A modal pushover analysis procedure to estimate seismic demands for unsymmetric‐plan buildings

An Erratum has been published for this article in Earthquake Engng. Struct. Dyn. 2004; 33:1429. Based on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric‐plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by non‐linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each floor level. These ‘modal’ demands due to the first few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems. When applied to elastic systems, the MPA procedure is equivalent to standard response spectrum analysis (RSA). The MPA estimates of seismic demand for torsionally‐stiff and torsionally‐flexible unsymmetric systems are shown to be similarly accurate as they are for the symmetric building; however, the results deteriorate for a torsionally‐similarly‐stiff unsymmetric‐plan system and the ground motion considered because (a) elastic modes are strongly coupled, and (b) roof displacement is underestimated by the CQC modal combination rule (which would also limit accuracy of RSA for linearly elastic systems). Copyright © 2004 John Wiley & Sons, Ltd.     

Elastic earthquake analysis of torsionally coupled multistorey buildings

With the aid of perturbation analysis of vibration frequencies and mode shapes it is shown that any lower vibration mode of a torsionally coupled building may be approximated as a linear combination of three vibration modes of the corresponding torsionally uncoupled system (a system with coincident centres of mass and resistance but all other properties are identical to the actual system): one translational mode along each of the two principal axes of resistance and one mode in torsional vibration. This result provides the motivation for a simpler—relative to the standard—procedure for analysing the response of torsionally coupled multistorey buildings to earthquake ground motion. To illustrate the application and accuracy of this procedure two numerical examples are presented.     

基于振动台实验的结构损伤识别研究

选择美国加州大学圣地亚哥分校7层钢筋混凝土剪力墙足尺结构振动台实验,开展结构损伤识别研究,实验采用白噪声、环境振动和不同强度的地震动交替激发,记录地震动激发实验前后的结构反应。基于该记录计算和对比自振频率和振型曲率的变化、剪切波走时及其变化和结构层间位移角,分析发现一层和二层振型曲率较大,走时较长,走时变化也较大,现场检查发现一层和二层的破坏也较为严重,这些参数可用于识别结构损伤程度和定位损伤位置,而自振频率和层间位移角变化仅可反映出结构损伤程度,难以揭示结构损伤位置。     

Generalized force vectors for multi‐mode pushover analysis of torsionally coupled systems

A generalized multi‐mode pushover analysis procedure was developed for estimating the maximum inelastic seismic response of symmetrical plan structures under earthquake ground excitations. Pushover analyses are conducted with story‐specific generalized force vectors in this procedure, with contributions from all effective modes. Generalized pushover analysis procedure is extended to three‐dimensional torsionally coupled systems in the presented study. Generalized force distributions are expressed as the combination of modal forces to simulate the instantaneous force distribution acting on the system when the interstory drift at a story reaches its maximum value during seismic response. Modal contributions to the generalized force vectors are calculated by a modal scaling rule, which is based on the complete quadratic combination. Generalized forces are applied to the mass centers of each story incrementally for producing nonlinear static response. Maximum response quantities are obtained when the individual frames attain their own target interstory drift values in each story. The developed procedure is tested on an eight‐story frame under 15 ground motions, and assessed by comparing the results obtained from nonlinear time history analysis. The method is successful in predicting the torsionally coupled inelastic response of frames responding to large interstory drift demands. Copyright © 2014 John Wiley & Sons, Ltd.     

Vibration‐based damage assessment of steel structure using global and local response measurements

Damage assessment of a structure involves acquiring and identifying dynamic characteristics of the structure and using these characteristics to evaluate behavior and performance. In this study, an unsymmetrical three‐story steel structure (fabricated with one weak column in the first floor) was tested on shaking table and subjected to a series of earthquake excitations with increasing level of excitation back to back. Besides, white noise excitation was also applied in between the earthquake excitation to serve as the reference state. Both the traditional sensing system (accelerometer and linear variable differential transformer) and the local optical tracker system were implemented in the structure to collect the vibration‐based responses. For operational modal analysis, structural response from white noise excitation will be used in this study. First, the traditional system identification using global response data is used (multivariate autoregressive (AR)‐model) to extract system natural frequencies and mode shapes from all different set of white noise responses after earthquake excitation. The migration of AR‐coefficient ellipse error from each sensor response was used to identify the damage location. Second, blind source separation technique was used to identify the modal contribution of the structure from each test, which provide information to detect the damage severity. Finally, from the local optical tracker array data, the principal component analysis was applied to quantify the earthquake‐induce local stress of the structural member. Combine the result from damage detection using global measurement and the identified local element stress, one can locate and quantify the damage. Copyright © 2015 John Wiley & Sons, Ltd.     

Modal identification of structures from ambient vibration,free vibration,and seismic response data via a subspace approach

This work presents a unified procedure for determining the natural frequencies, modal damping ratios and modal shapes of a structure from its ambient vibration, free vibration and earthquake response data. To evaluate the coefficient matrices of a state‐space model, the proposed procedure applies a subspace approach cooperating with an instrumental variable concept. The dynamic characteristics of a structure are determined from the coefficient matrices. The feasibility of the procedure is demonstrated through processing an in situ ambient vibration measurement of a five‐storey steel frame, an impulse response measurement of a three‐span continuous bridge, and simulated earthquake responses of five‐storey steel frames from shaking table tests. The excellent agreement of the results obtained herein with those published previously confirms the feasibility of the present procedure. Copyright © 2001 John Wiley & Sons, Ltd.     

Dynamic characteristics of a base isolated building from ambient vibration measurements and low level earthquake shaking

Ambient vibration tests were conducted on a base-isolated apartment building in Takamatsu, Japan, to determine the mode shapes and the associated natural frequencies and damping ratios at very low levels of excitation. The latest developments in signal analysis for modal decomposition are used to analyze the ambient response data. A finite element model of the building and isolators was calibrated and refined using the experimental results from the ambient vibration tests. This model was then used to simulate the recorded response of the building under excitation from a small earthquake. The finite element model, calibrated by ambient vibration data and the low level of earthquake shaking, provides the starting point for modelling the non-linear response of the building when subjected to strong shaking.     

Earthquake‐induced structural response output‐only identification by two different Operational Modal Analysis techniques

Output‐only system identification is developed here towards assessing current modal dynamic properties of buildings under seismic excitation. Earthquake‐induced structural response signals are adopted as input channels for two different Operational Modal Analysis (OMA) techniques, namely, a refined Frequency Domain Decomposition (rFDD) algorithm and an improved Data‐Driven Stochastic Subspace Identification (SSI‐DATA) procedure. Despite that short‐duration, non‐stationary, earthquake‐induced structural response signals shall not fulfil traditional OMA assumptions, these implementations are specifically formulated to operate with seismic responses and simultaneous heavy damping (in terms of identification challenge), for a consistent estimation of natural frequencies, mode shapes, and modal damping ratios. A linear ten‐storey frame structure under a set of ten selected earthquake base‐excitation instances is numerically simulated, by comparing the results from the two identification methods. According to this study, best up‐to‐date, reinterpreted OMA techniques may effectively be used to characterize the current dynamic behaviour of buildings, thus allowing for potential Structural Health Monitoring approaches in the Earthquake Engineering range.     

A note on the perturbation analysis of the mode shapes of torsionally coupled buildings

The application of perturbation analysis in torsionally coupled buildings makes it possible to obtain an approximation of the dynamic properties of the buildings in question by combining appropriately the dynamic properties of the corresponding torsionally uncoupled buildings. This note aims to clarify the results obtained from a second-order perturbation analysis of the mode shapes of torsionally coupled buildings. Numerical examples of building models are given to illustrate the theoretical points.     

Experimental study on multiple tuned mass dampers to reduce seismic responses of a three‐storey building structure

In this study, several mass dampers were designed and fabricated to suppress the seismic responses of a ¼‐scale three‐storey building structure. The dynamic properties of the dampers and structure were identified from free and forced vibration tests. The building structure with or without the dampers was, respectively, tested on a shake table under the white noise excitation, the scaled 1940 El Centro earthquake and the scaled 1952 Taft earthquake. The dampers were placed on the building floors using the sequential procedure developed by the authors in previous studies. Experimental results indicated that the multiple damper system is substantially superior to a single tuned mass damper in mitigating the floor accelerations even though the multiple dampers are sub‐optimal in terms of tuning frequency, damping and placement. These results validated the sequential procedure for placement of the multiple dampers. The structure was also analysed numerically based on the shake table excitation and the identified structure and damper parameters for all test cases. Numerical and experimental results are in good agreement, validating the dynamic properties identified. Copyright © 2003 John Wiley & Sons, Ltd.     

Two‐stage damage detection algorithms of structure using modal parameters identified from recursive subspace identification

Structural damage assessment under external loading, such as earthquake excitation, is an important issue in structural safety evaluation. In this regard, appropriate data analysis and feature extraction techniques are required to interpret the measured data and to identify the state of the structure and, if possible, to detect the damage. In this study, the recursive subspace identification with Bona‐fide LQ renewing algorithm (RSI‐BonaFide‐Oblique) incorporated with moving window technique is utilized to identify modal parameters such as natural frequencies, damping ratios, and mode shapes at each instant of time during the strong earthquake excitation. From which the least square stiffness method (LSSM) combined with the model updating technique, called efficient model correction method (EMCM), is used to estimate the first‐stage system stiffness matrix using the simplified model from the previously identified modal parameters (nominal model). In the second stage, 2 different damage assessment algorithms related to the nominal system stiffness matrix were derived. First, the model updating technique, called EMCM, is applied to correct the nominal model by the newly identified modal parameters during the strong motion. Second, the element damage index can be calculated using element damage index method (EDIM) to quantify the damage extent in each element. Verification of the proposed methods through the shaking table test data of 2 different types of structures and a building earthquake response data is demonstrated to specify its corresponding damage location, the time of occurrence during the excitation, and the percentage of stiffness reduction.     

Dynamic behavior of buildings with non-uniform stiffness along their height assessed through coupled flexural and shear beams

A novel model for assessing building behavior has been developed by coupling a Bernoulli beam with a quartic stiffness variation and a shear beam with a parabolic stiffness variation, trends that are expected in buildings designed for earthquake actions. Then the partial differential equation of motion governing the behavior of the model has been solved, obtaining analytic expressions (Closed form solutions) for mode shapes in terms of Legendre functions. These closed form solutions were validated with finite element model analyses and effects of non-uniformity of stiffness were assessed in a generalized manner. It was found that period lengthening is mild for the first mode, but for higher modes can be far more noticeable if shear stiffness at beam top is <20 % of its base value. Mode shapes also change notoriously for reductions beyond the same limit, potentially inducing large floor acceleration demands at unexpected locations. Also it was found that drift demands can be noticeably enhanced even if shear stiffness at top is 75 % of the base value, in what would be considered uniform buildings. This model has several applications for assessing the response or large stocks of buildings, calibrate complex models, assess damage on building contents, establishing in short time damage scenarios for large cities, and could be helpful for education, as emphasis is brought back on fundamental concepts.     

System identification of a building from multiple seismic records

This paper describes the identification of finite dimensional, linear, time‐invariant models of a 4‐story building in the state space representation using multiple data sets of earthquake response. The building, instrumented with 31 accelerometers, is located on the University of California, Irvine campus. Multiple data sets, recorded during the 2005 Yucaipa, 2005 San Clemente, 2008 Chino Hills and 2009 Inglewood earthquakes, are used for identification and validation. Considering the response of the building as the output and the ground motion as the input, the state space models that represent the underlying dynamics of the building in the discrete‐time domain corresponding to each data set are identified. The time‐domain Eigensystem Realization Algorithm with the Observer/Kalman filter identification procedure are adopted in this paper, and the modal parameters of the identified models are consistently determined by constructing stabilization diagrams. The four state space models identified demonstrate that the response of the building is amplitude dependent with the response frequency and damping, being dependent on the magnitude of ground excitation. The practical application of this finding is that the consistency of this building response to future earthquakes can be quickly assessed, within the range of ground excitations considered (0.005g–0.074g), for consistency with prior response—this assessment of consistent response is discussed and demonstrated with reference to the four earthquake events considered in this study. Inclusion of data sets relating to future earthquakes will enable the findings to be extended to a wider range of ground excitation magnitudes. Copyright © 2010 John Wiley & Sons, Ltd.     

Development of deformable connection for earthquake‐resistant buildings to reduce floor accelerations and force responses

This paper presents the development of a deformable connection that is used to connect each floor system of the flexible gravity load resisting system (GLRS) with the stiff lateral force resisting system (LFRS) of an earthquake‐resistant building. It is shown that the deformable connection acts as a seismic response modification device, which limits the lateral forces transferred from each floor to the LFRS and allows relative motion between the GLRS and LFRS. In addition, the floor accelerations and the LFRS story shears related to the higher‐mode responses are reduced. The dispersion of peak responses is also significantly reduced. Numerical simulations of the earthquake response of a 12‐story reinforced concrete shear wall example building with deformable connections are used to define an approximate feasible design space for the deformable connection. The responses of the example building model with deformable connections and the example building model with rigid‐elastic connections are compared. Two configurations of the deformable connection are studied. In one configuration, a buckling restrained brace is used as the limited‐strength load‐carrying hysteretic component of the deformable connection, and in the other configuration, a friction device is used. Low damping laminated rubber bearings are used in both configurations to ensure the out‐of‐plane stability of the LFRS and to provide post‐elastic stiffness to the deformable connection. Important experimental results from full‐scale tests of the deformable connections are presented and used to calibrate numerical models of the connections. Copyright © 2016 John Wiley & Sons, Ltd.     

云南漾濞地震大理某高层建筑结构地震响应观测数据初步分析

2021年5月21日21时21分至22时32分,云南漾濞先后发生了M5.6级、M6.4级、M5.0级和M5.2级地震,位于大理的某高层建筑结构地震反应观测台阵获取了这4次地震的结构动力响应,观测数据同步性好,数据质量高。该高层建筑为框架剪力墙结构,地上26层,地下1层,三分量加速度测点共8个分别位于建筑的第1层、4层、7层、10层、13层、17层、20层和25层,数据实时传输至中国地震局工程力学研究所燕郊数据中心。本文对结构台阵的观测记录进行了初步分析,绘制建筑结构观测楼层的三向绝对加速度及其傅里叶幅值谱,检验数据同步性和质量,通过滤波和积分得到相对速度和相对位移,利用功率谱方法分析得到频率响应函数,并利用复模态指数函数方法得到两水平方向前三阶模态频率和振型。通过4次地震结构模态频率和振型的初步对比结果表明:主体结构基本完好,这与现场调查结果吻合。该结构台阵获取的前震、主震和余震反应记录,为后续开展深入的模态参数分析、地震损伤识别以及研究框架剪力墙结构的振动特性和抗震性能提供了宝贵数据。     

Envelopes of maximum seismic response for a partially symmetric single storey building model

An analysis is made of the coupled lateral-torsional response of a partially symmetric single-storey building model to horizontal translatory earthquake excitation. Interest centres on the evaluation of realistic estimates for two equivalent static actions (a shear and a torque) which account for the worst dynamic consequences of torsional unbalance. The results substantiate the findings of previous investigations which have given rise to the belief that strong modal coupling and severely coupled lateral and torsional responses are possible even in nominally symmetric buildings. The response of the model is assumed to be linearly elastic and viscously damped. In a preliminary analysis the equations of motion are solved using the modal analysis technique and the conditions necessary for full modal coupling are ascertained. Then by employing the design spectrum concept, together with suitably conservative procedures for combining the modal maxima, dimensionless forms of the equivalent static actions are evaluated as functions of two independent parameters. The final results are furnished by modified square root of the sum of the squares (SRSS) combination functions which take account of the spacing between the translational and torsional frequencies. Examples at the end of the paper illustrate the practical significance of the work.     

A modified static procedure for the design of torsionally unbalanced multistorey frame buildings

Seismic building codes include design provisions to account for the torsional effects arising in torsionally unbalanced (asymmetric) buildings. These provisions are based on two alternative analytical procedures for determining the design load for the individual resisting structural elements. A previous study has shown that the linear elastic modal analysis procedure may not lead to conservative designs, even for multistorey buildings with regular asymmetry, when such structures are excited well into the inelastic range of response. The equivalent static force procedure as recommended by codes may also be deficient in accounting for additional ductility demand in the critical stiff-edge elements. This paper addresses the non-conservatism of existing static torsional provisions and examines aspects of element strength distribution and its influence on inelastic torsional effects. A recommendation is made for improving the effectiveness of the code-type static force procedure for torsionally unbalanced multistorey frame buildings with regular asymmetry, leading to a design approach which estimates conservatively the peak ductility demand of edge elements on both sides of the building. The modified approach also retains the simplicity of existing code provisions and results in acceptable levels of additional lateral design strength. It has recently been adopted by the new Australian earthquake code, which is due to be implemented early in 1993.     

Alternative method to locate centre of rigidity in asymmetric buildings

Response of asymmetric buildup under earthquake excitation often involves lateral vibration coupled with torsional vibration. Floor slab is, in general, assumed as rigid along the in‐plane direction. Building code provisions to account for the torsional effect in static force procedure are based on centre of rigidity or shear centre of the building. A convenient procedure is developed here to locate the centre of rigidity or shear centre, which can be implemented, using any standard building analysis software. The procedure is applicable for orthogonal as well as non‐orthogonal building systems and accounts for all possible definitions of static eccentricity to compute the design response. An irregular building is analysed to illustrate the proposed methodology. Significant variation in member force resultants is observed due to different definitions of static eccentricity. Finally, a mathematical proof is presented to substantiate the applicability of the proposed procedure to a non‐orthogonal building. Copyright © 2006 John Wiley & Sons, Ltd.     

A refined Frequency Domain Decomposition tool for structural modal monitoring in earthquake engineering

Output-only structural identification is developed by a refined Frequency Domain Decomposition(rFDD) approach, towards assessing current modal properties of heavy-damped buildings(in terms of identification challenge), under strong ground motions. Structural responses from earthquake excitations are taken as input signals for the identification algorithm. A new dedicated computational procedure, based on coupled Chebyshev Type Ⅱ bandpass filters, is outlined for the effective estimation of natural frequencies, mode shapes and modal damping ratios. The identification technique is also coupled with a Gabor Wavelet Transform, resulting in an effective and self-contained time-frequency analysis framework. Simulated response signals generated by shear-type frames(with variable structural features) are used as a necessary validation condition. In this context use is made of a complete set of seismic records taken from the FEMA P695 database, i.e. all 44 "Far-Field"(22 NS, 22 WE) earthquake signals. The modal estimates are statistically compared to their target values, proving the accuracy of the developed algorithm in providing prompt and accurate estimates of all current strong ground motion modal parameters. At this stage, such analysis tool may be employed for convenient application in the realm of Earthquake Engineering, towards potential Structural Health Monitoring and damage detection purposes.     

System identification applied to long‐span cable‐supported bridges using seismic records

This paper presents the application of system identification (SI) to long‐span cable‐supported bridges using seismic records. The SI method is based on the System Realization using Information Matrix (SRIM) that utilizes correlations between base motions and bridge accelerations to identify coefficient matrices of a state‐space model. Numerical simulations using a benchmark cable‐stayed bridge demonstrate the advantages of this method in dealing with multiple‐input multiple‐output (MIMO) data from relatively short seismic records. Important issues related to the effects of sensor arrangement, measurement noise, input inclusion, and the types of input with respect to identification results are also investigated. The method is applied to identify modal parameters of the Yokohama Bay Bridge, Rainbow Bridge, and Tsurumi Fairway Bridge using the records from the 2004 Chuetsu‐Niigata earthquake. Comparison of modal parameters with the results of ambient vibration tests, forced vibration tests, and analytical models are presented together with discussions regarding the effects of earthquake excitation amplitude on global and local structural modes. Copyright © 2007 John Wiley & Sons, Ltd.