Decoupling algorithm for evaluating multiple beam damages in steel moment‐resisting frames

Post‐earthquake safety evaluation of steel moment‐resisting frames mainly relies on the inspection of seismic damage to beam–column connections. Recently, in order to evaluate seismic damage of steel connections in a prompt and precise manner, a local damage evaluation method based on dynamic strain responses has been proposed and receives attention. In the evaluation method where strain responses are measured by piezoelectric strain sensors, a strain‐based damage index has been developed for evaluating individual seismic beam damage in a steel frame. However, for a steel frame suffering multiple beam damages, the damage index deteriorates its performance in identifying small damages with the presence of neighboring severe damages because of the moment redistributions induced by larger damages. This paper presents a decoupling algorithm that removes the issue of damage interaction and improves the performance of the damage index. The decoupling algorithm was derived on the basis of damage‐induced moment release and redistribution mechanism. The effectiveness of the decoupling algorithm was numerically and experimentally investigated using a nine‐story steel frame model and a large scale five‐story steel frame testbed that can simulate multiple fractures at beam ends. Copyright © 2016 John Wiley & Sons, Ltd.     

Residual structural capacity evaluation of steel moment‐resisting frames with dynamic‐strain‐based model updating method

This paper presents a method for evaluating the residual structural capacity of earthquake‐affected steel structures. The method first quantifies the damage severity of a beam by computing the dynamic‐strain‐based damage index. Next, the model used to analyze the structure is updated based on the damage index, to reflect the observed damage conditions. The residual structural capacity is then estimated in terms of changes in stiffness and strength, which can be applied by structural engineers, via a nonlinear static analysis of the updated model. The main contributions of this paper are in performance evaluation of the dynamic‐strain‐based damage index for seismically induced damage using a newly developed substructure testing environment, consideration of various damage patterns in composite beams, and extension of a local damage evaluation technique to a residual capacity estimation procedure by incorporating the model‐updating technique. In laboratory testing, the specimens were damaged quasi‐statically, and vibration tests were conducted as the damage proceeded. First, a bare steel beam–column connection was tested, and then a similar one with a floor slab was used for a more realistic case. The estimated residual structural capacities for these specimens were compared with the static test results. The results verified that the proposed method can provide fine estimates of the stiffness and strength deteriorations within 10% for the specimen without the floor slab and within 30% for that with the floor slab. Copyright © 2017 John Wiley & Sons, Ltd.     

Modeling level selection for seismic analysis of concrete‐filled steel tube/moment‐resisting frames by using fragility curves

The seismic behavior of plane moment‐resisting frames (MRFs) consisting of I steel beams and concrete‐filled steel tube (CFT) columns is investigated in this study. More specifically, the effect of modeling details of each individual component of CFT‐MRFs, such as the composite CFT columns, the beam‐column connections, the panel zones, and the steel I beams on their seismic behavior, is studied through comparisons against available experimental results. Then, fragility curves are constructed for three typical CFT‐MRFs, designed according to European codes, for various levels of modeling sophistication through nonlinear time‐history analyses. On the basis of these fragility curves, one can select the appropriate modeling level of sophistication that can lead to the desired seismic behavior for a given seismic intensity. Copyright © 2014 John Wiley & Sons, Ltd.     

Development of empirical and analytical fragility functions using kernel smoothing methods

Fragility functions that define the probabilistic relationship between structural damage and ground motion intensity are an integral part of performance‐based earthquake engineering or seismic risk analysis. This paper introduces three approaches based on kernel smoothing methods for developing analytical and empirical fragility functions. A kernel assigns a weight to each data that is inversely related to the distance between the data value and the input of the fragility function of interest. The kernel smoothing methods are, therefore, non‐parametric forms of data interpolation. These methods enable the implicit treatment of uncertainty in either or both of ground motion intensity and structural damage without making any assumption about the shape of the resulting fragility functions. They are particularly beneficial for sparse, noisy, or non‐homogeneous data sets. For illustration purposes, two types of data are considered. The first is a set of numerically simulated responses for a four‐story steel moment‐resisting frame, and the second is a set of field observations collected after the 2010 Haiti earthquake. The results demonstrate that these methods can develop continuous representations of fragility functions without specifying their functional forms and treat sparse data sets more efficiently than conventional data binning and parametric curve fitting methods. Moreover, various uncertainty analyses are conducted to address the issues of over‐fitting, bias, and confidence intervals. Copyright © 2014 John Wiley & Sons, Ltd.     

Uniform fragility spectra for the performance‐based seismic design of structures considering variabilities in structural properties

This paper presents a new methodology based on structural performance to determine uniform fragility design spectra, i.e., spectra with the same probability of exceedance of a performance level for a given seismic intensity. The design spectra calculated with this methodology provide directly the lateral strength, in terms of yield‐ pseudo‐accelerations, associated with the rate of exceedance of a specific ductility characterizing the performance level for which the structures will be designed. This procedure involves the assessment of the seismic hazard using a large enough number of seismic records of several magnitudes; these records are simulated with an improved empirical Green function method. The statistics of the performance of a single degree of freedom system are obtained using Monte Carlo simulation considering the seismic demand, the fundamental period, and the strength of the structure as uncertain variables. With these results, the conditional probability that a structure exceeds a specific performance level is obtained. The authors consider that the proposed procedure is a significant improvement to others considered in the literature and a useful research tool for the further development of uniform fragility spectra that can be used for the performance‐based seismic design and retrofit of structures.     

Development of seismic fragility surfaces for reinforced concrete buildings by means of nonlinear time‐history analysis

Fragility curves are generally developed using a single parameter to relate the level of shaking to the expected structural damage. The main goal of this work is to use several parameters to characterize the earthquake ground motion. The fragility curves will, therefore, become surfaces when the ground motion is represented by two parameters. To this end, the roles of various strong‐motion parameters on the induced damage in the structure are compared through nonlinear time‐history numerical calculations. A robust structural model that can be used to perform numerous nonlinear dynamic calculations, with an acceptable cost, is adopted. The developed model is based on the use of structural elements with concentrated nonlinear damage mechanics and plasticity‐type behavior. The relations between numerous ground‐motion parameters, characterizing different aspects of the shaking, and the computed damage are analyzed and discussed. Natural and synthetic accelerograms were chosen/computed based on a consideration of the magnitude‐distance ranges of design earthquakes. A complete methodology for building fragility surfaces based on the damage calculation through nonlinear numerical analysis of multi‐degree‐of‐freedom systems is proposed. The fragility surfaces are built to represent the probability that a given damage level is reached (or exceeded) for any given level of ground motion characterized by the two chosen parameters. The results show that an increase from one to two ground‐motion parameters leads to a significant reduction in the scatter in the fragility analysis and allows the uncertainties related to the effect of the second ground‐motion parameter to be accounted for within risk assessments. Copyright © 2009 John Wiley & Sons, Ltd.     

Tests and model calibration of high‐strength steel tubular beam‐to‐column and column‐base composite joints for moment‐resisting structures

Performance‐based engineering (PBE) methodologies allow for the design of more reliable earthquake‐resistant structures. Nonetheless, to implement PBE techniques, accurate finite element models of critical components are needed. With these objectives in mind, initially, we describe an experimental study on the seismic behaviour of both beam‐to‐column (BTC) and column‐base (CB) joints made of high‐strength steel S590 circular columns filled with concrete. These joints belonged to moment‐resisting frames (MRFs) that constituted the lateral‐force‐resisting system of an office building. BTC joints were conceived as rigid and of partial strength, whereas CB joints were designed as rigid and of full strength. Tests on a BTC joint composed of an S275 steel composite beam and high‐strength steel concrete‐filled tubes were carried out. Moreover, two seismic CB joints were tested with stiffeners welded to the base plate and anchor bolts embedded in the concrete foundation as well as where part of a column was embedded in the foundation with no stiffeners. A test programme was carried out with the aim of characterising these joints under monotonic, cyclic and random loads. Experimental results are presented by means of both force–interstory drift ratio and moment–rotation relationships. The outcomes demonstrated the adequacy of these joints to be used for MRFs of medium ductility class located in zones of moderate seismic hazard. Then, a numerical calibration of the whole joint subassemblies was successfully accomplished. Finally, non‐linear time‐history analyses performed on 2D MRFs provided useful information on the seismic behaviour of relevant MRFs. Copyright © 2015 John Wiley & Sons, Ltd.     

Need of performance‐based earthquake engineering in Taiwan: a lesson from the Chichi earthquake

The objectives of seismic engineering are to design and build better and more economic earthquake‐resistant structures. Performance, which is measured as the amount of damage of a facility and the impact of damage to the society after an earthquake, is the main concern. Performance‐based earthquake engineering (PBEE) implies design, evaluation, and construction of engineered facilities whose performance under common and extreme earthquake ground motions responds to the diverse needs and objectives of the owners, users and society. Observations on the performance or damage of structures after strong earthquake ground motions have always served as an effective means to evaluate the current seismic regulations and guidelines and make further improvements afterwards. This paper presents some of the typical damage evidence after the Chichi earthquake occurred recently in Taiwan. Important issues in performance‐based earthquake engineering that need to be considered in future seismic regulations of Taiwan are addressed accordingly. Copyright © 2000 John Wiley & Sons, Ltd.     

Vibration‐based damage assessment of steel structure using global and local response measurements

Damage assessment of a structure involves acquiring and identifying dynamic characteristics of the structure and using these characteristics to evaluate behavior and performance. In this study, an unsymmetrical three‐story steel structure (fabricated with one weak column in the first floor) was tested on shaking table and subjected to a series of earthquake excitations with increasing level of excitation back to back. Besides, white noise excitation was also applied in between the earthquake excitation to serve as the reference state. Both the traditional sensing system (accelerometer and linear variable differential transformer) and the local optical tracker system were implemented in the structure to collect the vibration‐based responses. For operational modal analysis, structural response from white noise excitation will be used in this study. First, the traditional system identification using global response data is used (multivariate autoregressive (AR)‐model) to extract system natural frequencies and mode shapes from all different set of white noise responses after earthquake excitation. The migration of AR‐coefficient ellipse error from each sensor response was used to identify the damage location. Second, blind source separation technique was used to identify the modal contribution of the structure from each test, which provide information to detect the damage severity. Finally, from the local optical tracker array data, the principal component analysis was applied to quantify the earthquake‐induce local stress of the structural member. Combine the result from damage detection using global measurement and the identified local element stress, one can locate and quantify the damage. Copyright © 2015 John Wiley & Sons, Ltd.     

A web‐based methodology for the prediction of approximate IDA curves

A web‐based methodology for the prediction of approximate IDA curves, which consists of two independent processes, is proposed. The result of the first process is a response database of the SDOF model, whereas the second process involves the prediction of approximate IDA curves from the response database by using n‐dimensional linear interpolation. Such an approach enables user‐friendly prediction of the seismic response parameters with high accuracy. In order to demonstrate the capabilities of the proposed methodology, a web application for the prediction of the approximate 16th, 50th and 84th fractile responses of an RC structure was developed. For the presented case study, the response database was computed for a set of 30 ground motion records and the discrete values of six structural parameters. Very good agreement between the computed and the approximated IDA curves of the four‐storey RC building was observed. Copyright © 2012 John Wiley & Sons, Ltd.     

Uniform hazard versus uniform risk bases for performance‐based earthquake engineering of light‐frame wood construction

This paper investigates the implications of designing for uniform hazard versus uniform risk for light‐frame wood residential construction subjected to earthquakes in the United States. Using simple structural models of one‐story residences with typical lateral force‐resisting systems (shear walls) found in buildings in western, eastern and central regions of the United States as illustrations, the seismic demands are determined using nonlinear dynamic time‐history analyses, whereas the collapse capacities are determined using incremental dynamic analyses. The probabilities of collapse, conditioned on the occurrence of the maximum considered earthquakes and design earthquakes stipulated in ASCE Standard 7‐05, and the collapse margins of these typical residential structures are compared for typical construction practices in different regions in the United States. The calculated collapse inter‐story drifts are compared with the limits stipulated in FEMA 356/ASCE Standard 41‐06 and observed in the recent experimental testing. The results of this study provide insights into residential building risk assessment and the relation between building seismic performance implied by the current earthquake‐resistant design and construction practices and performance levels in performance‐based engineering of light‐frame wood construction being considered by the SEI/ASCE committee on reliability‐based design of wood structures. Further code developments are necessary to achieve the goal of uniform risk in earthquake‐resistant residential construction. Copyright © 2010 John Wiley & Sons, Ltd.     

Accounting for directionality as a function of structural typology in performance‐based earthquake engineering design

For the seismic design of a structure, horizontal ground shaking is usually considered in two perpendicular directions, even though real horizontal ground motions are complex two‐dimensional phenomena that impose different demands at different orientations. While the issue of ground motion dependence on the orientation of the recording devices has been the focus of many significant developments during the last decade, the effects of directionality on the characteristics of the structure have received less attention. This work presents a proposal to calculate the probability of exceedance of elastic spectral displacements accounting for structural typology and illustrates its relevance by means of its application to two case‐study buildings. In order to ease its implementation in seismic design codes, a simplification is developed by means of a detailed statistical analysis of the results obtained using four sets of real hazard curves. The framework presented herein is considered to represent an important contribution to the field of performance‐based earthquake engineering, permitting improved treatment of directionality effects within seismic risk design and assessment. Copyright © 2016 John Wiley & Sons, Ltd.     

Active sensing using impedance‐based ARX models and extreme value statistics for damage detection

In this paper, the applicability of an auto‐regressive model with exogenous inputs (ARX) in the frequency domain to structural health monitoring (SHM) is established. Damage sensitive features that explicitly consider non‐linear system input/output relationships are extracted from the ARX model. Furthermore, because of the non‐Gaussian nature of the extracted features, Extreme Value Statistics (EVS) is employed to develop a robust damage classifier. EVS provides superior performance to standard statistical methods because the data of interest are in the tails (extremes) of the damage sensitive feature distribution. The suitability of the ARX model, combined with EVS, to non‐linear damage detection is demonstrated using vibration data obtained from a laboratory experiment of a three‐story building model. It is found that the vibration‐based method, while able to discern when damage is present in the structure, is unable to localize the damage to a particular joint. An impedance‐based active sensing method using piezoelectric (PZT) material as both an actuator and a sensor is then investigated as an alternative solution to the problem of damage localization. Copyright © 2005 John Wiley & Sons, Ltd.     

Probabilistic performance‐based optimum design of seismic isolation for a California high‐speed rail prototype bridge

Previous comparison studies on seismic isolation have demonstrated its beneficial and detrimental effects on the structural performance of high‐speed rail bridges during earthquakes. Striking a balance between these 2 competing effects requires proper tuning of the controlling design parameters in the design of the seismic isolation system. This results in a challenging problem for practical design in performance‐based engineering, particularly when the uncertainty in seismic loading needs to be explicitly accounted for. This problem can be tackled using a novel probabilistic performance‐based optimum seismic design (PPBOSD) framework, which has been previously proposed as an extension of the performance‐based earthquake engineering methodology. For this purpose, a parametric probabilistic demand hazard analysis is performed over a grid in the seismic isolator parameter space, using high‐throughput cloud‐computing resources, for a California high‐speed rail (CHSR) prototype bridge. The derived probabilistic structural demand hazard results conditional on a seismic hazard level and unconditional, i.e., accounting for all seismic hazard levels, are used to define 2 families of risk features, respectively. Various risk features are explored as functions of the key isolator parameters and are used to construct probabilistic objective and constraint functions in defining well‐posed optimization problems. These optimization problems are solved using a grid‐based, brute‐force approach as an application of the PPBOSD framework, seeking optimum seismic isolator parameters for the CHSR prototype bridge. This research shows the promising use of seismic isolation for CHSR bridges, as well as the potential of the versatile PPBOSD framework in solving probabilistic performance‐based real‐world design problems.