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1.
SPO2IDA is introduced, a software tool that is capable of recreating the seismic behaviour of oscillators with complex quadrilinear backbones. It provides a direct connection between the static pushover (SPO) curve and the results of incremental dynamic analysis (IDA), a computer‐intensive procedure that offers thorough demand and capacity prediction capability by using a series of nonlinear dynamic analyses under a suitably scaled suite of ground motion records. To achieve this, the seismic behaviour of numerous single‐degree‐of‐freedom (SDOF) systems is investigated through IDA. The oscillators have a wide range of periods and feature pinching hysteresis with backbones ranging from simple bilinear to complex quadrilinear with an elastic, a hardening and a negative‐stiffness segment plus a final residual plateau that terminates with a drop to zero strength. An efficient method is introduced to treat the backbone shape by summarizing the analysis results into the 16, 50 and 84% fractile IDA curves, reducing them to a few shape parameters and finding simpler backbones that reproduce the IDA curves of complex ones. Thus, vast economies are realized while important intuition is gained on the role of the backbone shape to the seismic performance. The final product is SPO2IDA, an accurate, spreadsheet‐level tool for performance‐based earthquake engineering that can rapidly estimate demands and limit‐state capacities, strength reduction R‐factors and inelastic displacement ratios for any SDOF system with such a quadrilinear SPO curve. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

2.
This paper investigates the seismic response of multi‐storey cross‐laminated timber (CLT) buildings and its relationship with salient ground‐motion and building characteristics. Attention is given to the effects of earthquake frequency content on the inelastic deformation demands of platform CLT walled structures. The response of a set of 60 CLT buildings of varying number of storeys and panel fragmentation levels representative of a wide range of structural configurations subjected to 1656 real earthquake records is examined. It is shown that, besides salient structural parameters like panel aspect ratio, design behaviour factor, and density of joints, the frequency content of the earthquake action as characterized by its mean period has a paramount importance on the level of nonlinear deformations attained by CLT structures. Moreover, the evolution of drifts as a function of building to ground‐motion periods ratio is different for low‐ and high‐rise buildings. Accordingly, nonlinear regression models are developed for estimating the global and interstorey drifts demands on multi‐storey CLT buildings. Finally, the significance of the results is highlighted with reference to European seismic design procedures and recent assessment proposals.  相似文献   

3.
The efficacy of various ground motion intensity measures (IMs) in the prediction of spatially distributed seismic demands (engineering demand parameters, (EDPs)) within a structure is investigated. This has direct implications to building‐specific seismic loss estimation, where the seismic demand on different components is dependent on the location of the component in the structure. Several common IMs are investigated in terms of their ability to predict the spatially distributed demands in a 10‐storey office building, which is measured in terms of maximum interstorey drift ratios and maximum floor accelerations. It is found that the ability of an IM to efficiently predict a specific EDP depends on the similarity between the frequency range of the ground motion that controls the IM and that of the EDP. An IMs predictability has a direct effect on the median response demands for ground motions scaled to a specified probability of exceedance from a ground motion hazard curve. All of the IMs investigated were found to be insufficient with respect to at least one of magnitude, source‐to‐site distance, or epsilon when predicting all peak interstorey drifts and peak floor accelerations in a 10‐storey reinforced concrete frame structure. Careful ground motion selection and/or seismic demand modification is therefore required to predict such a spatially distributed demands without significant bias. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

4.
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.  相似文献   

5.
This study explores seismic performance of steel frame buildings with SMA-based self-centering bracing systems using a probabilistic approach. The self-centering bracing system described in this study relies on superelastic response of large-diameter cables. The bracing systems is designed such that the SMA cables are always stressed in tension. A four-story steel frame building characterized until collapse in previous research is selected as a case-study building. The selected steel frame building is designed with SMA bracing systems considering various design parameters for SMA braces. Numerical models of these buildings are developed by taking into account the ultimate state of structural components and SMA braces as well as the effect of gravity frames on lateral load resistance. Nonlinear static analyses are conducted to assess the seismic characteristics of each frame and to examine the effect of SMA brace failure on the seismic load carrying capacity of SMA-braced frames. Incremental dynamic analyses (IDA) are performed to compute seismic response of the designed frames at various seismic intensity levels. The results of IDA are used to develop probabilistic seismic demand models for peak inter-story and residual inter-story drifts. Seismic demand hazard curves of peak and residual inter-story drifts are generated by convolving the ground motion hazard with the probabilistic seismic demand models. Results show that steel frames designed with SMA bracing systems provide considerably lower probability of reaching at a damage state level associated with residual drifts compared to a similarly designed steel moment resisting frame, especially for seismic events with high return periods. This indicates reduced risks for the demolition and collapse due to excessive residual drifts for SMA braced steel frames.  相似文献   

6.
An envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

7.
An Erratum has been published for this article in Earthquake Engineering and Structural Dynamics 2003; 32:1795. The recently developed modal pushover analysis (MPA) has been shown to be a significant improvement over the pushover analysis procedures currently used in structural engineering practice. None of the current invariant force distributions accounts for the contribution of higher modes—higher than the fundamental mode—to the response or for redistribution of inertial forces because of structural yielding. By including the contributions of a sufficient number of modes of vibration (generally two to three), the height‐wise distribution of responses estimated by MPA is generally similar to the ‘exact’ results from non‐linear response history analysis (RHA). Although the results of the previous research were extremely promising, only a few buildings were evaluated. The results presented below evaluate the accuracy of MPA for a wide range of buildings and ground motion ensembles. The selected structures are idealized frames of six different heights: 3, 6, 9, 12, 15, and 18 stories and five strength levels corresponding to SDF‐system ductility factor of 1, 1.5, 2, 4, and 6; each frame is analysed for 20 ground motions. Comparing the median values of storey‐drift demands determined by MPA to those obtained from non‐linear RHA shows that the MPA predicts reasonably well the changing height‐wise variation of demand with building height and SDF‐system ductility factor. Median and dispersion values of the ratios of storey‐drift demands determined by MPA and non‐linear‐RHA procedures were computed to measure the bias and dispersion of MPA estimates with the following results: (1) the bias and dispersion in the MPA procedure tend to increase for longer‐period frames and larger SDF‐system ductility factors (although these trends are not perfect); (2) the bias and dispersion in MPA estimates of seismic demands for inelastic frames are usually larger than for elastic systems; (3) the well‐known response spectrum analysis (RSA), which is equivalent to the MPA for elastic systems, consistently underestimates the response of elastic structures, e.g. up to 18% in the upper‐storey drifts of 18‐storey frames. Finally, the MPA procedure is simplified to facilitate its implementation in engineering practice—where the earthquake hazard is usually defined in terms of a median (or some other percentile) design spectrum for elastic systems—and the accuracy of this simplified procedure is documented. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

8.
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 Taver, mean period Tm, predominant period Tg, characteristic period Tc and smoothed spectral predominant period To 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.  相似文献   

9.
A process is outlined and evaluated for the estimation of seismic roof and storey drift demands for frame structures from the spectral displacement demand at the first mode period of the structure. The spectral displacement demand is related to the roof drift demand for the multi‐degree‐of‐freedom (MDOF) structure using three modification factors, accounting for MDOF effects, inelasticity effects, and P‐delta effects. Median values and measures of dispersion for the factors are obtained from elastic and inelastic time history analyses of nine steel moment resisting frame structures subjected to sets of ground motions representative of different hazard levels. The roof drift demand is related to the storey drift demands, with the results being strongly dependent on the number of stories and the ground motion characteristics. The relationships proposed in this paper should prove useful in the conceptual design phase, in estimating deformation demands for performance assessment, and in improving basic understanding of seismic behaviour. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

10.
Incremental dynamic analysis (IDA)—a procedure developed for accurate estimation of seismic demand and capacity of structures—requires non‐linear response history analysis of the structure for an ensemble of ground motions, each scaled to many intensity levels, selected to cover the entire range of structural response—all the way from elastic behaviour to global dynamic instability. Recognizing that IDA of practical structures is computationally extremely demanding, an approximate procedure based on the modal pushover analysis procedure is developed. Presented are the IDA curves and limit state capacities for the SAC‐Los Angeles 3‐, 9‐, and 20‐storey buildings computed by the exact and approximate procedures for an ensemble of 20 ground motions. These results demonstrate that the MPA‐based approximate procedure reduces the computational effort by a factor of 30 (for the 9‐storey building), at the same time providing results to a useful degree of accuracy over the entire range of responses—all the way from elastic behaviour to global dynamic instability—provided a proper hysteretic model is selected for modal SDF systems. The accuracy of the approximate procedure does not deteriorate for 9‐ and 20‐storey buildings, although their dynamics is more complex, involving several ‘modes’ of vibration. For all three buildings, the accuracy of the MPA‐based approximate procedure is also satisfactory for estimating the structural capacities for the limit states of immediate occupancy, collapse prevention, and global dynamic instability. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

11.
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.  相似文献   

12.
This paper summarizes the results of an extensive study on the inelastic seismic response of X‐braced steel buildings. More than 100 regular multi‐storey tension‐compression X‐braced steel frames are subjected to an ensemble of 30 ordinary (i.e. without near fault effects) ground motions. The records are scaled to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, brace slenderness ratio and column stiffness strongly influence the amplitude and heightwise distribution of inelastic deformation. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer a direct estimation of drift and ductility demands. The uncertainty of this estimation due to the record‐to‐record variability is discussed in detail. More specifically, given the strength (or behaviour) reduction factor, the proposed formulae provide reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum cyclic ductility of the diagonals along the height of the structure. The strength reduction factor refers to the point of the first buckling of the diagonals in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This design‐oriented feature enables both the rapid seismic assessment of existing structures and the direct deformation‐controlled seismic design of new ones. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

13.
Non‐linear dynamic time‐history analyses conducted as part of a performance‐based seismic design approach often require that the ground motion records are scaled to a specified level of seismic intensity. Recent research has demonstrated that certain ground motion scaling methods can introduce a large scatter in the estimated seismic demands. The resulting demand estimates may be biased, leading to designs with significant uncertainty and unknown margins of safety, unless a relatively large ensemble of ground motion records is used. This paper investigates the effectiveness of seven ground motion scaling methods in reducing the scatter in estimated peak lateral displacement demands. Non‐linear single‐degree‐of‐freedom systems and non‐linear multi‐degree‐of‐freedom systems are considered with different site conditions (site soil profile and epicentral distance) and structural characteristics (yield strength, period, and hysteretic behavior). It is shown that scaling methods that work well for ground motions representative of stiff soil and far‐field conditions lose their effectiveness for soft soil and near‐field conditions for a wide range of structural characteristics. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

14.
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.  相似文献   

15.
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.  相似文献   

16.
Incremental Dynamic Analysis (IDA) involves a series of nonlinear response history analyses with a suite of incrementally scaled ground motion records. Although IDA is perhaps the most comprehensive seismic performance assessment method, it receives criticism because several ground motion records are scaled up until the structure collapses. The scaling practice often results to unrealistic multipliers, thus modifying the amplitude of the ground motion and introducing bias on the structural performance estimation. Record scaling is a common practice in earthquake engineering due to the lack of natural records corresponding to large magnitudes and/or small distances from the fault rupture location. In this work we use a large number of ground motion records to compare the predictions of IDA with that of unscaled ground motions and we propose a new methodology in order to quantify the bias introduced in IDA. Apart from natural records, we have conducted broadband ground motion simulations for rupture scenarios of weak, medium and large magnitude events in order to expand our record database. The investigation is performed on a series of inelastic single-degree-of-freedom systems and on two multistory steel moment frame buildings. The results pinpoint both qualitatively and quantitatively, for the full range of limit-states, the bias that IDA introduces on the structural performance estimation.  相似文献   

17.
A generalized pushover analysis (GPA) procedure is developed for estimating the inelastic seismic response of structures under earthquake ground excitations. The procedure comprises applying different generalized force vectors separately to the structure in an incremental form with increasing amplitude until a prescribed seismic demand is attained for each generalized force vector. A generalized force vector is expressed as a combination of modal forces, and simulates the instantaneous force distribution acting on the system when a given response parameter reaches its maximum value during dynamic response to a seismic excitation. While any response parameter can be selected arbitrarily, generalized force vectors in the presented study are derived for maximum interstory drift parameters. The maximum value of any other response parameter is then obtained from the envelope of GPAs results. Each nonlinear static analysis under a generalized force vector activates the entire multi‐degree of freedom effects simultaneously. Accordingly, inelastic actions develop in members with the contribution of all ‘instantaneous modes’ in the nonlinear response range. Target seismic demands for interstory drifts at the selected stories are calculated from the associated drift expressions. The implementation of the proposed GPA is simpler compared with nonlinear response history analysis, whereas it is less demanding in computational effort when compared with several multi‐mode adaptive nonlinear static procedures. Moreover, it does not suffer from the statistical combination of inelastic modal responses obtained separately. The results obtained from building frames have demonstrated that GPA is successful in estimating maximum member deformations and member forces with reference to the response history analysis. When the response is linear elastic, GPA and response spectrum analysis produce identical results. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

18.
This paper examines the distribution of seismic drift demands in multi-storey steel moment frames designed to the provisions of Eurocode 8, with due account of the frequency content of ground motion. After providing an overview of current design rules, selected results from a detailed parametric investigation into inelastic drift demands are presented and discussed. The study includes extensive incremental dynamic analyses covering a wide range of structural characteristics and a large suite of ground motion records. The mean period is adopted in this work as a measure of the frequency content of ground motion. Prediction models for maximum global and inter-storey drift demands are presented and shown to be primarily affected by the fundamental-to-mean period ratio and the behaviour factor. Particular attention is given in this paper to the influence of the relative storey stiffness ratio on the distribution of drift demands over the height of the structure. In order to achieve a comparatively uniform drift distribution, a target relative storey stiffness ratio, incorporating the structural and ground motion characteristics, is proposed for design purposes. Finally, the implications of the findings on typical design procedures are highlighted, and possible improvements in codified guidance are discussed.  相似文献   

19.
By means of a graphical procedure, the capacity spectrum method compares the capacity of a structure with the demands of earthquake ground motion on it. In the present version of the method, highly damped elastic spectra have been used to determine seismic demand. A more straightforward approach for the determination of seismic demand is based on the use of the inelastic strength and displacement spectra which can be obtained directly by time-history analyses of inelastic SDOF systems, or indirectly from elastic spectra. The advantages of the two approaches (i.e. the visual representation of the capacity spectrum method and the superior physical basis of inelastic demand spectra) can be combined. In this paper, the idea of using inelastic demand spectra within the capacity spectrum method has been elaborated and is presented in an easy to use format. The approach represents the so-called N2 method formulated in the format of the capacity spectrum method. By reversing the procedure, a direct displacement-based design can be performed. The application of the modified capacity spectrum method is illustrated by means of two examples. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

20.
The seismic performance of existing structures can be assessed based on nonlinear static procedures, such as the Capacity Spectrum Method. This method essentially approximates peak responses of an inelastic single‐degree‐of‐freedom (SDOF) system using peak responses of an equivalent linear SDOF model. In this study, the equivalent linear models of inelastic SDOF systems are developed based on the constant strength approach, which does not require iteration for assessing the seismic performance of existing structures. To investigate the effects of earthquake type and seismic region on the equivalent linear models, four ground‐motion data sets—Japanese crustal/interface/inslab records and California crustal records—are compiled and used for nonlinear dynamic analysis. The analysis results indicate that: (1) the optimal equivalent linear model parameters (i.e. equivalent vibration period ratio and damping ratio) decrease with the natural vibration period, whereas they increase with the strength reduction factor; (2) the impacts of earthquake type and seismic region on the equivalent linear model parameters are not significant except for short vibration periods; and (3) the degradation and pinching effects affect the equivalent linear model parameters. We develop prediction equations for the optimal equivalent linear model parameters based on nonlinear least‐squares fitting, which improve and extend the current nonlinear static procedure for existing structures with degradation and pinching behavior. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

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