A rate‐dependent constitutive model of high damping rubber bearings: modeling and experimental verification

In this study, a constitutive model of high damping rubber bearings (HDRBs) is developed that allows the accurate representation of the force–displacement relationship including rate‐dependence for shear deformation. The proposed constitutive model consists of two hyperelastic springs and a nonlinear dashpot element and expresses the finite deformation viscoelasticity laws based on the classical Zener model. The Fletcher–Gent effect, manifested as high horizontal stiffness at small strains and caused by the carbon fillers in HDRBs, is accurately expressed through an additional stiffness correction factor α in the novel strain energy function. Several material parameters are used to simulate the responses of high damping rubber at various strain levels, and a nonlinear viscosity coefficient η is introduced to characterize the rate‐dependent property. A parameter identification scheme is applied to the results of the multi‐step relaxation tests and the cyclic shear tests, and a three‐dimensional function of the nonlinear viscosity coefficient η with respect to the strain, and strain rate is thus obtained. Finally, to investigate the accuracy and feasibility of the proposed model for application to the seismic response assessment of bridges equipped with HDRBs, an improved real‐time hybrid simulation (RTHS) test system based on the velocity loading method is developed. A single‐column bridge was used as a test bed and HDRBs was physically tested. Comparing the numerical and RTHS results, advantage of the proposed model in the accuracy of the predicted seismic response over comparable hysteretic models is demonstrated. Copyright © 2016 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.     

Modeling RC column flexural failure modes under intensive seismic loading

The aim of this work is to model beam‐column behavior in a computationally effective manner, revealing reliably the overall response of reinforced concrete members subjected to intensive seismic loading. In this respect, plasticity and damage are considered in the predominant longitudinal direction, allowing for fiber finite element modeling, while in addition the effect of inelastic buckling of longitudinal rebars, which becomes essential at later stages of intensive cyclic loading, is incorporated. Α smooth plasticity‐damage model is developed for concrete, accounting for unilateral compressive and tensile behavior, nonlinear unloading and crack closure phenomena. This is used to address concrete core crushing and spalling, which triggers the inelastic buckling of longitudinal rebars. For this reason, a uniaxial local stress‐strain constitutive relation for steel rebars is developed, which is based on a combined nonlinear kinematic and isotropic hardening law. The proposed constitutive model is validated on the basis of existing experimental data and the formulation of the buckling model for a single rebar is developed. The cross section of rebar is discretized into fibers, each one following the derived stress‐strain uniaxial law. The buckling curve is determined analytically, while equilibrium is imposed at the deformed configuration. The proposed models for concrete and rebars are embedded into a properly adjusted fiber beam‐column element of reinforced concrete members and the proposed formulation is verified with existing experimental data under intensive cyclic loading.     

Design of hysteretic dampers with optimal ductility for the transverse seismic control of cable‐stayed bridges

Cable‐stayed bridges require a careful consideration of the lateral force exerted by the deck on the towers under strong earthquakes. This work explores the seismic response of cable‐stayed bridges with yielding metallic dampers composed of triangular plates that connect the deck with the supports in the transverse direction. A design method based on an equivalent single‐degree of freedom approximation is proposed. This is proved valid for conventional cable‐stayed bridges with 200‐ and 400‐m main spans, but not 600 m. The height of the plates is chosen to (1) achieve a yielding capacity that limits the maximum force transmitted from the deck to the towers, and to (2) control the hysteretic energy that the dampers dissipate by defining their design ductility. In order to select the optimal ductility and the damper configuration, a multi‐objective response factor that accounts for the energy dissipation, peak damper displacement and low‐cycle fatigue is introduced. The design method is applied to cable‐stayed bridges with different spans and deck–support connections. The results show that the dissipation by plastic deformation in the dampers prevents significant damage in the towers of the short‐to‐medium‐span bridges under the extreme seismic actions. However, the transverse response of the towers in the bridge with a 600‐m main span is less sensitive to the dampers. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

Advanced frame element for seismic analysis of masonry structures: model formulation and validation

This paper presents a masonry panel model for the nonlinear static and dynamic analysis of masonry buildings suitable for the seismic assessment of new and existing structures. The model is based on an equivalent frame idealization of the structure and stems from previous research on force‐based frame elements. The element formulation considers axial, bending, and shear deformations within the framework of the Timoshenko beam theory. A phenomenological cyclic section law that accounts for the shear panel response is coupled, through equilibrium between shear and bending forces along the element, with a fiber‐section model that accounts for the axial and bending responses. The proposed panel model traces with a low computational burden and numerical stability the main aspects of the structural behavior of masonry panels and is suitable for analyses of multi‐floor buildings with a relatively regular distribution of openings and with walls and floors organized to grant a box‐like behavior under seismic loads. The model capabilities are validated though analyses of simple unreinforced masonry panels and comparisons with published experimental results. The model accuracy is strongly dependent on the fiber and shear constitutive laws used. However, the formulation is general, and laws different from those employed in this study are easily introduced without affecting the model formulation. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of horizontal stiffness of fibre‐reinforced elastomeric isolators

Unbonded fibre‐reinforced elastomeric isolator (U‐FREI) is relatively new seismic base isolator in which fibre layers are used as reinforcement to replace steel shims as are normally used in conventional isolators. Further, the top and bottom end steel connector plates of conventional isolators are also removed. In general, the horizontal response of U‐FREI is nonlinear because of reduction in contact area due to rollover deformation and reduction in shear modulus of isolator under large deformation. Thus, evaluation of horizontal stiffness of U‐FREI is a challenging problem. Most previous studies were focused on the investigation of horizontal response of scaled models of U‐FREIs with low shape factors. A few analytical approaches were suggested for predicting the horizontal response of U‐FREI; but their results were not in good agreement with experimental observations. In the present study, the horizontal responses of prototype U‐FREIs are evaluated under a constant vertical pressure and cyclic loading using both experiments and finite element analysis. Prototype U‐FREIs with different shear moduli and with different shape factors are considered. Finite element simulations of corresponding bonded FREIs are also performed under the same loadings as in U‐FREIs. A rational analytical approach including the influence of rollover deformation and simultaneous reduction in shear modulus is proposed as a basic analytical tool for predicting the horizontal stiffness of FREIs (both bonded and unbonded). It is in reasonably good agreement with the results obtained from experiments and numerical analysis. Copyright © 2017 John Wiley & Sons, Ltd.     

The damped cable system for seismic protection of frame structures — Part I: General concepts,testing and modeling

Research studies on the damped cable system (DCS) for seismic protection of frame structures are presented in this paper and the accompanying one. This technology includes prestressed steel cables linked to pressurized fluid viscous spring‐dampers fixed to the foundation at their lower ends, and to the top floor, or one of the upper floors, at their upper ends. The cables have sliding contacts with the floor slabs, to which they are joined by steel deviators. The general characteristics of the system, as well as of the constituting spring‐dampers and cables, are initially discussed. The results of a laboratory testing campaign developed on a DCS prototype are examined, and transferred into the formulation of the finite element model of the system, conceived to be easily generated by commercial structural analysis programs. A second dynamic experimental investigation follows, concerning a pilot installation of the system on a full‐scale mock‐up building. The benefits of the protective technology are evaluated in terms of maximum displacements and accelerations, as well as of equivalent viscous damping coefficient and MDOF transmissibility ratio. Further sections of the study, including a preliminary sizing criterion of DCS, additional numerical enquiries aimed at optimizing its geometrical layout, and the application to a real case study building, are offered in the companion paper. Copyright © 2011 John Wiley & Sons, Ltd.     

Probabilistic performance‐based optimum design of seismic isolation for a California high‐speed rail prototype bridge

Previous comparison studies on seismic isolation have demonstrated its beneficial and detrimental effects on the structural performance of high‐speed rail bridges during earthquakes. Striking a balance between these 2 competing effects requires proper tuning of the controlling design parameters in the design of the seismic isolation system. This results in a challenging problem for practical design in performance‐based engineering, particularly when the uncertainty in seismic loading needs to be explicitly accounted for. This problem can be tackled using a novel probabilistic performance‐based optimum seismic design (PPBOSD) framework, which has been previously proposed as an extension of the performance‐based earthquake engineering methodology. For this purpose, a parametric probabilistic demand hazard analysis is performed over a grid in the seismic isolator parameter space, using high‐throughput cloud‐computing resources, for a California high‐speed rail (CHSR) prototype bridge. The derived probabilistic structural demand hazard results conditional on a seismic hazard level and unconditional, i.e., accounting for all seismic hazard levels, are used to define 2 families of risk features, respectively. Various risk features are explored as functions of the key isolator parameters and are used to construct probabilistic objective and constraint functions in defining well‐posed optimization problems. These optimization problems are solved using a grid‐based, brute‐force approach as an application of the PPBOSD framework, seeking optimum seismic isolator parameters for the CHSR prototype bridge. This research shows the promising use of seismic isolation for CHSR bridges, as well as the potential of the versatile PPBOSD framework in solving probabilistic performance‐based real‐world design problems.     

Non‐linear‐Maxwell‐element‐type hysteretic control force

A simple non‐linear control law is proposed for reducing structural responses against seismic excitations. This law defines control force dynamics by one differential equation involving a non‐linear term that restrains the control force amplitude. If non‐linearity is neglected, the control force becomes the force in a Maxwell element, so it is called the non‐linear‐Maxwell‐element‐type (NMW) control force. The NMW control force vs. deformation relation plots hysteretic curves. The basic performance of an SDOF model with the NMW control force is examined for various conditions by numerical analyses. Furthermore, the control law is extended to fit an MDOF structural model, and an application example is shown. The computational results show that the NMW control force efficiently reduces structural responses. Copyright © 2000 John Wiley & Sons, Ltd.     

预应力混凝土圆形储煤筒仓地震反应分析

使用ANSYS软件对一大直径预应力混凝土圆形储煤筒仓结构建立了有限元模型,以储料质量沿高度分布不变为原则,采用施加质量单元的方法模拟储料的分布,通过对预应力混凝土筒仓进行地震作用下的受力、变形分析,研究了预应力混凝土筒仓结构的受力性能及整体抗震性能,同时分析了筒仓结构地震作用简化计算方法的可行性.分析结果表明,水平地震作用对筒仓预应力结构部分的环向力无显著影响,预应力筒仓结构具有良好的抗侧力性能;同时,在结构基本振型指数选取合理时,采用底部剪力法估算筒仓水平地震作用是可行的.所得结果可为同类筒仓结构的地震反应分析提供参考.     

地震动对锚索桩的响应特性研究

汶川地震震害调查表明使用预应力锚索的桩板墙变形协调性好,抗震性能高,但目前在预应力锚索桩板墙的抗震设计理论研究方面仍比较落后。鉴于此,利用FLAC3D对预应力锚索桩板墙的地震响应特征进行研究,包括桩身土压力分布、桩身变位及锚索内锚段应力的动力响应特性等,并通过改变地震动参数进行多种工况的分析,系统研究地震动参数对桩-土-锚动力耦合相互作用规律的影响。研究成果可加强对预应力锚索桩板墙抗震表现的认识,也为深化抗震机理研究提供可靠的依据。     

An isolation system for limited seismic gaps in near‐fault zones

The ability of a recently proposed seismic isolation system, with inherent self‐stopping mechanism, to mitigate or even eliminate seismic pounding of adjacent structures is investigated under severe near‐fault earthquakes. The isolation system is referred to as roll‐in‐cage (RNC) isolator. It is a rolling‐based isolator that provides in one unit the necessary functions of vertical rigid support, horizontal flexibility with enhanced stability, hysteretic energy dissipation, and resistance to minor vibration loads. In addition, the RNC isolator is distinguished by a self‐stopping (buffer) mechanism to limit the bearing displacement under excitations stronger than a design earthquake or at limited seismic gaps, and a linear gravity‐based self‐recentering mechanism to prevent permanent bearing displacement without causing vertical fluctuation of the isolated structure. A previously developed multifeature SAP2000 model of the RNC isolator is improved in this paper to account for the inherent buffer mechanism's damping. Then, the effectiveness of the isolator's buffer mechanism in limiting peak bearing displacements is studied together with its possibly arising negative influence on the isolation efficiency. After that, the study investigates how to alleviate or even eliminate those possibly arising drawbacks, due to the developed RNC isolator's inner pounding as a result of its buffer activation, to achieve efficient seismic isolation with no direct structure‐to‐structure pounding, considering limited seismic gaps with adjacent structures and near‐fault earthquakes. The results show that the RNC isolator could be an efficient solution for aseismic design in near‐fault zones considering limited seismic gaps. Earthquake Engineering and Structural Dynamics. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of lead core heating on the seismic performance of bridges isolated with LRB in near‐fault zones

In this paper, the effect of lead core heating and associated strength deterioration on the seismic response of bridges isolated with lead rubber bearings (LRB) is investigated as a function of the characteristics of the isolator and near fault ground motions with forward rupture directivity effect. Furthermore, the ability of bounding analyses to provide a design envelope for maximum isolator force and maximum isolator displacement is verified. For this purpose, a series of nonlinear dynamic analyses are conducted for LRB isolated bridges where both deteriorating and non‐deteriorating force‐deformation relationship of LRB were employed. The analyses are performed for both simulated and recorded ground motions. It is found that while the temperature rise in the lead core generally increases with increasing magnitude and number of near fault ground motion velocity pulses, it decreases with larger distances from the fault. It is also found that bounding analysis method provides conservative (envelope) estimates of maximum isolator displacement and maximum isolator force for design purposes that fulfill its intended purpose. Copyright © 2012 John Wiley & Sons, Ltd.     

Effects of seismic isolation on the seismic response of a California high‐speed rail prototype bridge with soil‐structure and track‐structure interactions

With the launch of the high‐speed train project in California, the seismic risk is a crucial concern to the stakeholders. To investigate the seismic behavior of future California High‐Speed Rail (CHSR) bridge structures, a 3D nonlinear finite‐element model of a CHSR prototype bridge is developed. Soil‐structure and track‐structure interactions are accounted for in this comprehensive numerical model used to simulate the seismic response of the bridge and track system. This paper focuses on examining potential benefits and possible drawbacks of the a priori promising application of seismic isolation in CHSR bridges. Nonlinear time history analyses are performed for this prototype bridge subjected to two bidirectional horizontal historical earthquake ground motions each scaled to two different seismic hazard levels. The effect of seismic isolation on the seismic performance of the bridge is investigated through a detailed comparison of the seismic response of the bridge with and without seismic isolation. It is found that seismic isolation significantly reduces the deck acceleration and the force demand in the bridge substructure (i.e., piers and foundations), especially for high‐intensity earthquakes. However, seismic isolation increases the deck displacement (relative to the pile cap) and the stresses in the rails. These findings imply that seismic isolation can be promisingly applied to CHSR bridges with due consideration of balancing its beneficial and detrimental effects through using appropriate isolators design. The optimum seismic isolator properties can be sought by solving a performance‐based optimum seismic design problem using the nonlinear finite‐element model presented herein. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonlinear seismic analysis of reinforced concrete frames using the force analogy method

A method of nonlinear seismic analysis for RC framed structures considering full‐range factors, including stiffness and strength degradation, geometric nonlinearity, and structural member failure, is established based on the fundamental concept of the force analogy method. The strong material nonlinearity, large geometric deformation, and internal forces redistribution due to the member failure can be depicted by the proposed local plastic mechanisms, the rotation hinges at the member ends and the slide hinges assigned to the columns, of which the measurement relationships are moment versus plastic rotation and shear force versus shear plastic deformation, respectively. They are capable of evaluating the exact response of RC structures. Because only unchanging initial stiffness matrices are used through the whole computation process, the state‐space formulation was used for solving the equations of motion. The advantages of the force analogy method, such as high efficiency and stability, are still retained. The exactness of the proposed local plastic mechanisms is verified against a group of tests data, and the application of the proposed procedure is performed to an RC framed structure to simulate the full‐range nonlinear response by increasing the excitation step by step until failure of partial structural members appear. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental study of deformable connection consisting of friction device and rubber bearings to connect floor system to lateral force resisting system

This paper presents experimental and numerical studies of a full‐scale deformable connection used to connect the floor system of the flexible gravity load resisting system to the stiff lateral force resisting system (LFRS) of an earthquake‐resistant building. The purpose of the deformable connection is to limit the earthquake‐induced horizontal inertia force transferred from the floor system to the LFRS and thereby to reduce the horizontal floor accelerations and the forces in the LFRS. The deformable connection that was studied consists of a friction device (FD) and carbon fiber‐reinforced laminated low‐damping rubber bearings (RB), denoted as the FD + RB connection. The test results show that the force‐deformation responses of the FD + RB connection are stable under quasi‐static sinusoidal and earthquake loading histories and dynamic sinusoidal loading histories. The FD + RB connection force‐deformation response is approximated with a bilinear elastic‐plastic force‐deformation response with kinematic hardening. The FD is axially stiff, compact, easy‐to‐assemble, and able to accommodate the FD + RB connection kinematic requirements. The FD elastic stiffness controls the FD + RB connection elastic stiffness. The FD friction force controls the force when the FD + RB connection force‐deformation response transitions from elastic to post elastic. The RB provide predictable and reliable post‐elastic stiffness to the FD + RB connection. The machining tolerances for the FD components, the “break‐in” effect, the sliding history, and the dwell time affect the FD friction force. Numerical simulation results for a 12‐story reinforced concrete wall building with FD + RB connections under seismic loading show that a reduction of the FD friction force increases the FD + RB connection deformation demand.     

Shaking table test and numerical simulation of a 1/2‐scale self‐centering reinforced concrete frame

Self‐centering reinforced concrete frames are developed as an alternative of traditional seismic force‐resisting systems with better seismic performance and re‐centering capability. This paper presents an experimental and computational study on the seismic performance of self‐centering reinforced concrete frames. A 1/2‐scale model of a two‐story self‐centering reinforced concrete frame model was designed and tested on the shaking table in State Key Laboratory of Disaster Reduction in Civil Engineering at Tongji University to evaluate the seismic behavior of the structure. A structural analysis model, including detailed modeling of beam–column joints, column–base joints, and prestressed tendons, was constructed in the nonlinear dynamic modeling software OpenSEES. Agreements between test results and numerical solutions indicate that the designed reinforced concrete frame has satisfactory seismic performance and self‐centering capacity subjected to earthquakes; the self‐centering structures can undergo large rocking with minor residual displacement after the earthquake excitations; the proposed analysis procedure can be applied in simulating the seismic performance of self‐centering reinforced concrete frames. To achieve a more comprehensive evaluation on the performance of self‐centering structures, research on energy dissipation devices in the system is expected. Copyright © 2015 John Wiley & Sons, Ltd.     

Cumulative damage‐based inelastic cyclic demand spectrum

The estimation of cyclic deformation demand resulting from earthquake loads is crucial to the core objective of performance‐based design if the damage and residual capacity of the system following a seismic event needs to be evaluated. A simplified procedure to develop the cyclic demand spectrum for use in preliminary seismic evaluation and design is proposed in this paper. The methodology is based on estimating the number of equivalent cycles at a specified ductility. The cyclic demand spectrum is then determined using well‐established relationships between seismic input energy and dissipated hysteretic energy. An interesting feature of the proposed procedure is the incorporation of a design spectrum into the proposed procedure. It is demonstrated that the force–deformation characteristics of the system, the ductility‐based force‐reduction factor R_μ, and the ground motion characteristics play a significant role in the cyclic demand imposed on a structure during severe earthquakes. Current design philosophy which is primarily based on peak response amplitude considers cyclic degradation only in an implicit manner through detailing requirements based on observed experimental testing. Findings from this study indicate that cumulative effects are important for certain structures, classified in this study by the initial fundamental period, and should be incorporated into the design process. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic response of rotating machines–structure–RFBI systems

The seismic response of a critical rotating machine either rigidly attached to a floor or independently isolated housed within an initially aseismically designed or uncontrolled structure are investigated. A particular isolation system, the Resilient‐Friction Base Isolator (RFBI), is employed. Finite element formulations of a rotor‐disk‐bearing model on a rigid base are developed. The equations of motion for the combined rotating machine–structure–RFBI systems are presented. Parametric studies are performed to investigate the effects of variations in system physical properties including friction coefficient, mass ratio, shaft flexibility, bearing rigidity, bearing damping and speed of rotation on the response of rotating machines for the combined rotating machine–structure–isolator systems. Comparative studies in the peak response of the rotating machine supported on various isolation systems and the corresponding fixed base system are carried out. The study indicates that the Resilient‐Friction Base Isolator can significantly reduce the seismic response of rotating components to potentially damaging ground excitations. Copyright © 2000 John Wiley & Sons, Ltd.