Real-time hybrid simulation of structures equipped with viscoelastic-plastic dampers using a user-programmable computational platform

A user-programmable computational/control platform was developed at the University of Toronto that offers real-time hybrid simulation (RTHS) capabilities. The platform was verified previously using several linear physical substructures. The study presented in this paper is focused on further validating the RTHS platform using a nonlinear viscoelastic-plastic damper that has displacement, frequency and temperature-dependent properties. The validation study includes damper component characterization tests, as well as RTHS of a series of single-degree-of-freedom (SDOF) systems equipped with viscoelastic-plastic dampers that represent different structural designs. From the component characterization tests, it was found that for a wide range of excitation frequencies and friction slip loads, the tracking errors are comparable to the errors in RTHS of linear spring systems. The hybrid SDOF results are compared to an independently validated thermalmechanical viscoelastic model to further validate the ability for the platform to test nonlinear systems. After the validation, as an application study, nonlinear SDOF hybrid tests were used to develop performance spectra to predict the response of structures equipped with damping systems that are more challenging to model analytically. The use of the experimental performance spectra is illustrated by comparing the predicted response to the hybrid test response of 2DOF systems equipped with viscoelastic-plastic dampers.     

Seismic response of light internal equipment in base-isolated structures

The seismic response of light secondary systems in a building is dependent on the response of the primary structural system to the seismic ground motion with the result that very high accelerations can be induced in such secondary systems. This response can be reduced through the use of aseismic base isolation which is a design strategy whereby the entire building can be decoupled from the damaging horizontal components of seismic ground motion by the use of some form of isolation system. The paper presents a theoretical analysis of the response of light equipment in isolated structures and a parallel experimental programme both of which show that the use of base isolation can not only attenuate the response of the primary structural system but also reduce the response of secondary systems. Thus, the design of equipment and piping in a base-isolated building is very much simpler than that for a conventionally founded structure: inelastic response and equipment-structure interaction need not be considered and multiple support response analysis is rendered unnecessary. Although an isolation system with linear elastic bearings can reduce the acceleration of the structure, it may be accompanied by large relative displacements between the structure and the ground. A system using lead-rubber hysteretic bearings, having a force-displacement relation which is approximately a bilinear loop, can reduce these displacements. A parallel experimental programme was carried out to investigate the response of light equipment in structures isolated using lead-rubber bearings. The experimental results show that these bearings can dissipate energy and limit the displacement and acceleration of the structure but are less effective in reducing the accelerations in the internal equipment. The results of both the analysis and the tests show that base isolation is a very effective method for the seismic protection of light equipment items in buildings.     

Experimental study on the aseismic capacity of a wooden house using shaking table

The aseismic capacity of a typical Korean wooden house built using traditional construction methods is quantitatively estimated. Tenon joints were used in wooden frames. Two 1:4 scale models were tested for rock and soil foundation conditions. Scaled real earthquake time histories were input for the tests. The natural frequency and modal damping ratio of the wooden house in the elastic range were 1·66 Hz and 7 per cent, respectively. The Peak Ground Acceleration (PGA) at the collapse of the house at the soil site was 0·25g, whereas PGA for moderate damage at the rock site was 0·6g. A significant reduction in acceleration response and increase in displacement response was observed for rock and soil foundation conditions, respectively. The wooden house studied is much more vulnerable at soil sites than at rock sites due to the rich low-frequency contents of the input motion and the flexible characteristics of the wooden house. Non-linear dynamic analyses using the modified Double-Target model were compared with test results. The modified Double-Target model appropriately simulates the non-linear inelastic behaviour of a wooden house with tenon joints. Copyright © 1999 John Wiley & Sons, Ltd.     

POST-EARTHQUAKE RESIDUAL DISPLACEMENTS OF BILINEAR OSCILLATORS

Structures subjected to large inelastic deformations during violent ground shaking do not always return to their initial ‘at-rest’ position but may have residual displacements. Even if collapse does not occur, large residual displacements may render them unusable or irreparable. In order to investigate the likely magnitude of residual displacement many bilinear single-degree-of-freedom oscillators with specified ductilities of 2·0, 4·0 and 6·0, stiffness ratios ranging from −0·25 to 1·0 and fundamental periods from 0 to 3·0s were subjected to 11 earthquake records from various ground types. It is shown that bilinear oscillators with positive stiffness ratios generally have small residual displacements, while those with negative stiffness ratios tend to undergo little inelastic reversal of deformation and have larger residual displacements. Reasons for this behaviour were able to be explained by means of a ‘hysteresis centre curve’. A design example for structures able to be modelled as single-degree-of-freedom oscillators is provided. © 1997 John Wiley & Sons, Ltd.     

Quantifying the seismic response of structures with flexible diaphragms

Floor diaphragm in-plane stiffness affects building response to horizontal ground accelerations. This paper describes a series of elastic and inelastic time history analyses of symmetric structures with different deformation types, configurations and heights to quantify these effects. It is shown that displacements of single storey elastically responding structures tend to be most significantly affected by diaphragm flexibility. Analyses of these structures were cross-verified by a closed-form mechanics-based formulation developed to describe the response. Simple relationships were proposed to allow designers to conservatively estimate the increase in peak in-plane displacement resulting from diaphragm flexibility. Copyright © 2012 John Wiley & Sons, Ltd.     

实时GNSS地震仪系统实现及精度分析

高频GNSS数据实时精密单点定位(RTPPP)可实时获得地表瞬时动态形变和地震波信号,为地震参数快速确定、地震快速响应及海啸预警提供实时的观测资料.本文构建了实时GNSS地震仪系统,主要包括RTPPP和实时探测两部分.利用RTPPP 方法处理了模拟的震动实验平台实验数据和2010年Baja California地震的数据,并与惯导(IMU)、事后PPP和差分相对定位结果比较,定量评估了实时GNSS地震仪系统的精度.结果表明,该系统可实现水平方向优于1cm,高程方向优于3cm的实时定位,且对Baja California地震的实时探测结果与南加州地震数据中心公布的结果相一致.     

Torsional mechanisms in ductile building systems

It is postulated that in order to estimate torsional effects on the seismic response of ductile building structures, the associated plastic mechanism to be developed in the three-dimensional system should be identified. The proposed approach is very different from that embodied in building codes. Inelastic structures are classified as either torsionally unrestrained or restrained. It is shown that clearly defined mechanisms that are to be mobilized, enable the acceptable system ductility demand to be estimated. This should ensure that the corresponding demands imposed on critical translatory elements of the system do not exceed their established displacement ductility capacity. To this end familiar quantities, such as element yield displacement and stiffness, are redefined. Comparisons are made of the intents of existing codified design approaches and those emphasising the role of imposed inelastic displacements. A simple treatment of the consequences of earthquake-induced inelastic skew displacements is also addressed. The primary aim of the paper is to offer very simple concepts, based on easily identifiable plastic mechanisms, to be utilized in structural design rather than advancement in analyses. Detailed design applications of these concepts are described elsewhere. The approach is an extension of the deterministic philosophy of capacity design, now used in some countries. © 1998 John Wiley & Sons, Ltd.     

Strong motion displacement waveforms using 10‐Hz precise point positioning GPS: an assessment based on free oscillation experiments

The recently developed precise point positioning (PPP) technique permits to compute instantaneous coordinates of a GPS station relatively to distant reference stations and waveforms of ground displacements during strong motions at the 1 Hz level. This is another application of GPS, different from the computation of static coseismic movements or of accurate monitoring of dynamic displacements of structures using a static receiver and a nearby moving receiver (DGPS). Recently, earthquake ground displacement waveforms using 10‐Hz GPS data have also been calculated, but no independent evidence to assess their quality exists. To overcome this problem, we evaluated the output of 10‐Hz PPP results on the basis of supervised learning experiments. Semistatic and dynamic displacements (damped harmonic oscillations) of known characteristics of the order of a few centimeter were produced and were recorded by GPS, an accelerometer, and a robotic total station. Time series of instantaneous displacements were analyzed using different PPP techniques and were compared with reference (true) values derived from DGPS and the other sensors. Our analysis revealed that the PPP‐derived coordinates are contaminated by long‐period noise but they can display the details of semistatic displacements, while their short‐period component describes well the pattern of waveforms and spectra (at least up to 4 Hz) of dynamic displacements, with up to 20 mm accuracy for isolated points. These results indicate that 10‐Hz PPP‐GPS is useful for earthquake engineering and can safely be used to reconstruct waveforms of deflections of the ground and of various points on structures during strong motions. Copyright © 2014 John Wiley & Sons, Ltd.     

A new simplified approach for assessing nonlinear seismic response of plan-asymmetric structures considering soil-structure interaction

An innovative approximate method is presented to consider the plan asymmetry, nonlinear structural behaviour and soil-structure interaction (SSI) effects simultaneously. The proposed method so-called Flexible base 2DMPA (F2MPA) is an extension of 2 degrees of freedom modal pushover analysis (2DMPA) approach to consider foundation flexibility in seismic response analysis of plan asymmetric structures which itself were developed based on Uncoupled Modal Response History Analysis method for inelastic fixed-base asymmetric structures. In F2MPA for each mode shape using 2DMPA procedure, the elastic and inelastic properties of 2DOF modal systems corresponding to the fixed-base structure are initially derived. Then in each time step, displacements and inelastic restoring forces of the superstructure are computed from modal equations of the flexibly-supported structure. In each time step, the nonlinear secant stiffness matrix corresponding to the n-th MDOF modal equations of soil-structure system is updated using the corresponding modal 2DOF system of fixed-base structure. To update the transformed modal stiffness matrix of the SSI system, this matrix is partitioned and it is assumed that the non-linear variation of the superstructure can be estimated from the variation of modal stiffness matrix of the fixed-base structure. Accuracy of the proposed method was verified on an 8-story asymmetric-plan building under different seismic excitations. The results obtained from F2MPA method were compared with those obtained by nonlinear response history analysis of the asymmetric soil-structure system as a reference response. It was shown that the proposed approach could predict the results of the nonlinear time history analysis with a good accuracy. The main advantage of F2MPA is that this method is much less time-consuming and useful for the practical aims such as massive analysis of a nonlinear structure under different records with multiple intensity levels.     

Bi-directional pseudodynamic test of a full-size three-storey building

The reliability of a Pseudodynamic (PsD) test depends primarily on the accuracy of the control system. Difficulties arise mainly when the method is applied to very stiff or very heavy structures or to structures with a high number of Degrees of Freedom (DoFs). This paper describes the bi-directional PsD testing of a full-size three-storey building. The tested specimen is a composite structure with plan dimensions of 12×16 m and height of 9·5 m, made of steel columns and beams combined with composite reinforced concrete slabs. The PsD test included the application of two uncorrelated accelerograms along the horizontal directions X and Y. Since the structure was not symmetric about the Y-axis, the possibility of torsion was considered by taking into account both horizontal displacements and the yaw rotation at every floor. Three displacement-controlled hydraulic actuators were thus used at each floor to impose these three DoFs while a fourth actuator with special control strategy was added to optimize the distribution of loads among the pistons. The validity of the testing methodology was verified by performing also a dynamic random burst test on the specimen which was afterwards pseudodynamically reproduced. Copyright © 1999 John Wiley & Sons, Ltd.     

Analysis of shaking table-structure interaction effects during seismic simulation tests

An analytical model is developed to evaluate performance characteristics of unidirectional seismic simulators (shaking tables). The validity of the model is verified with experimental measurements of the frequency response of the shaking table at the Catholic University of Peru. Interaction effects between shaking table and structure are first studied by analysing the response of a two DOF (degree of freedom) oscillator with mechanical properties representative of the actuator-table-structure system. A single DOF viscoelastic oscillator representing the structural test specimen is then included in the analytical model of the seismic simulator, and the behaviour of the combined system is evaluated, in the frequency domain, in terms of response stability and accuracy of reproduction of the command signal. Numerical simulations of system response under different load conditions are subsequently performed in order to study the influence of shaking table and test structure characteristics on the interaction phenomenon. The results obtained explain some of the performance degradation observed in seismic simulation tests involving very heavy structures and provide guidelines for the design of more reliable shaking table systems.     

Torsional balance of plan‐asymmetric structures with frictional dampers: analytical results

This investigation deals with the torsional balance of the earthquake response and design of elastic asymmetric structures with frictional dampers. Plan asymmetry leads to an uneven lateral deformation demand among structural members and to unbalanced designs with larger capacities in some resisting planes. Frictional dampers are capable of controlling lateral‐torsional coupling by placing the so‐called empirical center of balance (ECB) of the structure at equal distance from all edges of the building. This rule is developed for single‐story systems with linear and inelastic behavior. However, recently obtained theoretical and experimental results demonstrate that this rule carries over to multistory structures. Results show that the peak displacement demand at the building edges and that of resisting planes equidistant from the geometric center may be similar if the damper is optimally placed. It is also shown that torsional amplification of the edge displacements of arbitrary asymmetric structures relative to the displacement of the symmetric counterparts are approximately bound by a factor of 2. Furthermore, frictional dampers are equally effective in controlling lateral‐torsional coupling of torsionally flexible as well as stiff structures. Copyright © 2005 John Wiley & Sons, Ltd.     

Simplified seismic analysis of asymmetric building systems

The paper reviews the uncoupled modal response history analysis (UMRHA) and modal pushover analysis (MPA) procedure in the analysis of asymmetric structures. From the pushover curves in ADRS format, showing the relationships of base shear versus roof translation and base torque versus roof rotation, a bifurcating characteristic of the pushover curves of an asymmetric structure is observed. A two‐degree‐of‐freedom (2DOF) modal stick is constructed using lump mass eccentrically placed at the end of beam which is connected with the column by a rotational spring. By converting the equation of motion of a whole structure into 2DOF modal equations, all of the elastic properties in the 2DOF modal sticks can be determined accurately. A mathematical proof is carried out to demonstrate that the 2DOF modal stick is consistent with the single‐degree‐of‐freedom (SDOF) modal stick at elastic state. The bifurcating characteristic of modal pushover curves and the interaction of modal translation and rotation can be considered rationally by this 2DOF modal stick. In order to verify the effectiveness of this proposed 2DOF modal stick, a two‐storey asymmetric building structure was analysed by the UMRHA procedure incorporating this novel 2DOF modal sticks (2DMPA) and conventional SDOF modal sticks (SDMPA), respectively. The analytical results are compared with those obtained by nonlinear response history analysis (RHA). It is illustrated that the accuracy of the rotational response histories obtained by 2DMPA is much better than those obtained by SDMPA. Consequently, the estimations of translational response histories on flexible side (FS) and stiff side (SS) of the building structure are also improved. Copyright © 2006 John Wiley & Sons, Ltd.     

Predictive active control of MDOF structures

This paper presents a theoretical study of a predictive active control system used to improve the response of multi‐degree‐of‐freedom (MDOF) structures to earthquakes. As an example a building frame equipped with electrorheological (ER) dampers is considered. The aim of the design is to find a combination of forces that are produced by the ER dampers in order to obtain an optimal structural response. The mechanical response of ER fluid dampers is regulated by an electric field. Linear auto‐regressive model with exogenous input (ARX) is used to predict the displacements and the velocities of the frame in order to overcome the time‐delay problem in the control system. The control forces in the ER devices are calculated at every time step by the optimal control theory (OCT) according to the values of the displacements and of the velocities that are predicted at the next time step at each storey of the structure. A numerical analysis of a seven‐storey ER damped structure is presented as an example. It shows a significant improvement of the structural response when the predictive active control system is applied compared to that of an uncontrolled structure or that of a structure with controlled damping forces with time delay. The structure's displacements and velocities that were used to obtain the optimal control forces were predicted according to an ‘occurring’ earthquake by the ARX model (predictive control). The response was similar to that of the structure with control forces that were calculated from a ‘known’ complete history of the earthquake's displacement and velocity values, and were applied without delay (instantaneous control). Copyright © 2000 John Wiley & Sons, Ltd.     

Force–displacement mixed control for collapse tests of multistory buildings using quasi‐static loading systems

In quasi‐static tests for structures with multi‐DOF, the forces exerted to the structures commonly follow a prescribed force profile, for example, triangular pattern and/or uniform pattern. Therefore, force control is the natural choice. However, force control is no longer applicable when the specimens sustain significant stiffness and strength degradation, particularly in collapse tests. To solve this problem, a force–displacement mixed control algorithm is proposed, which is able to achieve stable control in quasi‐static tests following prescribed force profiles. On the basis of the FlexTest IIm platform of the MTS Systems Corporation (14000 Technology Dr, Eden Prairie, MN 55344 United States), a test program named Tsinghua University mixed control test program, which uses a mixed control algorithm, was developed. The algorithm was initially applied to an elastic test of a cantilever column to verify its accuracy and stability and then to a collapse test of a multistory RC frame to investigate its effectiveness. In the collapse test, the effects of major control parameters, that is, the number of iterative rounds and the loading time of each round on the control accuracy, were also studied. The test results show that the test program applying the mixed control algorithm can achieve stable control of the collapse tests maintaining the expected force profile. Increasing the number of iterative rounds and the loading time of each round can improve the control accuracy. Copyright © 2013 John Wiley & Sons, Ltd.     

Shake table testing of an elevator system in a full‐scale five‐story building

This paper investigates the seismic performance of a functional traction elevator as part of a full‐scale five‐story building shake table test program. The test building was subjected to a suite of earthquake input motions of increasing intensity, first while the building was isolated at its base and subsequently while it was fixed to the shake table platen. In addition, low‐amplitude white noise base excitation tests were conducted while the elevator system was placed in three different configurations, namely, by varying the vertical location of its cabin and counterweight, to study the acceleration amplifications of the elevator components due to dynamic excitations. During the earthquake tests, detailed observation of the physical damage and operability of the elevator as well as its measured response are reported. Although the cabin and counterweight sustained large accelerations because of impact during these tests, the use of well‐restrained guide shoes demonstrated its effectiveness in preventing the cabin and counterweight from derailment during high‐intensity earthquake shaking. However, differential displacements induced by the building imposed undesirable distortion of the elevator components and their surrounding support structure, which caused damage and inoperability of the elevator doors. It is recommended that these aspects be explicitly considered in elevator seismic design. Copyright © 2016 John Wiley & Sons, Ltd.     

基于HHT变换瞬时能量谱的长周期结构地震反应分析

基于HHT变换得到瞬时能量谱,并以简谐地震反应为理论基础进行多自由度体系在地震动作用下的瞬态反应计算。通过对一个长周期(十五层)结构工程实例的地震瞬态反应计算分析,揭示长周期结构有别于短周期结构动力响应的独特特性:长周期结构位移响应的瞬时能量峰值的时间滞后于地震动能量峰值的时间,且主要受到瞬态振动的控制,并以低阶振型的控制为主,第一阶振型峰值位移滞后的时间最长,滞后的时间主要取决于结构的第一阶自振周期。研究结果表明,长周期结构在强烈地震动作用下,地震动强度出现的最大时刻并不总是对应于结构破环与倒塌的时间。     

Comparison of displacement coefficient method and capacity spectrum method with experimental results of RC columns

For the performance‐based seismic design of buildings, both the displacement coefficient method used by FEMA‐273 and the capacity spectrum method adopted by ATC‐40 are non‐linear static procedures. The pushover curves of structures need to be established during processing of these two methods. They are applied to evaluation and rehabilitation of existing structures. This paper is concerned with experimental studies on the accuracy of both methods. Through carrying out the pseudo‐dynamic tests, cyclic loading tests and pushover tests on three reinforced concrete (RC) columns, the maximum inelastic deformation demands (target displacements) determined by the coefficient method of FEMA‐273 and the capacity spectrum method of ATC‐40 are compared. In addition, a modified capacity spectrum method which is based on the use of inelastic design response spectra is also included in this study. It is shown from the test specimens that the coefficient method overestimates the peak test displacements with an average error of +28% while the capacity spectrum method underestimates them with an average error of ‐20%. If the Kowalsky hysteretic damping model is used in the capacity spectrum method instead of the original damping model, the average errors become ‐11% by ignoring the effect of stiffness degrading and ‐1.2% by slightly including the effect of stiffness degrading. Furthermore, if the Newmark–Hall inelastic design spectrum is implemented in the capacity spectrum method instead of the elastic design spectrum, the average error decreases to ‐6.6% which undervalues, but is close to, the experimental results. Copyright © 2003 John Wiley & Sons, Ltd.     

On the response of yielding seismically isolated structures

This paper investigates the seismic response of yielding isolated structures. To establish a general understanding of the nonlinear response of seismically isolated structures, this study first investigates the nonlinear response of isolated structures subjected to steady‐state harmonic motion and nonlinear transient ground excitation. The response of both viscously damped and hysteretically damped isolation systems is investigated in three phases. Initially, basic insights are gained through simple nonlinear two degrees of freedom (2‐DOF) models subjected to harmonic motion of varying frequencies. Next, the transient response analysis of the nonlinear 2‐DOF model is investigated for a wide range of isolation system and superstructure properties. The results obtained from both approaches indicate that the yielding behavior of a structure on an isolation system is significantly different from that of the comparable fixed‐base structure. Finally, the response of the nonlinear 2‐DOF system model is compared with that of a 15‐story, three‐dimensional model. Based on the results of these analytical investigations, some important considerations for the design of seismically isolated structures are presented. Copyright © 2007 John Wiley & Sons, Ltd.