Spherical sliding isolation bearings with adaptive behavior: Experimental verification

This paper describes an experimental program to examine the force–displacement behavior of a class of multi‐spherical sliding bearings. The primary goal of the experiments is to test the validity of the theory developed in a companion paper that describes the behavior of these devices. Experimental work consisted of testing the three primary variations of these bearings in several configurations of different friction and displacement capacities. Most tests were carried out at slow speeds; however, some testing was also conducted at high speed (up to approximately 400 mm/s) to examine the behavior under dynamic conditions. The results of experimental testing were generally found to be in very good agreement with the analytical results. It is shown that the forces and displacements at which transitions in stiffness occur are predictable and therefore controllable in design. Furthermore, the underlying principles of operation were confirmed by the fact that starting and stopping of sliding on the different surfaces occurred as expected from theory. Copyright © 2007 John Wiley & Sons, Ltd.     

Improved numerical analysis for ultimate behavior of elastomeric seismic isolation bearings

Elastomeric isolation bearings consist of multiple rubber layers with their top and bottom surfaces bonded to steel plates to restrict compressive deformation. Deformation constraints result in a variation of elastic modulus over the cross section of the rubber layers. In this paper, we describe a normalized compression modulus distribution on a circular rubber pad. The compressive and bending moduli of the rubber pad can be reproduced by applying the distribution to a series of axial springs. We also present a mechanical model for predicting the behavior of elastomeric seismic isolation bearings subject to large shear deformation and high compressive load. The mechanical model consists of a series of multiple shear springs at midheight and a series of axial springs at the top and bottom interfaces of the bearing. Simulation analyses of bearing tests were conducted to validate the proposed model. The analyses demonstrated that a model for circular lead-rubber bearings can successfully capture the influence of the axial load magnitude on the bearing shear behavior. The new model can simulate much more realistic behavior than prior models based on a uniform modulus assumption.     

Behaviour of the double concave Friction Pendulum bearing

The double concave Friction Pendulum (DCFP) bearing is an adaptation of the well‐known single concave Friction Pendulum bearing. The principal benefit of the DCFP bearing is its capacity to accommodate substantially larger displacements compared to a traditional FP bearing of identical plan dimensions. Moreover, there is the capability to use sliding surfaces with varying radii of curvature and coefficients of friction, offering the designer greater flexibility to optimize performance. This paper describes the principles of operation of the bearing and presents the development of the force–displacement relationship based on considerations of equilibrium. The theoretical force–displacement relationship is then verified through characterization testing of bearings with sliding surfaces having the same and then different radii of curvature and coefficients of friction. Lastly, some practical considerations for analysis and design of DCFP bearings are presented. Copyright © 2006 John Wiley & Sons, Ltd.     

摩擦摆支座在单层球面网壳结构中的隔震分析

将摩擦摆支座（FPS）应用于单层球面网壳结构的隔震，给出了隔震网壳结构的运动方程。通过对比分析不同强度地震动输入条件下的结构动力响应特征，考察了FPS支座应用于网壳结构隔震的有效性和适用性。研究结果表明，在不同强度的地震动作用下，隔震结构的节点加速度峰值和杆件轴力峰值都得到了有效控制，且地震动强度越大，控制效果越好。     

Characterizing friction in sliding isolation bearings

The force–displacement behavior of the Friction Pendulum? (FP) bearing is a function of the coefficient of sliding friction, axial load on the bearing and effective radius of the sliding surface. The coefficient of friction varies during the course of an earthquake with sliding velocity, axial pressure and temperature at the sliding surface. The velocity and axial pressure on the bearing depend on the response of the superstructure to the earthquake shaking. The temperature at an instant in time during earthquake shaking is a function of the histories of the coefficient of friction, sliding velocity and axial pressure, and the travel path of the slider on the sliding surface. A unified framework accommodating the complex interdependence of the coefficient of friction, sliding velocity, axial pressure and temperature is presented for implementation in nonlinear response‐history analysis. Expressions to define the relationship between the coefficient of friction and sliding velocity, axial pressure, and temperature are proposed, based on available experimental data. Response‐history analyses are performed on FP bearings with a range of geometrical and liner mechanical properties and static axial pressure. Friction is described using five different models that consider the dependence of the coefficient of friction on axial pressure, sliding velocity and temperature. Frictional heating is the most important factor that influences the maximum displacement of the isolation system and floor spectral demands if the static axial pressure is high. Isolation system displacements are not significantly affected by considerations of the influence of axial pressure and velocity on the coefficient of friction. Copyright © 2014 John Wiley & Sons, Ltd.     

Hysteretic models for sliding bearings with varying frictional force

The friction pendulum system is a sliding seismic isolator with self‐centering capabilities. Under severe earthquakes, the movement may be excessive enough to cause the pendulum to hit the side rim of the isolator, which is provided to restrain the sliding. The biaxial behavior of a single friction pendulum, in which the slider contacts the restrainer, is developed using a smooth hysteretic model with nonlinear kinematic hardening. This model is extended to simulate the biaxial response of double and triple friction pendulums with multiple sliding surfaces. The model of a triple friction pendulum is based on the interaction between four sliding interfaces, which in turn is dependent upon the force and displacement conditions prevailing at these interfaces. Each of these surfaces are modeled as nonlinear biaxial springs suitable for a single friction pendulum, using the yield surface, based on the principles of the classical theory of plasticity, and amended for varying frictional yield force, due to variation in vertical load and/or velocity‐dependent friction coefficient. The participation of the nonlinear springs is governed by stick‐slip conditions, dictated by equilibrium and kinematics. The model can simulate the overall force‐deformation behavior, track the displacements in individual sliding surfaces, and account for the ultimate condition when the sliders are in contact with their restrainers. The results of this model are verified by comparison to theoretical calculations and to experiments. The model has been implemented in programs IDARC2D and 3D‐BASIS, and the analytical results are compared with shake table experimental results. Copyright © 2013 John Wiley & Sons, Ltd.     

A mathematical hysteretic model for elastomeric isolation bearings

An analytical model for high damping elastomeric isolation bearings is presented in this paper. The model is used to describe mathematically the damping force and restoring force of the rubber material and bearing. Ten parameters to be identified from cyclic loading tests are included in the model. The sensitivity of the ten parameters in affecting the model is examined. These ten parameters are functions of a number of influence factors on the elastomer such as the rubber compound, Mullins effect, scragging effect, frequency, temperature and axial load. In this study, however, only the Mullins effect, scragging effect, frequency and temperature are investigated. Both material tests and shaking table tests were performed to validate the proposed model. Based on the comparison between the experimental and the analytical results, it is found that the proposed analytical model is capable of predicting the shear force–displacement hysteresis very accurately for both rubber material and bearing under cyclic loading reversals. The seismic response time histories of the bearing can also be captured, using the proposed analytical model, with a practically acceptable precision. Copyright © 2002 John Wiley & Sons, Ltd.     

Coupling behavior of shear deformation and end rotation of elastomeric seismic isolation bearings

This paper presents a mechanical model for predicting the behavior of elastomeric seismic isolation bearings subject to combined end rotations and shear deformation. The mechanical model consists of a series of axial springs at the top, mid‐height and bottom of the bearing to vertically reproduce asymmetric bending moment distribution in the bearings. The model can take into account end rotations of the bearing, and the overall rotational stiffness includes the effect of the variation of vertical load on the bearing and the imposed shear deformation. Static bending tests under various combinations of vertical load and shear deformation were performed to identify the mechanical characteristics of bearings. The test results indicate that bearing rotational stiffness increases with increasing vertical load but decreases with increasing shear deformation. Simulation analyses were conducted to validate the new mechanical model. The results of analyses using the new model show very good agreement with experimental observations. A series of seismic response analyses were performed to demonstrate the dynamic behavior of top‐of‐column isolated structures, a configuration where the end rotations of isolation bearings are typically expected to be larger. The results suggest that the end rotations of elastomeric bearings used in practical top‐of‐column isolated structures do not reduce the stability limit of isolation system. Copyright © 2016 John Wiley & Sons, Ltd.     

Uplift‐restraining Friction Pendulum seismic isolation system

This paper extends the scope of seismic isolation by introducing an innovative uplift‐restraining Friction Pendulum system. Termed the XY‐FP isolator, the new isolation device consists of two orthogonal opposing concave beams interconnected through a sliding mechanism that permits tension to develop in the bearing, thereby preventing uplift. Owing to its distinct configuration, the XY‐FP isolator possesses unique properties for a seismic isolator, including uplift restraint, decoupling of the bi‐directional motion along two orthogonal directions, and capability of providing independent stiffness and energy dissipation along the principal horizontal directions of the bearing. The study concentrates on introducing the concept and establishing the underlying principles of operation of the new XY‐FP isolator, formulating the mathematical model for the XY‐FP isolator, and presenting its mechanical behaviour through a displacement‐control testing program on a single XY‐FP isolator. Copyright © 2005 John Wiley & Sons, Ltd.     

A parametric study of seismic behavior of roller seismic isolation bearings for highway bridges

A roller seismic isolation bearing is proposed for use in highway bridges. The bearing utilizes a rolling mechanism to achieve seismic isolation and has a zero post‐elastic stiffness under horizontal ground motions, a self‐centering capability, and unique friction devices for supplemental energy dissipation. The objectives of this research are to investigate the seismic behavior of the proposed bearing using parametric studies (1) with nonlinear response history analysis and (2) with equivalent linear analysis according to the AASHTO guide specifications, and by comparing the results from both analysis methods (3) to evaluate the accuracy of the AASHTO equivalent linear method for predicting the peak displacement of the proposed bearing during an earthquake. Twenty‐eight ground motions are used in the studies. The parameters examined are the sloping angle of the intermediate plate of the bearing, the amount of friction force for supplemental energy dissipation, and the peak ground acceleration levels of the ground motions. The peak displacement and base shear of the bearing are calculated. Results of the studies show that a larger sloping angle does not reduce the peak displacement for most of the parametric combinations without friction devices. However, for parametric combinations with friction devices, it allows for the use of a higher friction force, which effectively reduces the peak displacement, while keeping a self‐centering capability. The AASHTO equivalent linear method may underestimate the peak displacement by as much as 40%. Vertical ground motions have little effect on the peak displacement, but significantly increase the peak base shear. Copyright © 2009 John Wiley & Sons, Ltd.     

Study of the seismic performance of expansion double spherical seismic isolation bearings for continuous girder bridges

The development of an expansion double spherical seismic isolation (DSSI) bearing by modifying the fixed DSSI bearing is described in this paper.The expansion DSSI bearing is characterized by its good ...     

A mechanical model for elastomeric seismic isolation bearings including the influence of axial load

For the purpose of predicting the large‐displacement response of seismically isolated buildings, an analytical model for elastomeric isolation bearings is proposed. The model comprises shear and axial springs and a series of axial springs at the top and bottom boundaries. The properties of elastomeric bearings vary with the imposed vertical load. At large shear deformations, elastomeric bearings exhibit stiffening behavior under low axial stress and buckling under high axial stress. These properties depend on the interaction between the shear and axial forces. The proposed model includes interaction between shear and axial forces, nonlinear hysteresis, and dependence on axial stress. To confirm the validity of the model, analyses are performed for actual static loading tests of lead–rubber isolation bearings. The results of analyses using the new model show very good agreement with the experimental results. Seismic response analyses with the new model are also conducted to demonstrate the behavior of isolated buildings under severe earthquake excitations. The results obtained from the analyses with the new model differ in some cases from those given by existing models. Copyright © 2008 John Wiley & Sons, Ltd.     

隔震与非隔震支座对混凝土箱梁桥地震易损性的影响

为评估隔震和非隔震支座对桥梁地震易损性的影响,以一座3跨连续混凝土箱梁桥为分析对象,首先建立采用铅芯橡胶隔震支座与非隔震型盆式橡胶支座下桥梁的数值模型,求得不同程度地震作用下墩顶与支座的最大位移响应;再定义转角延性比损伤指标,结合支座剪应变,分析桥墩和支座的地震易损性情况;最后通过宽界限法建立全桥地震易损性曲线.研究结...     

Seismic isolation of bridges using isolation systems based on flat sliding bearings

Three different isolation systems (IS’s) for bridges and viaducts are considered in the present study. All of them are made of steel-PTFE sliding bearings (SB) to support the weight of the deck and auxiliary devices, based on different technologies and materials (i.e. rubber, steel and shape memory alloys), to provide re-centring and/or additional energy dissipating capability. An extensive numerical investigation has been carried out in order to (i) assess the reliability of different design approaches, (ii) compare the response of different types of IS’s, (iii) evaluate the sensitivity of the structural response to friction variability due to bearing pressure, air temperature and state of lubrication and (iv) identify the response variations caused by changes in the ground motion, bridge and isolation characteristics. The nonlinear time-history analyses have been carried out using a simplified pier-deck model, where the pier is modelled as an elastic cantilever beam and the mass of the deck is connected to the pier through suitable nonlinear elements, simulating the behaviour of the IS. Both artificial and natural seismic excitations have been used in the nonlinear dynamic analyses.     

隔震层位置与隔震支座选型

探讨隔震层的竖向设计位置,以期优化隔震设计,促进隔震技术的发展。隔震层设置在±0.00地板下和地下室板底相比:(1)在单层地下室部分不需设置隔震支座;(2)因减少地下室层的竖向荷载,竖向承载力的要求容易得到满足;(3)对于平面极不规则的结构,在±0.00板底隔震时,可以把上部结构分成几个平面相对比较规则的部分,因而隔震层扭转影响引起的位移可以减小;(4)对于文中算例,由于此3方面的原因,隔震支座选型后当隔震层处于±0.00地板下时可以降低隔震支座的费用达37.4%。对于平面尺寸大、平面极不规则的建筑结构把上部结构分割成若干规整的结构在首层地面以下进行隔震是一种经济可行的隔震方案。     

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.     

Nonlinear behavior of high-damping rubber bearings under horizontal bidirectional loading: full-scale tests and analytical modeling

Horizontal bidirectional loading tests are conducted for real-sized high-damping rubber (HDR) bearings with diameters of 700 mm (HDR700) and 1300 mm (HDR1300). The hysteresis loops of these bearings under bidirectional horizontal loadings are compared with those under unidirectional loadings. The results show that the bearing force measurement in the primary direction of loading increases when there is displacement in the orthogonal direction. Unusually, the maximum restoring force in the orthogonal direction to the primary loading direction occurs near zero displacement. On the basis of the observations of the restoring forces, a rate-independent model is proposed. This model simulates well the test results under both bidirectional loading and unidirectional loading. It can reproduce the irregular restoring forces characteristics around zero displacement as described above. Bidirectional loading induced twist deformation in the HDR bearings that increased local shear strains. This phenomenon results in an early failure as observed in HDR700. The additional shear strain is estimated based on the twist deformation measured by video image analysis. The comparison of the nominal total shear stress demonstrates that the increase of shear stress because of bidirectional loading occurs when the average shear strain is larger than about 200%. The larger the shear strain, the greater the bidirectional effect. It is shown that the nominal total shear stress of average strain of 350% under bidirectional circular loading pattern is approximately the same as the average shear strain of 400% under unidirectional loading. This means that the average shear strain of 350% under a bidirectional circular loading corresponds to a local shear strain of 400%. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Seismic isolation analysis of FPS bearings in spatial lattice shell structures

<正>A theoretical model of a friction pendulum system(FPS) is introduced to examine its application for the seismic isolation of spatial lattice shell structures.An equation of motion of the lattice shell with FPS bearings is developed.Then, seismic isolation studies are performed for both double-layer and single-layer lattice shell structures under different seismic input and design parameters of the FPS.The influence of frictional coefficients and radius of the FPS on seismic performance are discussed.Based on the study,some suggestions for seismic isolation design of lattice shells with FPS bearings are given and conclusions are made which could be helpful in the application of FPS.     

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.