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Dear all,

This thread I dedicated for sharing the materials from my mini-lib regarding the selection of ground motion acceleration for input motion of dynamic analysis in earthquake engineering field. It composes of technical reports, articles of journal, and conference proceedings, which is authored by well-known scientist and engineer in earthquake engineering and engineering seismology field from Stanford Univ., UC Berkeley, Imperial College, UCLA, etc. namely Professors Alin Cornell, J.W. Baker, Norm Abrahamson, J.J. Bommer, J.P. Stewart, J.D. Bray, etc.. It includes the selection method inside the coridor of GMSM (new USA style) as well as the method adopted in EC8. Due to my technical limitations, I will send the link in several times.

Regards,
adekajeng

======

1) PEER 2009/01 - Evaluation of Ground Motion Selection and Modification Methods: Predicting Median Interstory Drift Response of Buildings, Editor: Haselton, C.B.

-- Nonlinear structural response is often highly sensitive to the selection and modification of input ground motions, and many ground motion selection and modification (GMSM) methods have been proposed. No systematic studies exist that provide impartial guidance to engineers regarding appropriate methods for use in a specific analysis applicatio. The purpose of this report is to provide the engineering community with a foundation, backed by comprehensive research, for choosing appropriate ground motion selection and modification methods for predicting the median drift response of buildings. To this end, the approach taken in this report is [a] to select and scale ground motions using a wide variety of proposed methods, [b] to use these ground motions as inputs to nonlinear dynamic structural analyses, and then [c] to study differences in the resulting structural response predictions in order to identify what GMSM decisions are most crucial. By studying a large number of GMSM methods and analyzing a variety of structures, this report quantitatively compares many of the GMSM methods available to the engineering community. I believed the GMSM method will be a new norm in many seismic codes in the world soon.

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2) PEER 2001/09 - Ground Motion Evaluation Procedures for Performance-Based Design, Editor: J.P. Stewart

-- This report was prepared to synthesize contemporary procedures for ground motion analysis within a performance-based design framework, and to document the past and future role of PEER research in developing these procedures. Each component of ground motion analysis is described. The subjects of source, path, and site effects are discussed in six chapters organized according to a traditional breakdown of topics.

This report may be superceeded by the PEER 2009/01.

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3) Evaluation of Ground Motion Selection and Scaling Techniques for Long-Period Structures, Final Report to USGS by J.W. Baker.

-- the method inside the report suggest that records selected based on the ground motion parameter ε (or that otherwise account for the spectral shape implied by ε) can be safely scaled without introducing any bias, whereas the records selected using other methods have biased structural responses when scaled. Detailed methods presented herein also can be found in jounals of Earthquake Spectra and Earthq.Engrg. Struct.Dyn.

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.. to be continued
4) -- Shome N, Cornell CA, Bazzurro P, Carballo JE (1998). Earthquakes, Records, and Nonlinear Responses, Earthquake Spectra; 14(3):469-500.

The article explains how to obtain a set of ground-motion records for nonlinear structural dynamic analysis that will result in an accurate estimate of the cumulative distribution function (CDF) and the median of the engineering demand parameter (EDP) of interest for a given structure, earthquake magnitude (M), source-to-site distance [R], site classification (S) and style of faulting (F), or a given M, R, S, F and first-mode spectral acceleration (Sa(T1) ).

This is a famous paper that proposed the scalling method based on spectrum acceleration at structure's fundamental period or RSA(T1) and has been selected in GMSM method in the aforementioned PEER 2009/01.


5) -- Baker JW, Cornell CA (2006a). Spectral shape, epsilon and record selection. Earthquake Engineering & Structural Dynamics; 35(9):1077–95.

6) -- Baker JW, Cornell CA (2006b). Correlation of response spectral values for multi-component ground motions. Bulletin of the Seismological Society of America; 96(1):215-27.

7) -- Baker JW, Cornell CA (2005). A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon. Earthquake Engineering & Structural Dynamics; 34(10):1193-217.

These three articles explains about how to obtain the conditional mean values of spectral acceleration at all periods of interest, given the target spectral acceleration value at the first-mode period of the structure, Sa(T1), as well as causal magnitude and distance
values. This “conditional mean spectrum” is then used as a target for record selection and scaling. Records selected and scaled to match this spectrum provide median responses equal to the median responses of ground motions naturally at the target Sa(T1) level of interest. The conditional standard deviation of the spectrum given Sa(T1) can also be calculated and presumably ensembles of records selected to match this standard deviation would provide an accurate representation of the complete distribution of response given Sa(T1), but this has not been tested in practice.

The article has introduced the parameter epsilon in the selection of ground motion and has been selected in GMSM method as explained in the aforementioned PEER 2009/01.

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.. To be continued
8) -- Design Ground Motion Library (2008), Final Report Prepared for California Geological Survey – Strong Motion Instrumentation Program, and Pacific Earthquake Engineering
Research Center – Lifelines Program.

A modified application of the DGML software package was used to obtain a set of ground motion acceleration time histories for nonlinear dynamic structural analysis that will result in an estimate of the cumulative distribution function (CDF) and the median of the engineering demand parameter (EDP) of interest for a given structure, earthquake magnitude (M), source-to-site distance ®, site classification (S), and a given first-mode spectral acceleration Sa(T1). For the method application, the DGML was modified to provide a set of records that would approximately match the distribution about the conditional mean target spectrum.

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9) -- Naeim, F., A. Alimoradi, and S. Pezeshk, (2004). Selection and Scaling of Ground Motion Time Histories for Structural Design Using Genetic Algorithms, Earthquake Spectra, 20(2): 413-426.

This method is designed to provide the best median estimate and/or the PDF of response (GMSM method). This method has been coded as an in-house software developed by Alimoradi and Naeim at John A. Martin and Associates with support from the Mid-America Earthquake Center and The University of Memphis. The objective is to combine different ground motion records and scaling factors, using a genetic algorithm (GA) scheme, to match a given design response spectrum in an average sense, minimizing the mean
square error.

10) -- Kottke, A. and E.M. Rathje (2008). A Semi-Automated Procedure for Selecting and Scaling Recorded Earthquake Motions for Dynamic Analysis, Earthquake Spectra, 24(4): 911-932.

Method is to obtain a set of ground motion seismograms for nonlinear dynamic structural analysis that will result in an accurate estimate of the cumulative distribution function (CDF) (GMSM Methods) of the engineering demand parameter (EDP) of interest for a given elastic response spectra.

11) -- Watson-Lamprey, J.A. and N.A. Abrahamson (2006), Selection of Ground Motion Time Series and Limits on Scaling, Soil Dynamics and Earthquake Engineering; 26(5):477-482.

The method is to obtain a set of ground motion seismograms for nonlinear dynamic structural analysis that will result in an accurate estimate of the median of the engineering demand parameter (EDP) of interest for a given structure, earthquake magnitude (M), source-to-site distance [R], and elastic response spectrafirst-mode spectral acceleration [Sa(T1)]

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.. To be continued

As per request, thread moved to Magazine, Journals, Papers and Presentations section. (Grunf)
..

12) -- Bommer JJ, Acevedo AB. (2004) The use of real earthquake accelerograms as input to dynamic analysis. Journal of Earthquake Engineering, 8(S1):43–91.

This paper explains the criteria for selecting records in terms of earthquake scenarios and in terms of response spectral ordinates are presented, together with options and criteria for adjusting the selected accelerograms to match the elastic design spectrum. The application of both geophysical and response spectra search criteria is illustrated using compatible scenarios, and the selected records are analysed and adjusted to produce suites of acceleration time-series suitable for dynamic analyses. The paper concludes with suggestions for making use of real records in engineering analysis and design, and recommendations are given for improving the current guidelines provided in seismic design codes.

This well-known article addresses the methods adopted in EC8 and partially relevant with the PEER 2001/09.


13) -- Hancock J, Bommer JJ. (2007). Using spectral matched records to explore the influence of strong-motion duration on inelastic structural response. Soil Dynamics and Earthquake Engineering, 27(4):291–299.

This study investigates the influence of duration on damage to an 8-storey RC wall-frame structure using 30 recorded accelerograms with a wide range of durations. The primary influence of the spectral acceleration has been homogenized by scaling and adjusting the accelerograms with wavelets so that they all have a good match to the same smooth response spectra.


14) -- Beyer, K. and Bommer JJ. (2007). Selection and Scaling of Real Accelerograms for Bi-Directional Loading: A Review of Current Practice and Code Provisions, Journal of Earthquake Engineering, 11:13–45.

A review paper of code provisions regarding selection and scaling of ground motions for bi-directional analysis has, however, revealed that the guidelines provided are frequently inconsistent or are lacking transparency regarding the underlying assumptions. The aim of this study is to shed some light on a number of aspects involved when selecting and scaling records for bi-directional analysis and post-processing results of such analyses.


15) -- Hancock J, Bommer JJ., Stafford, PJ. (2008). Numbers of scaled and matched accelerograms required for inelastic dynamic analyses, Earthquake Engineering & Structural Dynamics, 37: 1585-1607.

This paper considers the response of an 8-storey MDOF RC structure to accelerograms selected, linearly scaled or spectrally matched using five different techniques. The first method consists of selecting real records on the basis of seismological characteristics, while the remaining methods make an initial selection on the basis of magnitude and spectral shape before (1) scaling to the target spectral acceleration at the initial period; (2) scaling to the target spectrum over a range of periods; (3) using wavelet adjustments to match the target spectrum and (4) using wavelet adjustments to match multiple target spectra for multiple damping ratios.

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..

16) -- Iervolino, I., and Cornell, C. A. (2005). Record selection for nonlinear seismic analysis of structures, Earthquake Spectra; 21(3): 685–713.

This study addresses the question of selection and amplitude scaling of accelerograms for predicting the nonlinear seismic response of structures. It hypothesizes that neither usual principal seismological characteristics nor scaling of records matters to the nonlinear response of structures. It then investigates under what conditions this hypothesis may not be sustainable. Results here show [1] little evidence to support the need for a careful site-specific process of record selection by magnitude and distance, and [2] that concern over scenario-to-scenario record scaling, at least within the limits tested, may not be justified.


17) -- Iervolino, I., Manfredi, G., and Cosenza, E. (2006). Ground-motion duration effects on nonlinear seismic response, Earthquake Engineering and Structural Dynamics; 35: 21–38.

The study presented in this paper addresses the question of which nonlinear demand measures are sensitive to ground motion duration by statistical analyses of several case studies. A number of single SDOF structures were selected considering: (1) four oscillation periods; (2) three evolutionary and non-evolutionary hysteretic behaviours; (3) two target ductility levels. Effects of duration are investigated, by nonlinear dynamic analysis, with respect to six different demand indices ranging from displacement ductility ratio to equivalent number of cycles. The results lead to the conclusion that duration content of ground motion is statistically insignificant to displacement ductility and cyclic ductility demand. The conclusions hold regardless of SDOF’s period and hysteretic relationship investigated.


18) -- Iervolino, I., Maddaloni, G., and Cosenza, E. (2008). Eurocode 8 compliant real record sets for seismic analysis of structures, Journal of Earthquake Engineering; 12(1): 54–90.

The study presented herein investigates the European Strong-Motion Database with the purpose of assessing whether it is possible to find real accelerogram sets complying with the EC8 spectra, while accounting for additional constraints believed to matter in the seismic assessment of buildings, as suggested by the current best practice. Original (un-scaled) accelerogram sets matching EC8 criteria were found, for the case of one-component (P-type) and spatial sets (S-type), for the spectra anchored to the Italian peak acceleration values. The average spectra for these sets tend to be as close as possible to the code spectrum. Other sets, requiring scaling, have been found to match the non dimensional (country-independent) EC8 spectral shape. These sets have also the benefit of reducing, in respect to the un-scaled sets, the record-to-record variability of spectra.


19) -- Iervolino, I., Maddaloni, G., and Cosenza, E. (2009). A Note on Selection of Time-Histories for Seismic Analysis of Bridges in Eurocode 8, Journal of Earthquake Engineering; 13:1125–1152.

This paper represents an extension of the same study to EC8 Part 2 and bridges. To this aim the European Strong-Motion Database is searched to identify real record sets matching the design spectral shapes for several hazard levels and site conditions in a broad
range of periods up to 4s. It resulted that combinations well approximating the target may be found for some soil classes, at least for low-to-moderate seismicity sites and if the condition of matching specific source parameters is released and large record-to-record variability is accepted. Finally the record sets presented have been used to compare spectral compatibility prescriptions of EC8 Part 1 and Part 2, which have been found to be equivalent to some extent.


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.. To be continued
..

20) -- Luco N, and Cornell CA. (2007). Structure-specific scalar intensity measures for
near-source and ordinary earthquake ground motions. Earthquake Spectra; 23(2):357–92.

This paper deals with several alternative ground-motion intensity measures (IMs) that are intended for use in assessing the seismic performance of a structure at a site susceptible to near-source and/or ordinary ground motions. The efficiency and sufficiency of each alternative IM, which are quantified via (i) nonlinear dynamic analyses of the structure under a suite of earthquake records and (ii) linear regression analysis, are demonstrated for the drift response of three different moderate- to long-period buildings subjected to suites of ordinary and of near-source earthquake records.


21) -- Luco, N. and Bazzuro, P. (2007). Does amplitude scaling of ground motion records result in biased nonlinear structural drift responses? Earthquake Engineering and Structural Dynamics; 36:1813–1835.

This article investigates whether scaling of records randomly selected from an Mw–R bin (or range) to a target fundamental-mode spectral acceleration (Sa) level introduces bias in the expected nonlinear structural drift response of both single-degree-of-freedom oscillators and one multi-degree-of-freedom building. The bias is quantified relative to unscaled records from the target Mw–R bin that are ‘naturally’ at the target Sa level. The results demonstrate that scaling can indeed introduce a bias that, for the most part, can be explained by differences between the elastic response spectra of the scaled versus unscaled records.


22) -- Baker, JW. (2007). Measuring Bias in Structural Response Caused by Ground Motion
Scaling, 8th Pacific Conference on Earthquake Engineering, December 5-7. Paper Number 056.

The paper proposes a method for detecting such scaling bias based on selecting a suite of ground motion records that have been scaled to all have the same intensity level (where here intensity is measured by spectral acceleration at the structure’s first-mode period). The structural responses associated with the records are plotted versus the records’ scale factors.


23) -- Baker, JW and Cornell, CA (2008). Vector-valued intensity measures for pulse-like near-fault ground motions, Engineering Structures 30: 1048–1057.

In this paper, an improved vector-valued measure of ground motion intensity is considered for structural response prediction, with attention also given to computing occurrence rates for this intensity measure using extensions of standard probabilistic seismic hazard analysis. It explains the possibility of accounting the near-fault effects when assessing the reliability of structures located at sites where pulse-like ground motions may occur.


24) -- Baker, JW and Cornell, CA (2008). Vector-Valued Intensity Measures Incorporating Spectral Shape for Prediction of Structural Response, Journal of Earthquake Engineering; 12(4): 534-554.

The article presents two methods for identifying effective periods and used to investigate intensity measures (IM) for example structures, and an improvement in the efficiency of structural response predictions is also shown. A method is presented for predicting the probability distribution of structural response using a vector IM while accounting for the effect of collapses. The ground motion parameter ε is also considered as part of a three-parameter vector.


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.. To be continued
..

25) -- Dhakal, R.P., Mander, JB, Mashiko, N. (2006). Identification of critical ground motions for seismic performance assessment of structures, Earthquake Engineering Structural Dynamics 35:989–1008.

The ground motion identification procedure consists of: choosing a suitable suite of ground motions and an appropriate intensity measure; selecting a computational tool and modelling the structure accordingly; performing Incremental Dynamic Analysis on a non-linear model of the structure; interpreting these results into 50th (median) and 90th percentile performance bounds; and identifying the critical ground motions that are close to these defining probabilistic curves at ground motion intensities corresponding to the design basis earthquake and the maximum considered earthquake.


26) -- Zhai, C-H., Xie, L-L. (2007). A new approach of selecting real input ground motions for seismic design: The most unfavourable real seismic design ground motions, Earthquake Engineering Structural Dynamics 36:1009–1027.

This paper presents a new way of selecting real input ground motions for seismic design and analysis of structures based on a comprehensive method for estimating the damage potential of ground motions, which takes into consideration of various ground motion parameters and structural seismic damage criteria in terms of strength, deformation, hysteretic energy and dual damage of Park & Ang damage index. The proposed comprehensive method fully involves the effects of the intensity, frequency content and duration of ground motions and the dynamic characteristics of structures.


27) -- Bradley, BA. (2010). Site-Specific and Spatially Distributed Ground-Motion Prediction of Acceleration Spectrum Intensity, Bulletin of the Seismological Society of America 100(2): 792–801.

This article presents a theoretical basis for predicting acceleration spectrum intensity (ASI), based on prediction equations for spectral acceleration, both for individual sites and spatially distributed regions. ASI is found to have a better predictability than conventional ground-motion intensity measure such as elastic pseudospectral acceleration at a specific period.


28) -- Catalan A., Benavent-Climent, A. Xavier Cahis, X. (2010). Selection and scaling of earthquake records in assessment of structures in low-to-moderate seismicity zones, Soil Dynamics and Earthquake Engineering 30:40–49.

In this work, the influence of selecting appropriate values for parameters T1 and Sa(T1) on the response of the building is investigated from the study of two structures, of 4 and 8 stories. The records are selected from a database of European earthquakes, and the failure of the structures is evaluated by statistical means. From the results of the analyses, it is proposed that in seismic assessment studies the reference period for scaling should be 1.1 times the fundamental period of the structure, and at least 30 records should be used to guarantee reliable results.


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.. To be continued
..

29) -- Naeim, F, Lew, M (1995). On the use of design spectrum compatible time histories, Earthquake Spectra 11(1): 111–127.

The paper explains a significant potential problem associated with uncontrolled use of design spectrum compatible time history (DSCTH) records in seismic design. It is shown that the use DSCTH can lead to exaggeration of displacement demand and energy input in analysis and design seismic-isolated buildings.


30) -- Kappos, AJ, Kyriakakis, P. (2000). A re-evaluation of scaling techniques for natural records, Soil Dynamics and Earthquake Engineering 20: 111-123.

The study focuses on the problem of reducing scatter in the response calculated from time history analysis using natural records, by proper scaling of these records. The firrst part of the study focuses on the effect of scaling on elastic and inelastic spectra for strength and displacement. It is found that in the intermediate and long period range any of the three velocity-related parameters studied are appropriate to use


31) -- Maholtra, PJ, (2003). Strong-Motion Records for Site-Specific Analysis, Earthquake Spectra 19(3): 557–578.

A procedure is presented to select and scale strong-motion records for site-specific analysis. The procedure matches records’ smooth response spectra with the site response spectrum by scaling of the acceleration histories. The parameters defining the smooth spectrum of various records are computed and tabulated to allow easy selection of records. Hazard de-aggregation is used to identify closer and distant seismic events, which are simulated by the scaled ground motion histories


32)-- Amiri, GG, Manouchehri Dana, F (2005). Introduction of the most suitable parameter for selection of critical earthquake, Computers and Structures 83: 613–626.

The main objective of this research is to apply a reasonable strategy for selecting a critical earthquake (the earthquake from which the designer obtains the maximum response) with the help of the most suitable parameter in earthquake, based on statistical studies of various earthquake parameters. various parameters including, PGA, EPA, PGV, EPV, PGD, Arias intensity, and Duration were obtained. EPA was chosen as the most suitable earthquake parameter for selection of the critical earthquake.


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.. To be continued
..

33) -- Gomes, RC, Santos, J, Oliveira, CS (2006). Design Spectrum-Compatible Time Histories for Numerical Analysis: Generation, Correction and Selection, Journal of Earthquake Engineering 10(6):843-865.

In nonlinear seismic analysis the ground motion has to be represented through time histories. In this paper, a high number of spectrum-compatible time histories were generated, based on random vibration theory.


34) -- Hancock, J, Watson-Lamprey, J, Abrahamson, NA, Bommer, JJ, Markatis, A, McCoy, E, Mendis, R (2006). An Improved Method of Matching Response Spectra of Recorded Earthquake Ground Motion Using Wavelets, Journal of Earthquake Engineering 10(S1): 67-89.

The advantages of using real accelerograms matched to the target response spectrum using wavelets for this purpose are discussed. The program RspMatch, which performs spectral matching using wavelets, is modified using new wavelets that obviate the need to subsequently apply a baseline correction. This paper proposed RspMatch2005 as a new version of RspMatch.

Currently, the method explained herein is used in SeismoMatch as an engine.


35) Hancock, J, Bommer, JJ (2008). A State-of-Knowledge Review of the Influence of Strong-Motion Duration on Structural Damage, Earthquake Spectra, 22(3): 827–845.

This review paper provides a summary and critical review of the literature on the influence of strong-motion duration on structural demand. It is found that studies employing damage measures related to cumulative energy usually find a positive correlation between strong-motion duration and structural damage, while studies employing damage measures using maximum response generally do not find strong correlations between duration and damage.


36)-- Tothong, P, Luco, N. (2007). Probabilistic seismic demand analysis using advanced ground motion intensity measures, Earthquake Engineering Structural Dynamics 36:1837–1860.

This paper compares and contrasts the use, in probabilistic seismic demand analysis, of certain advanced scalar versus vector and conventional scalar ground motion intensity measures (IMs). It demonstrates that this is true for ordinary and for near-source pulse-like earthquake records. The latter ground motions cannot be adequately characterized by either Sa alone.


37) -- Rezaeian, S, Der Kiureghian, A (2010). Simulation of synthetic ground motions for specified earthquake and site characteristics, Earthquake Engineering Structural Dynamics 39:1155–1180.

A method for generating a suite of synthetic ground motion time-histories for specified earthquake and site characteristics defining a design scenario is presented. The method employs a parameterized stochastic model that is based on a modulated, filtered white-noise process. The resulting synthetic acceleration as well as corresponding velocity and displacement time-histories capture the main features of real earthquake ground motions, including the intensity, duration, spectral content, and peak values. The proposed method can be used in seismic design and analysis in conjunction with or instead of recorded ground motions.


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.. To be continued.
..

38) -- Iervolino, I, De Luca, F., Cosenza, E., Manfredi, G (2010). Chapter 4: Real, Scaled, Adjusted and Artificial Records: A Displacement and Cyclic Response Assessment, in M.N. Fardis (ed.), Advances in Performance-Based Earthquake Engineering, Geotechnical, Geological, and Earthquake Engineering 13, Springer. thumbup

This work tries to address the spectral matching issue from the structural point of view in terms of non-linear peak and cyclic response, simply having as reference a code-based design spectrum. To this end, six categories of 28 accelerograms, each one consisting of four sets, were considered: 1] un-scaled real records; 2] moderately scaled real records; 3] largely scaled real records; 4] wavelet-adjusted real records (RSPMatch); 5] type 1 artificial records (Belfagor); and 6] type 2 artificial records (SIMQKE).

This article is -->> recommended to read <<-- for those who are intensively used spectral matching methods for their input motion in engineering design and assessment.


39) -- Douglas, J, Aochi, H (2010). A Survey of Techniques for Predicting Earthquake Ground Motions for Engineering Purposes, Survey in Geophysics 29:187–220.

The various techniques proposed in earthquake ground-motion prediction and a variety of procedures have their adherents and some of them are extensively used to estimate ground motions for engineering design purposes and in seismic hazard research. The purposes of this article are to: summarise existing methods and the most important references, provide a family tree showing the connections between different methods and, most importantly, to discuss the advantages and disadvantages of each method.

This is a good review-paper that will give us a broad information from seismology engineering to earthquake engineering.


40) -- Katsanos, E, Sextos, AG, Manolis, GD (2010). Selection of earthquake ground motion records: A state-of-the-art review from as structural engineering perspective. Soil Dynamics and Earthquake Engineering 30:157-169. thumbupthumbupthumbup

This paper reviews alternative selection procedures based on established methods for incorporating strong ground motion records within the frame work of seismic design of structures. the aim of this paper is to present the most recent methods developed for selecting an ‘appropriate’ set of records that can be used for dynamic analysis of structural systems in the context of performance-based design.

-- >> Highly recommended to read!! <<---- It is a very useful review-paper for structural dynamic analysis that contained almost all of the aforementioned papers in this thread.


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:clap::clap::clap::clap::clap::clap:


This is the end of my collection for the topic related to selection of ground motions for input motion of structural dynamic analysis.

It is welcome for you to add more links for articles with IDENTICAL TOPIC in this thread, especially articles from the peer-reviewed journals such as
- Structural Design of Tall Buildings (see in Katsanos et al. #40),
- Bulletin of the New Zealand Society for Earthquake Engineering,
- Japanese journal,
- Journal of Earthquake Technology (India),
- Chinese journals,
- or else
(must be in English of course).

Best regards.
I added 2 new papers to this thread regarding the selection of ground motion based on Prof. Baker's research group at Stanford Univ. The method can be very useful in assessing the collapse capacity of structural system.

41) Haselton, C., Baker, J. W., Liel, A. B., and Deierlein, G. G. (2011). Accounting for ground motion spectral shape characteristics in structural collapse assessment through an adjustment for epsilon, Journal of Structural Engineering, 137(3), 332-344.

42) Baker, J.W. (2011). Conditional Mean Spectrum: Tool for ground motion selection, Journal of Structural Engineering, 137(3), 322-331.

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Ciao!