AP/VP specific inelastic displacement ratio for seismic response estimation of structures

In this study, two new site specific statistical equations are proposed to estimate the inelastic displacement ratio, C₁ of structures subjected to far fault (FF) and near fault (NF) ground motions. The proposed equations consider the effects of fundamental vibration period of the structure, T, lateral strength ratio, R and frequency content of the design earthquake record represented by the A_p/V_p ratio (or T₀ = 2π/A_p/V_p), which is a function of the earthquake magnitude, distance to fault, faulting mechanism and site class. It was observed that the C₁ values obtained from the proposed equations are in good agreement with the calculated results. The flare of the plotted C₁ vs. T/T₀ curves enables the proposed equations to cover nearly all the calculated C₁ data range and give satisfactory results. However, the curves obtained using the C₁ equations of several codes and those available in the literature do not cover the whole calculated C₁ data range and generally give unconservative results (smaller C₁ values) especially in the shorter period range. For the longer period range, the predictions of C₁ obtained from the proposed equation and the ones available in the literature are in good agreement with the calculated C₁ data. Copyright © 2014 John Wiley & Sons, Ltd.     

Simplified inelastic seismic analysis of base‐isolated structures using the N2 method

In the paper a simplified nonlinear method has been applied to the analysis of base‐isolated structures. In the first part, a three‐linear idealization of the capacity curve is proposed. The initial stiffness is defined based on the first yielding point in the superstructure, whereas the secondary slope depends on the failure mechanism of the superstructure. A consequence is a much more pronounced secondary slope, which does not correspond to the presumptions used in the originally proposed N2 method. A parametric nonlinear dynamic study of single degree of freedom systems with different hardening slopes and damping has been performed for an ensemble of seven EC8 spectrum‐compatible artificial accelerograms. It was concluded that, in the long‐period range, the equal displacement rule could be assumed also for the proposed systems with non‐zero post‐yield stiffness. In the second part, the proposed idealization was used for the analysis of isolated RC frame buildings that were isolated with different (lead) rubber‐bearing isolation systems. The stiffness of the isolators was selected for three different protection levels and for three different ground motion intensities, which have resulted in elastic as well as moderately and fully damaged superstructure performance levels. Three different lateral load distributions were investigated. It was observed that a triangular distribution, with an additional force at the base, works best in the majority of practical cases. It was concluded that the N2 method can, in general, provide a reasonably accurate prediction of the actual top displacement, as well as of the expected damage to the superstructure. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparative response and performance of base‐isolated and fixed‐base structures

A building with a seismic isolation system, in an earthquake, is recognized as producing substantially smaller accelerations and deformations compared with a building that use other systems. This type of system is therefore expected to better protect the building's nonstructural components, equipment, and other contents that are essential for the activities conducted in the building. Unlike many available studies on building responses, only a small number of studies on a buildings' nonstructural component responses are available, and no study has directly addressed building performance with regard to nonstructural component protection. This paper therefore measures the performance of various seismically isolated buildings. Specifically, the effects of important structural parameters, namely, isolation stiffness, isolation damping ratio, and number of stories on the response of base‐isolated structures are investigated parametrically. Ground motions with 2% exceedence in 50years Maximum Considered Earthquake (MCE) are used. Performance is compared with that of fixed‐base structures in order to present data that will be useful in justifying the more costly technology. The buildings are 3, 9, and 20 stories, represented by MDOF shear‐beam models. As examples of displacement‐sensitive and acceleration‐sensitive components, partition walls and ceilings are considered, respectively. The Pacific Earthquake Engineering Research Center performance‐based earthquake engineering methodology is adopted to evaluate the failure return periods of the examples based on their available fragility curves. In addition, the curves are varied hypothetically to understand the sensitivity of the return period to the curve features. Then, the median and dispersion of fragility curves required to satisfy the components' desired failure return period are obtained. Copyright © 2015 John Wiley & Sons, Ltd.     

Probabilistic estimation of maximum inelastic displacement demands for performance‐based design

A probabilistic approach to estimate maximum inelastic displacement demands of single‐degree‐of‐freedom (SDOF) systems is presented. By making use of the probability of exceedance of maximum inelastic displacement demands for given maximum elastic spectral displacement and the mean annual frequency of exceedance of elastic spectral ordinates, a simplified procedure is proposed to estimate mean annual frequencies of exceedance of maximum inelastic displacement demands. Simplifying assumptions are thoroughly examined and discussed. Using readily available elastic seismic hazard curves the procedure can be used to compute maximum inelastic displacement seismic hazard curves and uniform hazard spectra of maximum inelastic displacement demands. The resulting maximum inelastic displacement demand spectra provide a more rational way of establishing seismic demands for new and existing structures when performance‐based approaches are used. The proposed procedure is illustrated for elastoplastic SDOF systems having known‐lateral strength located in a region of high seismicity in California. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamics of inelastic base‐isolated structures subjected to analytical pulse ground motions

Structural design code provisions worldwide prescribe relatively small seismic force reduction factors for seismically base‐isolated structures, making their response to design‐level earthquake excitation essentially elastic. This paper uses the method of dimensional analysis to prove that; in most cases, this is not a conservative design approach but a necessity that emerges from the dynamics of base‐isolated structures. It is shown that allowing typical base‐isolated structures to yield results in large displacement ductility demands for the structure. This phenomenon is caused by the change in the nature of the ground motion excitation as it is transmitted to the structure through the seismic base isolation system as well as by the change in the distribution of displacements between the structure and the isolation bearings caused by yielding of the isolated structure. Copyright © 2013 John Wiley & Sons, Ltd.     

Independent component regression for predicting the responses of biaxial base‐isolated buildings

This paper presents a regression model to predict the base displacement responses of biaxial base‐isolated buildings using independent component analysis. The model proposed utilizes multiple ground motion intensity measures from North American and Japanese earthquakes as inputs, and transforms them into an independent component space using independent component regression (ICR). Unlike other latent variable methods, such as principal component regression, ICR does not readily allow for dimensionality reduction of the components that do not contribute significantly to the explained variance of the original data set. Hence, a whitening‐step to transform the correlated variables into uncorrelated ones is introduced prior to performing ICR. Prediction results are presented and compared with the simulation results for two building models with increasing degree of complexity. The results show that the model based on ICR results in good estimates for the base displacement responses, and the standard errors remain relatively small and constant across a range of isolation periods. Copyright © 2009 John Wiley & Sons, Ltd.     

Inelastic displacement ratios for evaluation of existing structures

Results of a detailed statistical study of constant relative strength inelastic displacement ratios to estimate maximum lateral inelastic displacement demands on existing structures from maximum lateral elastic displacement demands are presented. These ratios were computed for single‐degree‐of‐freedom systems with different levels of lateral strength normalized to the strength required to remain elastic when subjected to a relatively large ensemble of recorded earthquake ground motions. Three groups of soil conditions with shear wave velocities higher than 180m/s are considered. The influence of period of vibration, level of lateral yielding strength, site conditions, earthquake magnitude, distance to the source, and strain‐hardening ratio are evaluated and discussed. Mean inelastic displacement ratios and those associated with various percentiles are presented. A special emphasis is given to the dispersion of these ratios. It is concluded that distance to the source has a negligible influence on constant relative strength inelastic displacement ratios. However, for periods smaller than 1s earthquake magnitude and soil conditions have a moderate influence on these ratios. Strain hardening decreases maximum inelastic displacement at a fairly constant rate depending on the level of relative strength for periods of vibration longer than about 1.0s while it decreases maximum inelastic displacement non‐linearly as the period of vibration shortens and as the relative‐strength ratio increases for periods of vibration shorter than 1.0s. Finally, results from non‐linear regression analyses are presented that provide a simplified expression to be used to approximate mean inelastic displacement ratios during the evaluation of existing structures built on firm sites. Copyright © 2003 John Wiley & Sons, Ltd.     

Improved evaluation of inelastic displacement demands for short‐period masonry structures

This work discusses the simplified estimation of earthquake‐induced nonlinear displacement demands as required by nonlinear static procedures, with particular attention on short‐period masonry structures. The study focuses on systems with fundamental periods between 0.1 and 0.5 s, for which inelastic amplification of the elastic displacement demand is more pronounced; hysteretic force‐displacement relationships characteristic of masonry structures are adopted, because these structures are more commonly found within the considered period range. Referring to the results of nonlinear dynamic analyses of single‐degree‐of‐freedom oscillators, some limitations of the Eurocode 8 and Italian Building Code formulations are first discussed, then an improved equation is calibrated that relates inelastic and elastic displacement demands. Numerical values of the equation parameters are obtained, considering the amount of hysteretic energy dissipation associated with various damage mechanisms observed in masonry structures. Safety factors are also calculated to determine several percentiles of the displacement demand. It is shown that the proposed equation can be extended to more dissipative systems. Finally, the same formulation is adapted to the estimation of seismic displacements when elastic analysis procedures are employed. Copyright © 2017 John Wiley & Sons, Ltd.     

Inelastic displacement demands in steel structures and their relationship with earthquake frequency content parameters

This paper deals with the estimation of peak inelastic displacements of SDOF systems, representative of typical steel structures, under constant relative strength scenarios. Mean inelastic deformation demands on bilinear systems (simulating moment resisting frames) are considered as the basis for comparative purposes. Additional SDOF models representing partially‐restrained and concentrically‐braced (CB) frames are introduced and employed to assess the influence of different force‐displacement relationships on peak inelastic displacement ratios. The studies presented in this paper illustrate that the ratio between the overall yield strength and the strength during pinching intervals is the main factor governing the inelastic deformations of partially‐restrained models and leading to significant differences when compared with predictions based on bilinear structures, especially in the short‐period range. It is also shown that the response of CB systems can differ significantly from other pinching models when subjected to low or moderate levels of seismic demand, highlighting the necessity of employing dedicated models for studying the response of CB structures. Particular attention is also given to the influence of a number of scalar parameters that characterise the frequency content of the ground motion on the estimated peak displacement ratios. The relative merits of using the average spectral period T_aver, mean period T_m, predominant period T_g, characteristic period T_c and smoothed spectral predominant period T_o of the earthquake ground motion, are assessed. This paper demonstrates that the predominant period, defined as the period at which the input energy is maximum throughout the period range, is the most suitable frequency content scalar parameter for reducing the variability in displacement estimations. Finally, noniterative equivalent linearisation expressions based on the secant period and equivalent damping ratios are presented and verified for the prediction of peak deformation demands in steel structures. Copyright © 2011 John Wiley & Sons, Ltd.     

Study on inelastic displacement ratio spectra for near-fault pulse-type ground motions

In displacement-based seismic design, inelastic displacement ratio spectra (IDRS) are particularly useful for estimating the maximum lateral inelastic displacement demand of a nonlinear SDOF system from the maximum elastic displacement demand of its counterpart linear elastic SDOF system. In this study, the characteristics of IDRS for near-fault pulse-type ground motions are investigated based on a great number of earthquake ground motions. The in? uence of site conditions, ratio of peak ground velocity (PGV) to peak ground acceleration (PGA), the PGV, and the maximum incremental velocity (MIV) on IDRS are also evaluated. The results indicate that the effect of near-fault ground motions on IDRS are signifi cant only at periods between 0.2 s - 1.5 s, where the amplifi cation can approach 20%. The PGV/PGA ratio has the most signifi cant in? uence on IDRS among the parameters considered. It is also found that site conditions only slightly affect the IDRS.     

On the evaluation of seismic response of structures by nonlinear static methods

In the most recent seismic codes, the assessment of the seismic response of structures may be carried out by comparing the displacement capacity, provided by nonlinear static analysis, with the displacement demand. In many cases the code approach is based on the N2 method proposed by Fajfar, which evaluates the displacement demand by defining, as an intermediate step, a single degree‐of‐freedom (SDOF) system equivalent to the examined structure. Other codes suggest simpler approaches, which do not require equivalent SDOF systems, but they give slightly different estimation of the seismic displacement demand. The paper points out the differences between the methods and suggests an operative approach that provides the same accuracy as the N2 method without requiring the evaluation of an equivalent SDOF system. A wide parametric investigation allows an accurate comparison of the different methods and demonstrates the effectiveness of the proposed operative approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Seismic reliability‐based ductility demand evaluation for inelastic base‐isolated structures with friction pendulum devices

The aim of this work is to propose seismic reliability‐based relationships between the strength reduction factors and the displacement ductility demand of nonlinear structural systems equipped with friction pendulum isolators (FPS) depending on the structural properties. The isolated structures are described by employing an equivalent 2dof model characterized by a perfectly elastoplastic rule to account for the inelastic response of the superstructure, whereas, the FPS behavior is described by a velocity‐dependent model. An extensive parametric study is carried out encompassing a wide range of elastic and inelastic building properties, different seismic intensity levels and considering the friction coefficient as a random variable. Defined a set of natural seismic records and scaled to the seismic intensity corresponding to life safety limit state for L'Aquila site (Italy) according to NTC08, the inelastic characteristics of the superstructures are designed as the ratio between the average elastic responses and increasing strength reduction factors. Incremental dynamic analyses (IDAs) are developed to evaluate the seismic fragility curves of both the inelastic superstructure and the isolation level assuming different values of the corresponding limit states. Integrating the fragility curves with the seismic hazard curves related to L'Aquila site (Italy), the reliability curves of the equivalent inelastic base‐isolated structural systems, with a design life of 50 years, are derived proposing seismic reliability‐based regression expressions between the displacement ductility demand and the strength reduction factors for the superstructure as well as seismic reliability‐based design (SRBD) abacuses useful to define the FPS properties. Copyright © 2016 John Wiley & Sons, Ltd.     

Influence of FPS bearing properties on the seismic performance of base‐isolated structures

The paper analyzes the influence of friction pendulum system (FPS) isolator properties on the seismic performance of base‐isolated building frames. The behavior of these systems is analyzed by employing a two‐degree‐of‐freedom model accounting for the superstructure flexibility, whereas the FPS isolator behavior is described by adopting a widespread model that considers the variation of the friction coefficient with the velocity. The uncertainty in the seismic input is taken into account by considering a set of natural records with different characteristics scaled to increasing intensity levels. The variation of the statistics of the response parameters relevant to the seismic performance is investigated through the nondimensionalization of the motion equation and an extensive parametric study carried out for different isolator and system properties. The proposed approach allows to explore a wide range of situations while limiting the required nonlinear response history analyses. Two case studies consisting of base‐isolated building frames described as shear‐type systems are finally investigated in order to demonstrate the capabilities of the proposed simplified model in unveiling the essential characteristics of the performance of buildings isolated with FPS bearings. Copyright © 2015 John Wiley & Sons, Ltd.     

Near-fault acceleration pulses and non-acceleration pulses: Effects on the inelastic displacement ratio

Near-fault ground motions can impose particularly high seismic demands on the structures due to the pulses that are typically observed in the velocity time-histories. The velocity pulses can be further categorized into either a distinct acceleration pulse (acc-pulse) or a succession of high-frequency, one-sided acceleration spikes (non-acc-pulse). The different characteristics of velocity pulses imply different frequency content of the ground motions, potentially causing different seismic effects on the structures. This study aims to investigate the characteristics of the two types of velocity pulses and their impacts on the inelastic displacement ratio (C_R) of single-degree-of-freedom systems. First, a new method that enables an automated classification of velocity pulses is used to compile a ground motion dataset which consists of 74 acc-pulses and 45 non-acc-pulses. Several intensity measures characterizing different seismological features are then compared using the two groups of records. Finally, the influences of acc-pulses and non-acc-pulses on the C_R spectra are studied; the effects of pulse period and hysteretic behavior are also considered. Results indicate that the characteristics of the two types of velocity pulses differ significantly, resulting in clearly distinct C_R spectral properties between acc-pulses and non-acc-pulses. Interestingly, mixing acc-pulses and non-acc-pulses can lead to local “bumps” that were found in the C_R spectral shape by previous studies. The findings of this study highlight the importance of distinguishing velocity pulses of different types when selecting near-fault ground motions for assessing the nonlinear dynamic response of structures.     

A simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures

A versatile, simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures is discussed in this work. A probabilistic foundation is used to address the various sources of uncertainties, either excitation or structural, and to characterize seismic risk. This risk is given, in this stochastic setting, by some statistics of the system response over the adopted probability models and stochastic simulation is implemented for its evaluation. An efficient, sampling‐based approach is also introduced for establishing a probabilistic sensitivity analysis to identify the importance of each of the uncertain model parameters in affecting the overall risk. This framework facilitates use of complex models for the structural system and the excitation. The adopted structural model explicitly addresses nonlinear characteristics of the isolators and of any supplemental dampers, and the effect of seismic pounding of the base to the surrounding retaining walls. An efficient stochastic ground motion model is also discussed for characterizing future near‐fault ground motions and relating them to the seismic hazard for the structural site. An illustrative example is presented that emphasizes the results from the novel probabilistic sensitivity analysis and their dependence on seismic pounding occurrences and on addition of supplemental dampers. Copyright © 2011 John Wiley & Sons, Ltd.     

On the inelastic torsional response of single‐storey structures under bi‐axial excitation

An attempt has been made to explore the general trends in the seismic response of plan‐asymmetric structures without any restrictions imposed by a particular code. Systems with structural elements in both orthogonal directions under bi‐directional excitation were studied. Idealized single‐storey models with bi‐axial eccentricity were employed. The systems were torsionally stiff and, in the majority of cases, mass‐eccentric. The main findings are: in general, inelastic torsional response is qualitatively similar to elastic torsional response. Quantitatively, the torsional effect on the flexible side, expressed as an increase of displacements due to torsion, decreases slightly with increasing plastic deformation, unless the plastic deformations are small. The response on the stiff side generally strongly depends on the effect of several modes of vibration and on the influence of the ground motion in the transverse direction. These influences depend on the structural and ground motion characteristics in both directions. Reduction of displacements due to torsion, typical for elastic torsionally stiff structures, usually decreases with increasing plastic deformations. As an additional effect of large plastic deformations, a flattening of the displacement envelopes in the horizontal plane usually occurs, indicating that torsional effects in the inelastic range are generally smaller than in the elastic range. The dispersion of the results of inelastic torsional response analysis is generally larger than that of elastic analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Inelastic displacement ratios for evaluation of structures built on soft soil sites

This paper summarizes the results of a comprehensive statistical study aimed at evaluating peak lateral inelastic displacement demands of structures with known lateral strength and stiffness built on soft soil site conditions. For that purpose, empirical information on inelastic displacement ratios which are defined as the ratio of peak lateral inelastic displacement demands to peak elastic displacement demands are investigated. Inelastic displacement ratios were computed from the response of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to 118 earthquake ground motions recorded on bay‐mud sites of the San Francisco Bay Area and on soft soil sites located in the former lake‐bed zone of Mexico City. Mean inelastic displacement ratios and their corresponding scatter are presented for both ground motion ensembles. The influence of period of vibration normalized by the predominant period of the ground motion, the level of lateral strength, earthquake magnitude, and distance to the source are evaluated and discussed. In addition, the effects of post‐yield stiffness and of stiffness and strength degradation on inelastic displacement ratios are also investigated. It is concluded that magnitude and distance to the source have negligible effects on constant‐strength inelastic displacement ratios. Results also indicate that weak and stiffness‐degrading structures in the short spectral region could experience inelastic displacement demands larger than those corresponding to non‐degrading structures. Finally, a simplified equation obtained using regression analyses aimed at estimating mean inelastic displacement ratios is proposed for assisting structural engineers in performance‐based assessment of structures built on soft soil sites. Copyright © 2006 John Wiley & Sons, Ltd.     

Residual displacement ratios for assessment of existing structures

Results of an analytical study aimed at evaluating residual displacement ratios, C_r, which allow the estimation of residual displacement demands from maximum elastic displacement demands is presented. Residual displacement ratios were computed using response time‐history analyses of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to an ensemble of 240 earthquake ground motions recorded in stations placed on firm sites. The results were statistically organized to evaluate the influence of the following parameters: period of vibration, level of relative lateral strength, site conditions, earthquake magnitude, and distance to the source. In addition, the influence of post‐yield stiffness ratio in bilinear systems and of the unloading stiffness in stiffness‐degrading systems was also investigated. A special emphasis is given to the uncertainty of these ratios. From this study, it is concluded that mean residual displacement ratios are more sensitive to changes in local site conditions, earthquake magnitude, distance to the source range and hysteretic behaviour than mean inelastic displacement ratios. In particular, residual displacement ratios exhibit large levels of record‐to‐record variability and, therefore, this dispersion should be taken into account when estimating residual displacements. A simplified expression is presented to estimate mean residual displacements ratios for elastoplastic systems during the evaluation of existing structures built on firm soil sites. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance‐based seismic assessment of conventional and base‐isolated steel buildings including environmental impact and resilience

Sustainability and resilience are issues that are recognized worldwide, and increased attention should be placed on strategies to design and maintain infrastructure systems that are hazard resilient, damage tolerant, and sustainable. In this paper, a methodology to evaluate the seismic sustainability and resilience of both conventional and base‐isolated steel buildings is presented. Furthermore, the proposed approach is used to explore the difference between the performance associated with these buildings by considering the three pillars of sustainability: economic, social, and environmental. Sustainability and resilience are both considered to cover a comprehensive performance‐based assessment content. The uncertainties associated with performance and consequence evaluation of structural and non‐structural components are incorporated within the assessment process. The proposed performance‐based assessment approach is illustrated on conventional and base‐isolated steel buildings under given seismic scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Experimental and computational verification of reasonable design formulae for base‐isolated structures

It is clear that base isolation is a sensible strategic design in attenuating the responses of a structural system induced by ground motions. The design of seismically isolated structures is mainly governed by the Uniform Building Code (UBC) published by the International Conference of Building Officials. The UBC code emphasizes a simple, statically equivalent design method that displacements of an isolated structure are concentrated at the isolation level. Therefore, the superstructure nearly moves as a rigid body and the design forces of elements above isolators are based on the behaviour of isolators at the design displacement. However, in the UBC code, the distribution of inertial (or lateral) forces over the height of the superstructure above isolation has been found to be too conservative for most isolated structures. In view of this, two simple and reasonable design formulae for the lateral force distribution on isolated structures have been proposed in this paper. Results obtained from a full‐scale isolated structure tested on the shaking table and numerical analyses of two additional examples verify the suitability of design formulae. It is illustrated that the proposed formulae can predict well the lateral force distribution on isolated structures during earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.