• International journal of steel structures
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• v.18 no.5
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• pp.1684-1698
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• 2018

Fragility functions are determined for braced steel moment frames (SMFs) with plans such as square-, T-, L-, U-, trapezoidal-, and semicircular-shaped, subjected to blast. The frames are designed for gravity and seismic loads, but not necessarily for the blast loads. The blast load is computed for a wide range of scenarios involving different parameters, viz. charge weight, standoff distance, and blast location relative to plan of the structure followed by nonlinear dynamic analysis of the frames. The members failing in rotation lead to partial collapse due to plastic mechanism formation. The probabilities of partial collapse of the SMFs, with and without bracing system, due to the blast loading are computed to plot fragility curves. The charge weight and standoff distance are taken as Gaussian random input variables. The extent of propagation of the uncertainties in the input parameters onto the response quantities and fragility of the SMFs is assessed by computing Sobol sensitivity indices. The probabilistic analysis is conducted using Monte Carlo simulations. The frames have least failure probability for blasts occurring in front of their corners or convex face. Further, the unbraced frames are observed to have higher fragility as compared to counterpart braced frames for far-off detonations.

• Earthquakes and Structures
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• v.14 no.3
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• pp.203-214
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• 2018

Predictive demand and collapse fragility functions are two essential components of the probabilistic seismic demand analysis that are commonly developed based on statistics with enormous, costly and time consuming data gathering. Although this approach might be justified for research purposes, it is not appealing for practical applications because of its computational cost. Thus, in this paper, Bayesian regression-based demand and collapse models are proposed to eliminate the need of time-consuming analyses. The demand model developed in the form of linear equation predicts overall maximum inter-story drift of the lowto mid-rise regular steel moment resisting frames (SMRFs), while the collapse model mathematically expressed by lognormal cumulative distribution function provides collapse occurrence probability for a given spectral acceleration at the fundamental period of the structure. Next, as an application, the proposed demand and collapse functions are implemented in a seismic fragility analysis to develop fragility and consequently seismic demand curves of three example buildings. The accuracy provided by utilization of the proposed models, with considering computation reduction, are compared with those directly obtained from Incremental Dynamic analysis, which is a computer-intensive procedure.

• Earthquakes and Structures
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• v.11 no.3
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• pp.445-459
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• 2016

Quantitative estimation of seismic response of various structural systems at the collapse limit state is one of the most significant objectives in Performance-Based Earthquake Engineering (PBEE). Assessing the effects of uncertainties, due to variability in ground motion characteristics and random nature of earthquakes, on nonlinear structural response is a pivotal issue regarding collapse safety prediction. Incremental Dynamic Analysis (IDA) and fragility curves are utilized to estimate demand parameters and seismic performance levels of structures. Since producing these curves based on a large number of nonlinear dynamic analyses would be time-consuming, selection of appropriate earthquake ground motion records resulting in reliable responses with sufficient accuracy seems to be quite essential. The aim of this research study is to propose a methodology to assess the seismic behavior of reinforced concrete frames at collapse limit state via accurate estimation of seismic fragility curves for different Engineering Demand Parameters (EDPs) by using a limited number of ground motion records. Research results demonstrate that accurate estimating of structural collapse capacity is feasible through applying the proposed method offering an appropriate suite of limited ground motion records.

• Earthquakes and Structures
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• v.15 no.5
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• pp.529-540
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• 2018

The influences of initial damage paths and aftershock (AS) spectral shape on the assessment of AS collapse fragility are investigated. To do this, a four-story ductile reinforced concrete (RC) frame structure is employed as the study case. The far-field earthquake records recommended by FEMA P695 are used as AS ground motions. The AS incremental dynamic analyses are performed for the damaged structure. To examine the effect of initial damage paths, a total of six kinds of initial damage paths are adopted to simulate different initial damage states of the structure by pushover analysis and dynamic analysis. For the pushover-based initial damage paths, the structure is "pushed" using either uniform or triangle lateral load pattern to a specified damage state quantified by the maximum inter-story drift ratio. Among the dynamic initial damage paths, one single mainshock ground motion or a suite of mainshock ground motions are used in the incremental dynamic analyses to generate a specified initial damage state to the structure. The results show that the structure collapse capacity is reduced as the increase of initial damage, and the initial damage paths show a significant effect on the calculated collapse capacities of the damaged structure (especially at severe damage states). To account for the effect of AS spectral shape, the AS collapse fragility can be adjusted at different target values of ${\varepsilon}$ by using the linear correlation model between the collapse capacity (in term of spectral intensity) and the AS ${\varepsilon}$ values, and coefficients of this linear model is found to be associated with the initial damage states.

• Earthquakes and Structures
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• v.15 no.3
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• pp.253-261
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• 2018

This article details a bridge-specific fragility method developed to enhance the seismic design and resilience of bridges. Current seismic design processes provide guidance for the design of a bridge that will not collapse during a design hazard event. However, they do not provide performance information of the bridge at different hazard levels or due to design changes. Therefore, there is a need for a supplement to this design process that will provide statistical information on the performance of a bridge, beyond traditional emphases on collapse prevention. This article proposes a bridge-specific parameterized fragility method to enable efficient estimation of various levels of damage probability for alternative bridge design parameters. A multi-parameter demand model is developed to incorporate bridge design details directly in the fragility estimation. Monte Carlo simulation and Logistic regression are used to determine the fragility of the bridge or bridge component. The resulting parameterized fragility model offers a basis for a bridge-specific design tool to explore the influence of design parameter variation on the expected performance of a bridge. When used as part of the design process, these tools can help to transform a prescriptive approach into a more performance-based approach, efficiently providing probabilistic performance information about a new bridge design. An example of the method and resulting fragility estimation is presented.

• Structural Engineering and Mechanics
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• v.71 no.3
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• pp.305-315
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• 2019

Extremely long-span transmission tower-line system is an indispensable portion of an electricity transmission system, and its failures or collapse can impact on the entire electricity grid, affect the modern life, and cause great economic losses. It is therefore imperative to investigate the failure and safety of the transmission tower subjected to ground motions. In the present study, a detailed finite element (FE) model of a representative extremely long-span transmission tower-line system is established. A segmental damage indicator (SDI) is proposed to quantitatively assess the damage level of each segment of the transmission tower under earthquakes. Additionally, parametric studies are conducted to investigate the influence of different ground motions and incident angles on the ultimate capacity and weakest segment of the transmission tower. Finally, the collapse fragility curve in terms of the maximum SDI value and PGA is plotted for the exampled transmission tower. The results show that the proposed SDI can quantitatively assess the damage level of the segments, and thus determine the ultimate capacity and weakest segment of the transmission tower. Moreover, the different ground motions and incident angles have a significant influence on the SDI values of the transmission tower, and the collapse fragility curve is utilized to evaluate the collapse resistant capacity of the transmission tower subjected to ground motions.

• Steel and Composite Structures
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• v.50 no.3
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• pp.249-263
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• 2024

This article presents a comparative analysis of seismic behavior in steel-beam reinforced concrete column (RCS) frames versus steel and reinforced concrete frames. The study evaluates the seismic response and collapse behavior of RCS frames of varying heights through nonlinear modeling. RCS, steel, and reinforced concrete special moment frames are considered in three height categories: 5, 10, and 20 stories. Two-dimensional frames are extracted from the three-dimensional structures, and nonlinear static analyses are conducted in the OpenSEES software to evaluate seismic response in post-yield regions. Incremental dynamic analysis is then performed on models, and collapse conditions are compared using fragility curves. Research findings indicate that the seismic intensity index in steel frames is 1.35 times greater than in RCS frames and 1.14 times greater than in reinforced concrete frames. As the number of stories increases, RCS frames exhibit more favorable collapse behavior compared to reinforced concrete frames. RCS frames demonstrate stable behavior and maintain capacity at high displacement levels, with uniform drift curves and lower damage levels compared to steel and reinforced concrete frames. Steel frames show superior strength and ductility, particularly in taller structures. RCS frames outperform reinforced concrete frames, displaying improved collapse behavior and higher capacity. Incremental Dynamic Analysis results confirm satisfactory collapse capacity for RCS frames. Steel frames collapse at higher intensity levels but perform better overall. RCS frames have a higher collapse capacity than reinforced concrete frames. Fragility curves show a lower likelihood of collapse for steel structures, while RCS frames perform better with an increase in the number of stories.

• Earthquakes and Structures
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• v.20 no.2
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• pp.175-185
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• 2021

This study strives to highlight the importance of considering the vertical ground motions (VGM) in the seismic evaluation of RC buildings. To this aim, IDA (Incremental Dynamic Analysis) is conducted on three code-based designed high-rise RC frame-core wall buildings using a suite of earthquake records comprising of significant VGMs. To unravel the significance of the VGM inclusion on the performance of the buildings, IDAs are conducted in two states (with and without the vertical component), and subsequently based on each analysis, fragility curves are developed. Non-simulated collapse criteria are used to determine the collapse state drift ratio and the area under the velocity spectrum (SIm) is taken into account as the intensity measure. The outcome of this study delineates that the inclusion of VGM leads to the increase in the collapse vulnerability of the structures as well as to the change in the pattern of inter-story drifts and failure mode of the buildings. The results suggested that it would be more conservative if the VGM is included in the seismic assessment and the fragility analysis of RC buildings.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.1063-1093
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• 2015

Structural robustness has become an important design variable. However, based on the existing definitions of structural robustness it is often difficult to analyse and evaluate structural robustness, and sometimes not efficient since they mix structural robustness with several other structural variables. This paper concerns the development of a new structural robustness definition, and structural robustness and structural fragility indices. The basis for the development of the new indices is the analysis of the damage energy of structural systems for a given hazard scenario and involves a criterion to define an "unavoidable collapse" state. Illustrative examples are given detailing the steps and calculations needed to obtain values for both the structural robustness and the structural fragility indices. Finally, this paper presents the main advantages of the newly proposed definition and indices for the structural risk analysis over existing traditional methods.

• Earthquakes and Structures
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• v.23 no.5
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• pp.463-472
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• 2022

Reinforced concrete (RC) beam column joints (BCJ) have mostly exhibited poor seismic performance during several past earthquakes, typically due to the poor-quality concrete or lack of reinforcement detailing typical of pre-code design practice. The present study is motivated towards numerical simulation and seismic fragility assessment of one such RC-BCJ. The BCJ is loaded to failure and strengthened using Ultra High Performance-Hybrid Fiber Reinforced Concrete (UHP-HFRC) jacketing. The strengthening is performed for four different BCJ specimens, each representing an intermediate damage state before collapse. viz., slight, moderate, severe, and collapse. From the numerical simulation of all the BCJ specimens, an attempt is made to correlate different modelling and design parameters of the BC joint with respect to the damage states. In addition, seismic fragility analysis of the original as well as the retrofitted damaged BCJ specimens show the relative enhancement achieved in each case.