• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.495-502
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• 2003

This study proposed the Probability Density Function (PDF) interpolation technique to evaluate the seismic fragility curves as a function of the return period. Seismic fragility curves have been developed as a function of seismic intensities such as peak ground acceleration, peak pound velocity, and pseudo-velocity spectrum. The return period of design earthquakes, however, can be more useful among those seismic intensity measurements, because the seismic hazard curves are generally represented with a return period of design earthquakes and the seismic design codes also require to consider the return period of design earthquake spectrum for a specific site. In this respect the PDF interpolation technique is proposed to evaluate the seismic fragility curves as a function of return period. Seismic fragility curves based on the return period are compared with ones based on the peak ground acceleration for the bridge model.

• Earthquakes and Structures
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• v.6 no.6
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• pp.689-713
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• 2014

The seismic vulnerability of stone masonry buildings is studied on the basis of their fragility curves. In order to account for out-of-plane failure modes, normally disregarded in past studies, linear static Finite Element analysis in 3D of prototype regular buildings is performed using a nonlinear biaxial failure criterion for masonry. More than 1100 analyses are carried out, so as to cover the practical range of the most important parameters, namely the number of storeys, percentage of side length in exterior walls taken up by openings, wall thickness, plan dimensions and number of interior walls, type of floor and pier height-to-length ratio. Results are presented in the form of damage and fragility curves. The fragility curves correspond well to the damage observed in masonry buildings after strong earthquakes and are in good agreement with other fragility curves in the literature. They confirm what is already known, namely that buildings with stiff floors or higher percentage of load-bearing walls are less vulnerable, and that large openings, taller storeys, larger number of storeys, higher wall slenderness and higher ratio of clear height to horizontal length of walls increase the vulnerability, but show also by how much.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.09a
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• pp.319-325
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• 2003

The fragility curves of seismic retrofitted bridges by steel jacketing of bridge columns and restrainers at expansion joints after the 1994 Northridge earthquake are developed. Fragility curves are represented by lognormal distribution functions with two parameters(fragility parameters consisting of median and log-standard deviation) and developed as a function of peak ground acceleration (PGA). Two parameters in the lognormal distribution are estimated by the maximum likelihood method. The sixty ground acceleration time histories for Los Angeles area developed for FEMA SAC project are used for the dynamic analysis of the bridges and a computer code is developed to calculate hysterestic parameters of bridge columns before and after steel jacketing. The effect of retrofit is expressed in terms of the increase of the median value of the fragility curve for the retrofitted bridge from that of the bridge before retrofit. The comparison of fragility curves of the bridges before and after column retrofit demonstrates that the improvement of the bridges with steel jacketing on the seismic performance is excellent for the damage states defined in this study. The comparison of fragility curves of the bridges before and after restrainers at expansion joints also shows the improvement in the seismic performance of restrained bridges for the severe damage states.

• Wind and Structures
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• v.9 no.3
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• pp.217-230
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• 2006

This paper describes a procedure to develop fragility curves for woodframe structures subjected to lateral wind loads. The fragilities are cast in terms of horizontal displacement criteria (maximum drift at the top of the shearwalls). The procedure is illustrated through the development of fragility curves for one and two-story residential woodframe buildings in high wind regions. The structures were analyzed using a monotonic pushover analysis to develop the relationship between displacement and base shear. The base shear values were then transformed to equivalent nominal wind speeds using information on the geometry of the baseline buildings and the wind load equations (and associated parameters) in ASCE 7-02. Displacement vs. equivalent nominal wind speed curves were used to determine the critical wind direction, and Monte Carlo simulation was used along with wind load parameter statistics provided by Ellingwood and Tekie (1999) to construct displacement vs. wind speed curves. Wind speeds corresponding to a presumed limit displacement were used to construct fragility curves. Since the fragilities were fit well using a lognormal CDF and had similar logarithmic standard deviations (${\xi}$), a quick analysis to develop approximate fragilities is possible, and this also is illustrated. Finally, a compound fragility curve, defined as a weighted combination of individual fragilities, is developed.

• Earthquakes and Structures
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• v.18 no.6
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• pp.709-718
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• 2020

Fragility curves are useful tools to estimate the damage probability of buildings owing to seismic actions. The purpose of this study is to investigate seismic vulnerability of reinforced concrete (RC) buildings, according to the 2007 and 2018 Turkish Seismic Codes, using fragility curves. For the numerical analyses, typical five- and seven-storey RC buildings were selected and incremental dynamic analyses (IDA) were performed. To complete the IDAs, eleven earthquake acceleration records multiplied by various scaling factors from 0.2g to 0.8g were used. To predict nonlinearity, a distributed hinge model that involves material and geometric nonlinearity of the structural members was used. Damages to confined concrete and reinforcement bar of structural members were obtained by considering the unit deformation demands of the 2007 Turkish Seismic Code (TSC-2007) and the 2018 Turkey Building Earthquake Code (TBEC-2018). Vulnerability evaluation of these buildings was performed using fragility curves based on the results of incremental dynamic analyses. Fragility curves were generated in terms of damage levels occurring in confined concrete and reinforcement bar of structural members with a lognormal distribution assumption. The fragility curves show that the probability of damage occurring is more according to TBEC-2018 than according to TSC-2007 for selected buildings.

• Journal of the Earthquake Engineering Society of Korea
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• v.14 no.5
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• pp.53-64
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• 2010

Seismic fragility curves of structures represent the probability of exceeding the prescribed structural damage state for a given various levels of ground motion intensity, such as peak ground acceleration (PGA). This means that seismic fragility curves are essential to the evaluation of structural seismic performance and assessments of risk. Most of existing studies have not considered the near- and far-fault earthquake effect on the seismic fragility curves. In order to evaluate the effect of near- and far-fault earthquakes, seismic fragility curves for PSC box girder bridges subjected to near- and far-fault earthquakes are calculated and compared. The seismic fragility curves are strongly dependent on the earthquake characteristics such as fault distance. This paper suggests that the effect of near- and far-fault earthquakes on seismic fragility curves of PSC box girder bridge structure should be considered.

• Journal of the Korean Society of Industry Convergence
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• v.9 no.3
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• pp.207-214
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• 2006

In this paper, the stability of SA(Spectral Acceleration) fragility curves is studied for the two sets of elastic modulus of concrete. In doing that, general purpose structural analysis program and generally used probability density function are used. The results of structural analysis are represented by Bernoulli distribution which says damage or no damage. By the use of Maximum Likelihood Method, two parameters of lognormal distribution - median and standard deviation - are found. With them, the fragility curves are constructed.

• Journal of the Earthquake Engineering Society of Korea
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• v.22 no.5
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• pp.271-280
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• 2018

This paper presents a framework for developing aftershock fragility curves for reinforced concrete bridges initially damaged by mainshocks. The presented aftershock fragility is a damage-dependent fragility function, which is conditioned on an initial damage state resulting from mainshocks. The presented framework can capture the cumulative damage of as-built bridges due to mainshock-aftershock sequences as well as the reduced vulnerability of bridges repaired with CFRP pier jackets. To achieve this goal, the numerical model of column jackets is firstly presented and then validated using existing experimental data available in literature. A four-span concrete box-girder bridge is selected as a case study to examine the application of the presented framework. The aftershock fragility curves are derived using response data from back-to-back nonlinear dynamic analyses under mainshock-aftershock sequences. The aftershock fragility curves for as-built bridge columns are firstly compared with different levels of initial damage state, and then the post-repair effect of FRP pier jacket is examined through the comparison of aftershock fragility curves for as-built and repaired piers.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.5
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• pp.75-83
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• 2003

The ultimate goal of this research is to improve highway system performance in earthquakes by evaluating the effectiveness of retrofitting bridges with column jacketing. The objective of the study is to determine if steel jacketing increases the ductility capacity of bridge columns and hence improves the fragility characteristics of the bridge. Analytical fragility curves are used to adjust the empirical fragility curves obtained for the unretrofitted bridges using seismic damage data collected following past earthquakes. The adjustment was carried out by increasing the median values of the empirical curves through comparison with the median values of the corresponding fragility curves obtained analytically, both before and after being retrofit.

• Nuclear Engineering and Technology
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• v.51 no.3
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• pp.894-903
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• 2019

An approach for collapse risk assessment is proposed to evaluate the vulnerability of electric cabinet in nuclear power plants. The lognormal approaches, namely maximum likelihood estimation and linear regression, are introduced to establish the fragility curves. These two fragility analyses are applied for the numerical models of cabinets considering various boundary conditions, which are expressed by representing restrained and anchored models at the base. The models have been built and verified using the system identification (SI) technique. The fundamental frequency of the electric cabinet is sensitive because of many attached devices. To bypass this complex problem, the average spectral acceleration $S_{\bar{a}}$ in the range of period that cover the first mode period is chosen as an intensity measure on the fragility function. The nonlinear time history analyses for cabinet are conducted using a suite of 40 ground motions. The obtained curves with different approaches are compared, and the variability of risk assessment is evaluated for restrained and anchored models. The fragility curves obtained for anchored model are found to be closer each other, compared to the fragility curves for restrained model. It is also found that the support boundary conditions played a significant role in acceleration response of cabinet.