Absolute Acceleration Response Research Articles

Performance analysis of a novel single-flywheel resettable-inertia damper with eddy-current damping

The clutching inertia model presents an ideal Bang-Bang control approach, but it is challenging to realize practically through passive means. In this paper, a single-flywheel resettable-inertia damper (SRID) is proposed on the basis of the clutching inertia model. This device is implemented with a rack-and-pinion system, a right-angle gearbox system, and a flywheel-mounted eddy-current damping system. Initially, a mechanical analysis model of this device is established according to its working mechanism. Subsequently, comparative analyses are performed on the performance of SRID in a single degree-of-freedom (SDOF) structure compared to viscous dampers (VDs) subjected to harmonic and seismic excitations. The results show that the SRID can achieve a comparable control effect as VDs with a much smaller need for the damping coefficient, reflecting a damping amplification effect over 100 times. The SRID is effective in controlling peak displacement and absolute acceleration responses, especially for long-period structures. Moreover, the control performance is significantly improved with increasing magnetic induction intensity.

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.

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.

Hybrid self-centering dual rocking core system for seismic resilience by controlling both structural and nonstructural damage

This study proposes a novel hybrid self-centering dual rocking core (HSDRC) system with structural and nonstructural damage control functions for the building structure’s seismic resilience. The rigid rocking cores (RCs), viscous dampers (VDs), and shear friction spring dampers (SFDs) are introduced in HSDRC systems. The rocking cores with pinned bases are adopted for promoting uniform inter-story drifts over the building height. The SFDs are introduced to dissipate hysteretic energy and bring self-centering capacity by eliminating residual deformation. The VD’s velocity-proportional damping can help HSDRC systems control the nonstructural damage and building content’s damage sensitive to absolute floor accelerations. The expected behavior of HSDRC systems is first described. A direct displacement-based design (DDBD) method is following proposed to achieve the desired nonlinear behavior of HSDRC. Following the developed DDBD procedure, six HSDRC systems are designed. For highlighting the advantages of HSDRC systems compared to the existing self-centering energy-absorbing rocking core (SEDRC) system, two SEDRC systems are also designed. Nonlinear dynamics were included for investigating the performance of the designed systems subjected to seismic events. The numerical results demonstrate that the designed HSDRC systems show the expected nonlinear behavior and achieve the design target, confirming the developed DDBD method’s effectiveness. Compared to SEDRC systems, the newly proposed HSDRC systems show smaller absolute floor acceleration responses while obtaining the comparative capacity in controlling both peak and residual inters-tory drifts, indicating the proposed HSDRC systems can be a promising seismic resilient structural system for both structural and nonstructural damage control.

Reduction of the seismic absolute acceleration response with supplemental viscous damping

The relationship between the seismic absolute acceleration response of single- and multi-degree-of freedom building models and the amount of supplemental viscous damping is analyzed. Possible influence of the fundamental period, the number of stories, and the frequency content of the excitation is evaluated. It was found that, qualitatively, the relationship between the absolute acceleration response and the amount of supplemental viscous damping is different from that between the displacement response and the amount of supplemental viscous damping. The implications of the findings of this study for the design of supplemental viscous damping systems aimed at reducing the absolute acceleration response of buildings are discussed.

Rapid seismic fragility curves assessment of eccentrically braced frames through an output-only nonmodel-based procedure and machine learning techniques

A nonmodel and output-only-based framework incorporating an Auto-Regressive model and roof absolute acceleration response are hired in this study to compute a robust wavelet-based damage-sensitive feature (rDSF) and estimate engineering demand parameters (EDPs) of buildings with eccentrically braced frames (EBFs). A large database is recruited to estimate the peak and residual story drift ratios and peak floor absolute accelerations as EDPs. The database comprises cmorfb-fc wavelet-based rDSF, number of stories, building heights, and EDPs of the 4- and 8-story EBF archetypes, resulting from 44 far-field ground motions through incremental dynamic analysis. The capability of both the closed-form equations and machine learning (ML) techniques is investigated to estimate the EDPs. The predictive equations are constructed using ordinary least squares linear regression, Symbolic and Bayesian regressions. To have a more accurate estimation of EDPs, 12 renowned ML-based regression algorithms are also implemented for training, validation, and test datasets. Sensitivity analysis using box-whisker plots on the validation dataset shows that Extreme Gradient Boosted Trees (ExGBT) ensemble has a remarkable efficiency to predict the EDPs and leads to the highest 10-fold correlation coefficient and the lowest root-mean-square error. Moreover, ExGBT has the lowest median absolute relative deviation in different damage states and consequently is selected as the best surrogate algorithm. The predicted EDPs can be further exploited to map rDSF-based fragility curves, a conditional probability at each defined damage state given the value of rDSF. The comparative results for the test data approve that the predicted fragility curves approximately match with those obtained from observed data and can be used for early decision-making in emergency operations.

Influence of spatially varying ground motions on the seismic responses of bridge structures with KDampers

KDamper has been applied to control the seismic responses of bridge structures very recently. However, previous studies considered its performance under uniform ground motions only, the influence of the inevitable spatially varying ground motions (SVGMs) is not yet explored. To address this issue, this study systematically investigates the seismic responses of a large-span bridge structure equipped with KDampers subjected to SVGMs. In particular, the analytical model of a classical bridge equipped with KDampers is developed, and the corresponding dynamic equations of motion are formulated. Subsequently, KDampers are optimized by minimizing the mean peak response of the bridge deck in the frequency domain. Finally, parametric analyses are performed to comprehensively evaluate the influence of SVGMs (including wave passage and coherency loss effects) on the seismic responses of the bridge in both the frequency and time domains. The analytical results reveal that the optimized KDampers are effective in reducing the displacement and absolute acceleration responses of the bridge. Moreover, the effectiveness of KDampers is more evident when SVGMs are considered as compared to the uniform ground motions. This research can contribute to an in-depth understanding of the control effectiveness of KDampers, especially for the cases considering SVGMs.

Seismic performance of column-bearing silo structure with granular materials considering SSI effect

This paper investigates the effects of different silo height-to-diameter ratios, different storage categories and different site soil categories on the seismic performance of column-bearing concrete grain vertical silo structures considering soil-structure dynamic interaction (SSI). The study reveals more comprehensive response mechanism of soil-pile-silo structure with grain storage system under earthquake actions. The numerical results indicate that for the full silo models with different height-diameter ratios, the SSI effect could reduce the absolute acceleration response, and the reducing rate at the top of the support column will be slightly larger than that of the top of the silo. In addition, the greater the height-diameter ratio, the more obvious the absolute acceleration damping effect of the SSI effect. The SSI effect has the greatest damping effect on the absolute acceleration response when the silo is filled with wheat. Moreover, the degree of softness and hardness of the soil affects the shock absorption effect of SSI on the absolute acceleration and elastic–plastic acceleration of the silo. The softer the soil, the more obvious the shock absorption effect of SSI. More interestingly, among the parameters of height-diameter ratio, storage material type and dynamic shear modulus of soil, the height-diameter ratio has the greatest influence on the seismic response and hysteretic energy dissipation performance of the column-bearing silo structure considering SSI effect, followed by the foundation soil. Dynamic shear modulus and the storage material category have the least influence.

Shaking table test study on seismic performance of RC frame structure with NES

A new type of nonlinear vibration absorber NES (Nonlinear Energy Sink) studied in this paper belongs to the structural passive control technology, which consists of a horizontal track and an additional mass block. Acting as a damper absorb and dissipate energy, the NES completes the target energy transfer by generating a horizontal nonlinear restoring force and reduces the response of the main structure. In this paper theoretical analysis of the new NES was analyzed by the expression of the restoring force of the NES and the equation of motion of the additional NES system are deduced. Shaking table test was carried out on the 1:4 scale RC frame structure model installed with the new NES shock absorber, focusing on the research on the energy dissipation and shock absorption effect of the NES shock absorber, and whether it can improve the seismic performance of the RC frame structure damaged in the earthquake. The results show that the NES installed in the RC frame structure has sufficient nonlinear displacement and energy dissipation capacity under the moderate and strong earthquakes, showing a very good energy dissipation and shock absorption effect. The NES can reduce the top story displacement and acceleration response of the main structure under the action of earthquake; the top story displacement and absolute acceleration response are related to the natural frequency of the frame and the spectral characteristics of seismic waves, so that the vibration control effect is affected by the frequency spectrum of seismic waves. In the frequency domain analysis of the frame dynamic response, the nonlinear energy well exhibits the characteristics of broadband control. This type of NES significantly reduces the seismic response of damaged structures, improves the seismic performance of damaged structures under moderate to strong earthquakes, and decreases the risk of potential collapse and construction costs during earthquake aftershocks.

Machine learning-driven performance-based seismic design of hybrid self-centering braced frames with SMA braces and viscous dampers

A hybrid self-centering braced frame equipped with shape memory alloy-based self-centering braces (SMA-SCBs) and viscous dampers is proposed to achieve enhanced seismic performance. Based on the proposed hybrid strategy combining the contributions of SMA-SCBs and viscous dampers, this paper investigates the advantages of such hybrid self-centering braced frames in achieving the desired maximum inter-story drift under a considered seismic intensity. To this end, the influence of design parameters of SMA-SCBs and viscous dampers on hybrid self-centering braced frames is examined through parametric dynamic analyses of equivalent single-degree-of-freedom systems. The analysis results indicate that the post-yield stiffness ratio α and energy dissipation factor β of SMA-SCB, and the contribution of viscous damper show significant influence on the peak displacement responses of hybrid self-centering braced frames. The constant inelastic displacement ratio prediction model for hybrid self-centering braced frames is developed using machine learning algorithms. A performance-based seismic design method is subsequently proposed for the hybrid self-centering braced frames to achieve the target displacement responses based on the developed machine learning models. Two hybrid self-centering braced frames are designed based on the proposed design method. Nonlinear dynamic analyses are conducted to investigate the seismic performance of the designed structures. To highlight the advantages of the hybrid self-centering braced frames, another six-story self-centering braced frame with SMA-SCBs only is also studied in this paper. The analysis results indicate that all the designed hybrid self-centering braced frames can achieve the desired performance objective. Compared to the self-centering braced frame with SMA-SCBs only, the hybrid self-centering braced frames can achieve much smaller base shear demand and absolute floor acceleration responses.

Energy analysis of an inerter‐enhanced floating floor structure (In‐FFS) under seismic loads

AbstractTo improve the seismic responses of the traditional floating floor structure (FFS), an inerter‐enhanced FFS, namely the In‐FFS, was recently proposed by the authors. The multifold improvements offered by the In‐FFS compared to the FFS have been investigated based on the seismic responses analysis. In this work, the superior performances of the In‐FFS are investigated and demonstrated based on the energy analysis method. It is found that, thanks to the dynamic equivalent mass effect of the inerter, the input energy of the entire system under seismic inputs is suppressed. Compared with the conventional frame structure (FS), the maximum mechanical energy of the primary structure is reduced by around 75% and 80% for the FFS and In‐FFS, respectively. As a result, dynamic responses of the primary structure are greatly mitigated. More importantly, the inerter attachment can effectively suppress the maximum kinetic energy of the FFSs (e.g., by more than 50%). The relative displacements between the floating floor slabs and the primary structure are reduced by more than a half. The energy dissipation capacity of the inerter attachment is much better (about two times) than that of the traditional isolator with the same damper. Compared to its two degenerated models, the proposed inerter attachment can suppress both the maximum mechanical energy of the primary structure and the maximum kinetic energy of the floating floor slab at the same time. Overall, the proposed In‐FFS outperforms the traditional FFS. It enhances the multifold advantages of the FFS (i.e., the small interstory drift responses of the primary structure and the limited absolute acceleration response of the floating floor slab); meanwhile, it also eliminates a main disadvantage of the FFS (i.e., the large relative displacement between the floated floor slabs and the primary structure).

Hybrid self-centering companion spines for structural and nonstructural damage control

This paper intends to develop a new lateral force-resisting system – the hybrid self-centering companion spines system (denoted as the HSCS system) – for obtaining better seismic resilience by controlling both structural and nonstructural damage. The HSCS system consists of two rigid spines pinned to the ground and several hybrid dampers. The two rigid spines can facilitate the structure to avoid soft-story mechanisms and control higher mode responses by promoting uniform inter-story drift distribution under strong earthquakes. The hybrid damper is made of a friction spring damper and a viscous damper in parallel and provides the self-centering feature, energy-absorbing capacity, and acceleration- and velocity-control capacity for reducing structural and nonstructural damage. A performance-based design (PBD) procedure was developed for the HSCS system based on the concept of the direct displacement-based design method. The three-story and six-story demonstration buildings were considered in this study to investigate the seismic performance of steel buildings equipped with the proposed HSCS systems. Four designs with different design parameters were performed for the demonstration buildings based on the proposed PBD procedure. The three- and six-story self-centering companion spines systems (denoted as SCS systems) were considered for highlighting the benefits of adopting HSCS systems. Nonlinear dynamic analyses were conducted to evaluate the structural and nonstructural damage of the designed buildings under earthquakes. The analysis results indicate that the designed HSCS systems can achieve the desired performance objective and nonlinear behavior under dynamic excitations. The HSCS systems can show excellent structural damage control performance and post-earthquake recoverability by controlling the residual inter-story drift much smaller than 0.2% even under MCE excitations. The excellent nonstructural damage control capacity can be also observed in the designed HSCS systems, while most of the nonstructural components are only slightly damaged even under MCE excitations. Moreover, the HSCS systems can achieve smaller absolute floor acceleration and floor velocity responses than SCS systems under both DBE and MCE although they are designed to achieve similar maximum inter-story drift responses under DBE.

Parametric study and prediction models of the seismic response of single-degree-of-freedom structural systems equipped with Maxwell material fluid viscous dampers

The addition of supplemental damping through fluid viscous dampers has been widely implemented as a seismic protection system for diverse typologies of structures. Typically, fluid viscous dampers are modelled using a Maxwell material model, which accounts for the stiffness of the damper device and its support assembly. However, the influence of the different parameters involved in the design of Maxwell fluid viscous dampers on the dynamic response of damped systems subjected to transient loads has not been studied thoroughly, especially regarding the acceleration response of dynamic systems. This paper discusses the results of a parametric study of the influence of several damper's design parameters, such as the velocity exponent, the supplemental damping level, the seismic intensity, and the Maxwell material stiffness, and the interaction among them, on the seismic response of viscously damped single-degree-of-freedom structural systems. Non-linear time history analyses were carried out using the FEMA P-695 far-field ground motion set scaled to four increasing intensities. The seismic response was measured in terms of peak relative displacements, peak relative velocities, peak damper forces, peak floor absolute accelerations, and peak floor absolute acceleration response spectra. Based on the obtained seismic responses, several prediction models were proposed using Gaussian Process Regression to provide an insight into the influence of the different design parameters of fluid viscous dampers on the seismic response of viscously damped single-degree-of-freedom structural systems. The results show that the different parameters involved in the design of Maxwell fluid viscous dampers significantly influence the efficiency of damper devices and the seismic response of the single-degree-of-freedom structural systems, especially in terms of acceleration response. For particular combinations of the damper's design parameters, significantly higher floor spectral accelerations can be observed in some period ranges compared to those of control systems without dampers. Additionally, the floor absolute acceleration response spectra exhibit a stiffening effect caused by the implementation of fluid viscous dampers, shifting peak floor spectral accelerations to shorter periods. The magnitude of the stiffening effect is proved to be correlated to the Maxwell material stiffness value.

Enhancement of nonlinear signal-based control to estimate earthquake excitations from absolute acceleration responses of nonlinear structures

This study constructs an inverse method for multi-storey structures with nonlinear hysteretic characteristics commonly used in earthquake and structural engineering. Constructing the inverse methods, which accurately reconstruct an input signal from a response and structural information, has been challenging owing to the severity of the nonlinear characteristics as well as structural complexity. Nonlinear signal-based control (NSBC) can achieve the exact input estimation from a nonlinear structural response when its linear model is exactly invertible. However, its estimation accuracy decreases when the exact inversion of the linear model is impossible, and an approximation is required. This study introduces a controller design consisting of three enhancements of NSBC to realise accurate input estimation even when the inversion requires an approximation; the estimation of an earthquake excitation from acceleration in the absolute coordinates of nonlinear structures is a typical example. The first enhancement is the improvement of a differentiator used to convert an improper inverse model into a proper one. The second is the zero-stiffness design wherein the stiffness of all storeys in the linear model is intentionally set to zero. The third is the addition of inner-error feedback actions to conventional NSBC controllers. The effectiveness of these enhancements is examined via numerical simulations of the input estimations of nonlinear 2/4-degree-of-freedom (2/4DOF) systems shaken by an earthquake excitation. The enhanced NSBC successfully estimates the earthquake excitation with 100% accuracy from one known absolute acceleration response of the nonlinear 2/4DOF systems. Its potential application for estimating earthquake excitations by realising a predetermined response on nonlinear structures is also analysed.

Shaking table test of concrete columns hybrid reinforced by steel/FRP bars

Post-earthquake residual deformation can be decreased due to the designable post-yield stiffness of concrete column reinforced by steel bars/fiber reinforced polymer (FRP) bars. Shaking table tests of three concrete columns with similar initial stiffnesses were conducted, where the longitudinal reinforcement included ordinary steel bars, steel-FRP composite bars (SFCBs) and hybrid reinforcement (steel bars and FRP bars, C–H). The measurements included acceleration response and strain development. The test results showed that the absolute and relative peak ground acceleration (PGA) responses of different columns were similar to one another. The residual strain in the anchorage region was not consistent (tension or compression) and was affected by the longitudinal reinforcement type and the amplitude of the input PGA. For ordinary reinforced concrete (RC) columns, the plastic strain of steel bars developed rapidly after the input ground motion PGA reached 100 Gal, and the corresponding residual strain also developed dramatically. For the SFCB column, even after the peak strain reached 15,000 με, the residual strain was still below 500 με. For hybrid column C–H, the residual strain of the FRP bar was similar to that of the SFCB column. Even when the input wave PGA reached 560 Gal with concrete cover spalling and steel bar buckling, no damage was observed on the FRP bars. In general, compared to ordinary RC columns, concrete columns with hybrid steel and FRP bar reinforcement can achieve a smaller residual deformation, while SFCB reinforced columns can be constructed in severe environments due to a good anti-corrosion performance, such as in offshore structures.

Earthquake ground motion estimation for buildings using absolute floor acceleration response data

AbstractEarthquake ground motion information is useful for structural vibration control during earthquakes and post‐earthquake inspections of structural damage. However, in practice, the ground input data on a specific location may not be available because of instrumentation limitations or technical issues. Numerous studies have been devoted to identifying the unknown excitation. Most of these studies required responses in relative coordinates or from systems with direct feedthrough. On the other hand, acceleration monitoring systems in applications measure global responses of buildings, which corresponds to the absolute acceleration of a point on a structure, that is, the measured floor acceleration is the sum of the unknown earthquake‐induced ground motion and acceleration relative to the ground when an earthquake happens. In this study, a ground motion estimation approach was developed based on an extended Kalman filter (EKF) with an embedded Bayesian noise parameter updating technique, which requires a relatively small number of sensors for absolute acceleration measurements. Numerical simulations, a shaking table test, and a real‐world application were performed to demonstrate the applicability and accuracy of the proposed method.

Experimental Research on Damping Effect of Double-Layer Tuned Mass Damper for High-Rise Structure

A double-layer tuned mass damper (DTMD) has advantages of wide damping frequency band and strong robustness. At present, there is a lack of seismic design methods for high-rise structures based on DTMDs. In this study, a DTMD parameter optimisation method was proposed, with the objective of minimising the peak displacement response of a first N-order vibration modal with a vibration mass participation factor of 85%. Then, a scale model of a high-rise structure was fabricated, along with a corresponding DTMD. Different types of excitations were chosen to clarify the dynamic responses of the model with and without the DTMD, including Site-II ground motions, long-period (LP) ground motions without pulses, and near-fault pulse-type (NFPT) ground motions. The results indicate that the dynamic responses of high-rise structures under LP and NFPT ground motions are much greater than those under Site-II ground motions. The DTMD can effectively reduce the absolute displacement response, acceleration response, and strain response at the top floor of the test model. However, the DTMD has a time delay in providing the damping effect. A smaller damping ratio between the upper TMD and the controlled structure will lead to a more significant damping effect for the DTMD.

Torsional response of a bisymmetric structure induced by bending–torsion interaction in vertical members

AbstractThe biaxially symmetric column induces torsional moment owing to the bending–torsion interaction when the top of the column is given horizontal displacement in the two directions of the principal axes of the cross section and the rotation of the column ends around the axes is constrained. Hence, horizontal ground motions in two directions can cause non‐negligible torsional vibration in a high‐rise building owing to autoparametric resonance. To investigate this phenomenon, in this study, we focus on a single‐story structure with an aggregated column, which is a model for columns or core structures in tall buildings and is assumed to be an elastic Euler beam; subsequently we derive the equations of motion under horizontal ground motions in two directions. The resonance condition in the torsional direction is also investigated. Time‐series response analyses are performed for input ground motions of harmonic waves, white noise, acceleration records of prior earthquakes, and a long‐period design wave, and the relationship between the ratio of two translational natural frequencies and the increase in maximum responses is explained. The results demonstrate that the absolute acceleration response to the long‐period design wave could increase by more than 50% in the worst‐case scenario.

Seismic acceleration demand and fragility assessment of storage tanks installed in industrial steel moment-resisting frame structures

Recent seismic events highlighted the importance of non-structural elements in seismic assessment and performance-based earthquake engineering. When referring to industrial facilities, storage tanks represent one of the most critical components for the continuous functionality of industrial and building plants after seismic events. At the same time, the dispersion of dangerous or inflammable materials, due to their collapse, could become a safety issue in terms of both human life and environmental impact. This study focuses on the seismic performance assessment of a liquid-storage tank installed in an industrial steel moment-resisting frame building. The performance is assessed in terms of fragility curves, that are provided for the meaningful limit states that affect the liquid-storage tank and considering several intensity measures. The results related to the structural performance are also discussed in detail in terms of fragility functions and floor response. The assessment is performed through nonlinear dynamic analyses using two different modelling approaches to evaluate the structural and non-structural performance. The first modelling approach explicitly accounts for the tank-structure interaction, while in the second one the tank is only modelled considering its seismic mass. The results show the importance of the modelling assumptions to accurately estimate the seismic demand on liquid-storage tanks and corresponding fragility, which is calculated in terms of different intensity measures (IM): average ground spectral acceleration, peak floor acceleration, and floor spectral accelerations. Peak floor acceleration, drift profiles, and absolute acceleration and relative displacement floor response spectra are instead scrutinised for what concerns demand. The comparison with the code formulations available in the literature for estimating the seismic demand to non-structural elements pointed out their inaccuracy for the analysed liquid-storage tank and the need for further efforts to develop more accurate procedures. Furthermore, the outcomes indicate that the IM adopted for secondary components, i.e. peak floor acceleration, may not always be the optimal one hence additional attention should also be paid to the definition of updated fragility curves for non-structural elements, identifying and adopting more suitable IMs.

Earthquake-induced economic loss estimation of eccentrically braced frames through roof acceleration-based nonmodel approach

This paper develops a nonmodel-based approach for seismic loss assessment of buildings with eccentrically braced frames (EBFs). An extensive database is utilized to predict engineering demand parameters (EDPs), including, peak and residual story drift ratios, peak story link rotations, and also peak floor absolute accelerations, along with the height of the buildings. The estimated EDPs are used to assess the total economic losses associated with the collapse, demolition, and repair of structural and/or non-structural components. The database includes seismic intensity measure, improved wavelet-based refined damage-sensitive feature (rDSF) assembled only by the roof absolute acceleration response, geometric information, and EDPs of the 4-, 8-, and 16-story prototype models, extracted from incremental dynamic analyses subjected to 44 far-field ground motions. The nonlinear model of the aforementioned structures was already developed by the authors to capture the response of the structures up to collapse. Symbolic and Bayesian regressions are carried out in addition to ordinary least square linear regression to develop the empirical equations. Moreover, a thorough study is performed on the optimal selection of the intensity measures proposed in the literature as the input variable of the predictive equations through reliability-based sensitivity analysis. To estimate the first mode period of the considered structures to compute the improved wavelet-based rDSF and promote a nonmodel-based approach, Auto-Regressive model with exogenous input is employed. The results show that the story-based EDPs and also the corresponding expected economic losses of EBF buildings are accurately predicted compared with those obtained from incremental dynamic analyses. Consequently, the proposed nonmodel-based approach paves the path for rapid earthquake-induced economic loss assessment of EBF buildings in emergency operations.