Risk‐based seismic design for collapse safety

Risk‐based seismic design, as introduced in this paper, involves the use of different types of analysis in order to satisfy a risk‐based performance objective with a reasonable utilization rate and sufficient reliability. Differentiation of the reliability of design can be achieved by defining different design algorithms depending on the importance of a structure. In general, the proposed design is iterative, where the adjustment of a structure during iterations is the most challenging task. Rather than using automated design algorithms, an attempt has been made to introduce three simple guidelines for adjusting reinforced concrete frames in order to increase their strength and deformation capacity. It is shown that an engineer can design a reinforced concrete frame in a few iterations, for example, by adjusting the structure on the basis of pushover analysis and checking the final design by means of nonlinear dynamic analysis. A possible variant of the risk‐based design algorithm for the collapse safety of reinforced concrete frame buildings is proposed, and its application is demonstrated by means of an example of an eight‐storey reinforced concrete building. Four iterations were required in order to achieve the risk‐based performance objective with a reasonable utilization rate. Copyright © 2016 John Wiley & Sons, Ltd.     

基于推覆分析的RC框架地震倒塌易损性预测

基于倒塌率的结构倒塌易损性分析是目前评价结构抗倒塌能力最合理的方法.但是,目前基于增量动力分析(IDA)的倒塌率分析方法,工作量和实施难度大,很难直接用于工程设计,因此有必要研究便于工程应用的新方法.本文基于18个典型多层RC框架结构的IDA倒塌率分析和静力推覆分析,发现RC框架在大震下的倒塌率及抗倒塌安全储备(CMR)与静力推覆得到的结构位移安全储备之间存在较好的相关关系.依据此关系,建议了保证大震倒塌率的推覆位移安全储备,并通过9个RC框架结构算例进行了验证.本文方法简单易行,可供规则多层RC框架结构抗倒塌设计参考.     

Effect of ground motion selection methods on seismic collapse fragility of RC frame buildings

Variation in the seismic collapse fragility of reinforced concrete frame buildings predicted using different ground motion (GM) selection methods is investigated in this paper. To simulate the structural collapse, a fiber‐element modelling approach with path‐dependent cyclic nonlinear material models that account for concrete confinement and crushing, reinforcement buckling as well as low cycle fatigue is used. The adopted fiber analysis approach has been found to reliably predict the loss in vertical load carrying capacity of structural components in addition to the sidesway mode of collapse due to destabilizing P–Δ moments at large inelastic deflections. Multiple stripe analysis is performed by conducting response history analyses at various hazard levels to generate the collapse fragility curves. To select GMs at various hazard levels, two alternatives of uniform hazard spectrum (UHS), conditional mean spectrum (CMS) and generalized conditional intensity measure (GCIM) are used. Collapse analyses are repeated based on structural periods corresponding to initial un‐cracked stiffness and cracked stiffness of the frame members. A return period‐based intensity measure is then introduced and applied in estimating collapse fragility of frame buildings. In line with the results of previous research, it is shown that the choice of structural period significantly affects the collapse fragility predictions. Among the GM selection methods used in this study, GCIM and CMS methods predict similar collapse fragilities for the case study building investigated herein, and UHS provides the most conservative prediction of the collapse capacity, with approximately 40% smaller median collapse capacity compared to the CMS method. The results confirm that collapse probability prediction of buildings using UHS offers a higher level of conservatism in comparison to the other selection methods. Copyright © 2017 John Wiley & Sons, Ltd.     

Simplified seismic sidesway collapse analysis of frame buildings

This paper presents the development and assessment of a simplified procedure for estimating the seismic sidesway collapse margin ratio of building structures. The proposed procedure is based on the development of a robust database of seismic peak displacement responses of nonlinear single‐degree‐of‐freedom systems for various seismic intensities and uses nonlinear static (pushover) analysis without the need for nonlinear time history dynamic analysis. The proposed simplified procedure is assessed by comparing its collapse capacity predictions on 72 different building structures with those obtained by nonlinear incremental dynamic analyses. The proposed simplified procedure offers a simple, yet efficient, computational/analytical tool that is capable of predicting collapse capacities with acceptable accuracy for a wide variety of frame building structures. Copyright © 2013 John Wiley & Sons, Ltd.     

A modal pushover analysis procedure to estimate seismic demands for unsymmetric‐plan buildings

An Erratum has been published for this article in Earthquake Engng. Struct. Dyn. 2004; 33:1429. Based on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric‐plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by non‐linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each floor level. These ‘modal’ demands due to the first few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems. When applied to elastic systems, the MPA procedure is equivalent to standard response spectrum analysis (RSA). The MPA estimates of seismic demand for torsionally‐stiff and torsionally‐flexible unsymmetric systems are shown to be similarly accurate as they are for the symmetric building; however, the results deteriorate for a torsionally‐similarly‐stiff unsymmetric‐plan system and the ground motion considered because (a) elastic modes are strongly coupled, and (b) roof displacement is underestimated by the CQC modal combination rule (which would also limit accuracy of RSA for linearly elastic systems). Copyright © 2004 John Wiley & Sons, Ltd.     

Integrating visual damage simulation,virtual inspection,and collapse capacity to evaluate post‐earthquake structural safety of buildings

A methodology is introduced to assess the post‐earthquake structural safety of damaged buildings using a quantitative relationship between observable structural component damage and the change in collapse vulnerability. The proposed framework integrates component‐level damage simulation, virtual inspection, and structural collapse performance assessment. Engineering demand parameters from nonlinear response history analyses are used in conjunction with component‐level damage simulation to generate multiple realizations of damage to key structural elements. Triggering damage state ratios, which describe the fraction of components within a damage state that results in an unsafe placard assignment, are explicitly linked to the increased collapse vulnerability of the damaged building. A case study is presented in which the framework is applied to a 4‐story reinforced concrete frame building with masonry infills. The results show that when subjected to maximum considered earthquake level ground motions, the probability of experiencing enough structural damage to trigger an unsafe placard, leading to building closure, is more than 2 orders of magnitude higher than the risk of collapse.     

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

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.     

Seismic response analysis using characteristic ground motion records for risk‐based decision‐making (3R method)

The concept of intensity‐based assessment for risk‐based decision‐making is introduced. It is realized by means of the so‐called 3R method (response analysis, record selection and risk‐based decision‐making), which can be used to check the adequacy of design of a new building or of the strengthening of an existing building by performing conventional pushover analysis and dynamic analysis for only a few ground motions, which are termed characteristic ground motions. Because the objective of the method is not a precise assessment of the seismic risk, a simple decision model for risk acceptability can be introduced. The engineer can decide that the reliability of a no‐collapse requirement is sufficient when collapse is observed in the case of less than half of, for example, seven characteristic ground motions. From the theoretical point of view, it is shown that the accuracy of the method is acceptable if the non‐linear response history analyses are performed at a low percentile of limit‐state intensity, which is also proven by means of several examples of multi‐storey reinforced concrete frame buildings. The 3R method represents a compromise between the exclusive use of either pushover analysis or dynamic analysis and can be easily introduced into building codes provided that its applicability is further investigated (e.g. asymmetric structures and other performance objectives) and that the procedure for the selection of characteristic ground motions is automated and readily available to engineers (www.smartengineering.si).     

Applicability of pushover methods for the seismic analysis of single‐column bent viaducts

An overview of the applicability of a typical single‐mode pushover method (the N2 method) and two typical multi‐mode pushover methods (the modal pushover analysis (MPA) and incremental response spectrum analysis (IRSA) methods) for the analysis of single column bent viaducts in the transverse direction is presented. Previous research, which was limited to relatively short viaducts supported by few columns, has been extended to longer viaducts with more bents. The single‐mode N2 method is accurate enough for bridges where the effective modal mass of the fundamental mode is at least 80% of the total mass. The applicability of this method depends on (a) the ratio of the stiffness of the superstructure to that of the bents and (b) the strength of the bents. In short bridges with few columns, the accuracy of the N2 method increases as the seismic intensity increases, whereas in long viaducts (e.g. viaducts with lengths greater than 500 m) the method is in general less effective. In the case of the analyzed moderately irregular long viaducts, which are common in construction design practice, the MPA method performed well. For the analysis of bridges where the modes change significantly, depending on the seismic intensity, the IRSA method is in principle more appropriate, unless a viaduct is torsionally sensitive. In such cases, all simplified methods should be used with care. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal seismic design of steel frame buildings based on life cycle cost considerations

A multi‐objective optimization procedure is presented for designing steel moment resisting frame buildings within a performance‐based seismic design framework. Life cycle costs are considered by treating the initial material costs and lifetime seismic damage costs as two separate objectives. Practical design/construction complexity, important but difficult to be included in initial cost analysis, is taken into due account by a proposed diversity index as another objective. Structural members are selected from a database of commercially available wide flange steel sections. Current seismic design criteria (AISC‐LRFD seismic provisions and 1997 NEHRP provisions) are used to check the validity of any design alternative. Seismic performance, in terms of the maximum inter‐storey drift ratio, of a code‐verified design is evaluated using an equivalent single‐degree‐of‐freedom system obtained through a static pushover analysis of the original multi‐degree‐of‐freedom frame building. A simple genetic algorithm code is used to find a Pareto optimal design set. A numerical example of designing a five‐storey perimeter steel frame building is provided using the proposed procedure. It is found that a wide range of valid design alternatives exists, from which a decision maker selects the one that balances different objectives in the most preferred way. Copyright © 2003 John Wiley & Sons, Ltd.     

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 simplified methd of evaluating the seismic performance of buildings

This paper presents a simplified method of evaluating the seismic performance of buildings. The proposed method is based on the transformation of a multiple degree of freedom (MDOF) system to an equivalent single degree of freedom (SDOF) system using a simple and intuitive process. The proposed method is intended for evaluating the seismic performance of the buildings at the intermediate stages in design, while a rigorous method would be applied to the final design. The performance of the method is evaluated using a series of buildings which are assumed to be located in Victoria in western Canada, and designed based on the upcoming version of the National Building Code of Canada which is due to be published in 2005. To resist lateral loads, some of these buildings contain reinforced concrete moment resisting frames,while others contain reinforced concrete shear walls. Each building model has been subjected to a set of site-specific seismic spectrum compatible ground motion records, and the response has been determined using the proposed method and the general method for MDOF systems. The results from the study indicate that the proposed method can serve as a useful tool for evaluation of seismic performance of buildings, and carrying out performance based design.     

Rigid‐plastic models for the seismic design and assessment of steel framed structures

This paper demonstrates the applicability of response history analysis based on rigid‐plastic models for the seismic assessment and design of steel buildings. The rigid‐plastic force–deformation relationship as applied in steel moment‐resisting frames (MRF) is re‐examined and new rigid‐plastic models are developed for concentrically‐braced frames and dual structural systems consisting of MRF coupled with braced systems. This paper demonstrates that such rigid‐plastic models are able to predict global seismic demands with reasonable accuracy. It is also shown that, the direct relationship that exists between peak displacement and the plastic capacity of rigid‐plastic oscillators can be used to define the level of seismic demand for a given performance target. Copyright© 2009 John Wiley & Sons, Ltd.     

Evaluation of predictors of non‐linear seismic demands using ‘fishbone’ models of SMRF buildings

Predictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 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.     

Pushover-based seismic risk assessment and loss estimation of masonry buildings

A pushover-based seismic risk assessment and loss estimation methodology for masonry buildings is introduced. It enables estimation of loss by various performance measures such as the probability of exceeding a designated economic loss, the expected annual loss, and the expected loss given a seismic intensity. The methodology enables the estimation of the economic loss directly from the results of structural analysis, which combines pushover analysis and incremental dynamic analysis of an equivalent SDOF model. The use of the methodology is demonstrated by means of two variants of a three-storey masonry building both of which have the same geometry, but they are built, respectively, from hollow clay masonry (model H) and solid brick masonry (model S). The probability of collapse given the selected design earthquake corresponding to a return period of 475 years was found to be negligible for model H, which indicates the proper behaviour of such a structure when designed according to the current building codes. However, the corresponding probability of collapse of model S was very high (46%). The expected total loss given the design earthquake was estimated to amount to 28 000 € and 290 000 €, respectively, for models H and S. The expected annual loss per 100 m² of gross floor area was estimated to amount to 75 € and 191 €, respectively, for models H and S. For the presented examples, it was also observed that nonstructural elements contributed more than 50% of the total loss.     

Alternative non‐linear demand estimation methods for probability‐based seismic assessments

Alternative non‐linear dynamic analysis procedures, using real ground motion records, can be used to make probability‐based seismic assessments. These procedures can be used both to obtain parameter estimates for specific probabilistic assessment criteria such as demand and capacity factored design and also to make direct probabilistic performance assessments using numerical methods. Multiple‐stripe analysis is a non‐linear dynamic analysis method that can be used for performance‐based assessments for a wide range of ground motion intensities and multiple performance objectives from onset of damage through global collapse. Alternatively, the amount of analysis effort needed in the performance assessments can be reduced by performing the structural analyses and estimating the main parameters in the region of ground motion intensity levels of interest. In particular, single‐stripe and double‐stripe analysis can provide local probabilistic demand assessments using minimal number of structural analyses (around 20 to 40). As a case study, the displacement‐based seismic performance of an older reinforced concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake, is evaluated. Copyright © 2008 John Wiley & Sons, Ltd.     

A probabilistic performance‐based approach for mitigating the seismic pounding risk between adjacent buildings

Existing design procedures for determining the separation distance between adjacent buildings subjected to seismic pounding risk are based on approximations of the buildings' peak relative displacement. These procedures are characterized by unknown safety levels and thus are not suitable for use within a performance‐based earthquake engineering framework. This paper introduces an innovative reliability‐based methodology for the design of the separation distance between adjacent buildings. The proposed methodology, which is naturally integrated into modern performance‐based design procedures, provides the value of the separation distance corresponding to a target probability of pounding during the design life of the buildings. It recasts the inverse reliability problem of the determination of the design separation distance as a zero‐finding problem and involves the use of analytical techniques in order to evaluate the statistics of the dynamic response of the buildings. Both uncertainty in the seismic intensity and record‐to‐record variability are taken into account. The proposed methodology is applied to several different buildings modeled as linear elastic single‐degree‐of‐freedom (SDOF) and multi‐degree‐of‐freedom (MDOF) systems, as well as SDOF nonlinear hysteretic systems. The design separation distances obtained are compared with the corresponding estimates that are based on several response combination rules suggested in the seismic design codes and in the literature. In contrast to current seismic code design procedures, the newly proposed methodology provides consistent safety levels for different building properties and different seismic hazard conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

A performance‐based framework for adaptive seismic aftershock risk assessment

Operative seismic aftershock risk forecasting can be particularly useful for rapid decision‐making in the presence of an ongoing sequence. In such a context, limit state first‐excursion probabilities (risk) for the forecasting interval (a day) can represent the potential for progressive state of damage in a structure. This work lays out a performance‐based framework for adaptive aftershock risk assessment in the immediate post‐mainshock environment. A time‐dependent structural performance variable is adopted in order to measure the cumulative damage in a structure. A set of event‐dependent fragility curves as a function of the first‐mode spectral acceleration for a prescribed limit state is calculated by employing back‐to‐back nonlinear dynamic analyses. An epidemic‐type aftershock sequence model is employed for estimating the spatio‐temporal evolution of aftershocks. The event‐dependent fragility curves for a given limit state are then integrated together with the probability distribution of aftershock spectral acceleration based on the epidemic‐type aftershock sequence aftershock hazard. The daily probability of limit state first‐excursion is finally calculated as a weighted combination of the sequence of limit state probabilities conditioned on the number of aftershocks. As a numerical example, daily aftershock risk is calculated for the L'Aquila 2009 aftershock sequence (central Italy). A representative three‐story reinforced concrete frame with infill panels, which has cyclic strength and stiffness degradation, is used in order to evaluate the progressive damage. It is observed that the proposed framework leads to a sound forecasting of limit state first‐excursion in the structure for two limit states of significant damage and near collapse. Copyright © 2014 John Wiley & Sons, Ltd.     

Modal pushover‐based scaling of earthquake records for nonlinear analysis of single‐story unsymmetric‐plan buildings

The modal pushover‐based scaling (MPS) procedure, currently restricted to symmetric‐plan buildings, is extended herein to unsymmetric‐plan buildings. The accuracy of the extended MPS procedure was evaluated for a large set of three‐degree‐of‐freedom unsymmetric‐plan structures with variable stiffness and strength. The structures were subjected to nonlinear response history analysis considering sets of seven records scaled according to the MPS procedure. Structural responses were compared against the benchmark values, defined as the median values of the engineering demand parameters due to 30 unscaled records. This evaluation of the MPS procedure has led to the following conclusions: (i) the MPS procedure provided accurate estimates of median engineering demand parameter values and reduced record‐to‐record variability of the responses; and (2) the MPS procedure is found to be much superior compared to the ASCE/SEI 7‐10 scaling procedure for three‐dimensional analysis of unsymmetric‐plan buildings. Copyright © 2013 John Wiley & Sons, Ltd.