Showing papers in "Journal of Earthquake Engineering in 2011"
TL;DR: In this paper, the authors present the damage of bridges resulting from the 2010 Maule, Chile earthquake based on site investigations and discuss the effect of in-plane rotation of skewed bridges, insufficient seat support length, absence of integrity of prestressed concrete girder bridges without diaphragms, and lack of bearing capacity of foundations.
Abstract: This article presents the damage of bridges resulting from the 2010 Maule, Chile earthquake based on site investigations. Features of bridge damage are presented and discussed with emphasis on the effect of in-plane rotation of skewed bridges, insufficient seat support length, absence of integrity of prestressed concrete girder bridges without diaphragms, and lack of bearing capacity of foundations.
124 citations
TL;DR: In this paper, the correlation of significant duration with several amplitude and cumulative-based ground motion intensity measures was examined and developed parametric equations for, and the correlations were determined using ground motions from active shallow crustal earthquakes in the Next Generation Attenuation database, and recently developed ground motion prediction equations.
Abstract: This manuscript examines, and develops parametric equations for, the correlation of significant duration with several amplitude- and cumulative-based ground motion intensity measures. The correlations are determined using ground motions from active shallow crustal earthquakes in the Next Generation Attenuation database, and recently developed ground motion prediction equations. It is found that significant durations tend to be negatively correlated with high-frequency amplitude-based intensity measures, weakly negatively correlated with moderate-frequency amplitude-based intensity measures, and weakly positively correlated with low-frequency amplitude-based intensity measures and cumulative absolute velocity. Particular attenuation is given to the physical interpretation of the observed correlations, which can largely be explained as a result of: (a) the 5–75% significant duration ( ) representing approximately the duration of body wave arrivals; and (b) the limited amount of energy contained in a ground ...
106 citations
TL;DR: In this paper, the results of an experimental program dealing with the ultimate behavior of bolted beam-to-column connections under cyclic actions are presented, and the design criteria adopted for tested specimens are discussed in detail, aiming to point out how the ultimate behaviour can be governed by properly strengthening the components for which yielding has to be prevented.
Abstract: In this paper, the results of an experimental program dealing with the ultimate behavior of bolted beam-to-column connections under cyclic actions are presented. The design criteria adopted for tested specimens are discussed in detail, aiming to point out how the ultimate behavior can be governed by properly strengthening the components for which yielding has to be prevented. To this scope, the component approach is adopted as a design tool for component hierarchy criteria. The aim of the paper is the investigation of the actual possibility of extending the component approach to the prediction of the cyclic response of beam-to-column joints. To this scope, the attention has been focused on the possibility to evaluate the overall energy dissipation capacity starting from the energy dissipation of the single joint components, provided that they are properly identified and their cyclic behavior is properly measured.
91 citations
TL;DR: In this paper, the in-plane response of unreinforced aerated concrete (AAC) panels has been assessed through an experimental test campaign aiming at obtaining a reliable description of the lateral cyclic behavior.
Abstract: The need to assess the seismic performance of autoclaved aerated concrete (AAC) masonry arose in different countries in the last years. The use of AAC for load-bearing walls is quite common in low seismicity areas in Central and Northern Europe, where its thermal insulation properties, together with lightness and workability, are particularly appreciated. Increasing attention to energy-efficient buildings is now supporting the adoption of a material with such characteristics also in higher seismicity regions. Hence, in order to correctly study the seismic performance of this constructive system, the in-plane response of unreinforced AAC masonry panels has been assessed through an experimental test campaign aiming at obtaining a reliable description of the lateral cyclic behavior. The experimental results are summarized in the article and the derived essential seismic design parameters are presented. The test results allowed the calibration of a macro-element model representative of the nonlinear response ...
90 citations
TL;DR: In this paper, a statistical study focused on evaluating inelastic displacement ratios (i.e., the ratio of maximum displacement with respect to maximum elastic displacement demand) of degrading and non-degrading single-degree-of-freedom (SDOF) systems subjected to forward-directivity near-fault ground motions is presented.
Abstract: This article presents results of a statistical study focused on evaluating inelastic displacement ratios (i.e., ratio of maximum inelastic displacement with respect to maximum elastic displacement demand) of degrading and non degrading single-degree-of-freedom (SDOF) systems subjected to forward-directivity near-fault ground motions. CR spectra are computed for normalized periods of vibration with respect to the predominant period of the ground motion to provide a better ground motion characterization. This period normalization allows reducing the record-to-record variability in the estimation of CR. An equation to obtain estimates of CR for the seismic assessment of structures exposed to forward-directivity near-fault ground motions is proposed.
81 citations
TL;DR: In this paper, a systematic study of buried pipeline response to strike-slip faulting was performed wherein advanced computational simulations were conducted in parallel with a series of physical tests employing split-boxes within the geotechnical centrifuge at Rensselaer Polytechnic Institute and the full-scale testing facility at Cornell University.
Abstract: A systematic study of buried pipeline response to strike-slip faulting was performed wherein advanced computational simulations were conducted in parallel with a series of physical tests employing split-boxes within the geotechnical centrifuge at Rensselaer Polytechnic Institute and the full-scale testing facility at Cornell University. This article describes the numerical modeling and simulations of the experimental tests. The buried pipeline and the surrounding soil are modeled using nonlinear beam (shell) elements and elasto-plastic springs distributed along the pipeline, respectively. Using the finite element method, reasonable predictions are obtained for the axial and bending strain distributions measured during the tests. It is also shown that finite element analysis using pipe beam elements and a modified soil spring model can accurately predict the pipeline seismic behavior due to strike-slip fault rupture, especially when the pipe is subjected to combined bending and tension. In addition, existi...
63 citations
TL;DR: In this paper, a model for predicting the cyclic response of bolted beam-to-column joints based on the knowledge of their geometrical and mechanical properties was developed. But the model was not applied to the prediction of cyclic responses of bolted connections, and accuracy of the developed model was investigated by means of the comparison between numerical and experimental results with reference to an experimental program carried out at Salerno University.
Abstract: The work is aimed at the prediction of the cyclic response of bolted beam-to-column joints starting from the knowledge of their geometrical and mechanical properties. To this scope a mechanical model is developed within the framework of the component approach already codified by Eurocode 3 for monotonic loadings. Accuracy of the developed mechanical model is investigated by means of the comparison between numerical and experimental results with reference to an experimental program carried out at Salerno University. The obtained results are encouraging about the possibility of extending the component approach to the prediction of the cyclic response of bolted connections.
63 citations
TL;DR: In this article, the effect of several characteristics on the nonlinear response of the equivalent SDOF is investigated, such as structural period, ground motion spectral shape, sensitivity of spectral shape to damping, and elastic damping ratio.
Abstract: The estimation of the maximum inelastic displacement response of structures is gaining increasing importance with the development and application of the so-called “Performance-Based Design” (PBD) procedures, in which important performance criteria are directly correlated to the seismic displacement demand. The maximum displacement of a MDOF structure is often estimated using the “equivalent SDOF system” concept, which reduces the problem to the prediction of the maximum inelastic displacement demand of an equivalent SDOF system with characteristics representative of the MDOF structure. This study focuses on the nonlinear response of SDOF systems with medium and long periods (T > 1 s), typical of tall buildings for which PBD is more widely adopted. In particular, the effect of several characteristics on the nonlinear response of the equivalent SDOF is investigated, such as structural period, ground motion spectral shape, sensitivity of spectral shape to damping, and elastic damping ratio. Design equations ...
62 citations
TL;DR: In this article, a critical evaluation of peak horizontal floor acceleration (PHFA) demands is conducted using representative numerical models of eight code-designed steel moment-resisting frame buildings and several ground motions.
Abstract: Using representative numerical models of eight code-designed steel moment-resisting frame buildings and several ground motions, time-history analyses are performed and a critical evaluation of Peak Horizontal Floor Acceleration (PHFA) demands is conducted. The frames are modeled alternatively as linear and nonlinear systems to isolate the effect of building nonlinearity on PHFA. In most cases, PHFA is reduced when nonlinear behavior of a building is considered; however, in some cases, significant amplification of PHFA is observed. Results from the numerical study provide insight into the trend of modal response modification factors presented taking ground motion spectral shape into account.
62 citations
TL;DR: In this article, a new technique for the strengthening of existing RC structures, based on the application of a high performance fiber reinforced concrete jacket, is investigated for the seismic retrofitting of existing columns and beam-column joints.
Abstract: A new technique for the strengthening of existing RC structures, based on the application of a high performance fiber reinforced concrete jacket, is investigated here The aim of the research is to study the possibility of using this technique for the seismic retrofitting of existing columns and beam-column joints Two full-scale tests have been performed: a column-to-foundation joint and a beam-column joint The specimens have been loaded with static horizontal cyclic loads with increasing amplitude The results show that with the adoption of this technique it is possible to significantly increase both bearing capacity and ductility of existing RC structures
54 citations
TL;DR: In this article, the seismic performance of scaled bridge columns using polypropylene fiber reinforced cement composite (PFRC), steel fiber reinforced concrete (SFRC), and reinforced concrete(RC) in combination with high strength longitudinal bars was presented.
Abstract: This article presents the seismic performance of scaled bridge columns using polypropylene fiber reinforced cement composite (PFRC), steel fiber reinforced concrete (SFRC), and reinforced concrete (RC) in combination with high strength longitudinal bars. The columns were subjected to combined axial and bilateral cyclic loading. Use of PFRC and SFRC mitigated damage of cover and core concrete, local buckling of longitudinal bars and strains induced in ties compared with the RC column. Damage mitigation and lateral confinement effect was superior in PFRC than SFRC. While PFRC and SFRC reduced the damage, their flexural strength and ductility capacity were similar with the RC column.
TL;DR: In this article, the differences in structural response to near-fault pulse-like, non-pulse-like and far-farfault ground motions are examined based on elastic and inelastic response spectra.
Abstract: The differences in structural response to near-fault pulse-like, near-fault non pulse-like, and far-fault ground motions are examined based on elastic and inelastic response spectra. As a first step, the criteria to identify pulse-like motions are examined. The influence of the ground motion orientation is also studied, considering the normal to strike orientation, and the principal directions of motion among others. The characteristics of the spectral shapes are synthesized constructing smoothed spectra using the Veletsos-Newmark-Hall methodology, i.e., considering response amplification factors for elastic systems and response reduction factors for inelastic systems.
TL;DR: In this article, a new shear strength model based on modifications to the UCSD shear model was proposed to calculate the shear capacity and predict the displacement ductility of reinforced concrete walls in diagonal tension.
Abstract: This research proposes a new shear strength model, based on modifications to the UCSD shear model by Kowalsky and Priestley [2000], to calculate the shear capacity and predict the displacement ductility of reinforced concrete walls in diagonal tension. An experimental database is created from a literature review of experimental tests of reinforced concrete walls that exhibit strength degradation and shear failure during cyclic loading. This experimental database is used in the formulation of the proposed shear model and to test the accuracy of the model. The proposed model improves the accuracy of calculating pre-emptive shear and flexure-shear strength, correctly identifies the failure mode for all collected specimens, and provides the closest prediction of the ultimate displacement ductility. Based on this research, the proposed shear model is recommended for the calculation of the shear strength of reinforced concrete walls for either the assessment of existing buildings or the design of new structures.
TL;DR: In this article, the authors present probabilistic performance-based proposals for seismic assessments of RC buildings based on the knowledge levels, which take advantage of the Bayesian framework for updating the probability distributions for structural modeling parameters based on results of tests and inspections.
Abstract: One of the most challenging aspects of the seismic assessment of existing buildings is the characterization of structural modeling uncertainties. Recent codes, such as Eurocode 8, seem to synthesize the effect of structural modeling uncertainties in the so-called confidence factors that are applied to mean material property estimates. The confidence factors are classified and tabulated as a function of discrete knowledge levels acquired based on the results of specific in-situ tests and inspections. In this approach, the effect of the application of the confidence factors on structural assessment is not explicitly stated. This work presents probabilistic performance-based proposals for seismic assessments of RC buildings based on the knowledge levels. These proposals take advantage of the Bayesian framework for updating the probability distributions for structural modeling parameters based on the results of tests and inspections. As structural modeling parameters, both the mechanical material properties a...
TL;DR: In this article, the effect of ground motion incidence angle for three-dimensional excitation and response is investigated for response of highway bridges in two-dimensional and single axis 3D finite element analyses, and the negligible effect of incidence angle on mean ensemble response was confirmed with a stochastic representation of the ground motions.
Abstract: In two-dimensional and single axis three-dimensional finite element analyses, the ground motion incidence angle can play a significant role in structural response. The effect of incidence angle for three-dimensional excitation and response is investigated in this paper for response of highway bridges. Single-degree-of-freedom elastic and inelastic mean spectra were computed from various orientation techniques and found indistinguishable for combinations of orthogonal horizontal components. Probabilistic seismic demand models were generated for the nonlinear response of five different bridge models. The negligible effect of incidence angle on mean ensemble response was confirmed with a stochastic representation of the ground motions.
TL;DR: In this paper, numerical site response analyses were carried out on the Nicastro ridge in Southern Italy in order to investigate topographic effects, separating topographic from stratigraphic amplification.
Abstract: Numerical site response analyses were carried out on the Nicastro ridge in Southern Italy in order to investigate topographic effects. First, the analyses were carried out on a simplified model by employing simple artificial signals, in order to get preliminary physical insights into the two-dimensional phenomena involved. Then, numerical analyses were carried out on a more realistic heterogeneous subsoil model developed on the basis of geotechnical and geophysical investigations. Real accelerograms were selected for these analyses. Particular attention was devoted to separating topographic from stratigraphic amplification. Finally, the topographic amplification factors were compared with literature data and Eurocode 8 recommendations.
TL;DR: In this paper, a case study of the statue of Apollo at the Academy of Athens is presented, showing that the earthquake of 1999 (MW = 5.9), at a source distance of about 10 km, caused the base of a statue to slide on the column capital and rotate, with no evidence of any damage having been done to the column or to the Academy Building proper.
Abstract: The seismic vulnerability of statues mounted on monolithic or multidrum columns is presented in this article. Emphasis is given to the procedure that should be followed for the assessment of the stability to future earthquakes, which is presented through the case study of the statue of Apollo at the Academy of Athens. The earthquake of 1999 (MW = 5.9), at a source distance of about 10 km, caused the base of the statue to slide on the column capital and rotate, with no evidence of any damage having been done to the column or to the Academy Building proper. Earthquake damage of monuments of this type is rarely noticed and, even if observed, is not reported in any detail. This particular case, therefore, offered the opportunity to investigate the stability of statues mounted on multi-drum columns, and also to present critical issues related to the assessment of their vulnerability, as the selection of the ground motions that should be used in the analysis, the determination of the parameters of the numerical...
TL;DR: In this article, high-precision attenuation models were derived to estimate peak ground acceleration (PGA), velocity (PGV), and displacement (PGD) using a new variant of genetic programming, namely multi expression programming (MEP).
Abstract: High-precision attenuation models were derived to estimate peak ground acceleration (PGA), velocity (PGV), and displacement (PGD) using a new variant of genetic programming, namely multi expression programming (MEP). The models were established based on an extensive database of ground-motion recordings released by Pacific Earthquake Engineering Research Center (PEER). For more validity verification, the models were employed to predict the ground-motion parameters of the Iranian plateau earthquakes. The results indicate that the MEP attenuation models are capable of effectively estimating the peak ground-motion parameters. The proposed models are able to reach a prediction performance comparable with the attenuation relationships found in the literature.
TL;DR: In this article, the experimental seismic responses of a full-scale, six-story, light-frame wood apartment building were compared against the predictions from a numerical model developed for performance-based seismic design applications.
Abstract: The experimental seismic responses of a full-scale, six-story, light-frame wood apartment building were compared against the predictions from a numerical model developed for performance based seismic design applications. The accuracy of the as-design model was evaluated. A comparison was conducted for the overall building displacement profile, inter-story drifts, global hysteretic responses, and anchor tie-down system behavior for three seismic excitation test levels. While the numerical model was shown to be able to predict the seismic response of the test specimen with reasonable accuracy, this study specifically highlights challenges in the prediction of mid-rise wood frame buildings seismic response.
TL;DR: In this paper, a seismic isolation device based on superelastic material components manufactured using shape memory alloys is proposed, which provides nonlinear flag-shaped lateral displacement-shear force hysteresis, additional damping and recentering properties to reduce or eliminate the residual deformations.
Abstract: The objective of the present work is to propose a new seismic isolation device based on superelastic material components manufactured using shape memory alloys. Seismic isolation is one of the most effective options for the passive protection of structures. Shape memory alloys (SMAs) are characterized by unique mechanical properties due to a solid-solid transformation. An isolation bearing system based on a SMA superelastic effect is intended to provide nonlinear flag-shaped lateral displacement-shear force hysteresis, additional damping, and recentering properties to reduce or eliminate the residual deformations. The device concept is based on two separate systems, one to transmit the vertical load and another to act as a lateral restrainer. This article presents in detail the mechanical components of the innovative device focusing on its main properties. The system theoretical response is computed, resulting very attractive from the earthquake engineering point of view, because of its capability in reac...
TL;DR: In this article, the influence of inelastic structural response on the seismic response of secondary systems and eventually develop an expression to estimate the seismic input on secondary systems that explicitly accounts for the level of inelinasticity in the primary structure in terms of the filtering phenomenon.
Abstract: Response of masonry walls to out-of-plane excitation is a complex, yet inadequately addressed theme in seismic analysis. The seismic input expected on an out-of-plane wall (or a generic “secondary system”) in a masonry building is the ground excitation filtered by the in-plane response of the walls and the floor diaphragm response. More generally, the dynamic response of the primary structure, which can be nonlinear, contributes to the filtering phenomenon. The current article delves into the details and results of several nonlinear dynamic time-history analyses executed within a parametric framework. The study addresses masonry structures with rigid diaphragm response to lateral loads. The scope of the parametric study is to demonstrate the influence of inelastic structural response on the seismic response of secondary systems and eventually develop an expression to estimate the seismic input on secondary systems that explicitly accounts for the level of inelasticity in the primary structure in terms of ...
TL;DR: In this article, the authors investigated the demand on shear panel dampers (SPDs) installed in steel structures under strong earthquake motions to serve as guidance for the recommended capacity of SPDs in seismic design.
Abstract: This study is aimed at investigating the demand on shear panel dampers (SPDs) installed in steel structures under strong earthquake motions to serve as guidance for the recommended capacity of SPDs in seismic design. For this purpose, an extensive dynamic analysis is carried out on steel bridge pier structures with SPD devices. To describe the restoring force characteristics of SPDs, the analysis uses a newly developed combined hardening model based on experimental data. The seismic demands made on SPD devices are examined and then summarized to give recommended values for determining the necessary deformation capacity of SPDs.
TL;DR: In this paper, a comparison of dynamic and pseudo-dynamic tests was conducted and it was shown that conventional construction materials exhibit pure hysteretic damping and consequently, when quasistatic restoring forces are measured directly, the addition of viscous damping in the equation of motion must be avoided unless it is intended to reflect missing physical elements.
Abstract: By comparison of dynamic and pseudo-dynamic tests, it is shown that conventional construction materials exhibit pure hysteretic damping and consequently, when quasistatic restoring forces are measured directly, the addition of viscous damping in the equation of motion must be avoided unless it is intended to reflect missing physical elements. Equally important in pseudo-dynamic testing is the fact that the apparent damping can be easily distorted by the inevitable control errors. The identification of a spatial model from the results of the tests allows obtaining a reliable estimation of the damping distortion for each vibration mode.
TL;DR: In this article, a model developed recently for conversion of instrumental data to Modified Mercalli Intensity data in North America has been evaluated in this study which employed strong motion recordings and matching intensity data from ten Iranian earthquakes.
Abstract: A model developed recently for conversion of instrumental data to Modified Mercalli Intensity data in North America has been evaluated in this study which employed strong motion recordings and matching Intensity data from ten Iranian earthquakes. Iranian data has also been used to develop new expressions for estimation of Intensity values for various peak ground motion parameters. Importantly, predictions from the new expression with peak ground velocity as the predictor is consistent with those from well-published models developed from data collected in North America. The demonstrated generality of existing conversion relationships has important implications to damage assessment across the globe.
TL;DR: In this paper, the importance of higher modes in the elastic response of tall buildings subjected to near-fault ground motions was investigated and it was found that higher modes contribute significantly to peak interstory drifts at the upper portions of the buildings.
Abstract: This article investigates the importance of higher modes in the elastic response of tall buildings subjected to near-fault ground motions. Building structures modeled as generic frames are analyzed using a large set of forward-directivity affected pulse-like ground-motion records. It is found that higher modes contribute significantly to peak interstory drifts at the upper portions of the buildings. The importance of higher modes increases as the height of the frame is increased. Equivalent pulses, often used to characterize structural response to near-fault ground motions, are found to underestimate peak interstory drifts at the roof level by a factor of 1.4.
TL;DR: In this article, the effect of two types of shear reinforcement, with reference to two type of masonry infills, on the seismic performance of reinforced concrete (RC) frames was experimentally investigated.
Abstract: The effect of two types of shear reinforcement, with reference to two types of masonry infills, on the seismic performance of reinforced concrete (RC) frames was experimentally investigated. Six single-story, one-bay, 1/3-scale frame specimens were tested under cyclic horizontal loading, up to a drift level of 40‰. Bare frames and infilled frames with two different infill compressive strengths were sorted into two groups based on stirrups or spirals as shear reinforcement. From the observed responses it can be deduced that rectangular spiral reinforcement is a first experience and more experiments are needed.
TL;DR: In this paper, the authors investigated the effectiveness of finite element modeling procedures in accurately capturing the nonlinear cyclic response of beam-column subassemblies under a wide range of conditions.
Abstract: Analytical studies are carried out to investigate the effectiveness of finite element modeling procedures in accurately capturing the nonlinear cyclic response of beam-column subassemblies. The analyses are performed using program VecTor2, employing only default or typical material constitutive models and behavior mechanisms in order to assess analysis capabilities without the need for special modeling techniques or program modifications. The specimens considered cover a wide range of conditions, and include interior and exterior seismically and non seismically designed beam-column subassemblies. It is shown that finite element analyses can achieve good accuracy in determining the strength, deformation response, energy dissipation, and failure mode of reinforced concrete beam-column subassemblies under seismic loading conditions.
TL;DR: In this paper, a nonlinear static procedure was proposed to predict the peak response of a multi-story asymmetric frame building with regular elevation subjected to bi-directional ground motion.
Abstract: The present article focuses on a nonlinear static procedure (NSP) for a multi-story asymmetric frame building with regular elevation subjected to bi-directional ground motion. In this procedure, two simplified models—an equivalent single-story model and an equivalent single-degree-of-freedom (SDOF) model—are used to predict the peak response of multi-story asymmetric buildings. The peak response is predicted through pushover analysis of an equivalent single-story model considering the effect of bi-directional excitations and an estimation of the nonlinear response of equivalent SDOF models. The predicted results are compared with the nonlinear dynamic analysis results, and satisfactory predictions can be obtained by the proposed procedure.
TL;DR: In this paper, a finite element analysis was carried out to assess the seismic behavior of Mustafa Pasha mosque in Skopje and the efficiency of a CFRP-based strengthening technique, and numerical models of the as-built and retrofitted mosque were calibrated and validated against the results of an extensive experimental investigation based on shaking table tests on a large-scale physical model.
Abstract: A finite element analysis was carried out to assess the seismic behavior of Mustafa Pasha mosque in Skopje and the efficiency of a CFRP-based strengthening technique The numerical models of the as-built and retrofitted mosque were calibrated and validated against the results of an extensive experimental investigation based on shaking table tests on a large-scale physical model Linear dynamic and nonlinear static analyses were performed to design the retrofitting intervention and to analyze the seismic behavior of the large-scale model before and after strengthening Experimental and numerical results were compared to assess the accuracy of the models The formation of crack patterns observed on the large-scale model in the different phases of the testing program was analysed and the responses to lateral load were compared Finally, the numerical models were used to predict the seismic behavior and the effectiveness of the retrofitting system on the full-scale prototype
TL;DR: In this article, a semi-analytical formulation is proposed to estimate the acceleration demand on an out-of-plane URM wall that explicitly takes into account the level of inelasticity in the primary structure in terms of the displacement ductility demand.
Abstract: The seismic input expected on an out-of-plane wall (or a generic secondary element) in a URM building is the ground excitation filtered by the in-plane response of the walls and the response of the floor diaphragms. More generally, the dynamic response of the primary structure, which can be nonlinear, contributes to the filtering phenomenon. Inelastic response of the primary structure can alter the secondary system response considerably in comparison to that under elastic structural response. The current article proposes a semi-analytical formulation to estimate the acceleration demand on an out-of-plane URM wall that explicitly takes into account the level of inelasticity in the primary structure in terms of the displacement ductility demand. A simplified approach to determine the acceleration profile over the height of a structure is also introduced. The formulation is based on statistical evaluation of the results of several inelastic time-history analyses treated within a parametric framework, which a...