Limitations on linear elastic procedures in performance assessment of regular frames

Linear elastic analysis procedures are employed exclusively in the traditional seismic design of new structures and widely employed in the seismic assessment of existing structures. It is also a convenient tool for the initial checking of deformations in displacement‐based design. The limitations that should be imposed on linear elastic procedures have been evaluated in this study by comparing the deformation‐based response quantities obtained from response spectrum analysis with those from the nonlinear time history analysis. Both procedures were applied to different design variants of 5, 8, and 12 story moment frames, subjected to 20 strong motion components exhibiting a variety of intensities. Member plastic rotations and interstory drift ratios were employed as the basic response parameter in performance assessment. It has been found that average column demand to capacity ratio (DCR) (the ratio of flexural demand from linear elastic analysis to flexural capacity) and average beam DCR at the critical story are the most effective parameters in determining the validity range of linear elastic procedures in regular moment frames. Limiting values for these response parameters are proposed. Furthermore, amplification factors for member rotation demands predicted by the linear procedures are suggested for moment frames when these limiting values are exceeded. These factors ensure that the amplified linear elastic rotations are not smaller than 84 percentile (mean – 1sigma) of the rotations obtained from nonlinear time history analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Cursory seismic drift assessment for buildings in moderate seismicity regions

This paper outlines a methodology to assess the seismic drift of reinforced concrete buildings with limited structural and geotechnical information. Based on the latest and the most advanced research on predicting potential near-field and far field earthquakes affecting Hong Kong, the engineering response spectra for both rock and soil sites are derived. A new step-by-step procedure for displacement-based seismic hazard assessment of building structures is proposed to determine the maximum inter-storey drift demand for reinforced concrete buildings. The primary information required for this assessment is only the depth of the soft soil above bedrock and the height of the building. This procedure is further extended to assess the maximum chord rotation angle demand for the coupling beam of coupled shear wall or frame wall structures, which may be very critical when subjected to earthquake forces. An example is provided to illustrate calibration of the assessment procedure by using actual engineering structural models.     

Displacement limits and performance displacement profiles in support of direct displacement‐based seismic assessment of bridges

Displacement limits and performance displacement profiles (PDPs) for the direct displacement‐based assessment of existing bridges are proposed. The PDPs are defined as the bridge inelastic deformed shapes associated with the attainment of selected damage states in some critical elements of the bridge. In the paper, displacement limits are provided for piers, abutments, joints, bearing devices and shear keys. Moreover, different approaches for the definition of the PDP are examined, including adaptive pushover analysis, effective modal analysis, and rational analysis of simplified bridge models. In the paper, the key aspects and modeling assumptions of the proposed direct displacement‐based assessment procedure are presented first. This is followed by some examples of application to typical Italian highway bridge configurations, differing in pier layout, deck type, and pier‐deck connections. Copyright © 2013 John Wiley & Sons, Ltd.     

A comparison of intensity‐based demand distributions and the seismic demand hazard for seismic performance assessment

This paper compares the seismic demands obtained from an intensity‐based assessment, as conventionally considered in seismic design guidelines, with the seismic demand hazard. Intensity‐based assessments utilize the distribution of seismic demand from ground motions that have a specific value of some conditioning intensity measure, and the mean of this distribution is conventionally used in design verification. The seismic demand hazard provides the rate of exceedance of various seismic demand values and is obtained by integrating the distribution of seismic demand at multiple intensity levels with the seismic hazard curve. The seismic demand hazard is a more robust metric for quantifying seismic performance, because seismic demands from an intensity‐based assessment: (i) are not unique, with different values obtained using different conditioning intensity measures; and (ii) do not consider the possibility that demand values could be exceeded from different intensity ground motions. Empirical results, for a bridge‐foundation‐soil system, illustrate that the mean seismic demand from an intensity‐based assessment almost always underestimates the demand hazard value for the exceedance rate considered, on average by 17% and with a large variability. Furthermore, modification factors based on approximate theory are found to be unreliable. Adopting the maximum of the mean values from multiple intensity‐based assessments, with different conditional intensity measures, provides a less biased prediction of the seismic demand hazard value, but with still a large variability, and a proportional increase the required number of analyses. For an equivalent number of analyses, direct computation of the seismic demand hazard is a more logical choice and provides additional performance insight. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental multi‐level seismic performance assessment of 3D RC frame designed for damage avoidance

This paper experimentally investigates the application of damage avoidance design (DAD) philosophy to moment‐resisting frames with particular emphasis on detailing of rocking interfaces. An 80% scale three‐dimensional rocking beam–column joint sub‐assembly designed and detailed based on damage avoidance principles is constructed and tested. Incremental dynamic analysis is used for selecting ground motion records to be applied to the sub‐assembly for conducting a multi‐level seismic performance assessment (MSPA). Analyses are conducted to obtain displacement demands due to the selected near‐ and medium‐field ground motions that represent different levels of seismic hazard. Thus, predicted displacement time histories are applied to the sub‐assembly for conducting quasi‐earthquake displacement tests. The sub‐assembly performed well reaching drifts up to 4.7% with only minor spalling occurring at rocking beam interfaces and minor flexural cracks in beams. Yielding of post‐tensioning threaded bars occurred, but the sub‐assembly did not collapse. The externally attached energy dissipators provided large hysteretic dissipation during large drift cycles. The sub‐assembly satisfied all three seismic performance requirements, thereby verifying the superior performance of the DAD philosophy. Copyright © 2007 John Wiley & Sons, Ltd.     

Simplified procedure for the estimation of local inelastic deformation demands for seismic performance assessment of buildings

The implementation of performance‐based design and assessment procedures in seismic codes leads to the need for an accurate estimation of local component demands. According to Part 3 of Eurocode 8 safety checks should be always conducted in terms of plastic rotations, even when linear elastic methods of analysis are used. This paper demonstrates that linear analysis fails to predict inelastic deformation demands at the member level. Therefore, a simplified procedure that allows for the estimation of beam inelastic deformation demands using linear elastic methods of analysis in a simple and conservative way is presented herein. A number of moment‐resisting steel frames designed according to different criteria and exhibiting different column‐to‐beam strength ratios were analysed and used for the derivation of the proposed procedure. A comparative study between alternative methods of quantifying inelastic deformation demands using linear analysis is also carried out. The results obtained allow concluding about the efficiency and conservativeness of the proposed procedure which makes it attractive to be employed in engineering practice. Copyright © 2016 John Wiley & Sons, Ltd.     

A displacement‐based seismic design procedure for RC buildings and comparison with EC8

A procedure for displacement‐based seismic design (DBD) of reinforced concrete buildings is described and applied to a 4‐storey test structure. The essential elements of the design procedure are: (a) proportioning of members for gravity loads; (b) estimation of peak inelastic member deformation demands in the so‐designed structure due to the design (‘life‐safety’) earthquake; (c) revision of reinforcement and final detailing of members to meet these inelastic deformation demands; (d) capacity design of members and joints in shear. Additional but non‐essential steps between (a) and (b) are: (i) proportioning of members for the ULS against lateral loads, such as wind or a serviceability (‘immediate occupancy’) earthquake; and (ii) capacity design of columns in flexure at joints. Inelastic deformation demands in step (b) are estimated from an elastic analysis using secant‐to‐yield member stiffnesses. Empirical expressions for the deformation capacity of RC elements are used for the final proportioning of elements to meet the inelastic deformation demands. The procedure is applied to one side of a 4‐storey test structure that includes a coupled wall and a two‐bay frame. The other side is designed and detailed according to Eurocode 8. Major differences result in the reinforcement of the two sides, with significant savings on the DBD‐side. Pre‐test calculations show no major difference in the seismic performance of the two sides of the test structure. Copyright © 2001 John Wiley & Sons, Ltd.     

Procedures for calibration of linear models for damage limitation in design of masonry‐infilled RC frames

Recent earthquakes have confirmed the role played by infills in the seismic response of reinforced concrete buildings. The control and limitation of damage to such nonstructural elements is a key issue in performance‐based earthquake engineering. The present work is focused on modeling and analysis of damage to infill panels, and, in particular, it is aimed towards linear analysis procedures for assessing the damage limitation limit state of infilled reinforced concrete frames. First, code provisions on infill modeling and acceptance criteria at the damage limitation limit state are reviewed. Literature contributions on damage to unreinforced masonry infill panels and corresponding displacement capacity are reported and discussed. Two procedures are then proposed aiming at a twofold goal: (i) the determination of ‘equivalent’ interstory drift ratio limits for a bare frame model and (ii) the estimation of the stiffness of equivalent struts representing infill walls in a linear model. These two quantities are determined such that a linear model ensures a reliable estimation of seismic capacity at the damage limitation limit state, providing the same intensity level as that obtained from nonlinear analyses carried out on structural models with infills. Finally, the proposed procedures are applied to four‐story and eight‐story case study‐infilled frames, designed for seismic loads according to current technical codes. The results of these application examples are presented and discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Direct displacement‐based seismic assessment procedure for multi‐span reinforced concrete bridges with single‐column piers

In Italy, as in other high seismic risk countries, many bridges, nowadays deemed ‘strategic’ for civil protection interventions after an earthquake, were built without antiseismic criteria, and therefore their seismic assessment is mandatory. Accordingly, the development of a seismic assessment procedure that gives reliable results and, at the same time, is sufficiently simple to be applied on a large population of bridges in a short time is very useful. In this paper, a displacement‐based procedure for the assessment of multi‐span RC bridges, satisfying these requirements and called direct displacement‐based assessment (DDBA), is proposed. Based on the direct displacement‐based design previously developed by Priestley et al., DDBA idealizes the multi DOF bridge structure as an equivalent SDOF system and hence defines a safety factor in terms of displacement. DDBA was applied to hypothetical bridge configurations. The same structures were analyzed also using standard force‐based approach. The reliability of the two methods was checked performing IDA with response spectrum compatible accelerograms. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance‐based seismic assessment method for Taiwanese historic Dieh‐Dou timber structures

Lateral force, response spectrum and step‐by‐step pushover analyses are performed and compared with the post‐earthquake survey of two Dieh‐Dou buildings seriously affected in the 1999 Chi‐Chi earthquake in Taiwan. The results show that the proposed FE model with finite translational and rotational stiffness can successfully be employed to assess the vulnerability of the frames. The fundamental period of Dieh‐Dou structures is about 1.0 s higher than that calculated by the simplified approach of the codes for regular frames; a modal analysis is, therefore, essential for this typology of structure. The elastic analysis, either lateral force or response spectrum, is shown to be reliable to assess Dieh‐Dou frames when quick results are desired. However, a non‐linear step‐by‐step pushover analysis has the advantage of greater accuracy, as it allows mapping the failure trend and indicating the critical elements. The lateral drifts are compared with the actual observed damage pattern and when the damage level is related to the peak ground acceleration on a vulnerability curve plot, it is shown that the joint failure combined with the lateral drift gives an indication of the global structural behaviour of this historic construction typology. Owing to the unique construction features of the Dieh‐Dou, the joint failure represents also a critical criterion in terms of maximum retention for conservation. Based on a damage level approach, an assessment methodology is suggested that would allow optimizing a strengthening strategy, for protection of these precious structures from future earthquakes while avoiding unnecessary interventions. Copyright © 2010 John Wiley & Sons, Ltd.     

Use of the conditional spectrum to incorporate record‐to‐record variability in simplified seismic assessment of RC wall buildings

A procedure for incorporating record‐to‐record variability into the simplified seismic assessment of RC wall buildings is presented. The procedure relies on the use of the conditional spectrum to randomly sample spectral ordinates at relevant periods of vibration. For inelastic response, displacement reduction factors are then used to relate inelastic displacement demand to the spectral displacement at the effective period for single‐degree‐of‐freedom systems. Simple equations are used to convert back and forth between multi‐degree‐of‐freedom RC wall buildings and equivalent single‐degree‐of‐systems so that relevant engineering demand parameters can be obtained. Consideration is also given to higher‐mode effects by adapting existing modal combination rules. The proposed method is applied to several case study buildings, showing promising results in the examination of inter‐storey drift ratio and shear forces. The proposed method captures the variation in the distribution of structural response parameters that occurs with variations in structural configuration, intensity, engineering demand parameter of interest and site characteristics. Discussion is provided on possible ways to improve the accuracy of the procedure and suggestions for additional future work. Copyright © 2015 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.     

Code‐based record selection methods for seismic performance assessment of buildings

The recent concerns regarding the seismic safety of the existing building stock have highlighted the need for an improvement of current seismic assessment procedures. Alongside with the development of more advanced commercial software tools and computational capacities, nonlinear dynamic analysis is progressively becoming a common and preferable procedure in the seismic assessment of buildings. Besides the complexity associated with the formulation of the mathematical model, major issues arise related with the definition of the seismic action, which can lead to different levels of uncertainty in terms of local and global building response. Aiming to address this issue, a comparative study of different code‐based record selection methods proposed by Eurocode 8, ASCE41‐13 and NZS1170.5:2004 is presented herein. The various methods are employed in the seismic assessment of four steel buildings, designed according to different criteria, and the obtained results are compared and discussed. Special attention is devoted to the influence of the number of real ground motion records selected on the estimation of the mean seismic response and, importantly, to the efficiency that is achieved when an additional selection criteria, based on the control of the spectral mismatch of each individual record with respect to the reference response spectrum, is adopted. The sufficiency of the methods with respect to the pairs of M–R of the selected group of records and the robustness of the scaling procedure are also examined. The paper closes with a study which demonstrates the suitability of a simplified probability‐based approach recently proposed for estimating mean seismic demands. Copyright © 2015 John Wiley & Sons, Ltd.     

Simulations of non‐stationary frequency content and its importance to seismic assessment of structures

To verify the importance of the non‐stationary frequency characteristic of seismic ground motion, a joint time–frequency analysis technique of time signals, called chirplet‐based signal approximation, is developed to extract the non‐stationary frequency information from the recorded data. The chirplet‐based signal approximation is clear in concept, similar to Fourier Transform in mathematical expressions but with different base functions. Case studies show that the chirplet‐based signal approximation can represent the joint time–frequency variation of seismic ground motion quite well. Both the random models of uniform modulating process and evolutionary process are employed to generate artificial seismic waves. The joint time–frequency modulating function in the random model of evolutionary process is determined by chirplet‐based signal approximation. Finally, non‐linear response analysis of a SODF system and a frame structure is performed based on the generated artificial seismic waves. The results show that the non‐stationary frequency characteristic of seismic ground motion can significantly change the non‐linear response characteristics of structures, particularly when a structure goes into collapse phase under seismic action. It is concluded that non‐stationary frequency characteristic of seismic ground motion should be considered for the assessment of seismic capacity of structures. Copyright © 2002 John Wiley & Sons, Ltd.     

A fuzzy–random analysis model for seismic performance of framed structures incorporating structural and non‐structural damage

Past earthquake experiences indicate that most buildings designed in accordance with modern seismic design codes could survive moderate‐to‐strong earthquakes; however, the financial loss due to repairing cost and the subsequent business interruption can be unacceptable. Designing building structures to meet desired performance targets has become a clear direction in future seismic design practice. As a matter of fact, the performance of buildings is affected by structural as well as non‐structural components, and involves numerous uncertainties. Therefore, appropriate probabilistic approach taking into account structural and non‐structural damages is required. This paper presents a fuzzy–random model for the performance reliability analysis of RC framed structures considering both structural and non‐structural damages. The limit state for each performance level is defined as an interval of inter‐storey drift ratios concerning, respectively, the non‐structural and structural damage with a membership function, while the relative importance of the two aspects is reflected through the use of an appropriate cost function. To illustrate the methodology, herein the non‐structural damage is represented by infill masonry walls. The probabilistic drift limits for RC components and masonry walls from the associated studies are employed to facilitate the demonstration of the proposed model in an example case study. The results are compared with those obtained using classical reliability model based on single‐threshold performance definition. The proposed model provides a good basis for incorporating different aspects into the performance assessment of a building system. Copyright © 2005 John Wiley & Sons, Ltd.     

Evaluation of a recently proposed record selection and scaling procedure for low‐rise to mid‐rise reinforced concrete buildings and its use for probabilistic risk assessment studies

This paper evaluates a recent record selection and scaling procedure of the authors that can determine the probabilistic structural response of buildings behaving either in the elastic or post‐elastic range. This feature marks a significant strength on the procedure as the probabilistic structural response distribution conveys important information on probability‐based damage assessment. The paper presents case studies that show the utilization of the proposed record selection and scaling procedure as a tool for the estimation of damage states and derivation of site‐specific and region‐specific fragility functions. The method can be used to describe exceedance probabilities of damage limits under a certain target hazard level with known annual exceedance rate (via probabilistic seismic hazard assessment). Thus, the resulting fragility models can relate the seismicity of the region (or a site) with the resulting building performance in a more accurate manner. Under this context, this simple and computationally efficient record selection and scaling procedure can be benefitted significantly by probability‐based risk assessment methods that have started to be considered as indispensable for developing robust earthquake loss models. Copyright © 2013 John Wiley & Sons, Ltd.     

Modified three‐dimensional seismic assessment method for buildings based on ambient vibration tests: extrapolation to higher shaking levels and measuring the dynamic amplification portion of natural torsion

This paper presents applications of the modified 3D‐SAM approach, a three‐dimensional seismic assessment methodology for buildings directly based on in situ experimental modal tests to calculate global seismic demands and the dynamic amplification portion of natural torsion. Considering that the building modal properties change from weak to strong motion levels, appropriate modification factors are proposed to extend the application of the method to stronger earthquakes. The proposed approach is consistent with the performance‐based seismic assessment approach, which entails the prediction of seismic displacements and drift ratios that are related to the damage condition and therefore the functionality of the building. The modified 3D‐SAM is especially practical for structures that are expected to experience slight to moderate damage levels and in particular for post‐disaster buildings that are expected to remain functional after an earthquake. In the last section of this paper, 16 low to mid‐rise irregular buildings located in Montreal, Canada, and that have been tested under ambient vibrations are analyzed with the method, and the dynamic amplification portion of natural torsion of the dataset is reported and discussed. The proposed methodology is appropriate for large‐scale assessments of existing buildings and is applicable to any seismic region of the world. Copyright © 2016 John Wiley & Sons, Ltd.