A response‐based decoupling criterion for multiply‐supported secondary systems

It is often infeasible to carry out coupled analyses of multiply‐supported secondary systems for earthquake excitations. ‘Approximate’ decoupled analyses are then resorted to, unless the response errors due to those are significantly high. This study proposes a decoupling criterion to identify such cases where these errors are likely to be larger than an acceptable level. The proposed criterion is based on the errors in the primary system response due to decoupling and has been obtained by assuming (i) the input excitation to be an ideal white noise process, (ii) cross‐modal correlation to be negligible, and (iii) the combined system to be classically damped. It uses the modal properties of the undamped combined system, and therefore, a perturbation approach has been formulated to determine the combined system properties in case of light to moderately heavy secondary systems. A numerical study has been carried out to illustrate the accuracy achieved with the proposed perturbation formulation. The proposed decoupling criterion has been validated with the help of two example primary‐secondary systems and four example excitation processes. Copyright © 2002 John Wiley & Sons, Ltd.     

Response of multiply supported secondary systems to earthquakes in frequency domain

A new formulation of the transfer function has been proposed for the seismic analysis of linear, multiply supported secondary systems. The transfer function for a given response quantity has been formulated by directly using the fixed-base modes of the primary and secondary systems. This approach is exact and does not involve the determination of the combined system properties. Further, it is applicable to the secondary systems with various mass ratios and configurations. A few example primary–secondary systems have been considered to illustrate the proposed formulation in case of different mass ratios. It has also been shown how the proposed formulation can be used to obtain reasonably accurate stochastic estimates of the secondary system responses. © 1998 John Wiley & Sons, Ltd.     

Stochastic seismic response of multiply-supported secondary systems in flexible-base structures

A formulation has been proposed for the transfer function of a secondary system response while the primary system is supported on a compliant soil and the excitation comprises of translational ground motion at its base. For this purpose, the earlier formulation of the authors for the fixed-base case, which exactly considers the interaction between the two sub-systems and is based on the use of their individual modal properties, has been extended. Also, the concept of modifying the input excitation for the interaction accelerations (associated with the soil–structure interaction) has been used. An example P–S system and three example earthquake excitations have been considered to illustrate the proposed formulation and to estimate the expected response peak amplitudes in the secondary system. This study shows that ‘detuning’ of the tuned systems may occur in case of significant soil–structure interaction. Further, for the reasons of both safety and economy, ignoring the interaction effects in designing the secondary systems may not always be justified. Copyright © 1999 John Wiley & Sons, Ltd.     

Evaluation of vertical seismic response for a large‐scale beam‐supported aqueduct

By the theories of potential flow and structural vibration, the formulae for evaluating the ‘wet’ (with water) frequencies and mode shapes of the beam‐supported aqueduct are derived through a simplified fluid‐structure interaction analysis. The time‐history formulae of structural responses to the vertical seismic excitation are obtained. Applying the response‐spectrum principle, the equivalent vertical earthquake load exerted on the beam and the corresponding effects are also derived. Several illustrative examples are conducted. The analytical results show that: (i) The ‘wet’ frequencies of the structure are lower than the corresponding ‘dry’ (without water) frequencies due to the participating water mass, but the ‘wet’ mode shapes are identical to the corresponding ‘dry’ ones. (ii) The water mass plays an important role in the vertical seismic response, which varies with the different geological sites. For the different seismic inputs, the deeper the water is, the greater are the structural responses. (iii) The vertical seismic effects on the beam are generally not too small to be neglected and should be considered in the structural designs of a beam‐supported aqueduct. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

非比例阻尼线性体系地震反应计算的振型分解反应谱法

以非比例阻尼线性体系地震反应计算实数形式的一般解答为基础,推导得到了非比例阻尼线性体系水平地震作用计算的多种形式,建立了非比例阻尼线性体系地震反应计算振型分解反应谱法的基本过程与步骤。最后,以一个五层剪切型结构为例,通过与各种常用直接积分方法计算结果的比较,证实了本文非比例阻尼线性体系地震反应计算实数形式的一般解答的高精度与可靠性。通过对多种形式地震作用所得地震效应的比较,证实了非比例阻尼线性体系地震反应振型分解反应谱方法的可靠性及可行性。     

Estimation of strength reduction factors via normalized pseudo‐acceleration response spectrum

Estimation of design forces in ductility‐based earthquake‐resistant design continues to be carried out with the application of response modification factors on elastic design spectra, and it remains interesting to explore how best to estimate strength reduction factors (SRFs) for a design situation. This paper considers the relatively less explored alternative of modelling SRF spectrum via a given response spectrum. A new model is proposed to estimate the SRF spectrum in terms of a pseudo‐spectral acceleration (PSA) spectrum and ductility demand ratio with the help of two coefficients. The proposed model is illustrated for an elasto‐plastic oscillator, in case of 10 recorded accelerograms and three ductility ratios. The proposed model is convenient and is able to predict SRF spectrum reasonably well, particularly at periods up to 1.0 s. Coefficients of the proposed model may also be determined in case of a given design spectrum when there is uncertainty in SRF spectrum due to uncertainty in temporal characteristics of the ground motion. This is illustrated with the help of 474 accelerograms recorded in western U.S.A. and different scaled PSA spectra. It is shown that probabilistic estimates may be obtained in this situation for SRF spectrum by assuming the error residuals to be log normally distributed with period‐dependent parameters. Copyright © 2006 John Wiley & Sons, Ltd.     

A probabilistic approach for estimating the seismic response of elasto‐plastic SDOF systems

The seismic response of elasto‐plastic structures to both recorded and generated accelerograms is characterized by a large scattering of the results, even for accelerograms with similar peak ground acceleration values and frequency content. According to current code recommendations a design value of the seismic response of an elasto‐plastic structure can be computed as the mean of the responses to a certain number of spectrum‐fitting generated accelerograms. A more effective probabilistic approach is presented herein. It allows the analyst to calculate a design value of the seismic response characterized by a predefined non‐exceedance probability using a limited number of generated accelerograms. The results of the performed analyses are presented in diagrams that can be used for structural design applications. The applicability of the proposed method is demonstrated in the case of an elasto‐plastic structural system and the results are compared with those obtained applying current code recommendations. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic response of self‐centring hysteretic SDOF systems

The seismic response of single‐degree‐of‐freedom (SDOF) systems incorporating flag‐shaped hysteretic structural behaviour, with self‐centring capability, is investigated numerically. For a SDOF system with a given initial period and strength level, the flag‐shaped hysteretic behaviour is fully defined by a post‐yielding stiffness parameter and an energy‐dissipation parameter. A comprehensive parametric study was conducted to determine the influence of these parameters on SDOF structural response, in terms of displacement ductility, absolute acceleration and absorbed energy. This parametric study was conducted using an ensemble of 20 historical earthquake records corresponding to ordinary ground motions having a probability of exceedence of 10% in 50 years, in California. The responses of the flag‐shaped hysteretic SDOF systems are compared against the responses of similar bilinear elasto‐plastic hysteretic SDOF systems. In this study the elasto‐plastic hysteretic SDOF systems are assigned parameters representative of steel moment resisting frames (MRFs) with post‐Northridge welded beam‐to‐column connections. In turn, the flag‐shaped hysteretic SDOF systems are representative of steel MRFs with newly proposed post‐tensioned energy‐dissipating connections. Building structures with initial periods ranging from 0.1 to 2.0s and having various strength levels are considered. It is shown that a flag‐shaped hysteretic SDOF system of equal or lesser strength can always be found to match or better the response of an elasto‐plastic hysteretic SDOF system in terms of displacement ductility and without incurring any residual drift from the seismic event. Copyright © 2002 John Wiley & Sons, Ltd.     

Modal response analysis of multi‐support structures using a random vibration approach

A formulation is developed for modal response analysis of multi‐support structures using a random vibration approach. The spectral moments of the structural response are rigorously decomposed into contributions from spectral moments of uncoupled modal responses. An advantage of the proposed formulation is that the total dynamic response can be obtained on the basis of mode by mode uncoupled analyses. The contributions to the total response from modal responses under individual support ground motions and under cross‐correlated pairs of support ground motions can be recognized explicitly. The application and performance of the formulation is illustrated by means of an example using a well‐established coherency spectrum model and widely known power spectra models, such as white noise and Kanai–Tajimi. The first three spectral moments of displacement, shear, and bending moment responses are computed, showing that the formulation produces the same results as the exact solution. Copyright © 2015 John Wiley & Sons, Ltd.     

Assessment of a capacity spectrum seismic design approach against cyclic and seismic experiments on full‐scale precast RC structures

Within the last decades, simplified methods alternative to dynamic nonlinear analysis have been developed to estimate the seismic performance of structures toward a performance‐oriented design. Considering drift as the main parameter correlated with structural damage, its estimation is of main importance to assess the structural performance. While traditional force‐based design deals with calibrated force reduction factors based on the expected structural ductility, other methods are based on the definition of a viscous damping factor defined as a function of the expected energy dissipated by the structure. An example is the capacity spectrum method. This method can be applied even without any a priori calibration or designer arbitrariness. This allows considering several peculiarities of the seismic behavior of precast structures, which may be influenced by nontraditional hysteresis of connections and members, interaction with the cladding panels, P‐δ effects, etc. The paper aims at verifying the soundness and accuracy of this method through the comparison of its predictions against the results of cyclic and pseudodynamic tests on precast structures, including single‐ and multistory buildings either stiff or flexible, obtained on full‐scale building prototypes tested within the framework of recent research projects (namely, “Precast Structures EC8,” “Safecast,” and “Safecladding”). Two simple methodologies of determination of the equivalent viscous damping from a force‐displacement cycle, based on the dissipated energy in relation to 2 different estimates of the elastic strain energy, are addressed and compared. Comments on the possible use of this procedure for the estimation of the seismic performance of precast structures are provided.     

A response spectrum approach for seismic performance evaluation of actively controlled structures

To evaluate and measure the effectiveness of active control schemes in reducing the response of structures subjected to earthquake excitations, it is common to use recorded or artificially generated earthquakes as input motions. This paper introduces the response spectrum analysis to evaluate linear control systems for seismic inputs defined by code‐prescribed or site‐specific ground response spectra. Using such a method one can evaluate a control system in a single analysis for the ensemble of time histories that are represented by the input response spectra. The response spectrum analysis can also facilitate the implementation of comprehensive parametric studies. A generalized response spectrum method is used to analyse systems with non‐symmetrical matrices that are caused by the general nature of the control actions imposed on the structure. The application of the method is demonstrated on several numerical examples of a building structure where the control force is applied through an active tuned‐mass damper. Copyright © 2000 John Wiley & Sons, Ltd.     

A method for the transfer function matrix of combined primary–secondary systems using classical modal decomposition

An iterative method is presented to compute the transfer function matrix of combined primary–secondary systems for seismic response analysis. It accounts for non‐proportional damping and dynamic interaction of the combined system. A closed form sequence is developed for the iterative computation of the transfer function matrix. Such sequence is assembled using independently the real classical mode frequencies, shapes and damping ratios of the primary system, and the natural frequency and critical damping ratio of the SDOF secondary system. The necessary and sufficient condition for convergence of the sequence is given in the paper. The method is illustrated through a couple of examples, including one of an appendix connected to a multi‐storey shear building. Convergence of the method is thoroughly analysed and peak responses are obtained using a spectral density function approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Wavelet‐based non‐stationary seismic rocking response of flexibly supported tanks

The non‐stationary rocking response of liquid storage tanks under seismic base excitations including soil interaction has been developed based on the wavelet domain random vibration theory. The ground motion has been characterized through statistical functionals of wavelet coefficients of the ground acceleration history. The tank–liquid–foundation system is modelled as a multi‐degree‐of‐freedom (MDOF) system with both lateral and rocking motions of vibration of the foundation. The impulsive and convective modes of vibration of the liquid in the tank have been considered. The wavelet domain coupled dynamic equations are formulated and then solved to get the expressions of instantaneous power spectral density function (PSDF) in terms of functionals of input wavelet coefficients. The moments of the instantaneous PSDF are used to obtain the stochastic responses of the tank in the form of coefficients of hydrodynamic pressure, base shear and overturning base moment for the largest expected peak responses. Parametric variations are carried out to study the effects of various governing parameters like height of liquid in the tank, height–radius ratio of the tank, ratio of total liquid mass to mass of foundation, and shear wave velocity in the soil medium, on the responses of the tank. Copyright © 2003 John Wiley & Sons, Ltd.     

Bi‐directional coupled tuned mass dampers for the seismic response control of two‐way asymmetric‐plan buildings

This paper proposes bi‐directional coupled tuned mass dampers (BiCTMDs) for the seismic response control of two‐way asymmetric‐plan buildings subjected to bi‐directional ground motions. The proposed BiCTMD was developed from the three‐degree‐of‐freedom modal system, which represents the vibration mode of a two‐way asymmetric‐plan building. The performance of the proposed BiCTMD for the seismic response control of elastic two‐way asymmetric‐plan buildings was verified by investigating the reductions of the amplitudes of the associated frequency response functions. In addition, the investigation showed that the proposed BiCTMD is effective in reducing the seismic damage of inelastic asymmetric‐plan buildings. Therefore, the BiCTMD is an effective approach for the seismic response control of both elastic and inelastic two‐way asymmetric‐plan buildings. Copyright © 2010 John Wiley & Sons, Ltd.     

Nonstationary stochastic response of structural systems equipped with nonlinear viscous dampers under seismic excitation

Nonlinear viscous dampers are supplemental devices widely used for enhancing the performance of structural systems exposed to seismic hazard. A rigorous evaluation of the effect of these damping devices on the seismic performance of a structural system should be based on a probabilistic approach and take into account the evolutionary characteristics of the earthquake input and of the corresponding system response. In this paper, an approximate analytical technique is proposed for studying the nonstationary stochastic response characteristics of hysteretic single degree of freedom systems equipped with viscous dampers subjected to a fully nonstationary random process representing the seismic input. In this regard, a stochastic averaging/linearization technique is utilized to cast the original nonlinear stochastic differential equation of motion into a simple first‐order nonlinear ordinary differential equation for the nonstationary system response variance. In comparison with standard linearization schemes, the herein proposed technique has the significant advantage that it allows to handle realistic seismic excitations with time‐varying frequency content. Further, it allows deriving a formula for determining the nonlinear system response evolutionary power spectrum. By this way, ‘moving resonance’ effects, related to both the evolutionary seismic excitation and the nonlinear system behavior, can be observed and quantified. Several applications involving various system and input properties are included. Furthermore, various response parameters of interest for the seismic performance assessment are considered as well. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the proposed technique. Copyright © 2014 John Wiley & Sons, Ltd.     

Effective use of seismic response envelopes for reinforced concrete structures

By exploiting the theory of the response envelopes formulated by Menun and Der Kiureghian [Envelopes for seismic response vectors. I–Theory, J. Str. Engrg. 2000; 126(3); 467–473], an algorithmic approach for seismic analysis of reinforced concrete frames is presented. It aims to fill a gap between research on spectral analysis of structures and current design practice in which the use of seismic response envelopes, available since early 2000s, is hampered by the lack of efficient and robust implementations. The proposed strategy is based on customary features (such as modal shapes and response spectra) currently adopted in professional practice, and it takes advantage of recently published formulations for the evaluation of stress resultants in arbitrarily shaped reinforced concrete cross‐sections subjected to axial force and biaxial bending. Numerical applications are illustrated in order to show the procedure's efficiency and effectiveness. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic response of multi‐supported structures by proper orthogonal decomposition

The seismic analysis of structures is usually carried out considering the ground motion as fully‐correlated in space and determining the structural response by pseudo‐deterministic methods such as the response spectrum technique. Actually, the partial correlation of the seismic acceleration may influence heavily the behaviour of spatially extended structures, such as bridges, viaducts or pipelines. In order to take its partial correlation into account, the seismic ground motion is schematized as a stochastic process dependent on time and on space; the hypotheses of stationarity and homogeneity are used to obtain simple and general results. The influence of the partial correlation of the seismic ground motion on the structural response is investigated by introducing suitable Equivalent Spectra. The acceleration of the support‐points of the structure is represented by the Proper Orthogonal Decomposition (POD), defining the modes of the earthquake. The method is formulated for any kind of multi‐degree‐of‐freedom system and is applied, as a case study, to an ideal single‐storey multi‐supported frame with an axially rigid beam. In the case of two supports, the POD decouples the pseudo‐static and the dynamic contributions to the structural response. This property is preserved for structural systems with many supports, where only the lower modes of the earthquake, usually the first two POD modes, are responsible for the structural response. Copyright © 2003 John Wiley & Sons, Ltd.     

Application of wavelet theory to identify yielding in seismic response of bi‐linear structures

The time–frequency and the time‐scale analysis methods are used in this paper to identify the dynamic characteristics of non‐linear seismic response of structural systems with single degree of freedom (SDOF) and multiple degrees of freedom (MDOF). Based on the floor acceleration response time histories of bi‐linear SDOF and MDOF structures, the current study compares the results of system identification using the short‐time Fourier transform (STFT), continuous wavelet transform (CWT) and discrete wavelet transform (DWT) methods. The aim is to identify the frequency variations and the time at on‐set of yielding and unloading of a bi‐linear structural system during seismic response. The results demonstrate that the CWT method is better than the STFT method in both time and frequency resolutions, and that the DWT method is the best at detecting the time at on‐set of yielding and unloading. Combining the results of CWT and DWT methods therefore provides accurate information of both frequency variations and yielding time in non‐linear seismic response. To alleviate the problems associated with noise‐contaminated signals, e.g. seismic response data recorded on site, the study suggests that low‐pass filtering be carried out before applying the DWT method to decompose the signals into multiple levels of details. Copyright © 2001 John Wiley & Sons, Ltd.     

Out‐of‐plane seismic response of vertically spanning URM walls connected to flexible diaphragms

A simplified numerical model was used to investigate the out‐of‐plane seismic response of vertically spanning unreinforced masonry (URM) wall strips. The URM wall strips were assumed to span between two flexible diaphragms and to develop a horizontal crack above the wall mid‐height. Three degrees of freedom were used to accommodate the wall displacement at the crack height and at the diaphragm connections, and the wall dynamic stability was studied. The equations of dynamic motion were obtained using principles of rocking mechanics of rigid bodies, and the formulae were modified to include semi‐rigid wall behaviour. Parametric studies were conducted that included calculation of the wall response for different values of diaphragm stiffness, wall properties, applied overburden, wall geometry and earthquake ground motions. The results of the study suggest that stiffening the horizontal diaphragms of typical low‐rise URM buildings will amplify the out‐of‐plane acceleration demand imposed on the wall and especially on the wall–diaphragm connections. It was found that upper‐storey walls connected to two flexible diaphragms had reduced stability for applied earthquake accelerograms having dominant frequency content that was comparable with the frequency of the diaphragms. It was also found that the applied overburden reduced wall stability by reducing the allowable wall rotations. The results of this study suggest that the existing American Society of Civil Engineers recommendations for assessment of vertically spanning walls overestimate the stability of top‐storey walls in multi‐storey buildings in high‐seismic regions or for walls connected to larger period (less stiff) diaphragms. Copyright © 2015 John Wiley & Sons, Ltd.