Equivalent Frame Model Research Articles

Damage survey and seismic vulnerability assessment of unreinforced masonry structures in low-intensity Ambasa earthquake of northeast India

Unreinforced masonry (URM) buildings in many developing countries are susceptible to severe damage during earthquakes as these are designed and constructed without considering the earthquake risk of that region. Many low-rise URM buildings in Tripura, a northeast state of India, have suffered substantial damage during the recent low-intensity Ambasa earthquake (Mw 5.7). In this context, a damage survey was conducted at first to assess the cause behind the damaged URM buildings. Thereafter, a publicly funded three-storied URM building in Kumarghat, Tripura, has been chosen as a typical representative case for the vulnerability assessment. The Equivalent Frame Modelling approach has been used to model the building in SAP2000 with three different sets of material properties. The Incremental Dynamic Analysis is performed considering seven ground motions to obtain the damage measures for fragility analysis. The visual observations and numerical results match well for the damaged building. In fact, the modelling and analysis technique seems to predict the reasonably accurate damage scenario within a limited computational effect. This opened up a possibility for assessing seismic of masonry buildings on a regular basis which was otherwise a challenge. It has been found that the use of poor quality materials is the primary reason behind the damage to the buildings in such earthquakes. The derived fragility curves also show that with the deterioration of material quality, the probability of suffering moderate to extensive damage increased significantly at the PGA level of 0.052 g that was recorded during the earthquake. Hence, this paper may help the practising engineer to understand several cruxes of vulnerability involved in the design and construction of structures. Further, the method summarized in this study may be extended for the vulnerability assessment of all the building typologies of the earthquake-prone areas of developing countries.

Required building separations and observed seismic pounding on the soft soils of Mexico City

In this paper, the authors discuss the extensive structural pounding observed in Mexico City during the September 19, 2017 earthquake. A critical review of the recommendations available for required separations between adjacent buildings in the seismic codes of Mexico City since 1966 is offered. The reasons why these recommendations have not been effectively enforced since then are also addressed. A parametric study was conducted to understand better the structural pounding phenomena for strong ground motions which have been recorded in soft soils in Mexico City during the 1985 and 2017 earthquakes. For this purpose, equivalent frame models for existing reinforced concrete and structural steel flatslab buildings with nonlinear pounding contacts were used. Some well-known proposed equations for building separations were evaluated based upon the results of these parametric studies for pounding. The evaluated equations were the ABS, SRSS and DDC rules, as well as the absolute difference combination (ADC) rule proposed by the authors. From the obtained results, it was found that the minimum building separation between adjacent buildings established in the seismic code of Mexico City should be raised to avoid strong pounding on soft soils. Also, it was found that both the DDC and ADC rules are promising in defining building separations closer to the one obtained from dynamic simulations. These equations are less conservative than the version of the absolute sum rule currently established in Mexican seismic codes.

Modelling and Seismic Response Analysis of Existing URM Structures. Part 2: Archetypes of Italian Historical Buildings

ABSTRACT This work presents a comprehensive strategy for analysing the complex seismic response of five Italian historical URM buildings, corresponding to different periods until 1920s. One distinctive feature of historical buildings is the need for integrating global modelling and local response of structural portions, due to possible activation of local failure modes interacting with the overall dynamic building response. Global behaviour is analysed via pushover and dynamic analyses of 3D equivalent-frame models. An original approach is adopted for assessing local out-of-plane mechanisms, accounting for their dynamic response to input time histories, filtered by the global response of the 3D model.

A methodological framework to relate the earthquake-induced frequency reduction to structural damage in masonry buildings

The diffusion of seismic structural health monitoring systems, evaluating the dynamic response of engineering structures to earthquakes, is growing significantly among strategic buildings. The increasing availability of valuable vibration data is being backed by continuously evolving techniques for analysing and assessing structural health and damage. Within this framework, the paper proposes a novel model-driven vibration-based methodology to support the assessment of the damage level in masonry buildings hit by earthquakes. The leading idea is to exploit, in the pre-event phase, synthetic equivalent-frame modelling and nonlinear dynamic analyses to systematically relate the gradual reduction of natural frequencies to increasing levels of structural damage. The resulting behavioural chart (seismic chart) of the building, constructed by employing computational tools and robustly defined on a statistical base, may provide the theoretical expectation to ascertain a certain level of seismic damage, based on the decrease in vibration frequency experimentally identified in the post-event phase. The methodology is firstly formalized, integrating common identification techniques with a novel damage grade estimation procedure, and finally exemplified for a monitored strategic masonry building damaged by the 2016–2017 Central Italy earthquake sequence. The outcomes of this application confirm the operational validity of the methodology, which can be intended as effective support for the decision-making process regarding structural usability and safety in the post-earthquake scenario.

Equivalent frame discretisation for URM fa\xe7ades with irregular opening layouts

Researchers and practitioners widely employ simplified Equivalent Frame Models (EFM) for reproducing the in-plane governed response of unreinforced brick masonry (URM) structures, as they typically represent an acceptable compromise between numerical accuracy and computational cost. However, when considering URM structural systems with irregular opening distribution, the definition of the effective height and length of deformable components (i.e. pier and spandrel elements) still represents an open challenge. In this work, the influence of irregular distribution of openings on the predicted lateral response of full-scale URM façades was investigated. To this end, several geometrical combinations characterised by various degrees of irregularity were considered and idealised according to commonly employed EF discretisation approaches. Then, after a preliminary calibration process against experimental tests on both individual piers and a full-scale building façade, EFM results were compared with micro-modelling predictions, carried out within the framework of the Applied Element Method and used as a benchmark. Although in specific irregular configurations using some discretisation approaches, macro and micro-models converge to similar results, non-negligible differences in terms of initial lateral stiffness, base-shear and damage distribution were observed with other EF schemes or opening layouts, thus indicating that a careful selection of appropriate criteria is indeed needed when performing in-plane analyses of URM systems with irregular opening distributions. Finally, building on inferred simulated data, potential solutions are given to overcome typical EF discretisation issues and better approximate micro-modelling outcomes.

Validation of non-linear equivalent-frame models for irregular masonry walls

This article compares the results obtained from the analyses of seven two-story masonry walls with an asymmetric arrangement of the openings. The walls are modelled with finite elements detailed micromodels and equivalent frame models. The equivalent frame model reliability is evaluated by comparing the results obtained with the two modelling strategies assuming the detailed micromodel’s results as reference. Namely, the equivalent frame models of the walls, subjected to nonlinear static analyses, were developed in Scientific Toolkit for OpenSees (STKO) and the OpenSees framework using a macroelement, widely accepted by the literature. The macroelement is based on the idealization of the equivalent frame model with fiber modeling of wall panels to capture bending behavior and a phenomenological law to describe shear behavior. It also provides a model for comparison and validation able to correctly describe the nonlinear behavior of fragile materials that exhibit softening in the response. The micromodeling approach was used as the reference as it is particularly efficient from a computation point of view.The numerical models were validated by comparing pseudo-static experimental tests present in the literature concerning walls with a symmetric arrangement of openings. After the preliminary calibration, the numerical comparisons of the irregular walls generally demonstrate a good correspondence between the equivalent frame model and finite element results. The most relevant differences arise for the walls with masonry panels that exhibit a mixed compression-shear damage mechanism because the simplified frame model cannot capture both behaviors, as it privileges the mechanism that activates first. The differences between the maximum shears, however, range from approximately 1% to 12%.

Operational Modal Analysis and Non-Linear Dynamic Simulations of a Prototype Low-Rise Masonry Building

This paper focuses on the dynamic behaviour of a low-rise masonry building representing the Italian residential heritage through experimental and numerical analyses. The authors discuss an application of combined Operational Modal Analysis and Finite Element Model updating for indirect estimation of the structural parameters. Two ambient vibration tests were carried out to estimate the structure’s dynamic behaviour in operational conditions. The first experimental setup consisted of accelerometers gathered in a row along the first floor to characterize the local dynamic of the floor. Conversely, the second setup had the accelerometers placed at the building’s corners to characterize the global dynamics. The outcomes of the first setup were used to estimate the mechanical parameters of the floor, while the ones form the second were used to characterize the mechanical parameters of the masonry piers. Therefore, two finite element models were implemented: (i) a single beam with an equivalent section of the floor to grasp the local behaviour of the investigated horizontal structure; (ii) an equivalent frame model of the entire building to characterise the global dynamic behaviour. The model updating process was developed in two phases to seize local and global dynamic responses. The updated numerical model formed the basis for a sensitivity analysis using the modelling parameters. The authors chose to delve into the influence of the floor on the dynamic behaviour of low-rise masonry buildings. With this aim, non-linear dynamic analyses were carried out under different mechanical characteristics of floors, expressing the scatter for ordinary masonry buildings. The displacements’ trends along the height of the building evidenced the notable role of the floor’s stiffness in the non-linear dynamic behaviour of the building. Lastly, the authors derived the fragility curves predicting the seismic performance in failure probability under a highly severe damage state.

Seismic fragility assessment of existing masonry buildings in aggregate

The paper describes the derivation of fragility curves useful for the seismic risk analyses of existing unreinforced masonry buildings inserted in aggregate. The L-shaped examined aggregate consists of three adjacent structural units that may mutually interact during seismic events. The seismic assessment is focused on the corner unit. The effects of different connection types between the adjacent units on the structural response were investigated. The seismic vulnerability of the masonry aggregate was assessed through nonlinear dynamic analyses (NDA) performed according to the multi-stripes approach. Both the in-plane and out-of-plane mechanisms were analyzed. The in-plane response of the corner unit is assessed through a 3D equivalent frame model of the entire aggregate, while the evaluation of its out-of-plane response makes use of the rigid-block assumption. Although evaluated in a separate way, the NDAs performed on the latter are based on the time histories derived from the global 3D model. The results are then processed in order to derive fragility curves, firstly, of the single failure mechanisms and, then, of the overall combined behavior. To this aim, various performance conditions are examined. For the reference building, the damage limit state is mainly governed by the in-plane behavior, while the collapse limit state by out-of-plane mechanisms. Moreover, the higher the connection level between adjacent structural units, the higher the interaction between in-plane and out-of-plane mechanisms at the collapse limit state.

Proposal for an equivalent frame model for the analysis of multi-storey monolithic CLT shearwalls

The paper presents a simple yet robust frame model to be used as an alternative to continuous 2D or 3D finite element models for the purpose of analyzing multi-storey cross-laminated timber (CLT) shearwalls with openings when subjected to lateral loads. The proposed model is applicable to monolithic CLT walls and takes into account the mechanical interaction between wall segments and lintel/parapet elements as well as the non-linear behaviour of the mechanical anchors, while the contribution of the vertical load is omitted. Pushover numerical analyses were conducted on the proposed equivalent frame model (EFM) and 2-D finite element model, and the results showed good agreement between the two models along the entire force-displacement curves. The failure conditions were found to be consistent in all cases, and the distribution of the internal forces were found to be reasonable. The proposed EFM was also compared with published test results on CLT shearwalls and the fit was deemed reasonable, with a slight tendency to underestimating the ultimate capacity of the shearwalls.

Modelling the seismic response of a 2-storey URM benchmark case study: comparison among different equivalent frame models

The paper presents the comparison of the results of non-linear static analyses performed with different software based on the equivalent frame (EF) modelling approach on a simple two-story unreinforced masonry building with rigid diaphragms. This study is part of a wider research activity carried out in the framework of the Italian Network of Seismic Laboratories (ReLUIS) projects, funded by the Italian Department of Civil Protection. Different configurations have been considered varying the layout of the openings on the bearing walls and the structural details. The EF models have been defined adopting as much as possible common assumptions, in order to reduce the epistemic modelling uncertainties and to facilitate the interpretation of the differences in the results obtained by the software. The comparison involved different aspects: the global scale response, in terms of capacity curves, the predicted damage pattern as well as checks at the local scale, in terms of distribution of the generalized forces. Moreover, in order to assess the reliability of the obtained results, the numerical predictions have been compared to an analytical upper bound reference solution. Finally, the sensitivity of the numerical response to the criterion adopted for the EF idealization of masonry walls has been investigated.

Integration of Modelling Approaches for the Seismic Assessment of Complex URM Buildings: The Podestà Palace in Mantua, Italy

This study investigated seismic assessments of the Podestà Palace in Mantua (Italy). This masonry palace has a complex geometrical configuration that resulted from the addition of various units stratified over centuries. This feature makes seismic assessment challenging from a modelling perspective due to the interaction among units. Here, an integrated use of three modelling strategies characterised by a different computational effort and degree of accuracy was employed: (i) the Structural Element Model, according to the Equivalent Frame Approach, to study the global response of the whole structure and to estimate the mutual dynamic interactions among units; (ii) the Macro-Block Model, to assess the out-of-plane response of facades prone to the activation of local mechanisms; and (iii) the Finite Element Model, to deepen the seismic response of some critical parts, highlighted by a global analysis but also roughly described by the Equivalent Frame Model. This integrated approach consists in the use of results achieved from one modelling approach as input for another. For example, the floor spectra estimated by (i) were used to define the seismic input in (ii); for assessing the most critical portions, more accurate models were addressed (as in case (iii)). The comprehensive interpretation of the seismic behaviour obtained by these models also allowed us to address more rationally possible strengthening solutions, such as the in-plane stiffening of vaults (particularly spread in the building), aimed to guarantee a better redistribution of seismic actions in such a complex building.

Dynamic calibration and seismic validation of numerical models of URM buildings through permanent monitoring data

AbstractThe construction of reliable numerical models is a key aspect within the seismic assessment of existing unreinforced masonry buildings. However, it is also a complex process due to the many uncertainties involved that can affect the structural response. In situ tests allow for the acquisition of data at a local scale. Nonetheless, supplementary information representing the global response is necessary to overcome other uncertainties (i.e., wall‐to‐wall connections or floor stiffness). To this end, data from ambient vibration tests (AVT) are useful to support seismic assessments. In fact, they allow for the identification of dynamic structural properties, which are useful in refining the calibration of numerical models. In addition, they address solutions for the aforementioned uncertainties. In this context, the paper presents how to efficiently exploit AVT data by using the case study of the former Courthouse of Fabriano (Ancona, Marche). This structure has been monitored since 2010 by the Italian Department of Civil Protection with a network of 28 seismic accelerometers. As a result, the equivalent frame (EF) model was calibrated in the linear field thanks to the dynamic identification provided under operational conditions. Subsequently, nonlinear dynamic analyses were performed using the recordings acquired during the Central Italy earthquake in 2016/2017. Even if the building experienced only a slight nonlinear behaviour, this comparison between the simulated and actual seismic response made it possible to validate the EF model, especially with reference to the capability in reproducing the amplification phenomena, which is extremely important for the assessment of structural and non‐structural components.

On the reliability of the equivalent frame models: the case study of the permanently monitored Pizzoli\u2019s town hall

This paper presents the comparison of the results of modal and nonlinear analyses carried out on a 2-story masonry building with rigid diaphragms, inspired by the Pizzoli’s town hall (AQ, Italy). The case study is one of the Benchmark Structures (labeled BS6) in the “URM nonlinear modelling–Benchmark project” funded by the Italian Department of Civil Protection (DPC) within the framework of the ReLUIS projects. The building has been instrumented since 2009 with a permanent monitoring system by the Osservatorio Sismico delle Strutture (OSS) of the DPC and was hit by the 2016/2017 Central Italy earthquake sequence. In the research first phase, modal and nonlinear static analyses were carried out in a blind prediction, without any preliminary calibration of the models, but referring only to commonly made assumptions on materials and modelling. Five computer programs based on the Equivalent Frame Model (EFM) approach were used. Four different structural configurations were considered: with weak spandrels (A), with tie rods coupled to spandrels (B), with RC ring beams coupled to spandrels (C) and with “shear type” idealization (D). In the research second phase, two of the developed EFMs were calibrated in the elastic range using the results of available Ambient Vibration Tests (AVTs). The models were then validated in the nonlinear range by simulating the dynamic response of the structure recorded during the mainshocks of the 2016/2017 Central Italy earthquake. Recorded and numerical results were compared at both the global and local scale.

A comparative study on a complex URM building: part I\u2014sensitivity of the seismic response to different modelling options in the equivalent frame models

The paper presents the comparison of the results of nonlinear static analyses carried out using six software packages (SWs) available at professional level and operating in the field of the equivalent frame (EF) approach on a model representative of a complex masonry building. The structure is inspired by the school “P. Capuzi” in Visso (MC, Italy), proposed as one of the benchmark structures in the “URM nonlinear modelling—Benchmark project” funded by the Italian Department of Civil Protection within the context of the ReLUIS projects. The 2-stories building is characterized by an irregular T-shaped plan and load-bearing walls consisting of two-leaf stone masonry with a rather regular bond scheme. The school was severely damaged by the seismic sequence that hit Central Italy in 2016/2017 and essentially exhibited a global in-plane box-type response, with a clear evidence of cracks concentrated in piers and spandrels. The availability of an accurate survey of the crack extension represents a precious and rare reference to firstly address in the paper the rules to be adopted in the EF models for the definition of the structural elements geometry. Then, the comparison of results is made with a twofold aim: firstly, by setting the models adopting shared and consistent modelling assumptions across the SWs; secondly, by investigating the sensitivity of the seismic response to some common epistemic and modelling uncertainties (namely: the adoption of various EF idealization rules for walls, the out-of-plane contribution of piers, the flange effect). In both cases, results are post-processed to define reference values of the achievable dispersion. The comparison is carried out in relation to a wide set of parameters, namely: global parameters (e.g. dynamic properties, pushover curves and equivalent bilinear curves); synthetic parameters of the structural safety (i.e. the maximum acceleration compatible with the ultimate limit state); the damage pattern simulated by SWs.

Numerical Simulation of Unreinforced Masonry Buildings with Timber Diaphragms

Though flexible diaphragms play a role in the seismic behaviour of unreinforced masonry buildings, the effect of the connections between floors and walls is rarely discussed or explicitly modelled when simulating the response of such buildings. These flexible diaphragms are most commonly timber floors made of planks and beams, which are supported on recesses in the masonry walls and can slide when the friction resistance is reached. Using equivalent frame models, we capture the effects of both the diaphragm stiffness and the finite strength of wall-to-diaphragm connections on the seismic behaviour of unreinforced masonry buildings. To do this, we use a newly developed macro-element able to simulate both in-plane and out-of-plane behaviour of the masonry walls and non-linear springs to simulate wall-to-wall and wall-to-diaphragm connections. As an unretrofitted case study, we model a building on a shake table, which developed large in-plane and out-of-plane displacements. We then simulate three retrofit interventions: Retrofitted diaphragms, connections, and diaphragms and connections. We show that strengthening the diaphragm alone is ineffective when the friction capacity of the wall-to-diaphragm connection is exceeded. This also means that modelling an unstrengthened wall-to-diaphragm connection as having infinite stiffness and strength leads to unrealistic box-type behaviour. This is particularly important if the equivalent frame model should capture both global in-plane and local out-of-plane failure modes.

Numerical modeling of the seismic performance of Romanian timber-framed masonry walls

Traditional architecture with timber-framed masonry (TFM) system was used in many countries prone to seismic events due to its earthquake-resistant performance. In this context, Romanian TFM buildings were constructed by local builders applying non-engineered measures to reduce seismic vulnerability. However, the seismic safety assessment of these buildings still presents open issues due to material modeling, and in simulating the complex interaction between structural elements. Although the seismic response at building scale depends on a combination of factors such as geometry, boundary conditions, quality of construction, structural connections and interactions, it is significantly influenced by the in-plane behavior of TFM walls. The present paper aims to investigate the seismic performance of Romanian TFM walls by using a simplified equivalent frame model, in OpenSEES software, with linear elastic elements and nonlinear behavior lumped at the connections. Indeed each joint is modeled with nonlinear springs, one per degree of freedom, for which the parameters were initially calibrated based on representative experimental tests in literature. After this calibration, the resulting parameters were updated to approach the local and global responses from the experimental campaign performed at the Technical University of Civil Engineering of Bucharest in terms of initial stiffness, maximum base shear, and total dissipated energy. The simplified modeling strategy requires limited computational efforts and provides information about the role of each connection.

On the use of continuum Finite Element and Equivalent Frame models for the seismic assessment of masonry walls

The assessment of the seismic vulnerability of masonry buildings requires reliable and computationally efficient numerical models. Different modelling strategies can be adopted when studying the global response of these structures, such as Continuum Constitutive Laws Models (CCLM) belonging to Finite Element (FE) models, which may be very accurate but whose use in practice presents several issues (high computational burden, requirement of many input data), and Equivalent Frame (EF) Models, that, even if based on strong simplifications, are now widespread in engineering practice, thanks to their computational efficiency and the need of few mechanical parameters for the structural analysis. The paper discusses the consistent use of these modelling techniques for the seismic analysis of masonry structures . To this aim, a comparison of two approaches (CCL and EF models) is presented focusing at first the attention on the calibration of the constitutive laws through analyses on single panels and then moving to the validation of some simplified assumptions made in the EFM through the analysis of a 2D regular URM wall. For the aim of validation, the CCL model is considered as the reference solution making an accurate comparison with the EF model in terms of generalized forces, drift and damage occurred at element scale and of pushover curve at global scale. • A procedure for cross-calibrating the mechanical parameters in Finite Element (FE) and Equivalent Frame (EF) models is discussed in the paper. • The procedure guarantees a consistent use of two modelling approaches for the seismic assessment of URM buildings. • The reliability of EF model in case of regular 2D URM walls is confirmed through a very detailed comparison with the FE model. • Different rules for the EF idealization of regular URM walls are tested and criteria to orient the choice on the most reliable ones are proposed.

PROS and CONS of linear and nonlinear seismic analyses for existing URM structures: Application to a historical building

Seismic capacity assessment of existing buildings is of paramount importance for mitigating the seismic risk in earthquake-prone areas. In Europe, the next version of Eurocode 8 and the current version of the Italian standards suggest the adoption of both linear and nonlinear approaches to perform seismic analyses of existing masonry buildings.This paper discusses with the main issues concerning linear and nonlinear analyses methodologies provided by the Italian standards for existing unreinforced masonry buildings. An historical building located in Southern Italy, representative of the Mediterranean basin buildings, has been chosen as a case study and modelled through the equivalent frame model. According to the Italian standards, the influence of in-plane stiffness of floors and spandrels on the overall seismic capacity of the structure has been considered in the analyses. Beyond the code prescriptions, the effect of different ultimate drifts values assumed for the spandrels on nonlinear behavior of the structure has been analysed.The results of two types of linear analyses (lateral static force method and modal response spectrum analysis) have been compared among them and with those provided by the nonlinear static method. Conclusions show that either behavior and overstrength factors provided by the Italian standards are conservative than those estimated through the nonlinear static analyses. Moreover, it has been remarked that the value of ultimate drift adopted for the spandrel can affect significantly the nonlinear response of the structures, although this topic still represents an open issue.

New Elastoplastic Analysis of Two-Dimensional Frames When Some Plastic Hinges Unload Elastically

Two-dimensional frames are made of elastic and perfectly plastic materials. Frames are analized by using the step by step elastoplastic analysis method where the applied loads are gradually increased at each step until a plastic hinge is developed. Then an equivalent frame model is generated by placing a mechanical hinge at the location of the plastic hinge and the increased external loads and the reduced plastic moments acting at the plastic hinge sections are applied to this model and elastoplastic analysis is performed. This elastoplastic analysis is repeated by incrementally increasing the external loads and applying the new reduced plastic moments, until the next plastic hinge is developed. Then a new equivalent frame model is generated to search for the following plastic hinge. This step by step elastoplastic analysis continues until the frame partially or totally collapses. When a plastic hinge is developed, it means that the section is at a fully plastic stress state. In the following small load increment: if this fully plastic stress state moves to another fully plastic stress state then this movement is called plastic flow. But if this fully plastic stress state moves to an elastic–plastic stress state then this movement is called elastic unloading. During the search of the next plastic hinge if one of the plastic hinges begins to unload elastically then the current equivalent frame model must be revised. For this the frame member which contains the elastically unloading plastic hinge is replaced by the equivalent frame member carrying balancing loads.

An approach to derive seismic fragility curves

Seismic risk assessment is needed for the evaluation of disaster management, emergency preparedness and prior retrofitting. Based on feasible collapse mechanisms and calculation of their associated seismic parameter Peak Ground Displacement, the failure analysis of the structure is identified. Further, the outputs are manipulated to produce a measure vulnerability obtained from failure analysis. In regions of moderate and high seismicity, Zone – III Fragility analysis is used. An investigation is made on low rise Unreinforced masonry (URM) structure located in Zone – III, particularly in Chennai. To obtain capacity curve and bi-linear capacity curve the structure is modelled as Equivalent Frame Model (EFM), and non – linear static pushover analysis (NPOA).The structure damages, under various level of seismic excitation was developed by an analytical seismic fragility curve. For prioritizing retrofit, pre-earthquake planning, and loss estimation tools such as cost-benefit analysis this curve is utilized. The damage states considered for determining probability of exceeding a specified damage state involved in fragility curve generation are slight, moderate, extreme and collapse.