Seismic analysis of multiply supported secondary systems with dynamic interaction effects

For a proper response spectrum analysis of a secondary system with multiple supports, the seismic inputs are required to be defined in terms of the auto and cross floor response spectra. If no feed-back or interaction effect from the secondary system to its supporting primary structure is suspected, these inputs can be developed by a direct analysis of the supporting structure alone. However, sometimes the effect of the interaction on the secondary system response can be quite significant. Herein, a method is developed to incorporate the feed-back effect, through proper modification of the interaction-free floor spectrum inputs. The interaction coefficients are used to effect such modifications in different floor spectral quantities. A procedure for the calculation of the interaction coefficients is proposed. The modified floor spectra when used as inputs to the secondary system do introduce the interaction effect in the secondary system response. A successful application of this method is demonstrated by numerical examples of secondary systems with three different secondary-to-primary system mass ratios.     

Median floor acceleration spectra of linear structures with uncertain properties

Response parameters used to estimate nonstructural damage differ depending on whether deformation‐sensitive or acceleration‐sensitive components are considered. In the latter case, seismic demand is usually represented through floor spectra, that is response spectra in terms of pseudo‐acceleration, which are calculated at the floor levels of the structure where the nonstructural components are attached to. Objective of this paper is to present a new spectrum‐to‐spectrum method for calculating floor acceleration spectra, which is able to explicitly account for epistemic uncertainties in the modal properties of the supporting structure. By using this method, effects on the spectra of possible variations from nominal values of the periods of vibration of the structure can be estimated. The method derives from the extension of closed‐form equations recently proposed by the authors to predict uniform hazard floor acceleration spectra. These equations are built to rigorously account for the input ground motion uncertainty, that is the record‐to‐record variability of the nonstructural response. In order to evaluate the proposed method, comparisons with exact spectra obtained from a standard probabilistic seismic demand analysis, as well as spectra calculated using the Eurocode 8 equation, are finally shown. Copyright © 2017 John Wiley & Sons, Ltd.     

Seismic response analysis of structure–equipment systems with non-classical damping effects

A method is presented to obtain the exact complex-valued eigenproperties of a classically damped structure and equipment system. The non-classically damped character of the combined system as well as the effect of dynamic interaction between primary structure and equipment are properly included in the calculation of these eigenproperties. It is necessary only to know the classical modal properties of the structure and, of course, the equipment characteristics. The eigenvalues are obtained as the solution of a non-linear equation which can be easily solved by the Newton–Raphson algorithm. Once the eigenvalues are known, the corresponding eigenvectors are obtained from simple closed-form expressions. The method can be used equally effectively with light as well as heavy equipment. Numerical results demonstrating the effectiveness of the method are presented. A procedure which utilizes the complex-valued eigenproperties is developed for calculating the floor response spectra directly from the ground spectra. Numerical results of floor response spectra obtained from this procedure are presented. The floor spectra calculated by this approach include the structure–equipment interaction effect.     

Uniform hazard floor acceleration spectra for linear structures

This paper presents a practical method to compute uniform hazard floor acceleration spectra for linear oscillators attached to a linear structure. The method builds on a probabilistic seismic demand model that relates the acceleration response of the oscillator with that of the generic mode of vibration of the supporting structure. Interaction between oscillator and structure is ignored. Independency of the model on the specific characteristics of seismic hazard at the site is shown. By using the method floor spectra are determined through a closed‐form expression, given the mean annual frequency of interest, the damping ratio of the oscillators, the modal properties of the structure, and three uniform hazard spectra representing seismic hazard at the site. Copyright © 2016 John Wiley & Sons, Ltd.     

Consistent floor response spectra for performance-based seismic design of nonstructural elements

The achievement of adequate performance objectives for buildings under increasing seismic intensities is not only related to the performance of structural members but also to the behavior of nonstructural elements. The need to properly design nonstructural elements for earthquakes has been largely demonstrated in the last few years and has become an important objective within the earthquake engineering community. A crucial aspect in the proper design of nonstructural elements is the definition of the seismic demand in terms of both absolute acceleration and relative displacement floor response spectra. In the first part of this study, relative displacement and absolute acceleration floor response spectra were computed for four reinforced concrete moment-resisting archetype frames via dynamic time-history analyses and were compared with floor response spectra predicted by means of two recent simplified methodologies available in the literature. It was observed that one of the existing methodologies is generally unable to predict consistent absolute acceleration and relative displacement floor response spectra. An improved procedure is developed for estimating consistent floor response spectra for building structures subjected to low and medium-high seismic intensities. This new procedure improves the predictions of a relative displacement floor response spectrum by constraining its ordinates at long nonstructural periods to the expected peak absolute displacement of the floor. The resulting acceleration and relative displacement response spectra are then consistently related by the well-known pseudo-spectral relationship over the entire nonstructural period range. The effectiveness of the proposed methodology was appraised against floor response spectra computed from nonlinear time-history analyses.     

Generation of floor response spectra including oscillator-structure interaction

A method is presented for generating floor response spectra for aseismic design of equipment attached to primary structures. The method accurately accounts for tuning, interaction and non-classical damping, which are inherent characteristics of composite oscillator-structure systems. Modal synthesis and perturbation techniques are used to derive the modal properties of the composite system in terms of the known properties of the structure and the oscillator. Floor spectra are generated directly in terms of these derived properties and the input ground response spectrum using modal combination rules that account for modal correlations and non-classical damping. The computed spectra, in general, are considerably lower than conventional floor response spectra due to the effect of interaction. They provide more realistic and economical criteria for design of equipment. The method is accurate to the order of perturbation and is computationally efficient, as it avoids time-history analysis and does not require numerical eigenvalue evaluation of the composite oscillator-structure system. The results of a parametric study demonstrate the accuracy of the method and illustrate several key features of floor response spectra.     

Floor response spectra for base-isolated multi-storey structures

A study of floor response spectra for a base-isolated multi-storey structure under sinusoidal and seismic ground excitations is carried out. Several base isolation systems including the laminated rubber bearing, the pure-friction, the resilient-friction, the Électricité de France and the sliding resilient-friction systems are considered. A sinusoidal ground acceleration and several earthquake accelerograms (including those of El Centro 1940, Pacoima Dam 1971 and Mexico City 1985) are used to evaluate the floor response spectra. The characteristics of the spectra generated by different base isolation systems are studied, and the results are compared with those for the fixed-base structure. It is shown that the structural contents can be protected against earthquakes by the use of properly designed base isolation systems. In particular, the laminated rubber bearing system appears to be remarkably effective in protecting the secondary systems under a variety of conditions.     

Effect of irregular structural configuration on floor acceleration demand in hill‐side buildings

A suite of reinforced‐concrete frame buildings located on hill sides, with 2 different structural configurations, viz step‐back and split‐foundation, are analyzed to study their floor response. Both step‐back and split‐foundation structural configurations lead to torsional effects in the direction across the slope due to the presence of shorter columns on the uphill side. Peak floor acceleration and floor response spectra are obtained at each storey's center of rigidity and at both its stiff and flexible edges. As reported in previous studies as well, it is observed that the floor response spectra are better correlated with the ground response spectrum. Therefore, the floor spectral amplification functions are obtained as the ratio of spectral ordinates at different floor levels to the one at the ground level. Peaks are observed in the spectral amplification functions corresponding to the first 2 modes in the upper portion of the hill‐side buildings, whereas a single peak corresponding to a specific kth mode of vibration is observed on the floors below the uppermost foundation level. Based on the numerical study for the step‐back and split‐foundation hill‐side buildings, simple floor spectral amplification functions are proposed and validated. The proposed spectral amplification functions take into account both the buildings' plan and elevation irregularities and can be used for seismic design of acceleration‐sensitive nonstructural components, given that the supporting structure's dynamic characteristics, torsional rotation, ground‐motion response spectrum, and location of the nonstructural components within the supporting structure are known, because current code models are actually not applicable to hill‐side buildings.     

Probabilistic seismic demand model for nonstructural components

Past earthquakes have shown the importance for critical facilities to remain functional during seismic events. In the performance assessment of these facilities, it is therefore essential to accurately evaluate the seismic demand of nonstructural components. Evaluation of these components is also important when estimation of nonstructural repair costs is a concern. In this paper, the use of a multivariate demand model for nonstructural components is proposed, in which demand is expressed in terms of both interstory drifts and floor acceleration spectra. A model is built using statistics of the demand vector derived from the results of a limited number of inelastic response history analyses of a structure. The model is then used to simulate any number of additional realizations of the demand vector required for an accurate estimation of the probability of functionality loss. A new proposal for a predictive equation to generate approximate realizations of floor response spectra is presented. A reinforced concrete frame is selected as an illustrative example to show the implementation of the probabilistic seismic demand model and to evaluate the proposed predictive equation for the floor response spectra. The results of the case study are used to demonstrate the importance of accounting for the correlation among the demand parameters when realizations of the seismic demand of nonstructural components are simulated. Copyright © 2015 John Wiley & Sons, Ltd.     

Eigenproperties of non-classically damped primary structure and equipment systems by a perturbation approach

Closed-form expressions are obtained to calculate the approximate complex eigenvalues and eigenvectors of a system composed of a non-classically damped primary structure and a single degree of freedom oscillator. The expressions are obtained through a systematic second order perturbation analysis of a transformed eigenvalue problem of the combined system. The possibility of tuning between the structure and equipment is considered. The dynamic properties of the combined system are derived in terms of the complex eigenvalues and eigenvectors of the supporting structure and the frequency, mass and damping ratio of the equipment. Examples demonstrating the accuracy of the expressions for the eigenvalues and eigenvectors are presented. These eigenproperties are used for generation of floor response spectra for non-classically damped structures to incorporate the dynamic interaction effects between the structure and equipment.     

A method for the direct estimation of floor acceleration spectra for elastic and inelastic MDOF structures

This paper deals with floor acceleration spectra, which are used for the seismic design and assessment of acceleration‐sensitive equipment installed in buildings. In design codes and in practice, not enough attention has been paid to the seismic resistance of such equipment. An ‘accurate’ determination of floor spectra requires a complex and quite demanding dynamic response history analysis. The purpose of the study presented in this paper is the development of a direct method for the determination of floor acceleration spectra, which enables their generation directly from the design spectrum of the structure, by taking into account the structure's dynamic properties. The method is also applicable to inelastic structures, which can greatly improve the economic aspects of equipment design. A parametric study of floor acceleration spectra for elastic and inelastic single‐degree‐of‐freedom (SDOF) and multiple‐degree‐of‐freedom structures was conducted by using (non)linear response history analysis. The equipment was modelled as an elastic single‐degree‐of‐freedom system. The proposed method was validated by comparing the results obtained with the more accurate results obtained in a parametric study. Due to its simplicity, the method is an appropriate tool for practice. In the case of inelastic structural behaviour, the method should be used in combination with the N2 method, or another appropriate method for simplified nonlinear structural analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

Strength-reduction factors for the design of light nonstructural elements in buildings

Strength-reduction factors that reduce ordinates of floor spectra acceleration due to nonlinearity in the secondary system are investigated. In exchange for permitting some inelastic deformation to occur in the secondary system or its supports, these strength reduction factors allow to design the nonstructural elements or their supports for lateral forces that are smaller than those that would be required to maintain them elastically during earthquakes. This paper presents the results of a statistical analysis on component strength-reduction factors that were computed considering floor motions recorded on instrumented buildings in California during various earthquakes. The effect of yielding in the component or its anchorage/bracing in offering protection against excessive component acceleration demands is investigated. It is shown that strength-reduction factors computed from floor motions are significantly different from those computed from ground motions recorded on rock or on firm soils. In particular, they exhibit much larger reductions for periods tuned or nearly tuned to the dominant modal periods of the building response. This is due to the large differences in frequency content of ground motions and floor motions, with the former typically characterized by wide-band spectra whereas the latter are characterized by narrow-band spectra near periods of dominant modes in the response of the building. Finally, the study provides approximate equations to estimate component strength-reduction factors computed through nonlinear regression analyses.     

Nonlinear rooftop tuned mass damper frame for the seismic retrofit of buildings

Numerical studies of existing buildings demonstrate the effectiveness of nonlinear/inelastic rooftop tuned mass damper frames (NRTMDF) used as a retrofit for reducing seismic response. The technique utilizes a rooftop penthouse as a tuned mass damper with mass incorporated as the roof deck of the penthouse while targeted nonlinearity and energy dissipation are introduced through buckling restrained braces (BRBs) linking the penthouse mass to the structure below. The writers summarize numerical studies of ten existing buildings modified with a specifically tuned NRTMDF. The studies demonstrate the effectiveness of the technique that stems from elastic and transient inelastic period shifts enabled by the damper coupled with targeted energy dissipation in the penthouse BRBs. Numerical simulations using response nonlinear time‐history analysis techniques show that for many structures and sites, the NRTMDF decreases peak transient response and overall seismic demand of the original structure. The technique also reduces seismic demand on nonstructural elements and components, manifested as reductions in floor acceleration spectra. Energy methods show that the approach enables significant reductions in energy demand on the original structure through the complete earthquake acceleration history. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiply supported secondary systems part I: Response spectrum analysis

A response spectrum procedure is developed for seismic analysis of multiply supported secondary systems. The formulation is based on the random vibration analysis of structural systems subjected to correlated inputs applied at several supports. For a proper response spectrum analysis of a multiple support system, the support inputs are required to be defined in terms of the auto and cross pseudo-acceleration and relative velocity floor response spectra. Also information about the floor displacements and velocities as well as their correlations is required. The response of the secondary system is expressed as a combination of the dynamic and pseudo-static response components. The dynamic component is associated with the inertial effects of the support accelerations, whereas the pseudo-static component is due to the displacement of the supports relative to each other. Herein, the correlation between these two parts of the response is included through a term called the cross response component. Each of these components of the response can be calculated by a response spectrum method. The application of the proposed method is demonstrated by numerical examples.     

楼板谱研究述评

介绍了楼板谱方法的发展与研究现状。详细阐述了主附结构系统的相互作用、调谐、非经典阻尼、多点支撑等动力特性问题,分别介绍了传统楼板谱与新型楼板谱以及多维地震动下楼板谱的研究方法,给出了有待进一步研究的课题。     

Floor response spectra of a partially embedded seismically isolated nuclear plant

This paper deals with the effects of foundation embedment on the floor response spectra of big base isolated structures such as nuclear power plants. Analyses of a finite element model, representative of a real nuclear power plant, have been carried out. It has been demonstrated that, in agreement with previous work, base rocking excitation, induced by soil–structure interaction, may amplify the non-isolated modes׳ response and thus it must not be overlooked.     

考虑土-结构相互作用和岩土参数不确定性的核电厂结构地震响应分析

针对核电厂结构,在考虑土-结构相互作用(SSI)的情况下进行随机地震反应分析,探讨地基岩土参数的不确定性对反应堆厂房楼层反应谱(FRS)的影响。运用ANSYS软件模块建立核电厂(NPP)结构有限元模型,通过设置边界弹簧单元和阻尼装置来考虑SSI效应;并且通过设置具有概率意义的弹簧刚度和阻尼系数,来模拟土特性参数的不确定性。随机响应分析与确定性分析的结果对比,揭示了岩性地基条件下SSI效应对核电厂FRS的影响以及地基岩土参数不确定性对FRS的影响程度。研究表明,在岩性地基条件下,亦不应忽略SSI效应;考虑SSI效应的随机分析模型同确定性模型相比,二者的分析结果较为接近,两方法都可用于NPP的FRS敏感性分析评估之中,并可进行相互比照。     

Effect of viscous damping devices on the response of seismically isolated structures

Viscous and other damping devices are often used as elements of seismic isolation systems. Despite the widespread application of nonlinear viscous systems particularly in Japan (with fewer applications in the USA and Taiwan), the application of viscous damping devices in isolation systems in the USA progressed intentionally toward the use of supplementary linear viscous devices due to the advantages offered by these devices. This paper presents experimental results on the behavior of seismically isolated structures with low damping elastomeric (LDE) and single friction pendulum (SFP) bearings with and without linear and nonlinear viscous dampers. The isolation systems are tested within a six‐story structure configured as moment frame and then again as braced frame. Emphasis is placed both on the acquisition of data related to the structural system (drifts, story shear forces, and isolator displacements) and on non‐structural systems (floor accelerations, floor spectral accelerations, and floor velocities). Moreover, the accuracy of analytical prediction of response is investigated based on the results of a total of 227 experiments, using 14 historic ground motions of far‐fault and near‐fault characteristics, on flexible moment frame and stiff braced frame structures isolated with LDE or SFP bearings and linear or nonlinear viscous dampers. It is concluded that when damping is needed to reduce displacement demands in the isolation system, linear viscous damping results in the least detrimental effect on the isolated structure. Moreover, the study concludes that the analytical prediction of peak floor accelerations and floor response spectra may contain errors that need to be considered when designing secondary systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic response of nonstructural components in case of nonlinear structures based on floor response spectra method

This paper investigates the response of nonstructural components in the presence of nonlinear behavior of the primary structure using floor response spectra method (FRS). The effect of several parameters such as initial natural frequency of the primary structure, natural frequency of the nonstructural components (subsystem), strength reduction factor and hysteretic model have been studied. A database of 164 registered ground acceleration time histories from the European Strong-Motion Database is used. Results are presented in terms of amplification factor and resonance factor. Amplification factor quantifies the effect of inelastic deformations of the primary structure on subsystem response. Resonance factor quantifies the variation of the subsystem response considering the primary structure acceleration. Obtained results differed from precedent studies, particularly for higher primary structure periods. Values of amplification factor are improved. Obtained results of resonance factor highlight an underestimation of peak values according to current design codes such as Eurocode 8. Therefore a new formulation is proposed.