Seismic response analysis of bridges isolated with friction pendulum bearings

A systematic method is developed for the dynamic analysis of the structures with sliding isolation which is a highly non-linear dynamic problem. According to the proposed method, a unified motion equation can be adapted for both stick and slip modes of the system. Unlike the traditional methods by which the integration interval has to be chopped into infinitesimal pieces during the transition of sliding and non-sliding modes, the integration interval remains constant throughout the whole process of the dynamic analysis by the proposed method so that accuracy and efficiency in the analysis of the non-linear system can be enhanced to a large extent. Moreover, the proposed method is general enough to be adapted for the analysis of the structures with multiple sliding isolators undergoing independent motion conditions simultaneously. The superiority of the proposed method for the analysis of sliding supported structures is verified by a three-span continuous bridge subjected to harmonic motions and real earthquakes. In addition, the side effect of excessive displacement of the superstructure induced by the sliding isolation is eliminated by replacing one of the roller supports on the abutments with hinge support. Therefore, both reductions in the forces of the substructure and the displacements of the superstructure can be achieved simultaneously. © 1998 John Wiley & Sons, Ltd.     

Evaluation of simplified methods of analysis for structures with triple friction pendulum isolators

Triple friction pendulum isolators, that exhibit behavior with amplitude‐dependent strength and instantaneous stiffness, represent a new development in seismic isolation. The application of simplified methods of analysis for this type of seismically isolated structures requires development of tools of simplified analysis and demonstration of their accuracy. This paper describes these tools and presents validation studies based on a large number of nonlinear response history analysis results. It is shown that simplified methods of analysis systematically provide good and often conservative estimates of isolator displacement demands and good estimates of isolator peak velocities. Copyright © 2009 John Wiley & Sons, Ltd.     

A model of triple friction pendulum bearing for general geometric and frictional parameters

Current models describing the behavior for the triple friction pendulum (TFP) bearing are based on the assumption that the resultant force of the contact pressure acts at the center of each sliding surface. Accordingly, these models only rely on equilibrium in the horizontal direction to arrive at the equations describing its behavior. This is sufficient for most practical applications where certain constraints on the friction coefficient values apply as a direct consequence of equilibrium. This paper presents a revised model of behavior of the TFP bearing in which no assumptions are made on the location of the resultant forces at each sliding surface and no constraints on the values of the coefficient of friction are required, provided that all sliding surfaces are in full contact. To accomplish this, the number of degrees of freedom describing the behavior of the bearing is increased to include the location of the resultant force at each sliding surface and equations of moment equilibrium are introduced to relate these degrees of freedom to forces. Moreover, the inertia effects of each of the moving parts of the bearing are accounted for in the derivation of the equations describing its behavior. The model explicitly calculates the motion of each of the components of friction pendulum bearings so that any dependence of the coefficient of friction on the sliding velocity and temperature can be explicitly accounted for and calculations of heat flux and temperature increase at each sliding surface can be made. This paper presents (a) the development of the revised TFP bearing model, (b) the analytic solution for the force–displacement relations of two configurations of the TFP bearing, (c) a model that incorporates inertia effects of the TFP bearing components and other effects that are useful in advanced response history analysis, and (d) examples of implementation of the features of the presented model. Copyright © 2016 John Wiley & Sons, Ltd.     

摩擦摆基础隔震结构双向地震反应分析

采用双向耦合力学模型模拟摩擦摆支座的双向耦合效应,对摩擦摆基础隔震结构进行了单向和双向地震反应对比分忻,分析表明在双向地震作用下结构各层的加速度反应较小,隔震层的层间位移较大,而上部结构的层间位移较小,并且在双向地震作用下,支座的最大位移明显大于单向地震作用时的支座最大位移,因而应考虑双向地震作用对摩擦摆基础隔震结构地震反应和隔震支座性能的影响。     

Extreme behavior in a triple friction pendulum isolated frame

While isolation can provide significantly enhanced performance compared to fixed‐base counter parts in design level or even maximum considered level earthquakes, there is still uncertainty over the performance of isolation systems in extreme events. Researchers have looked at component level stability of rubber bearings and on the effect of moat impact on behavior of structures isolated on general bilinear isolators. However, testing of triple friction pendulum (TFP) sliding bearings has not been done dynamically or incorporated into a building system. Here, one‐third scale laboratory tests were conducted to on a 2‐story 2‐bay TFP‐isolated structure. Input motions were increasingly scaled until failure occurred at the isolation level. As the superstructure was designed with a yield force equivalent to the force of the bearing just at their ultimate displacement capacity, there was minimal yielding. A numerical model is presented to simulate the isolated building up to and including bearing failure. Forces transferred to the superstructure in extreme motions are examined using both experimental and numerical data. Additionally, the effect of the hardening stage of the TFP bearing is evaluated using the numerical model, finding slight benefits.     

Shake table testing on restoring capability of double concave friction pendulum seismic isolation systems

After an earthquake, non‐negligible residual displacements may affect the serviceability of a base isolated structure, if the isolation system does not possess a good restoring capability. The permanent offset does not affect the performance unless the design is problematic for utilities, also considering possible concerns related to the maintenance of the devices. Starting from experimental and analytical results of previous studies, the restoring capability of Double Concave Friction Pendulum bearings is investigated in this paper. A simplified design suggestion for the estimation of maximum expected residual displacements for currently used friction pendulum systems is then validated. The study is based on controlled‐displacement and seismic input experiments, both performed under unidirectional motion. Several shaking table tests have been carried out on a three‐dimensional isolated specimen structure. The same sequence of seismic inputs was applied considering three different conditions of sliding surfaces corresponding to low, medium and high friction. The accumulation of residual displacements is also investigated by means of nonlinear dynamic analysis. Copyright © 2017 John Wiley & Sons, Ltd.     

Experimental and analytical study of the bi‐directional behavior of the triple friction pendulum isolator

This paper presents a non‐linear, kinematic model for triple friction pendulum isolation bearings. The model, which incorporates coupled plasticity and circular restraining surfaces for all sliding surfaces, is capable of capturing bi‐directional behavior and is able to explicitly track the movement of each internal component. The model is general so that no conditions regarding bearing properties, which effect the sequence of sliding stages, are required for the validity of the model. Controlled‐displacement and seismic‐input experiments were conducted using the shake table at the University of California, Berkeley to assess the fidelity of the proposed model under bi‐directional motion. Comparison of the experimental data with the corresponding results of the kinematic model shows good agreement. Additionally, experiments showed that the performance of TFP bearings is reliable over many motions, and the behavior is repeatable even when initial slider offsets are present. Copyright © 2011 John Wiley & Sons, Ltd.     

摩擦摆基础隔震结构多维地震反应分析

对摩擦摆基础隔震结构进行了单向、双向和三向地震反应对比分析,表明考虑双向水平地震动时摩擦摆基础隔震结构的支座位移增大,而结构的加速度和楼层剪力减小,其中对支座位移和结构加速度影响较大;考虑竖向地震动时摩擦摆基础隔震结构的支座位移略有减小,而结构的加速度和楼层剪力增大,其中对结构加速度影响较大.因而,在进行摩擦摆基础隔震结构地震反应分析时,应考虑多维地震动的影响.     

Experimental study of the effect of restraining rim design on the extreme behavior of pendulum sliding bearings

While the performance of sliding isolators has been extensively validated under typical levels of ground motion, there have been very few experimental studies on the extreme behavior of sliding isolation bearings when the displacement limit is reached. However, to appropriately design isolated systems, from selecting the displacement capacity of the bearing to sizing the superstructure members, the behavior of the bearing as it reaches, and in some cases exceeds, the displacement limit should be well understood. A series of shake table tests to investigate the extreme behavior of double pendulum sliding bearings under strong ground motions were conducted at McMaster University. One major difference in sliding bearings around the world is how the motion of the bearing is restrained at the bearing's displacement capacity. Scaled bearings with four different types of restraining rim designs were included, representing typical sliding restraining rims found in Europe, Japan, and the United States. Experimental observation shows that the restraining rim has a significant influence on the extreme behavior of sliding isolation bearing. Key response parameters such as impact force and uplift are evaluated and compared between the different sliding bearing designs. While the bearing with no rim bearing imparts the lowest forces to the superstructure, it loses its functionality at a lower amplitude input than all the other rim types. For the other rim designs, the impact forces are significantly higher but they remained operational although damaged.     

Development of a tunable friction pendulum system for semi‐active control of building structures under earthquake ground motions

The Friction Pendulum System (FPS) isolator is commonly used as a base isolation system in buildings. In this paper, a new tunable FPS (TFPS) isolator is proposed and developed to act as a semi‐active control system by combining the traditional FPS and semi‐active control concept. Theoretical analysis and physical tests were carried out to investigate the behavior of the proposed TFPS isolator. The experimental and theoretical results were in good agreement, both suggesting that the friction force of the TFPS isolator can be tuned to achieve seismic isolation of the structure. A series of numerical simulations of a base‐isolated structure equipped with the proposed TFPS isolator and subjected to earthquake ground motions were also conducted. In the analyses, the linear quadratic regulator (LQR) method was adopted to control the friction force of the proposed TFPS, and the applicability and effectiveness of the TFPS in controlling the structure's seismic responses were investigated. The simulation results showed that the TFPS can reduce the displacement of the isolation layer without significantly increasing the floor acceleration and inter‐story displacement of the superstructure, confirming that the TFPS can effectively control a base‐isolated structure under earthquake ground motions.     

Dynamic analysis of sliding structures with unsynchronized support motions

The dynamic analysis of sliding structures is complicated due to the presence of friction. Synchronization of the kinematics of all the isolation bearings is often granted to simplify the task. This, however, may lead to inaccurate prediction of the structural responses under certain circumstances. Stepped structures or continuous bridges with seismic isolation are notable examples where unsynchronized bearing motions are expected. In this paper, a logically simple and numerically efficient procedure is proposed to solve the dynamic problem of sliding systems with unsynchronized support motions. The motion equations for the sliding and non‐sliding modes of the isolated structure are unified into a single equation that is represented as a difference equation in a discrete‐time state‐space form and the base shear forces between the sliding interfaces can be determined through simple matrix algebraic analysis. The responses of the sliding structure can be obtained recursively from the discrete‐time version of the motion equation with constant integration time step even during the transitions between the non‐sliding and sliding phases. Therefore, both accuracy and efficiency in the dynamic analysis of the highly non‐linear system can be enhanced to a large extent. Rigorous assessment of seismic structures with unsynchronized support motions has been carried out for both a stepped structure and a continuous bridge. Effectiveness of friction pendulum bearings for earthquake protection of such structures has been verified. Moreover, evident unsynchronized sliding motions of the friction bearings have been observed, confirming the necessity to deal with each of the bearings independently in the analytical model. Copyright © 2000 John Wiley & Sons, Ltd.     

超弹性-复摩擦摆隔震支座的性能试验与数值模拟

利用复摩擦支座（Double friction pendulum bearing,DFPB）和形状记忆合金（Shape Memory alloy,SMA）拉索,提出了一种超弹性-复摩擦支座（Superelastic-double friction pendulum bearing,SDFPB）。该新型滑动隔震支座在水平方向可适应多水准地震激励,且在竖向拥有抵抗拉拔的功能。阐述了SDFPB的构造特点和工作原理。通过性能试验考察了这一隔震装置的力学特性。建立了SDFPB的恢复力模型,利用其模拟了试验条件下的滞回响应。研究结果表明:SDFPB的耗能能力优良,且具有较好的多级抗震自适应能力;模拟值与试验值吻合较好,验证了上述力学模型的正确性。     

摩擦摆隔震双层球面网壳结构的多维地震响应

将摩擦摆(FPS)引入到网壳结构的隔震控制中。文中首先阐明了FPS的工作机理和本构关系,建立了FPS隔震网壳结构的振动方程。通过双层球面网壳结构的数值算例考察了隔震和无控结构在单向和三向地震作用下的振动响应以及FPS的控制效果。研究结果表明,FPS具有良好的隔震和耗能效果,可有效地应用于球面网壳结构的振动控制。     

Seismic isolation of rigid cylindrical tanks using friction pendulum bearings

Storage tanks are vulnerable to earthquakes, as numerous major earthquakes have demonstrated. The trend of recent revisions to make seismic design criteria for large‐scale industrial storage tanks increasingly stringent has made development of cost‐effective earthquake‐resistant design and retrofit techniques for industrial tanks imperative. This study assesses the feasibility of seismic base isolation for making liquid‐filled storage tanks earthquake resistant. The sliding‐type friction pendulum seismic (FPS) bearings are considered rather than the elastomeric bearings because the dynamic characteristics of an FPS‐isolated tank remain unchanged regardless of the storage level. This work has devised a hybrid structural‐hydrodynamic model and solution algorithm, which would permit simple, accurate and efficient assessment of the seismic response of rigid cylindrical storage tanks in the context of seismic isolation. Extensive numerical simulations confirm the effectiveness of seismic base isolation of rigid cylindrical tanks using FPS bearings. Copyright © 2001 John Wiley & Sons, Ltd.     

Experimental and analytical studies of structures seismically isolated with an uplift‐restraining friction pendulum system

This paper presents findings from a comprehensive analytical and experimental study on the uplift‐restraining XY‐FP sliding isolation system. To investigate the effectiveness of the XY‐FP isolator and provide a rational basis for evaluating the efficacy of the developed mathematical model, an extensive experimental program was conducted on the earthquake simulator at the University at Buffalo. The experimental program involved a slender, five‐storey, scale‐model frame seismically isolated with four XY‐FP isolators subjected to simulations of historical horizontal and vertical ground motions. The experimental response demonstrates the validity of the concept and provides evidence for the effectiveness of the XY‐FP isolator in preventing uplift. A comprehensive analytical model capable of emulating the mechanical behaviour of the XY‐FP isolator is developed and implemented in program 3D‐BASIS‐ME. The newly enhanced program is used to predict the dynamic response of the seismically‐isolated model structure. Comparison of analytical predictions with experimental results attests to the efficacy of the analytical model for simulating the response of the XY‐FP isolator. With its appealing conceptual simplicity and its proven effectiveness, the new uplift‐restraining isolator has the potential to facilitate the application of seismic isolation even under the most extreme of conditions, including but not limited to near‐fault strong ground motions and uplift‐prone structural systems. Copyright © 2005 John Wiley & Sons, Ltd.     

Component and shaking table tests for full‐scale multiple friction pendulum system

The use of base isolation in developed countries including the U.S. and Japan has already been recognized as a very effective method for upgrading the seismic resistance of structures. In this study, an advanced base‐isolation system called the multiple friction pendulum system (MFPS) is investigated to understand its performance on seismic mitigation through full‐scale component and shaking table tests. The component tests of the advanced Teflon composite coated on the sliding surface show that the friction coefficient of the lubricant material is a function of the sliding velocity in the range of 0.03–0.12. The experimental results also indicate that there were no signs of degradation of the sliding interface observed after 2000 cycles of sliding displacements. A full‐scale MFPS isolator under a vertically compressive load of 8830 KN (900 tf) and horizontally cyclic displacements was tested in order to assess the feasibility of the MFPS isolator for its practical use. After 248 cycles of horizontal displacement reversals, the behaviour of the base isolator was almost identical to its behaviour during the first few cycles. The experimental results of the shaking table tests of a full‐scale steel structure isolated with MFPS isolators show that the MFPS device can isolate seismic transmitted energy effectively under soft‐soil‐deposit site earthquakes with long predominant periods as well as strong ground motions with short predominant periods. These test results demonstrate that the MFPS isolator possesses excellent durability and outstanding earthquake‐proof capability. Furthermore, the numerical results show that the mathematical model proposed in this study can well predict the seismic responses of a structure isolated with MFPS isolators. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of support rotation on triple friction pendulum bearing behavior

This paper presents numerical modeling techniques to capture the behavior of the triple friction pendulum (TFP) isolation bearing when rotation is permitted about the horizontal axes of the top and bottom components. This paper builds on a previous model for the TFP bearing presented by the authors that is based on the kinematic and constitutive relationships of the individual components of the TFP bearing. The effect of rotation on cyclic bearing behavior and seismic system behavior are investigated numerically for two cases: constant support rotation and variable support rotation. It is found that constant support rotations should be limited in amplitude to ensure standard TFP bearing behavior. Results suggest that flexible supports may not have a large effect on global structure performance as long as typical deformation limits for the supporting members are met. In cases of both constant support rotations and flexible supports, the hardening stages of TFP bearing behavior are diminished. Copyright © 2013 John Wiley & Sons, Ltd.     

支座摩擦系数对摩擦摆基础隔震结构地震反应的影响

对不同地震烈度作用下的摩擦摆基础隔震结构进行了地震反应分析,分析了支座摩擦系数对支座位移、楼层加速度和楼层剪力的影响。结果表明随着摩擦摆支座摩擦系数的增大,支座位移逐渐减小,而结构的加速度和楼层剪力逐渐增大;随着地震作用强度的提高,摩擦系数对支座位移的影响逐渐增大,而摩擦系数对结构加速度和楼层剪力的影响逐渐减小。     

Correct treatment of rotation of sliding surfaces in a kinematic model of the triple friction pendulum bearing

This paper addresses the treatment of the rotation of the internal components of the triple friction pendulum (TFP) isolation bearing in a numerical model previously presented by the authors. The numerical model is based on the kinematic behavior of the individual sliding surfaces and the constitutive relationships between them. The modification suggested in this paper improves the performance of the model so that the results exactly match that of the one‐dimensional piecewise linear behavior previously derived for the TFP bearing for restricted properties. The improved numerical model simulates bidirectional shear response and places no a priori restrictions on the bearing properties. The modification is put in the form of a technical communication so that the notation used and the basis of the correction could be presented with adequate clarity and so that an example of the benefit of the correction could be presented. Copyright © 2012 John Wiley & Sons, Ltd.