• Earthquakes and Structures
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• v.10 no.2
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• pp.429-450
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• 2016

An attempt has been made to incorporate the concept of collapse safety margin into the procedures proposed in the performance-based earthquake engineering (PBEE) framework for direct earthquake loss estimation, in which the collapse probability curve obtained from incremental dynamic analysis (IDA) is mathematically characterized with the S-type fitting model. The regressive collapse probability curve is then used to identify non-collapse cases and collapse cases. With the assumed lognormal probability distribution for non-collapse damage indexes, the expected direct earthquake loss ratio is calculated from the weighted average over several damage states for non-collapse cases. Collapse safety margin is shown to be strongly related with sustained damage endurance of structures. Such endurance exhibits a strong link with expected direct earthquake loss. The results from the case study on three concrete frames indicate that increase in cross section cannot always achieve a more desirable output of collapse safety margin and less direct earthquake loss. It is a more effective way to acquire wider collapse safety margin and less direct earthquake loss through proper enhancement of reinforcement in structural components. Interestingly, total expected direct earthquake loss ratio seems to be insensitive a change in cross section. It has demonstrated a consistent correlation with collapse safety margin. The results also indicates that, if direct economic loss is seriously concerned, it is of much significance to reduce the probability of occurrence of moderate and even severe damage, as well as the probability of structural collapse.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.771-776
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• 2007

Widespread propagation of failure can be triggered by localized damage to a structure because of fires, impact and explosion etc. In this paper, the progressive collapse analysis program is developed to automatically check the failed members and construct the modified structural model at each step. OpenSees, that is widely used in many research groups, was used for the developed progressive collapse analysis control program. The control program developed in this study automatically computes the damage indices of all the structural members and performance a progressive collapse analysis after the first failed member is selected. Using the developed program, we compared the progressive collapse behaviors of the example structures considering dynamic effects or not, and the difference of progressive collapse mechanism according to the modeling method of the failed members.

• Earthquakes and Structures
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• v.5 no.3
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• pp.277-296
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• 2013

Margin of safety against potential of progressive collapse is among important features of a structural system. Often eccentricity in plan of a building causes concentration of damage, thus adversely affects its progressive collapse safety margin. In this paper the progressive collapse of symmetric and asymmetric 3-story reinforced concrete ordinary moment resisting frame buildings subjected to the earthquake ground motions are studied. The asymmetric buildings have 5%, 15% and 25% mass eccentricity. The distribution of the damage and spread of the collapse is investigated using nonlinear time history analyses. Results show that potential of the progressive collapse at both stiff and flexible edges of the buildings increases with increase in the level of asymmetry in buildings. It is also demonstrated that "drift" as a more easily available global response parameter is a good measure of the potential of progressive collapse rather than much difficult-to-calculate local response parameter of "number of collapse plastic hinges".

• Structural Engineering and Mechanics
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• v.67 no.6
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• pp.587-601
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• 2018

Elevated water tanks are inverted pendulum type structures where drift limit is an important criterion for seismic design and performance evaluation. Explicit drift criteria for elevated water tanks are not available in the literature. In this study, probabilistic approach is used to determine maximum drift limit for damage state of yielding and damage state of collapse for the elevated water tanks supported on RC frame staging. The two damage states are defined using results of incremental dynamic analysis wherein a total of 2160 nonlinear time history analyses are performed using twelve artificial spectrum compatible ground motions. Analytical fragility curves are developed using two-parameter lognormal distribution. The maximum allowable drifts corresponding to yield and collapse level requirements are estimated for different tank capacities. Finally, a single fragility curve is developed which provides maximum drift values for the different probability of damage. Further, for rational consideration of the uncertainties in design, three confidence levels are selected and corresponding drift limits for damage states of yielding and collapse are proposed. These values of maximum drift can be used in performance-based seismic design for a particular damage state depending on the level of confidence.

• Structural Engineering and Mechanics
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• v.32 no.2
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• pp.193-212
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• 2009

The resilience of a city confronted with a terrorist bomb attack is the background of the paper. The resilience strongly depends on vital infrastructure and the physical protection of people. The protection buildings provide in case of an external explosion is one of the important elements in safety assessment. Besides the aspect of protection, buildings facilitate and enable many functions, e.g., offices, data storage, -handling and -transfer, energy supply, banks, shopping malls etc. When a building is damaged, the loss of functions is directly related to the location, amount of damage and the damage level. At TNO Defence, Security and Safety methods are developed to quantify the resilience of city infrastructure systems (Weerheijm et al. 2007b). In this framework, the dynamic response, damage levels and residual bearing capacity of multi-storey RC buildings is studied. The current paper addresses the aspects of dynamic response and progressive collapse, as well as the proposed method to relate the structural damage to a volume-damage parameter, which can be linked to the loss of functionality. After a general introduction to the research programme and progressive collapse, the study of the dynamic response and damage due to blast loading for a single RC element is described. Shock tube experiments on plates are used as a reference to study the possibilities of engineering methods and an explicit finite element code to quantify the response and residual bearing capacity. Next the dynamic response and progressive collapse of a multi storey RC building is studied numerically, using a number of models. Conclusions are drawn on the ability to predict initial blast damage and progressive collapse. Finally the link between the structural damage of a building and its loss of functionality is described, which is essential input for the envisaged method to quantify the resilience of city infrastructure.

• 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.

• Earthquakes and Structures
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• v.13 no.2
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• pp.211-220
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• 2017

Observations from past strong earthquakes revealed that near-fault ground motions could lead to the failure, or even collapse of electricity transmission towers which are vital components of an overhead electric power delivery system. For assessing the performance and robustness, a high-fidelity three-dimension finite element model of a long span transmission tower-line system is established with the consideration of geometric nonlinearity and material nonlinearity. In the numerical model, the Tian-Ma-Qu material model is utilized to capture the nonlinear behaviours of structural members, and the cumulative damage D is defined as an index to identify the failure of members. Consequently, incremental dynamic analyses (IDAs) are conducted to study the collapse fragility, damage positions, collapse margin ratio (CMR) and dynamic robustness of the transmission towers by using twenty near-fault ground motions selected from PEER. Based on the bending and shear deformation of structures, the collapse mechanism of electricity transmission towers subjected to Chi-Chi earthquake is investigated. This research can serve as a reference for the performance of large span transmission tower line system subjected to near-fault ground motions.

• Steel and Composite Structures
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• v.21 no.3
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• pp.553-571
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• 2016

The progressive collapse potential of steel moment framed structures due to abrupt removal of a column is investigated based on the energy principle. Based on the changes of component's internal energy, this paper analyzes structural member's sensitivity to abrupt removal of a column to determine a sub-structure resisting progressive collapse. An energy-based structural damage index is defined to judge whether progressive collapse occurs in a structure. Then, a simplified beam damage model is proposed to analyze the energies absorbed and dissipated by structural beams at large deflections, and a simplified modified plastic hinges model is developed to consider catenary action in beams. In addition, the correlation between bending moment and axial force in a beam during the whole deformation development process is analyzed and modified, which shows good agreement with the experimental results.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2001.10a
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• pp.202-206
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• 2001

In this study, the risk assessment of small reservoir by collapse using GIS is evaluated. Direct damage distance from collapsed reservoir is estimated by empirical USBR equations and submerged area is calculated by USBR's idea. The amount of damage by collapsed reservoir is figured out by damage assessment of National Institute for Disaster Prevention.