resultant accelerations across the three conditions (PASSIVE, ACTIVE, and FREE) resulted in a significant omnibus difference, F(2, 19) = [116], p < .001, η2 = .86, and in all pairwise post hoc comparisons (all p < .001). The machine-learning model using 5-s epochs resulted in 94% accuracy for the classification of PASSIVE versus ACTIVE standing. Model application to the FREE data resulted in an absolute average difference of 4.8% versus direct observation and an area under the curve value of 0.71. Conclusions: Active standing in three planes of movement can be identified from thigh-worn accelerometry via a machine-learning model, yet model refinement is warranted.

FINDING THE RELATIVE TRAJECTORY OF THE CARGO IN THE BODY OF A VEHICLE WHICH IS GOING DOWN OR UP ON A CURVED SECTION OF THE ROAD

With a certain assumption, the load, which during relative movement along the bottom of the body makes translational movement, can be taken as a material point. In this case, finding the relative movement of the load in the body when the car moves along the road with a spatial axis is reduced to finding the relative trajectory of the material point. In known works, it is proposed to use the accompanying trihedron of the trajectory of the transfer motion and Frenet's formula to find the absolute acceleration vector of a point. The independent variable is not time, as in traditional problems, but the arc coordinate of the transfer trajectory, since only under this condition can Frenet's formulas be applied. The vector of absolute acceleration is obtained in projections onto the vertices of the moving accompanying trihedron, without looking for individual components (transfer, relative, and Coriolis acceleration), as is done in traditional approaches. The purpose of the study is to investigate the relative movement of the load, taken as a material point, along the bottom of the body of a truck moving along a curvilinear section of the road with a spatial axis during its ascent or descent. The spatial curve is characterized by two parameters that depend on the kinematics of the accompanying Frenet trihedron. These parameters are the curvature k and the twist σ of the curve. Their values at any point of the curve will be determined if the dependencies k=k(s) and σ=σ(s) are known, where s is the arc coordinate (the arc length of the curve). It is assumed that such a spatial curve is the axis of a curved section of the road that goes uphill or downhill. The application of the accompanying trihedron of the curve and Frenet's formulas made it possible to describe the relative motion of the cargo in the body of a car moving along a road having a spatial axis with constant and variable speeds. The regularities of the relative movement of the cargo when the car is moving on the road, the axis of which is a helical line with constant curvature and twist, have been found. It was found that there is no significant difference between the value of the relative speed of the cargo when the car moves at a constant speed down or uphill at the initial stage. When braking on a descent, a significant relative movement of the cargo is observed, which increases with an increase in the braking acceleration, and when climbing, on the contrary, the relative movement decreases with an increase in the braking acceleration. The regularity of the relative movement of the cargo when the car moves along the road with variable curvature and torsion of the axis line depends on the type of these dependencies as a function of the length of the arc of the axis line.

Development of a simple algorithm to detect big air jumps and jumps during skiing.

Jumping is an important task in skiing, snowboarding, ski jumping, figure skating, volleyball and many other sports. In these examples, jumping tasks are a performance criterion, and therefore detailed insight into them is important for athletes and coaches. Therefore, this paper aims to introduce a simple and easy-to-implement jump detection algorithm for skiing using acceleration data from inertial measurement units attached to ski boots. The algorithm uses the average of the absolute vertical accelerations of the two boots. We provide results for different parameter settings of the algorithm and two types of jumps: Big Air jumps and jumps during skiing. The latter are divided into small (time of flight < 500 ms) and medium (time of flight ≥ 500 ms) jumps. The algorithm detects 100% of Big Air, 94% of medium and 44% of small jumps. In addition, the settings with the highest detection rates also have the highest number of overdetected jumps. To resolve this conflict, a penalty-adjusted score that considers the number of overdetected jumps in the final performance analysis is proposed.

Study of complex motion of a plane point at rotation of a supporting body

The paper studies the kinematic characteristics of the complex motion of a point under the rotation of a supporting body. The trajectory of the point performing complex motion is obtained, and the graphs of changes in absolute velocity, absolute acceleration of the point and their components in time are obtained. The solution of the problem was carried out in Mathcad package, for which the problem formulation and solution was carried out by the matrix method. The use of the mathematical package allowed us to take chronograms of the processes of relative motion of the point, translational motion of the body and absolute motion of the point.

DESIGN OF VISCO-ELASTIC SUPPORTS FOR TIMOSHENKO CANTILEVER BEAMS

The appropriate design of supports, upon which beams are usually placed as structural components in many engineering scenarios, has substantial significance in terms of both structural efficacy and cost factors. When beams experience various dynamic vibration effects, it is crucial to contemplate appropriate support systems that will effectively adapt to these vibrations. The present work investigates the most suitable support configuration for a cantilever beam, including viscoelastic supports across different vibration modes. Within this particular framework, a cantilever beam is simulated using beam finite elements. The beam is positioned on viscoelastic supports, which are represented by simple springs and damping elements. These supports are then included in the overall structural model. The equation of motion for the beam is first formulated in the temporal domain and then converted to the frequency domain via the use of the Fourier Transform. The basic equations used in the frequency domain are utilized to establish the dynamic characteristics of the beam by means of transfer functions. The determination of the ideal stiffness and damping coefficients of the viscoelastic components is achieved by minimizing the absolute acceleration at the free end of the beam. In order to minimize the objective function associated with acceleration, the nonlinear equations derived from Lagrange multipliers are solved using a gradient-based technique. The governing equations of the approach need partial derivatives with respect to design variables. Consequently, analytical derivative equations are formulated for both the stiffness and damping parameters. The present work introduces a concurrent optimization approach for both stiffness and damping. Passive constraints are established inside the optimization problem to impose restrictions on the lower and higher boundaries of the stiffness and damping coefficients. On the other hand, active constraints are used to ascertain the specific values of the overall stiffness and damping coefficients. The efficacy of the established approach in estimating the ideal spring and damping coefficients of viscoelastic supports and its ability to provide optimal support solutions for various vibration modes have been shown via comparative experiments with prior research.

A new probabilistic long-period critical excitation procedure for isolated building structures

The present paper develops a new procedure for finding the most unfavorable long-period excitation for isolated building structures based on the probabilistic critical excitation method. The upper bound of earthquake input energy per unit mass is considered the problem’s constraint, and a modified power spectral density (PSD) function is proposed to conform to the new constraint. It is shown that the new constraint can be used as a criterion to estimate the possible range of input energy of similar earthquakes. In addition, the new PSD function can control the excitation’s intensity. Finally, three base-isolated shear buildings modeled as multi degree of freedom systems with nonproportional damping are considered, and the critical excitations for each model are found based on the proposed method. To examine the reliability of the results, three actual accelerograms with a considerably high level of total input energy are selected as benchmarks and linear dynamic analyses are conducted using these accelerograms along with the generated critical excitations. The results show that the generated long-period excitations can better estimate the structural behavior (i.e., maximum displacement, drift, and absolute acceleration of stories) than the actual benchmark accelerograms.

Experimental Study and Seismic Design of Swing Story-Lateral Force Resisting Structural System

A seismic vibration control system, consisting of a swing story substructure, a lateral force resisting substructure and connecting dampers, is recently proposed. The analytical model and optimization method based on the stability maximization and H2 criteria have been established. In this paper, excellent vibration control effects of the proposed system are verified through the small-scale shaking table tests on a two-story model. Experimental results demonstrate the accuracy of the analytical model and the validity of the vibration control strategy. Through numerical analyses of benchmark structures, the input energy of the optimally designed system is remarkably mitigated, and favorable vibration control effects for reducing both inter-story drifts and absolute floor accelerations under earthquake ground motions are verified by comparing with conventional moment-resisting frame structures. In addition, significant control effects can be achieved when the optimal stiffness is greater than the critical buckling stiffness. A seismic design flow chart of the intensity-reduced design method is proposed based on the numerical analyses and the Chinese Seismic Design Code of Buildings. The results indicate that the seismic intensity-reduced design for the proposed system is feasible.

Performance assessment of steel frame buildings with hybrid self-centering braces under extremely rare far-field earthquakes

This paper investigates the seismic performance enhancement of steel frame buildings using a novel hybrid self-centering braces (HSBs) under extremely rare earthquake events. The hybrid self-centering brace consists of shape memory alloy (SMA) cables and viscoelastic (VE) dampers. A prototype bracing system is designed and fabricated to explore its basic mechanical behavior and working mechanism under cyclic loading, with a focus on its failure modes under large deformation loading condition. A multi-material mechanical model is developed to capture the mechanical behavior and failure of the HSB. Furthermore, five steel frame buildings with different parameterized HSBs are designed and modeled in OpenSees. Nonlinear dynamic analyses and incremental dynamic analyses are conducted on the five case-study frames using 44 far-field ground motions. The risk-based seismic performances of steel buildings with HSB are evaluated to assess the performance of HSB during extremely rare seismic events. The results show that the hybrid self-centering brace exhibits excellent self-centering and energy dissipation capabilities with the maximum equivalent viscous damping ratio reaching 9.4 %. Even under large deformations, VE dampers continue to work effectively after the failure of SMA cables, demonstrating remarkable redundancy. Numerical simulations further reveal that the redundancy of HSB can improve the structural seismic resilience in terms of inter-story drift ratio, residual drift, and floor absolute acceleration. The higher the redundancy of HSB in the case-study frames, the smaller the seismic response and mean annual frequency of exceedance of the engineering demand parameters, thereby indicating a significant improvement in seismic performance.

Seismic design and performance evaluation of hybrid braced frames having buckling-restrained braces and self-centering viscous energy-dissipative braces

Hybrid braced frames (HBFs) emerge as an innovative seismic-resilient system, synergizing the strengths of buckling-restrained braces (BRBs) and self-centering viscous energy-dissipative braces (SCVDBs). This novel system has the potential to simultaneously manage three key seismic demand parameters: peak inter-story drift (PID), residual inter-story drift (RID), and peak absolute floor acceleration (PFA). Nevertheless, a dedicated seismic design method for HBFs is yet to be developed. This research proposes a performance-based seismic design (PBSD) method specifically tailored for HBFs. The method's core relies on energy decoupling in the HBFs using a proposed energy distribution factor (η). To validate the proposed design method, sets of 4-, 8-, and 12-story braced frames are designed using varied η. A comprehensive seismic performance evaluation is conducted, utilizing nonlinear static and nonlinear time-history analyses. The findings indicate that the HBFs, designed utilizing different values of η, consistently meet predefined performance objectives. Within the scope of this study, the η value of 0.5 is shown to be optimal, enhancing the structural resilience of HBFs against PIDs and PFAs while exhibiting excellent self-centering performance comparable to the self-centering viscous energy-dissipative braced frame (SCVDF). Additionally, the HBFs demonstrate superior control over PFA compared to pure buckling-restrained braced frame (BRBF) and SCVDF.