Damping‐adjusted combination rule for the response spectrum analysis of base‐isolated buildings

The classical response spectrum method continues to be the most popular approach for designing base‐isolated buildings, therefore avoiding computationally expensive nonlinear time‐history analyses. In this framework, a new method for the seismic analysis and design of building structures with base isolation system (BIS) is formulated and numerically validated, which enables one to overcome the main shortcomings of existing techniques based on the response spectrum method. The main advantages are the following: first, reduced computational effort with respect to an exact complex‐valued modal analysis, which is obtained through a transformation of coordinates in two stages, both involving real‐valued eigenproblems; second, effective representation of the damping, which is pursued by consistently defining different viscous damping ratios for the modes of vibration of the coupled BIS‐superstructure dynamic system; and third, ease of use, because a convenient reinterpretation of the combination coefficients leads to a novel damping‐adjusted combination rule, in which just a single response spectrum is required for the reference value of the viscous damping ratio. The proposed approach is specifically intended for design situations where (i) the dynamic behaviour of seismic isolators can be linearised and (ii) effects of nonproportional damping, as measured by modal coupling indexes, are negligible in the BIS‐superstructure assembly. Copyright © 2012 John Wiley & Sons, Ltd.     

Inelastic response of RC frame buildings with seismic isolation

A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (F_y/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.     

Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation

The Rayleigh damping model, which is pervasive in nonlinear response history analysis (RHA) of buildings, is shown to develop ‘spurious’ damping forces and lead to inaccurate response results. We prove that a viscous damping matrix constructed by superposition of modal damping matrices—irrespective of the number of modes included or values assigned to modal damping ratios—completely eliminates the ‘spurious’ damping forces. This is the damping model recommended for nonlinear RHA. Replacing the stiffness‐proportional part of Rayleigh damping by the tangent stiffness matrix is shown to improve response results. However, this model is not recommended because it lacks a physical basis and has conceptual implications that are troubling: hysteresis in damping force–velocity relationship and negative damping at large displacements. Furthermore, the model conflicts with the constant‐damping model that has been the basis for fundamental concepts and accumulated experience about the inelastic response of structures. With a distributed plasticity model, the structural response is not sensitive to the damping model; even the Rayleigh damping model leads to acceptable results. This perspective on damping provides yet another reason to employ the superior distributed plasticity models in nonlinear RHA. OpenSees software has been extended to include a damping matrix defined as the superposition of modal damping matrices. Although this model leads to a full populated damping matrix, the additional computational demands are demonstrated to be minimal. Copyright © 2015 John Wiley & Sons, Ltd.     

Damage detection of base‐isolated buildings using multi‐input multi‐output subspace identification

A damage detection algorithm of structural health monitoring systems for base‐isolated buildings is proposed. The algorithm consists of the multiple‐input multiple‐output subspace identification method and the complex modal analysis. The algorithm is applicable to linear and non‐linear systems. The story stiffness and damping as damage indices of a shear structure are identified by the algorithm. The algorithm is further tuned for base‐isolated buildings considering their unique dynamic characteristics by simplifying the systems to single‐degree‐of‐freedom systems. The isolation layer and the superstructure of a base‐isolated building are treated as separate substructures as they are distinctly different in their dynamic properties. The effectiveness of the algorithm is evaluated through the numerical analysis and experiment. Finally, the algorithm is applied to the existing 7‐story base‐isolated building that is equipped with an Internet‐based monitoring system. Copyright © 2004 John Wiley & Sons, Ltd.     

Predominant period and equivalent viscous damping ratio identification for a full‐scale building shake table test

The predominant period and corresponding equivalent viscous damping ratio, also known in various loading codes as effective period and effective damping coefficient, are two important parameters employed in the seismic design of base‐isolated and conventional building structures. Accurate determination of these two parameters can reduce the uncertainty in the computation of lateral displacement demands and interstory drifts for a given seismic design spectrum. This paper estimates these two parameters from data sets recorded from a full‐scale five‐story reinforced concrete building subjected to seismic base excitations of various intensities in base‐isolated and fixed‐base configurations on the outdoor shake table at the University of California, San Diego. The scope of this paper includes all test motions in which the yielding of the reinforcement has not occurred and the response can still be considered ‘elastic’. The data sets are used with three system identification methods to determine the predominant period of response for each of the test configurations. One of the methods also determines the equivalent viscous damping ratio corresponding to the predominant period. It was found that the predominant period of the fixed‐base building lengthened from 0.52 to 1.30 s. This corresponded to a significant reduction in effective system stiffness to about 16% of the original stiffness. The paper then establishes a correlation between predominant period and peak ground velocity. Finally, the predominant periods and equivalent viscous damping ratios recommended by the ASCE 7‐10 loading standard are compared with those determined from the test building. Copyright © 2017 John Wiley & Sons, Ltd.     

Seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions

An approximation approach of seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions is proposed. The procedures of uncoupled modal response history analysis (UMRHA) are extended to two‐way asymmetric buildings simultaneously excited by two horizontal components of ground motion. Constructing the relationships of two‐way base shears versus two‐way roof translations and base torque versus roof rotation in ADRS format for a two‐way asymmetric building, each modal pushover curve bifurcates into three curves in an inelastic state. A three‐degree‐of‐freedom (3DOF) modal stick is developed to simulate the modal pushover curve with the stated bifurcating characteristic. It requires the calculation of the synthetic earthquake and angle β. It is confirmed that the 3DOF modal stick is consistent with single‐degree‐of‐freedom modal stick in an elastic state. A two‐way asymmetric three‐story building was analyzed by UMRHA procedure incorporating the proposed 3DOF modal sticks. The analytical results are compared with those obtained from nonlinear response history analysis. It is shown that the 3DOF modal sticks are more rational and effective in dealing with the assessment of two‐way asymmetric building systems under two‐directional seismic ground motions. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of near‐fault ground motions on the nonlinear dynamic response of base‐isolated r.c. framed buildings

Near‐fault ground motions are characterized by long‐period horizontal pulses and high values of the ratio between the peak value of the vertical acceleration, PGA_V, and the analogous value of the horizontal acceleration, PGA_H, which can become critical for base‐isolated (BI) structures. The objective of the present work is to check the effectiveness of the base isolation of framed buildings when using High‐Damping‐Rubber Bearings (HDRBs), taking into consideration the combined effects of the horizontal and vertical components of near‐fault ground motions. To this end, a numerical investigation is carried out with reference to BI reinforced concrete buildings designed according to the European seismic code (Eurocode 8). The design of the test structures is carried out in a high‐risk region considering (besides the gravity loads) the horizontal seismic loads acting alone or in combination with the vertical ones and assuming different values of the ratio between the vertical and horizontal stiffnesses of the HDRBs. The nonlinear seismic analysis is performed using a step‐by‐step procedure based on a two‐parameter implicit integration scheme and an initial‐stress‐like iterative procedure. At each step of the analysis, plastic conditions are checked at the potential critical sections of the girders (i.e. end sections of the sub‐elements in which a girder is discretized) and columns (i.e. end sections), where a bilinear moment–curvature law is adopted; the effect of the axial load on the ultimate bending moment (M‐N interaction) of the columns is also taken into account. The response of an HDRB is simulated by a model with variable stiffness properties in the horizontal and vertical directions, depending on the axial force and lateral deformation, and linear viscous damping. Copyright © 2011 John Wiley & Sons, Ltd.     

Stiffness‐damping simultaneous identification using limited earthquake records

A new method of stiffness‐damping simultaneous identification of building structures is proposed using limited earthquake records. It is shown that when horizontal accelerations are recorded at the floors just above and below a specific storey in a shear building model, the storey stiffness and the damping ratio can be identified uniquely. The viscous damping coefficient and the linear hysteretic damping ratio can also be identified simultaneously in a numerical model structure. The accuracy of the present identification method is investigated through the actual limited earthquake records in a base‐isolated building. It is further shown that an advanced identification technique for mechanical properties of a Maxwell‐type model can be developed by combining the present method with a perturbation technique. Copyright © 2000 John Wiley & Sons, Ltd.     

Approximating peak responses in seismically isolated buildings using generalized modal analysis

Although the ability to simulate accurately the detailed behavior of nonlinear isolation bearings and the effects of this nonlinearity on dynamic response of the isolated building is desirable, such detailed analyses are not feasible during initial design stages when bearing properties are being selected. However, it would be very beneficial to be able to estimate accurately key engineering demand parameters at the early stages of design to understand the dynamic response characteristics of the isolated structure and to balance and optimize the bearing and structural characteristics to achieve the performance goals set for the building. Unfortunately, classical modal response spectrum analysis methods do not provide accurate results for problems with large, nonclassical damping, as is characteristic of isolated buildings. To find a method capable of predicting peak building responses even with large nonclassical damping, generalized modal response spectrum analysis is implemented. The responses of several buildings having different heights and isolated by linear viscous as well as triple friction pendulum and single friction pendulum isolation systems are investigated. Generalized modal response spectrum analysis methods were found to give significantly better predictions for all systems compared with classical methods. The behavior of buildings isolated with single friction pendulum systems exhibiting sudden changes in stiffness could not be well predicted by either general or classical modal response spectrum analysis when effective damping was increased. Copyright © 2013 John Wiley & Sons, Ltd.     

Effects of brace stiffness on performance of structures with supplemental Maxwell model‐based brace–damper systems

Shear‐type buildings with Maxwell model‐based brace–damper systems are studied in this paper with a primary emphasis on the effects of brace stiffness. A single‐story building with a viscous damper installed on top of a Chevron‐brace is first investigated. Closed‐form solutions are derived for the simple structure, relating the brace stiffness and damper coefficient to the targeted reduction in response displacement or acceleration. For a given brace stiffness, the solution is minimized to give a set of formulae that will allow the optimal damper coefficient to be determined, assuring the desired performance. The model is subsequently extended to multistory buildings with viscous dampers installed on top of Chevron‐braces. For a targeted reduction in the mean square of the interstory drift, floor acceleration or base shear force, the minimum brace stiffness and optimal damper coefficients are obtained through an iterative procedure. The response reduction, which signifies the improved performance, is achieved by a combination of brace stiffness and viscous damper coefficients, unlike conventional approaches where damper coefficients are typically optimized independent of brace stiffnesses. Characteristics of multi‐degree‐of‐freedom systems are studied using a 2‐story and a 10‐story buildings where the effects of brace stiffness on the overall performance of the building can be quantified. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimum viscous damper for connecting adjacent SDOF structures for harmonic and stationary white‐noise random excitations

The dynamic behaviour of two adjacent single‐degree‐of‐freedom (SDOF) structures connected with a viscous damper is studied under base acceleration. The base acceleration is modelled as harmonic excitation as well as stationary white‐noise random process. The governing equations of motion of the connected system are derived and solved for relative displacement and absolute acceleration responses of connected structures. The response of structures is found to be reduced by connecting with a viscous damper having appropriate damping. For undamped SDOF structures, the closed‐form expressions for optimum damping of viscous damper for minimum steady state as well as minimum mean square relative displacement and absolute acceleration of either of the connected SDOF structures are derived. The optimum damper damping is found to be functions of mass and frequency ratio of two connected structures. Further, numerical results had indicated that the damping of the connected structures does not have noticeable effects on the optimum damper damping and the corresponding optimized response. This implies that the derived closed‐form expressions for optimum damper damping of undamped structures can also be used in practical applications for damped structures. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Simplified analysis of mid‐story seismically isolated buildings

The mid‐story isolation design method is recently gaining popularity for the seismic protective design of buildings located in the areas of high population. In a mid‐story isolated building, the isolation system is incorporated into the mid‐story rather than the base of the building. In this paper, the dynamic characteristics and seismic responses of mid‐story isolated buildings are investigated using a simplified three‐lumped‐mass structural model for which equivalent linear properties are formulated. From the parametric study, it is found that the nominal frequencies of the superstructure and the substructure, respectively, above and below the isolation system have significant influences on the isolation frequency and equivalent damping ratio of a mid‐story isolated building. Moreover, the mass and stiffness of the substructure are of greater significance than the superstructure in affecting the dynamic characteristics of the isolated building. Besides, based on the response spectrum analysis, it is noted that the higher mode responses may contribute significantly to the story shear force of the substructure. Consequently, the equivalent lateral force procedure of design codes should carefully include the effects of higher modes. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic response of 20‐story base‐isolated and fixed‐base reinforced concrete structural wall buildings at a near‐fault site

This paper investigates numerically the seismic response of six seismically base‐isolated (BI) 20‐story reinforced concrete buildings and compares their response to that of a fixed‐base (FB) building with a similar structural system above ground. Located in Berkeley, California, 2 km from the Hayward fault, the buildings are designed with a core wall that provides most of the lateral force resistance above ground. For the BI buildings, the following are investigated: two isolation systems (both implemented below a three‐story basement), isolation periods equal to 4, 5, and 6 s, and two levels of flexural strength of the wall. The first isolation system combines tension‐resistant friction pendulum bearings and nonlinear fluid viscous dampers (NFVDs); the second combines low‐friction tension‐resistant crosslinear bearings, lead‐rubber bearings, and NFVDs. The designs of all buildings satisfy ASCE 7‐10 requirements, except that one component of horizontal excitation, is used in the 2D nonlinear response history analysis. Analysis is performed for a set of ground motions scaled to the design earthquake and to the maximum considered earthquake (MCE). At both the design earthquake and the MCE, the FB building develops large inelastic deformations and shear forces in the wall and large floor accelerations. At the MCE, four of the BI buildings experience nominally elastic response of the wall, with floor accelerations and shear forces being 0.25 to 0.55 times those experienced by the FB building. The response of the FB and four of the BI buildings to four unscaled historical pulse‐like near‐fault ground motions is also studied. Copyright © 2013 John Wiley & Sons, Ltd.     

System identification of linear structures based on Hilbert–Huang spectral analysis. Part 1: normal modes

Based on the Hilbert–Huang spectral analysis, a method is proposed to identify multi‐degree‐of‐freedom (MDOF) linear systems using measured free vibration time histories. For MDOF systems, the normal modes have been assumed to exist. In this method, the measured response data, which are polluted by noises, are first decomposed into modal responses using the empirical mode decomposition (EMD) approach with intermittency criteria. Then, the Hilbert transform is applied to each modal response to obtain the instantaneous amplitude and phase angle time histories. A linear least‐square fit procedure is proposed to identify the natural frequency and damping ratio from the instantaneous amplitude and phase angle for each modal response. Based on a single measurement of the free vibration time history at one appropriate location, natural frequencies and damping ratios can be identified. When the responses at all degrees of freedom are measured, the mode shapes and the physical mass, damping and stiffness matrices of the structure can be determined. The applications of the proposed method are illustrated using three linear systems with different dynamic characteristics. Numerical simulation results demonstrate that the proposed system identification method yields quite accurate results, and it offers a new and effective tool for the system identification of linear structures in which normal modes exist. Copyright © 2003 John Wiley & Sons, Ltd.     

Validation of nonlinear time history analysis models for single‐storey concentrically braced frames using full‐scale shake table tests

The concentrically braced frame (CBF) structure is one of the most efficient steel structural systems to resist earthquakes. This system can dissipate energy during earthquakes through braces, which are expected to yield in tension and buckle in compression, while all other elements such as columns, beams and connections are expected to behave elastically. In this paper, the performance of single‐storey CBFs is assessed with nonlinear time‐history analysis, where a robust numerical model that simulates the behaviour of shake table tests is developed. The numerical model of the brace element used in the analysis was calibrated using data measured in physical tests on brace members subjected to cyclic loading. The model is then validated by comparing predictions from nonlinear time‐history analysis to measured performance of brace members in full scale shake table tests. Furthermore, the sensitivity of the performance of the CBF to different earthquake ground motions is investigated by subjecting the CBF to eight ground motions that have been scaled to have similar displacement response spectra. The comparative assessments presented in this work indicate that these developed numerical models can accurately capture the salient features related to the seismic behaviour of CBFs. A good agreement is found between the performance of the numerical and physical models in terms of maximum displacement, base shear force, energy dissipated and the equivalent viscous damping. The energy dissipated and, more particular, the equivalent viscous damping, are important parameters required when developing an accurate displacement‐based design methodology for CBFs subjected to earthquake loading. In this study, a relatively good prediction of the equivalent viscous damping is obtained from the numerical model when compared with data measured during the shake table tests. However, it was found that already established equations to determine the equivalent viscous damping of CBFs may give closer values to those obtained from the physical tests. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental tests on full‐scale RC unretrofitted frame and retrofitted with buckling‐restrained braces

The results of experimental tests carried out on reinforced concrete (RC) full‐scale 2‐storey 2‐bays framed buildings are presented. The unretrofitted frame was designed for gravity loads only and without seismic details; such frame was assumed as a benchmark system in this study. A similar RC frame was retrofitted with buckling‐restrained braces (BRBs). The earthquake structural performance of both prototypes was investigated experimentally using displacement‐controlled pushover static and cyclic lateral loads. Modal response properties of the prototypes were also determined before and after the occurrence of structural damage. The results of the dynamic response analyses were utilized to assess the existing design rules for the estimation of the elastic and inelastic period of vibrations. Similarly, the values of equivalent damping were compared with code‐base relationships. It was found that the existing formulations need major revisions when they are used to predict the structural response of as‐built RC framed buildings. The equivalent damping ratio ξ_eq was augmented by more than 50% when the BRBs was employed as bracing system. For the retrofitted frame, the overstrength Ω and the ductility µ are 1.6 and 4.1, respectively; the estimated R‐factor is 6.5. The use of BRBs is thus a viable means to enhance efficiently the lateral stiffness and strength, the energy absorption and dissipation capacity of the existing RC substandard frame buildings. The foundation systems and the existing members of the superstructure are generally not overstressed as the seismic demand imposed on them can be controlled by the axial stiffness and the yielding force of the BRBs. Copyright © 2011 John Wiley & Sons, Ltd.     

Understanding and predicting effects of supplemental viscous damping on seismic response of asymmetric one‐storey systems

Supplemental damping could mitigate the earthquake‐induced damage in buildings with asymmetric plan, known to be more vulnerable to damage than comparable symmetric‐plan buildings. This investigation aims to improve the understanding of how and why planwise distribution of fluid viscous dampers (FVDs) influences the response of linearly elastic, one‐storey, asymmetric‐plan systems. Starting with vibration mode shapes, we predict this influence on the modal damping ratios, and in turn on the individual modal responses and the total response. These predictions are confirmed by the computed responses, which demonstrated that the reduction in earthquake response of the system achieved by supplemental damping is strongly influenced by its planwise distribution, which is characterized by four parameters. Identified are asymmetric distributions of supplemental damping that are more effective in reducing the response compared to symmetric distribution. The percentage reduction achieved by a judiciously selected asymmetric distribution can be twice or even larger compared to symmetric distribution. Copyright © 2001 John Wiley & Sons, Ltd.     

Higher-mode effect on the seismic responses of buildings with viscoelastic dampers

In conventional modal analysis procedures, usually only a few dominant modes are required to describe the dynamic behavior of multi-degrees-of-freedom buildings. The number of modes needed in the dynamic analysis depends on the higher-mode contribution to the structural response, which is called the higher-mode effect. The modal analysis approach, however, may not be directly applied to the dynamic analysis of viscoelastically damped buildings. This is because the dynamic properties of the viscoelastic dampers depend on their vibration frequency. Therefore, the structural stiffness and damping contributed from those dampers would be different for each mode. In this study, the higher-mode effect is referred to as the response difference induced by the frequency-dependent property of viscoelastic dampers at higher modes. Modal analysis procedures for buildings with viscoelastic dampers distributed proportionally and non-proportionally to the stiffness of the buildings are developed to consider the higher-mode effect. Numerical studies on shear-type viscoelastically damped building models are conducted to examine the accuracy of the proposed procedures and to investigate the significance of the higher-mode effect on their seismic response. Two damper models are used to estimate the peak damper forces in the proposed procedures. Study results reveal that the higher-mode effect is significant for long-period viscoelastically damped buildings. The higher-mode effect on base shear is less significant than on story acceleration response. Maximum difference of the seismic response usually occurs at the top story. Also, the higher-mode effect may not be reduced by decreasing the damping ratio provided by the viscoelastic dampers. For practical application, it is realized that the linear viscous damping model without considering the higher-mode effect may predict larger damper forces and hence, is on the conservative side. Supported by: Science Council, Chinese Taipei, grant no. 88-2625-2-002-006     

Systematic assessment of irregular building–soil interaction using efficient modal analysis

In this paper an efficient methodology applying modal analysis is developed to assess systematically the combined soil–structure interaction and torsional coupling effects on asymmetric buildings. This method is implemented in the frequency domain to accurately incorporate the frequency‐dependent foundation impedance functions. For extensively extracting the soil–structure interaction effects, a diagonal transfer matrix in the modal space is derived. A comprehensive investigation of asymmetric building–soil interaction can then be conveniently conducted by examining various types of response quantities. Results of parametric study show that the increasing height‐to‐base ratio of a structure generally amplifies its translational and torsional responses. Moreover, both the translational and torsional responses are reduced for the case where the two resonant frequencies are well separated and this reduction is enhanced with the decreasing values of the relative soil stiffness and the height‐to‐base ratio. The most noteworthy phenomenon may be the fact that the SSI effects can enlarge the translational response if the structure is slender and the two resonant frequencies are very close. Copyright © 2001 John Wiley & Sons, Ltd.