Probabilistic collapse resistance and residual drift assessment of buildings with fluidic self‐centering systems

The seismic performance of three‐ and six‐story buildings with fluidic self‐centering system is probabilistically assessed. The fluidic self‐centering systems consist of devices that are based on the technology of fluid viscous dampers but built in a way that pressurization of the devices results in preload that is explored to reduce or eliminate residual drift. The design of these buildings followed a procedure that parallels the design for structures with damping systems in ASCE 7 but modified to include the preload effect. Reference conventional buildings were also designed per ASCE 7 for comparison. These buildings were then analyzed to examine and compare their seismic collapse resistance and residual drift, where the residual drift limits of 0.2, 0.5, 1.0 and 2.0% of story height were selected as important thresholds. The study further calculated the mean annual frequency of collapse and corresponding exceedance probability over 50 years, and the mean annual frequency of exceeding the threshold residual story drift limits and the corresponding exceedance probability over 50 years. Variations in the design procedures by considering increased displacement capacity or damping or preload of the devices, different types of damping, increased ultimate strength of the self‐centering device–brace systems and increased frame strength were considered. It was found that increasing either the ultimate force capacity of the self‐centering device–brace system or the frame strength results in important improvements in the collapse resistance and in minimizing residual drift, whereas the variation of other design parameters has minor effects. Copyright © 2016 John Wiley & Sons, Ltd.     

A noniterative design procedure for supplemental brace–damper systems in single‐degree‐of‐freedom systems

In this paper, a method for designing supplemental brace–damper systems in single‐degree‐of‐freedom (SDOF) structures is presented. We include the effects of the supporting brace stiffness in the dynamic response by using a viscoelastic Maxwell model. On the basis of the study of an SDOF under ground excitation, we propose a noniterative design procedure for simultaneously specifying both the damper and the brace while assuring a desired structural performance. It is shown that to increase the damper size beyond the value delivered by the proposed criteria will not provide any improvement but actually worsen the structural response. The design method presented here shows excellent agreement with the FEMA 273 design approach but offers solutions closer to optimality. Copyright © 2013 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.     

An equivalent SDOF system model for estimating the response of R/C building structures with proportional hysteretic dampers subjected to earthquake motions

For the purpose of estimating the earthquake response, particularly the story drift demand, of reinforced concrete (R/C) buildings with proportional hysteretic dampers, an equivalent single‐degree‐of‐freedom (SDOF) system model is proposed. Especially in the inelastic range, the hysteretic behavior of an R/C main frame strongly differs from that of hysteretic dampers due to strength and stiffness degradation in R/C members. Thus, the proposed model, unlike commonly used single‐spring SDOF system models, differentiates the restoring force characteristics of R/C main frame and hysteretic dampers to explicitly take into account the hysteretic behavior of dampers. To confirm the validity of the proposed model, earthquake responses of a series of frame models and their corresponding equivalent SDOF system models were compared. 5‐ and 10‐story frame models were studied as representative of low‐ and mid‐rise building structures, and different mechanical properties of dampers—yield strength and yield deformation—were included to observe their influence on the effectiveness of the proposed model. The results of the analyses demonstrated a good correspondence between estimated story drift demands using the proposed SDOF system model and those of frame models. Moreover, the proposed model: (i) led to better estimates than those given by a single‐spring SDOF system model, (ii) was capable of estimating the input energy demand and (iii) was capable of estimating the total hysteretic energy and the participation of dampers into the total hysteretic energy dissipation, in most cases. Results, therefore, suggest that the proposed model can be useful in structural design practice. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic response of linear and non‐linear asymmetric systems with non‐linear fluid viscous dampers

This investigation is concerned with the seismic response of one‐story, one‐way asymmetric linear and non‐linear systems with non‐linear fluid viscous dampers. The seismic responses are computed for a suite of 20 ground motions developed for the SAC studies and the median values examined. Reviewed first is the behaviour of single‐degree‐of‐freedom systems to harmonic and earthquake loading. The presented results for harmonic loading are used to explain a few peculiar trends—such as reduction in deformation and increase in damper force of short‐period systems with increasing damper non‐linearity—for earthquake loading. Subsequently, the seismic responses of linear and non‐linear asymmetric‐plan systems with non‐linear dampers are compared with those having equivalent linear dampers. The presented results are used to investigate the effects of damper non‐linearity and its influence on the effects of plan asymmetry. Finally, the design implications of the presented results are discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

Evaluation of residual drift demands in regular multi‐storey frames for performance‐based seismic assessment

This paper summarizes results of a comprehensive analytical study aimed at evaluating the amplitude and heightwise distribution of residual drift demands in multi‐storey moment‐resisting frames after earthquake excitation. For that purpose, a family of 12 one‐bay two‐dimensional generic frame models was subjected to an ensemble of 40 ground motions scaled to different intensities. In this investigation, an inelastic ground motion intensity measure was employed to scale each record, which allowed reducing the record‐to‐record variability in the estimation of residual drift demands. The results were statistically processed in order to evaluate the influence of ground motion intensity, number of stories, period of vibration, frame mechanism, system overstrength, and hysteretic behaviour on central tendency of residual drift demands. In addition, a special emphasis was given to evaluate the uncertainty in the estimation of residual drift demands. Results of incremental dynamic analyses indicate that the amplitude and heightwise distribution of residual drift demands strongly depends on the frame mechanism, the heightwise system structural overstrength and the component hysteretic behaviour. An important conclusion for performance‐based assessment is that the evaluation of residual drift demands involves significantly larger levels of uncertainty (i.e. record‐to‐record variability) than that of maximum drift demands, which suggests that this variability and corresponding uncertainty should be explicitly taken into account when estimating residual drift demands during performance‐based seismic assessment of frame buildings. Copyright © 2006 John Wiley & Sons, Ltd.     

Damping reduction factors and code‐based design equation for structures using semi‐active viscous dampers

This study uses a semi‐active viscous damper with three different control laws to reshape the structural hysteresis loop and mitigate structural response, referred to as 1–4, 1–3 and 2–4 devices, respectively. The 1–4 control law provides damping in all four quadrants of the force‐displacement graph (it behaves like a standard viscous damper), the 1–3 control law provides resisting forces only in the first and third quadrants, and the 2–4 control law provides damping in the second and fourth quadrants. This paper first outlines the linear single degree of freedom structural performance when the three types of semi‐active viscous dampers are applied. The results show that simultaneous reduction in both displacement and base‐shear demand is only available with the semi‐active 2–4 device. To enable guidelines for adding a 2–4 device into the design procedure, damping reduction factors (RF_ξs) are developed, as they play an important role and provide a means of linking devices to design procedures. Three methods are presented to obtain RF_ξ and equivalent viscous damping of a structure with a 2–4 semi‐active viscous damper. In the first method, the relationship between RF_ξ and the damping of a semi‐active structure can be obtained by calculating the area under the force‐deformation diagram. The second and third method modified the Eurocode8 formula of RF_ξ and smoothed results from analysis, respectively. Finally, a simple method is proposed to incorporate the design or retrofit of structures with simple, robust and reliable 2–4 semi‐active viscous dampers using standard design approaches. Copyright © 2016 John Wiley & Sons, Ltd.     

Improved dynamic correction method in seismic analysis of both classically and non‐classically damped structures

A step‐by‐step approximate procedure taking into consideration high‐frequency modes, usually neglected in the modal analysis of both classically and non‐classically damped structures, is presented. This procedure can be considered as an extension of traditional modal correction methods, like the mode‐acceleration method and the dynamic correction method, which are very effective for structural systems subjected to forcing functions described by analytical laws. The proposed procedure, herein called improved dynamic correction method, requires two steps. In the first step, the number of differential equations of motion are reduced and consequently solved by using the first few undamped mode‐shapes. In the second step, the errors due to modal truncation are reduced by correcting the dynamic response and solving a new set of differential equations, formally similar to the original differential equations of motion. The difference between the two groups of differential equations lies in the forcing vector, which is evaluated in such a way as to correct the effects of modal truncation on applied loads. Copyright © 2001 John Wiley & Sons, Ltd.     

Performance spectra based method for the seismic design of structures equipped with passive supplemental damping systems

A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd.     

Isoductile strengths and strength reduction factors of elasto‐plastic SDOF systems subjected to simple waveforms

The inelastic response of elasto‐plastic SDOF oscillators subjected to 24 simple waveforms was studied. The waveforms contain linear, quadratic, sinusoidal, and triangular acceleration components that repeat for not more than several cycles. Similarities and differences in oscillator response characteristics are presented, organized by a characteristic period. The strengths and corresponding strength reduction factors required for constant ductility responses are discussed. Response data are compared with expectations based on the concepts of equal energy, equal displacement, and preservation of force. Limitations on the applicability of the equal energy concept are identified. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

A probabilistic framework for correlated seismic downtime and repair cost estimation of geo‐structures

An important component of probabilistic risk assessment methods is the development of models to quantify the direct consequences of damage to geo‐structural components for a given intensity of the hazard. This paper presents a general probabilistic framework for correlated repair cost and downtime estimation of geo‐structures exposed to seismic hazards. The framework uses as input the results of nonlinear time‐history analysis of geo‐structures for the set of earthquake records that are representative of the seismic hazard models for the region of interest. The repair cost and downtime are estimated for individual earthquakes probabilistically considering the uncertainties associated with damage states. In addition, the formulation of the repair cost and downtime accounts for the reduction in the repair requirements as the number of damaged components in the given damage state increases. An analytical linear and two bilinear regression models are proposed for conditional correlated seismic repair cost and downtime estimation of geo‐structures given the intensity measure. The proposed framework is demonstrated by developing seismic repair models of a typical pile‐supported wharf structure on the west coast of the United States. The presented framework is general and can be applied to other types of geo‐structures and hazards and can include other decision variables such as loss of life as well. Copyright © 2013 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.     

An accurate strength amplification factor for the design of SDOF systems with P–Δ effects

The response of structures subjected to seismic actions is always influenced by P–Δ effects. The importance of this effect is generally modest for structures experiencing an elastic response but often relevant for structures responding well within the inelastic range of behaviour. Seismic codes indicate that P–Δ effects may be counterbalanced through an increase in the structural strength required by a first order analysis. This increase is calculated by means of a strength amplification factor. The expressions suggested in codes for this factor are simplistic and often criticized by researchers. In this paper, the effectiveness of some of the provisions reported in the literature or suggested in seismic codes is evaluated on single degree of freedom systems with different periods of vibration. As suggested by past studies, attention is focused on the influence of the interstorey drift sensitivity coefficient, significant duration of the ground motion, class of the site soil, displacement ductility and equivalent viscous damping ratio of the system. Finally, an accurate expression of the strength amplification factor is proposed. Copyright © 2013 John Wiley & Sons, Ltd.     

The effects of repeated earthquake ground motions on the non‐linear response of SDOF systems

In many parts of the world, the repetition of medium–strong intensity earthquake ground motions at brief intervals of time has been observed. The new design philosophies for buildings in seismic areas are based on multi‐level design approaches, which take into account more than a single damageability limit state. According to these approaches, a sequence of seismic actions may produce important consequences on the structural safety. In this paper, the effects of repeated earthquake ground motions on the response of single‐degree‐of‐freedom systems (SDOF) with non‐linear behaviour are analysed. A comparison is performed with the effect of a single seismic event on the originally non‐damaged system for different hysteretic models in terms of pseudo‐acceleration response spectra, behaviour factor q and damage parameters. The elastic–perfect plastic system is the most vulnerable one under repeated earthquake ground motions and is characterized by a strong reduction of the q‐factor. A moment resisting steel frame is analysed as well, showing a reduction of the q‐factor under repeated earthquake ground motions even larger than that of an equivalent SDOF system. Copyright © 2002 John Wiley & Sons, Ltd.     

Loss estimation for non‐ductile reinforced concrete building in Victoria,British Columbia,Canada: effects of mega‐thrust Mw9‐class subduction earthquakes and aftershocks

This paper presents, within the performance‐based earthquake engineering framework, a comprehensive probabilistic seismic loss estimation method that accounts for main sources of uncertainty related to hazard, vulnerability, and loss. The loss assessment rigorously integrates multiple engineering demand parameters (maximum and residual inter‐story drift ratio and peak floor acceleration) with consideration of mainshock–aftershock sequences. A 4‐story non‐ductile reinforced concrete building located in Victoria, British Colombia, Canada, is considered as a case study. For 100 mainshock and mainshock–aftershock earthquake records, incremental dynamic analysis is performed, and the three engineering demand parameters are fitted with a probability distribution and corresponding dependence computed. Finally, with consideration of different demolition limit states, loss assessment is performed. From the results, it can be shown that when seismic vulnerability models are integrated with seismic hazard, the aftershock effects are relatively minor in terms of overall seismic loss (1–4% increase). Moreover, demolition limit state parameters, uncertainties of collapse fragility, and non‐collapse seismic demand prediction models have showed significant contribution to the loss assessment. The seismic loss curves for the reference case and for cases with the varied parameters can differ by as large as about 150%. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of the structural response under seismic actions using non‐linear static methods

The paper investigates the degree of accuracy achievable when some non‐linear static procedures based on a pushover analysis are used to evaluate the seismic performance. In order to assess the significance of different sources of errors, three types of structural systems are analysed: (i) single‐degree‐of‐freedom (SDOF) systems with different hysteretic behaviour; (ii) shear‐type multi‐degree‐of‐freedom (MDOF) systems with elastic–perfect plastic (EPP) shear force–interstorey drift relationships; (iii) a steel moment‐resisting frame with rigid joints and EPP moment–curvature relationship. In SDOF systems, the source of approximation comes only from the calibration of the demand spectrum, while in MDOF systems some further errors are introduced by the schematization with an equivalent SDOF system. The non‐linear static procedures are compared with rigorous time‐history analyses carried out by considering ten generated earthquake ground motions compatible with the Eurocode 8 elastic spectra. It was found that SDOF systems with longer periods satisfy the equal displacement approximation regardless of the hysteretic model, while hysteresis loops with smaller energy dissipated indicate lower response for shorter periods. This is the opposite of what predicted by the ATC‐40 capacity spectrum method, which underestimates and overestimates, respectively, the actual response of low‐ and high‐ductility systems. Conversely, the inelastic spectrum method proposed by Vidic, Fajfar and Fischinger leads to the most accurate results for all types of structural systems. The analyses carried out on EPP shear‐type frames point out a large concentration of the ductility demand on some storeys. However, such a concentration markedly reduces when some hardening is accounted for. Copyright © 2006 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.