DYNAMIC RESPONSE OF EQUIPMENT IN STRUCTURES WITH SLIDING SUPPORT

The dynamic behaviour of a single degree-of-freedom (DOF) equipment mounted on a sliding primary structures subjected to harmonic and earthquake ground motions is studied numerically. To deal with the discontinuity nature of sliding structural systems, in this work the fictitious spring model is adopted. With the problem formulated in a state space form, an incremental numerical scheme capable of dealing with multi-DOF sliding structural systems is proposed for solving the time history responses. Numerical examples excited by harmonic and real earthquake ground motions are considered in order to study the following three effects: (1)the variation of the frictional coefficient of the sliding support, (2)subharmonic resonance and (3)effect of tuning (i.e. when the frequency of the equipment is coincident with or close to the fundamental frequency of the primary structure) on the mounted equipment. The dynamic characteristics of the mounted equipment are highlighted in the analysis of the numerical examples. © 1997 by John Wiley & Sons, Ltd.     

Experimental and analytical studies on the response of 1/4-scale models of freestanding laboratory equipment subjected to strong earthquake shaking

This paper investigates the seismic response of freestanding equipment when subjected to strong earthquake motions (2% probability of being exceeded in 50 years). A two-step approach is followed because the displacement limitations of the shake table do not permit full-scale experiments. First, shake table tests are conducted on quarter-scale wooden block models of the equipment. The results are used to validate the commercially available dynamic simulation software Working Model 2D. Working Model is then used to compute the response of the full-scale freestanding equipment when subjected to strong, 2% in 50 years hazard motions. The response is dominated by sliding, with sliding displacements reaching up to 70 cm. A physically motivated dimensionless intensity measure and the associated engineering demand parameter are identified with the help of dimensional analysis, and the results of the numerical simulations are used to obtain a relationship between the two that leads to ready-to-use fragility curves.     

考虑不同固定条件的核电设备多维地震响应振动台试验研究

在核电站中:核电设备通过不同的固定条件与结构相连,地震作用时设备与结构动力相互作用复杂,为分析核电设备多维地震响应并鉴定其抗震性能,进行了考虑不同固定条件的核电设备多维地震响应振动台试验研究。振动台试验进行了5次运行基准地震和1次安全停堆地震的动力时程激振,以及试验首末2次动力特性测试。试验结果表明:不同固定条件会影响核电设备多维地震响应的加速度峰值、反应谱特性和动力放大系数,与设备直接固定于振动台相比,将核电设备悬挂固定于剪力墙再与振动台连接的固定条件,改变了设备反应谱特性,且放大了响应的加速度峰值,具有显著的动力放大效应,使核电设备多维地震响应更为强烈。因此,对此类固定条件的核电设备,在产品设计及安装固定时要充分考虑动力放大效应,以提高设备的抗震韧性。抗震试验前后,核电设备功能运行正常,结构完整性好,抗震性能满足要求。     

Experimental and analytical studies on the response of freestanding laboratory equipment to earthquake shaking

This paper presents results of a comprehensive experimental program on the seismic response of full‐scale freestanding laboratory equipment. First, quasi‐static experiments are conducted to examine the mechanical behavior of the contact interface between the laboratory equipment and floors. Based on the experimental results, the response analysis that follows adopts two idealized contact friction models: the elastoplastic model and the classical Coulomb friction model. Subsequently, the paper presents shake table test results of full‐scale freestanding equipment subjected to ground and floor motions of hazard levels with corresponding displacements that can be accommodated by the shake table at the UC Berkeley Earthquake Engineering Research Center. For the equipment tested, although some rocking is observed, sliding is the predominant mode of response, with sliding displacements reaching up to 60 cm. Numerical simulations with the proposed models are performed. Finally, the paper identifies a physically motivated intensity measure and the associated engineering demand parameter with the help of dimensional analysis and presents ready‐to‐use fragility curves. Copyright © 2008 John Wiley & Sons, Ltd.     

Model‐based multi‐metric control of uniaxial shake tables

Shake tables provide a direct means by which to evaluate structural performance under earthquake excitation. Because the entire structure is mounted on the base plate and subjected to the ground motion in real time, dynamic effects and rate‐dependent behavior can be accurately represented. Shake table control is not straightforward as the desired signal is an acceleration record, while most actuators operate in displacement feedback for stability. At the same time, the payload is typically large relative to the capacity of the actuator, leading to pronounced control‐structure interaction. Through this interaction, the dynamics of the specimen influence the dynamics of the shake table, which can be problematic when specimens change behavior because of damage or other nonlinearities. Moreover, shake tables are themselves inherently nonlinear, making it difficult to accurately recreate a desired acceleration record over a broad range of amplitudes and frequencies. A model‐based multi‐metric shake table control strategy is proposed to improve tracking of the desired acceleration of a uniaxial shake table, remaining robust to nonlinearities including changes in specimen condition. The proposed strategy is verified for the shake table testing of both linear and nonlinear structures. Copyright © 2013 John Wiley & Sons, Ltd.     

Full‐scale shaking table test of a base‐isolated medical facility subjected to vertical motions

Base isolation is a well known technology that has been proven to reduce structural response to horizontal ground accelerations. However, vertical response still remains a topic of concern for base‐isolated buildings, perhaps more so than in fixed‐base buildings as isolation is often used when high performance is required. To investigate the effects of vertical response on building contents and nonstructural components, a series of full‐scale shaking table tests were conducted at the E‐Defense facility in Japan. A four‐story base‐isolated reinforced concrete building was outfitted as a medical facility with a wide variety of contents, and the behavior of the contents was observed. The rubber base isolation system was found to significantly amplify vertical accelerations in some cases. However, the damage caused by the vertical ground motions was not detrimental when peak vertical floor accelerations remained below 2 g with three exceptions: (1) small items placed on shelves slid or toppled; (2) objects jumped when placed on nonrigid furniture, which tended to increase the response; and (3) equipment with vertical eccentricities rocked and jumped. In these tests, all equipment and nonstructural components remained functional after shaking. Copyright © 2013 John Wiley & Sons, Ltd.     

Shake table investigation on the seismic performance of hospital equipment supported on wheels/casters

This paper presents an experimental investigation on the seismic response of medical equipment supported on wheels and/or casters. Two pieces of equipment were tested: a large ultrasound machine and a cart carrying smaller medical equipment. In the first phase, the resistance of the wheels and casters of the equipment was characterized through a controlled‐displacement procedure on the shake table. In the second phase, an extensive shake table test program was carried out to investigate the seismic response of the equipment. The input signals for the shake table tests included floor motions of a four‐story steel braced‐frame hospital designed to satisfy seismic requirements of a site in the Los Angeles area. The results of 96 shake table tests reported in this study include the seismic performance of the equipment under both unlocked and locked conditions, located on various floor levels of the building. It was observed that engaging the casters' locking mechanism does not necessarily decrease the relative displacement. The displacement response was sensitive to the excitation intensity and the orientation of the equipment with respect to the input excitation. Based on the experimental observations, appropriate structural engineering demand parameters associated with the relative displacement and relative velocity demands of the equipment are proposed and used to develop conditional probability curves. Finally, in an effort to extend the results of this experimental study to similar equipment on wheels/casters, the performance of a simple numerical model in predicting the peak seismic demands is evaluated. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal cost‐effective topology of column bearings for reducing vertical acceleration demands in multistory base‐isolated buildings

Base‐isolation is regarded as one of the most effective methods for protecting the structural and nonstructural building elements from design level horizontal earthquake ground shaking. However, base‐isolation as currently practiced does not offer unlimited protection for these buildings, especially when the ground shaking includes a strong vertical component. The vulnerability of nonstructural systems in a base‐isolated building was made evident during recent shake table testing of a full‐scale five‐story base‐isolated steel moment frame where nonstructural system damage was observed following tests including vertical excitation. Past research efforts have attempted to achieve 3D isolation of buildings and nuclear structures by concentrating both the horizontal and vertical flexibility at the base of the building that are either quite limited or not economically viable. An approach whereby the vertical flexibility is distributed up the height of the building superstructure to passively reduce vertical acceleration demands in base‐isolated buildings is presented. The vertical flexibility is achieved by placing laterally restrained elastomeric ‘column’ bearings at one or more floor levels along the height of the building. To broadly investigate the efficacy of the vertically distributed flexibility concept and the trade‐off between mitigation and cost, a multi‐objective optimization study was conducted considering 3‐story, 9‐story, and 20‐story archetype buildings that aimed to minimize the median peak vertical floor acceleration demands and to minimize the direct cost of column bearings. Based on the results of the optimization study, a practical rule for determining the number of levels and locations of column bearings is proposed and evaluated. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic characteristics and seismic behavior of prefabricated steel stairs in a full‐scale five‐story building shake table test program

This paper investigates the dynamic characteristics and seismic behavior of prefabricated steel stairs in a full‐scale five‐story building shake table test program. The test building was subjected to a suite of earthquake input motions and low‐amplitude white noise base excitations first, while the building was isolated at its base, and subsequently while it was fixed to the shake table platen. This paper presents the modal characteristics of the stairs identified using the data recorded from white noise base excitation tests as well as the physical and measured responses of the stairs from the earthquake tests. The observed damage to the stairs is categorized into three distinct damage states and is correlated with the interstory drift demands of the building. These shake table tests highlight the seismic vulnerability of modern designed stair systems and in particular identifies as a key research need the importance of improving the deformability of flight‐to‐building connections. Copyright © 2015 John Wiley & Sons, Ltd.     

Shake table testing of un‐reinforced brick masonry building test model isolated by U‐FREI

This paper presents a detailed study on feasibility of un‐bonded fiber reinforced elastomeric isolator (U‐FREI) as an alternative to steel reinforced elastomeric isolator (SREI) for seismic isolation of un‐reinforced masonry buildings. Un‐reinforced masonry buildings are inherently vulnerable under seismic excitation, and U‐FREIs are used for seismic isolation of such buildings in the present study. Shake table testing of a base isolated two storey un‐reinforced masonry building model subjected to four prescribed input excitations is carried out to ascertain its effectiveness in controlling seismic response. To compare the performance of U‐FREI, same building is placed directly on the shake table without isolator, and fixed base (FB) condition is simulated by restraining the base of the building with the shake table. Dynamic response characteristic of base isolated (BI) masonry building subjected to different intensities of input earthquakes is compared with the response of the same building without base isolation system. Acceleration response amplification and peak response values of test model with and without base isolation system are compared for different intensities of table acceleration. Distribution of shear forces and moment along the height of the structure and response time histories indicates significant reduction of dynamic responses of the structure with U‐FREI system. This study clearly demonstrates the improved seismic performance of un‐reinforced masonry building model supported on U‐FREIs under the action of considered ground motions. Copyright © 2015 John Wiley & Sons, Ltd.     

Experimental assessment of the seismic performance of hospital cabinets using shake table testing

An experimental investigation of hospital building equipment is presented. Dynamic properties and seismic performance of typical ambulatory freestanding cabinets are assessed by unidirectional and bidirectional shake table tests, also considering the presence of internal partitions and cabinet contents. Vulnerability analysis is performed according to the most recent and reliable assessment methods, evaluating the influence of different parameters of the sample cabinets. The performance criteria referred within this research are the limit states reached by the specimens (ie, rocking and overturning) and by their contents (ie, overturning and breaking). Fragility curves are evaluated for the components and the contents, considering both acceleration and velocity intensity measures, and also using dimensionless intensity measures developed in recent studies. The outcomes of the present study confirm the findings of previous laboratory tests and numerical simulations carried out by the same authors and provide a further insight for the reliable seismic performance assessment of hospital cabinets and their contents.     

Seismic response of sliding equipment and contents in base‐isolated buildings subjected to broadband ground motions

Base isolation has been established as the seismic design approach of choice when it comes to protecting nonstructural contents. However, while this protection technology has been widely shown to reduce seismic demands on attached oscillatory equipment and contents (EC), its effectiveness in controlling the response of freestanding EC that are prone to sliding has not been investigated. This study examines the seismic behavior of sliding EC inside base‐isolated buildings subjected to broadband ground motions. The effect of isolation system properties on the response of sliding EC with various friction coefficients is examined. Two widely used isolation models are considered: viscously damped linear elastic and bilinear. The study finds isolation to be generally effective in reducing seismic demands on sliding EC, but it also exposes certain situations where isolation in fact increases demands on EC, most notably for low friction coefficients and high earthquake intensities. Damping at the isolation level is effective in controlling the EC sliding displacements, although damping over about 20% is found to be superfluous. The study identifies a physically motivated dimensionless intensity measure and engineering demand parameter for sliding equipment in base‐isolated buildings subjected to broadband ground motions. Finally, the paper presents easy‐to‐use design fragility curves and an example that illustrates how to use them. Copyright © 2014 John Wiley & Sons, Ltd.     

Influence of the construction process and nonstructural components on the modal properties of a five‐story building

A full‐scale five‐story reinforced concrete building was built and tested on the NEES‐UCSD shake table during the period from May 2011 to May 2012. The purpose of this test program was to study the response of the structure and nonstructural components and systems (NCSs) and their dynamic interaction during seismic base excitation of different intensities. The building specimen was tested first under a base‐isolated condition and then under a fixed‐based condition. As the building was being erected, an accelerometer array was deployed on the specimen to study the evolution of its modal parameters during the construction process and placement of major NCSs. A sequence of dynamic tests, including daily ambient vibration, shock (free vibration) and forced vibration tests (low‐amplitude white noise and seismic base excitations), were performed on the building at different stages of construction. Different state‐of‐the‐art system identification methods, including three output‐only and two input‐output methods, were used to estimate the modal properties of the building. The obtained results allow to investigate in detail the effects of the construction process and NCSs on the dynamic parameters of this building system and to compare the modal properties obtained from different methods, as well as the performance of these methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparison between real‐time dynamic substructuring and shake table testing techniques for nonlinear seismic applications

Results from real‐time dynamic substructuring (RTDS) tests are compared with results from shake table tests performed on a two‐storey steel building structure model. At each storey, the structural system consists of a cantilevered steel column resisting lateral loads in bending. In two tests, a slender diagonal tension‐only steel bracing member was added at the first floor to obtain an unsymmetrical system with highly variable stiffness. Only the first‐storey structural components were included in the RTDS test program and a Rosenbrock‐W linearly implicit integration scheme was adopted for the numerical solution. The tests were performed under seismic ground motions exhibiting various amplitude levels and frequency contents to develop first and second mode‐dominated responses as well as elastic and inelastic responses. A chirp signal was also used. Coherent results were obtained between the shake table and the RTDS testing techniques, indicating that RTDS testing methods can be used to successfully reproduce both the linear and nonlinear seismic responses of ductile structural steel seismic force resisting systems. The time delay introduced by actuator‐control systems was also studied and a novel adaptive compensation scheme is proposed. Copyright © 2010 John Wiley & Sons, Ltd.     

土石坝振动台模型试验颗粒流数值模拟分析

目前一般采用振动台试验、离心振动台试验和有限元动力分析来获得土石坝在设计地震荷载作用下的形态和抗震性能。本文结合孔宪京等的土石坝振动台试验结果开展了颗粒流细观数值模拟研究,克服了传统连续介质力学的宏观连续性假设,形象而直观地表现出坝体在动力荷载作用下的破坏特征。数值模拟规律与振动台试验规律基本一致。同时还分析了坝体颗粒粘结强度和地震峰值加速度变化对坝体破坏特征的影响。数值结果表明,当颗粒间粘结强度较低时,表现为坝体表面颗粒的滑动破坏,粘结强度稍大时,会出现局部的小块颗粒团整体滑动破坏;随着峰值加速度的增大,坝顶沉降量在增大,坝体破坏特征不变。     

Shake‐table tests of a three‐story reinforced concrete frame with masonry infill walls

This paper presents the shake‐table tests of a 2/3‐scale, three‐story, two‐bay, reinforced concrete frame infilled with unreinforced masonry walls. The specimen is representative of the construction practice in California in the 1920s. The reinforced concrete frame had nonductile reinforcement details and it was infilled with solid masonry walls in one bay and infill walls with window openings in the other bay. The structure was subjected to a sequence of dynamic tests including white‐noise base excitations and 14 scaled historical earthquake ground motion records of increasing intensity. The performance of the structure was satisfactory considering the seismic loads it was subjected to. The paper summarizes the design of the specimen and the major findings from the shake‐table tests, including the dynamic response, the load resistance, the evolution of damage, and the final failure mechanism. Copyright © 2011 John Wiley & Sons, Ltd.     

Ground motion scaling methods for linear‐elastic structures: an integrated experimental and analytical investigation

The task of selecting and scaling an appropriate set of ground motion records is one of the most important challenges facing practitioners in conducting dynamic response history analyses for seismic design and risk assessment. This paper describes an integrated experimental and analytical evaluation of selected ground motion scaling methods for linear‐elastic building frame structures. The experimental study is based on the shake table testing of small‐scale frame models with four different fundamental periods under ground motion sets that have been scaled using different methods. The test results are then analytically extended to a wider range of structural properties to assess the effectiveness of the scaling methods in reducing the dispersion and increasing the accuracy in the seismic displacement demands of linear‐elastic structures, also considering biased selection of ground motion subsets. For scaling methods that are based on a design estimate of the fundamental period of the structure, effects of possible errors in the estimated period are investigated. The results show that a significant reduction in the effectiveness of these scaling methods can occur if the fundamental period is not estimated with reasonable certainty. Copyright © 2012 John Wiley & Sons, Ltd.     

Coupled shear‐bending formulation for seismic analysis of stacked wood shear wall systems

A summary of the development of a new coupled shear‐bending model for analysis of stacked wood shear walls and multi‐story wood‐frame buildings is presented in this paper. The model focuses on dynamic response of light‐frame wood structures under seismic excitation. The formulation is intended to provide a more versatile option than present pure shear models in that the new model is capable of accurately capturing the overall lateral response of each story diaphragm and separates the inter‐story shear deformation and the deformation associated with rotation of the diaphragm due to rod elongation, which is an analogue to the bending deformation in an Euler–Bernoulli beam model. Modeling the coupling of bending and shear deformation is shown to provide more accurate representation of stacked shear wall system behavior than a pure shear model, particularly for the upper stories in the assembly. The formulation is coupled with the newly developed evolutionary parameter hysteretic model for wood shear walls. Existing data from a shake table test of an isolated three‐story wood shear wall were used to verify the accuracy of the model prediction. The numerical results agreed very well with shake table test measurements. The influence of a continuous rod hold‐down system on the dynamic behavior of the three‐story stacked wood shear wall was also successfully simulated. Copyright © 2009 John Wiley & Sons, Ltd.     

Real-time dynamic hybrid testing for soil–structure interaction analysis

Simulating dynamic soil–structure interaction (SSI) problems is a challenge when using a shaking table because of the semi-infinity of soil foundations. This paper develops real-time dynamic hybrid testing (RTDHT) for SSI problems in order to consider the radiation damping effect of the semi-infinite soil foundation using a shaking table. Based on the substructure concept, the superstructure is physically tested and the semi-infinite foundation is numerically simulated. Thus, the response of the entire system considering the dynamic SSI is obtained by coupling the numerical calculation of the soil and the physical test of the superstructure. A two-story shear frame on a rigid foundation was first tested to verify the developed RTDHT system, in which the top story was modeled as the physical substructure and the bottom story was the numerical substructure. The RTDHT for a two-story structure mounted on soil foundation was then carried out on a shaking table while the foundation was numerically simulated using a lumped parameter model. The dynamic responses, including acceleration and shear force, were obtained under soft and hard soil conditions. The results show that the soil–structure interaction should be reasonably taken into account in the shaking table testing for structures.     

Development of high‐performance shake tables using the hierarchical control strategy and nonlinear control techniques

Conventional shake tables employ linear controllers such as proportional‐integral‐derivative or loop shaping to regulate the movement. However, it is difficult to tune a linear controller to achieve accurate and robust tracking of different reference signals under payloads. The challenges are mainly due to the nonlinearity in hydraulic actuator dynamics and specimen behavior. Moreover, tracking a high‐frequency reference signal using a linear controller tends to cause actuator saturation and instability. In this paper, a hierarchical control strategy is proposed to develop a high‐performance shake table. A unidirectional shake table is constructed at the University of British Columbia to implement and evaluate the proposed control framework, which consists of a high‐level controller and one or multiple low‐level controller(s). The high‐level controller utilizes the sliding mode control (SMC) technique to provide robustness to compensate for model nonlinearity and uncertainties experienced in experimental tests. The performance of the proposed controller is compared with a state‐of‐the‐art loop‐shaping displacement‐based controller. The experimental results show that the proposed hierarchical shake table control system with SMC can provide superior displacement, velocity and acceleration tracking performance and improved robustness against modeling uncertainty and nonlinearities. Copyright © 2015 John Wiley & Sons, Ltd.