Seismic reliability assessment of a steel moment-resisting frame with two different ductility levels using a cloud analysis approach
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摘要
A cloud method for generating percentile engineering demand parameter versus intensity measure(EDP-IM) curves of a structure subjected to a set of synthetic ground motions is presented. To this end, an ensemble of synthetic ground motions based on available real ones is generated. This is done by using attenuation relationships, duration and suitable Gutenberg-Richter relations attributed to the considered seismic hazard at a given site by estimating a suitable distribution of magnitude and site to source distance. The study aims to clarify the significance of the duration and frequency content on the seismic performance of structures, which were not considered in developing percentile incremental dynamic analysis(IDA) curves. The collapse probabilities of two steel moment-resisting frames with different ductility levels generated by IDA and the proposed cloud method are compared at different intensity levels. When compared with conventional IDA, the suggested cloud analysis(SCA) methodology with the same run number of dynamic analyses was able to develop response hazard curves that were more consistent with site-specific seismic hazards. Eliminating the need to find many real records by generating synthetic records consistent with site-specific seismic hazards from a few available recorded ground motions is another advantage of using this scheme over the IDA method..
A cloud method for generating percentile engineering demand parameter versus intensity measure(EDP-IM) curves of a structure subjected to a set of synthetic ground motions is presented. To this end, an ensemble of synthetic ground motions based on available real ones is generated. This is done by using attenuation relationships, duration and suitable Gutenberg-Richter relations attributed to the considered seismic hazard at a given site by estimating a suitable distribution of magnitude and site to source distance. The study aims to clarify the significance of the duration and frequency content on the seismic performance of structures, which were not considered in developing percentile incremental dynamic analysis(IDA) curves. The collapse probabilities of two steel moment-resisting frames with different ductility levels generated by IDA and the proposed cloud method are compared at different intensity levels. When compared with conventional IDA, the suggested cloud analysis(SCA) methodology with the same run number of dynamic analyses was able to develop response hazard curves that were more consistent with site-specific seismic hazards. Eliminating the need to find many real records by generating synthetic records consistent with site-specific seismic hazards from a few available recorded ground motions is another advantage of using this scheme over the IDA method..
A cloud method for generating percentile engineering demand parameter versus intensity measure(EDP-IM) curves of a structure subjected to a set of synthetic ground motions is presented. To this end, an ensemble of synthetic ground motions based on available real ones is generated. This is done by using attenuation relationships, duration and suitable Gutenberg-Richter relations attributed to the considered seismic hazard at a given site by estimating a suitable distribution of magnitude and site to source distance. The study aims to clarify the significance of the duration and frequency content on the seismic performance of structures, which were not considered in developing percentile incremental dynamic analysis(IDA) curves. The collapse probabilities of two steel moment-resisting frames with different ductility levels generated by IDA and the proposed cloud method are compared at different intensity levels. When compared with conventional IDA, the suggested cloud analysis(SCA) methodology with the same run number of dynamic analyses was able to develop response hazard curves that were more consistent with site-specific seismic hazards. Eliminating the need to find many real records by generating synthetic records consistent with site-specific seismic hazards from a few available recorded ground motions is another advantage of using this scheme over the IDA method..
引文
American Institute of Steel Construction(AISC,2010),Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications(ANSI/AISC 358-10),Including Supplement No.1,(AISC),Chicago,Illinois.
American Society of Civil Engineers(ASCE,2010),Minimum Design Loads for Buildings and Other Structures(ASCE 7-10),American Society of Civil Engineers,Reston,Virginia.
Applied Technology Council(ATC,2010),Modeling and Acceptance Criteria for Seismic Design and Analysis of Tall Buildings(ATC 72-1),Redwood City,California,Applied Technology Council(ATC,2012),Guidelines for Seismic Performance Assessment of Buildings(ATC58),Redwood City,California.
Aslani H and Miranda E(2003),“Probabilistic Response Assessment for Building-Specific Loss Estimation,”PEER Report,Pacific Earthquake Engineering Research(PEER)Center,University of California Berkeley.
Azarbakht A and Dol?ek M(2011),“Progressive Incremental Dynamic Analysis for First-Mode Dominated Structures,”Journal of Structural Engineering,3(137):445-455,DOI:10.1061/(ASCE)ST.1943-541X.0000282.
Bahramirad A,Tehranizadeh M and Moshref A(2015),“Equating Incremental Dynamic Analysis with Static Nonlinear Analysis at Near-Field Excitation,”Earthquake Engineering&Engineering Vibration,14(3):465-476,DOI:10.1007/s11803-015-0037-y.
Baker JW and Cornell CA(2006),“Vector-Valued Gound Motion Intensity Measures for Probabilistic Seismic Demand Analysis,”Blume Center Technical,Stanford University Report No.150.
Baker JW(2008),“An Introduction to Probabilistic Seismic Hazard Analysis(PSHA),”White Paper,Stanford Edu.,Version 1.3,72 pp,October 1St.
Barkhordary M and Tariverdilo S(2011),“Vulnerability of Ordinary Moment Resistant Concrete Frames,”Earthquake Engineering&Engineering Vibration,10(4):519-533,DOI:10.1007/s11803-011-0086-9.
Beheshti Aval SB,Sadegh Kouhestani H and Mottaghi L(2017),“Effectiveness of Two Conventional Methods for Seismic Retrofit of Steel and RC Moment Resisting Frames Based on Damage Control Criteria,”Earthquake Engineering&Engineering Vibration,16(3):537-555,DOI:10.1007/s11803-017-0404-y
Cosic M,Foli?R and Foli?B(2014),“Seismic Performances of the Structures at Variation of Artificial Accelerograms,”GRA?EVINAR,66(9):787-800.
Cornell CA,Jalayer F,Hamburger RO and Foutch DA(2004),“Hazard Ground Motions,and Probabilistic Assessments for PBSD,Performance Based Seismic Design Concepts and Implementation,”PEER Report2004/05,Pacific Earthquake Engineering Research(PEER)Center,University of California Berkeley,CA:39-52.
Cornell CA,Jalayar F,Hamburger Ro and Foutch DA(2002),“Probabilistic Basis for 2000 SAC Federal Emergency Management Agency Steel Moment Frame Guidelines,”Journal of Structural Engineering ASCE,128(4):526-533.
Dolsek M and Fajfar P(2004),“IN2-A Simple Alternative for IDA,”13th World Conference on Earthquake Engineering,Paper No.3353,Vancouver,B.C.,Canada.
Der Kiureghian A and Keshishian P(1996),“Effect of Site Response on Spatial Variability of Ground Motion,”11th.World Conference on Earthquake Engineering,Berkeley,Alcapulco,Mexico.
De Luca F,Iervolino and I and Cosenza E(2010),“Compared Seismic Response of Degrading Systems to Artificial and Real Records,”14th European Conference on Earthquake Engineering,Ohrid,Republic of Macedonia.
Elefante L,Jalayer F,Iervolino L and Manfredi G(2010),“Disaggregation-Based Response Weighting Scheme for Seismic Risk Assessment of Structures,”Journal of Soil Dynamics and Earthquake Engineering,30(12):1513-1527.
Ellingwood B(1990),“Validation Studies of Seismic PRAs,”Nuclear Engineering and Design,132(2):189-196.
Enderami SA,Beheshti Aval SB and Ala Saadeghvaziri M(2014)“New Energy Based Approach to Predict Seismic Demands of Steel Moment Resisting Frames Subjected to Near-Fault Ground Motions,”Engineering Structures,Elsevier,72:182-192.DOI:https://doi.org/10.1016/j.engstruct.2014.04.029
European Committee for Standardization(CEN,2003),Eurocode 8:Design of Structures for Earthquake Resistance.Part 1:General Rules,Seismic Actions and Rules for Buildings,EN 1998-1,Brussels,Belgium.
Fayun L,Haibing C and Maosong H(2017),“Accuracy of Three-Dimensional Seismic Ground Response Analysis in Time Domain Using Nonlinear Numerical Simulations,”Earthquake Engineering&Engineering Vibration,16(3):487-498,DOI:10.1007/s11803-017-0401-1
Federal Emergency Management Agency(FEMA,2009),Quantification of Building Seismic Performance Factors(FEMA-P695),Washington,D.C.
Federal Emergency Management Agency(FEMA,2003),NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures(FEMA 450),Washington,D.C.
Federal Emergency Management Agency(FEMA,2000),Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings(FEMA 350),Washington,D.C.
Gutenberg B and Richter CF(1954),Seismicity of the Earth and Associated Phenomena,Princeton University Press,Princeton,New Jersey.
Ghodrati Amiri G,Mahdavian A and Manouchehri Dana F(2007),“Attenuation Relationships for Iran,”Journal of Earthquake Engineering,11(4):469-492.
Gasparini DA and Vanmarcke EH(1976),“Simulated Earthquake Motions Compatible with Prescribed Response Spectra,”Publication No.R76-4,Massachusetts Institute of Technology,Cambridge.
Gentle JE(2005),Random Number Generation and Monte Carlo Methods(Statistics and Computing),2nd ed.,New York,USA.Springer Science and Business Media,Inc.
Han S and Chopra AK(2006),“Approximate Incremental Dynamic Analysis Using the Modal Pushover Analysis Procedure,”Earthquake Engineering and Structural Dynamics,35(15):1853-1873.
Hernandez B and Cotton F(2000),“Empirical Determination of the Ground Shaking Duration due to an Earthquake Using Strong Motion Accelerograms for Engineering Applications,”12th World Conference on Earthquake Engineering,Auckland,New Zealand;2254/4/A.
Jalayer F(2003),“Direct Probabilistic Seismic Analysis:Implementing Non-Linear Dynamic Assessments,”PhDThesis,Dept.of Civil and Environmental Engr.,Stanford University.
Jalayer F and Cornell CA(2009),“Alternative NonLinear Demand Estimation Methods for Probability-
Based Seismic Assessments,”Earthquake Engineering and Structural Dynamics,38(8):951-972.
Jalayer F,De Risi R and Manfredi G(2015),“Baysian Cloud Analysis:Efficient Structural Fragility Assessment Using Linear Regression,”Bull Earthquake Engineering,13(4):1183-1203.
Jalayer F,Franchin P and Pinto PE(2007),“A Scalar Decision Variable for Seismic Reliability Analysis of RCFrames,”Special Issue of Earthquake Engineering and Structural Dynamics on Structural Reliability,36(13):2050-2079.
Johari A and Khodaparast AR(2014),“Analytical Reliability Assessment of Liquefaction Potential Based on Cone Penetration Test Results,”Scientia Iranica A,21(5):1549-1565.
Katsanos E,Sextos AG,and Manolis GD(2010),“Selection of Earthquake Ground Motion Records,”Soil Dynamics and Earthquake Engineering,40(4):157-169.
Li B,Xie W and Pandey MD(2016),“Newmark Design Spectra Considering Earthquake Magnitudes and Site Categories,”Earthquake Engineering&Engineering Vibration,15(3):519-535,DOI:10.1007/s11803-016-0341-1.
Lin T and Baker JW(2013),“Introducing Adaptive Incremental Dynamic Analysis:A New Tool for Linking Ground Motion sSelection and Structural Response Assessment,”11th International Conference on Structural Safety&Reliability,New York,NY,USA.
Lee K and Foutch DA(2002),“Seismic Performance Evaluation of Pre-Northridge Steel Frame Buildings with Brittle Connections,”Journal of Structural Engineering,ASCE,128(4):546-555.
Mazzoni S,McKenna F,Scott MH and Fenves GL(2006),OpenSees Command Language Manual,Pacific Earthquake Engineering Research(PEER)Center,California,Berkeley.
McGuire RK and Arabasz WJ(1990),“An Introduction to Probabilistic Seismic Hazard Analysis,in Geotechnical and Environmental Geophysics,”Society of Exploration Geophysicists,Tulsa,1:333-353.
Merz H and Cornell CA(1973),“Seismic Risk Analysis Based on a Quadratic Magnitude-Frequency Law,”Bulletin of the Seismological Society of America,63(6):1999-2006.
Mezgebo MG and Lui EM(2017),“A New Methodology for Energy-Based Seismic Design of Steel Moment Frames,”Earthquake Engineering&Engineering Vibration,16(1):131-152,DOI:10.1007/s11803-017-0373-1.
Mousavi M,Ghafory-Ashtiany M and Azarbakht A(2011),“A New Indicator of Elastic Spectral Shape for the Reliable Selection of Ground Motion Records,”Earthquake Engineering&Structural Dynamics,40(12):1403-1416.
Pisarenko V,Sornette D and Rodkin MV(2010),“Distribution of Maximum Earthquake Magnitudes in Future Time Intervals,”Application to the Seismicity of Japan(1923-2007),Earth Planets Space,62:567-578.
Raghunandan M and Liel LB(2013),“Effect of Ground Motion Duration on Earthquake-Induced Structural Collapse,”Structural Safety,41:119-133.
Rathje E,Farai F,Russell S and Bray JD(2004),“Empirical Relationships for Frequency Content Parameters of Earthquake Ground Motions,”Earthquake Spectra,20(1):119-144.
Rezaeian S and Der Kiureghian A(2010),“Stimulation of Ground Motions for Specified Earthquake and Site Characteristics,”Earthquake Engineering&Structural Dynamics,39:1155-1180.
Shinozuka M,Feng M,Lee J and Naganuma T(2000),“Statistical Analysis of Fragility Curves,”Journal of Engineering Mechanics,ASCE,126(12):1224-1231.
Shome N,Cornell CA,Bazzurro P and Carballo JE(1998),“Earthquakes Records and Nonlinear Responses,”Earthquake Spectra,14(3):469-500.
Shome N and Cornell CA(1999),“Probabilistic Seismic Demand Analysis of Nonlinear Structures,”Reliability of Marine Structures,Deptartment of Civil and Environmental Engineering,Stanford University.
Stefano D and Pintucchi B(2010),“Predicting TorsionInduced Lateral Displacements for Pushover Analysis:Influence of Torsional System Characteristics,”Earthquake Engineering&Structural Dynamics,39(12):1369-1394.
Sullivan TJ,Welch DP and Calvi GM(2014),“Simplified Seismic Performance Assessment and Implications for Seismic Design,”Earthquake Engineering&Engineering Vibration,13(1):95-122,DOI:10.1007/s11803-014-0242-0.
Tafakori E,Pourzeynali S and Estekanchi HE(2017),
“Probabilistic Seismic Loss Estimation via Endurance Time Method,”Earthquake Engineering&Engineering Vibration,16(1):233-245,DOI:10.1007/s11803-017-0379-8.
Taflampas I,Maniatakis CH and Spyrakos CC(2008),"Estimation of Input Seismic Energy by Means of a New Definition of Strong Motion Duration,”14th World Conference on Earthquake Engineering,Beijing,China Report No.S10-065:12-17.
Vamvatsikos D and Cornell CA(2002),“Incremental Dynamic Analysis,”Earthquake Engineering and Structural Dynamics,31(3):491-514.
Vamvatsikos D and Cornell CA(2005),“Developing Efficient Scalar and Vector Intensity Measures for IDACapacity Estimation by Incorporating Elastic Spectral Shape Information,”Earthquake Engineering and Structural Dynamics,34(13):1-22.
Vamvatsikos D(2007),“SPO2IDA Software for Short,Moderate and Long Periods,”Report,http://blume.stanford.edu/pdffiles/Tech%20Reports/TR151_spo2idaallt.xls.
Vejdani-Noghreiyan HR and Shooshtari A(2008),“Comparison of Exact IDA and Approximate MPA-Based IDA for Reinforced Concrete Frames,”Proceedings of 14th WCEE,Beijing,China.
Vamvatsikos D(2012),“Accurate Application and Higher-Order Solutions of the SAC/FEMA Probabilistic Format for Performance Assessment,"15 WCEE,LISBOA.
Zareian F,Krawinkler H,Ibarra L and Lignos D(2010),“Basic Concept and Performance Measures in Prediction of Collapse of Buildings under Earthquake Ground Motions,”The Structural Design of Tall and Special Buildings Journal,19(1-2):167-181,DOI:10.1002/tal.546.
American Society of Civil Engineers(ASCE,2010),Minimum Design Loads for Buildings and Other Structures(ASCE 7-10),American Society of Civil Engineers,Reston,Virginia.
Applied Technology Council(ATC,2010),Modeling and Acceptance Criteria for Seismic Design and Analysis of Tall Buildings(ATC 72-1),Redwood City,California,Applied Technology Council(ATC,2012),Guidelines for Seismic Performance Assessment of Buildings(ATC58),Redwood City,California.
Aslani H and Miranda E(2003),“Probabilistic Response Assessment for Building-Specific Loss Estimation,”PEER Report,Pacific Earthquake Engineering Research(PEER)Center,University of California Berkeley.
Azarbakht A and Dol?ek M(2011),“Progressive Incremental Dynamic Analysis for First-Mode Dominated Structures,”Journal of Structural Engineering,3(137):445-455,DOI:10.1061/(ASCE)ST.1943-541X.0000282.
Bahramirad A,Tehranizadeh M and Moshref A(2015),“Equating Incremental Dynamic Analysis with Static Nonlinear Analysis at Near-Field Excitation,”Earthquake Engineering&Engineering Vibration,14(3):465-476,DOI:10.1007/s11803-015-0037-y.
Baker JW and Cornell CA(2006),“Vector-Valued Gound Motion Intensity Measures for Probabilistic Seismic Demand Analysis,”Blume Center Technical,Stanford University Report No.150.
Baker JW(2008),“An Introduction to Probabilistic Seismic Hazard Analysis(PSHA),”White Paper,Stanford Edu.,Version 1.3,72 pp,October 1St.
Barkhordary M and Tariverdilo S(2011),“Vulnerability of Ordinary Moment Resistant Concrete Frames,”Earthquake Engineering&Engineering Vibration,10(4):519-533,DOI:10.1007/s11803-011-0086-9.
Beheshti Aval SB,Sadegh Kouhestani H and Mottaghi L(2017),“Effectiveness of Two Conventional Methods for Seismic Retrofit of Steel and RC Moment Resisting Frames Based on Damage Control Criteria,”Earthquake Engineering&Engineering Vibration,16(3):537-555,DOI:10.1007/s11803-017-0404-y
Cosic M,Foli?R and Foli?B(2014),“Seismic Performances of the Structures at Variation of Artificial Accelerograms,”GRA?EVINAR,66(9):787-800.
Cornell CA,Jalayer F,Hamburger RO and Foutch DA(2004),“Hazard Ground Motions,and Probabilistic Assessments for PBSD,Performance Based Seismic Design Concepts and Implementation,”PEER Report2004/05,Pacific Earthquake Engineering Research(PEER)Center,University of California Berkeley,CA:39-52.
Cornell CA,Jalayar F,Hamburger Ro and Foutch DA(2002),“Probabilistic Basis for 2000 SAC Federal Emergency Management Agency Steel Moment Frame Guidelines,”Journal of Structural Engineering ASCE,128(4):526-533.
Dolsek M and Fajfar P(2004),“IN2-A Simple Alternative for IDA,”13th World Conference on Earthquake Engineering,Paper No.3353,Vancouver,B.C.,Canada.
Der Kiureghian A and Keshishian P(1996),“Effect of Site Response on Spatial Variability of Ground Motion,”11th.World Conference on Earthquake Engineering,Berkeley,Alcapulco,Mexico.
De Luca F,Iervolino and I and Cosenza E(2010),“Compared Seismic Response of Degrading Systems to Artificial and Real Records,”14th European Conference on Earthquake Engineering,Ohrid,Republic of Macedonia.
Elefante L,Jalayer F,Iervolino L and Manfredi G(2010),“Disaggregation-Based Response Weighting Scheme for Seismic Risk Assessment of Structures,”Journal of Soil Dynamics and Earthquake Engineering,30(12):1513-1527.
Ellingwood B(1990),“Validation Studies of Seismic PRAs,”Nuclear Engineering and Design,132(2):189-196.
Enderami SA,Beheshti Aval SB and Ala Saadeghvaziri M(2014)“New Energy Based Approach to Predict Seismic Demands of Steel Moment Resisting Frames Subjected to Near-Fault Ground Motions,”Engineering Structures,Elsevier,72:182-192.DOI:https://doi.org/10.1016/j.engstruct.2014.04.029
European Committee for Standardization(CEN,2003),Eurocode 8:Design of Structures for Earthquake Resistance.Part 1:General Rules,Seismic Actions and Rules for Buildings,EN 1998-1,Brussels,Belgium.
Fayun L,Haibing C and Maosong H(2017),“Accuracy of Three-Dimensional Seismic Ground Response Analysis in Time Domain Using Nonlinear Numerical Simulations,”Earthquake Engineering&Engineering Vibration,16(3):487-498,DOI:10.1007/s11803-017-0401-1
Federal Emergency Management Agency(FEMA,2009),Quantification of Building Seismic Performance Factors(FEMA-P695),Washington,D.C.
Federal Emergency Management Agency(FEMA,2003),NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures(FEMA 450),Washington,D.C.
Federal Emergency Management Agency(FEMA,2000),Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings(FEMA 350),Washington,D.C.
Gutenberg B and Richter CF(1954),Seismicity of the Earth and Associated Phenomena,Princeton University Press,Princeton,New Jersey.
Ghodrati Amiri G,Mahdavian A and Manouchehri Dana F(2007),“Attenuation Relationships for Iran,”Journal of Earthquake Engineering,11(4):469-492.
Gasparini DA and Vanmarcke EH(1976),“Simulated Earthquake Motions Compatible with Prescribed Response Spectra,”Publication No.R76-4,Massachusetts Institute of Technology,Cambridge.
Gentle JE(2005),Random Number Generation and Monte Carlo Methods(Statistics and Computing),2nd ed.,New York,USA.Springer Science and Business Media,Inc.
Han S and Chopra AK(2006),“Approximate Incremental Dynamic Analysis Using the Modal Pushover Analysis Procedure,”Earthquake Engineering and Structural Dynamics,35(15):1853-1873.
Hernandez B and Cotton F(2000),“Empirical Determination of the Ground Shaking Duration due to an Earthquake Using Strong Motion Accelerograms for Engineering Applications,”12th World Conference on Earthquake Engineering,Auckland,New Zealand;2254/4/A.
Jalayer F(2003),“Direct Probabilistic Seismic Analysis:Implementing Non-Linear Dynamic Assessments,”PhDThesis,Dept.of Civil and Environmental Engr.,Stanford University.
Jalayer F and Cornell CA(2009),“Alternative NonLinear Demand Estimation Methods for Probability-
Based Seismic Assessments,”Earthquake Engineering and Structural Dynamics,38(8):951-972.
Jalayer F,De Risi R and Manfredi G(2015),“Baysian Cloud Analysis:Efficient Structural Fragility Assessment Using Linear Regression,”Bull Earthquake Engineering,13(4):1183-1203.
Jalayer F,Franchin P and Pinto PE(2007),“A Scalar Decision Variable for Seismic Reliability Analysis of RCFrames,”Special Issue of Earthquake Engineering and Structural Dynamics on Structural Reliability,36(13):2050-2079.
Johari A and Khodaparast AR(2014),“Analytical Reliability Assessment of Liquefaction Potential Based on Cone Penetration Test Results,”Scientia Iranica A,21(5):1549-1565.
Katsanos E,Sextos AG,and Manolis GD(2010),“Selection of Earthquake Ground Motion Records,”Soil Dynamics and Earthquake Engineering,40(4):157-169.
Li B,Xie W and Pandey MD(2016),“Newmark Design Spectra Considering Earthquake Magnitudes and Site Categories,”Earthquake Engineering&Engineering Vibration,15(3):519-535,DOI:10.1007/s11803-016-0341-1.
Lin T and Baker JW(2013),“Introducing Adaptive Incremental Dynamic Analysis:A New Tool for Linking Ground Motion sSelection and Structural Response Assessment,”11th International Conference on Structural Safety&Reliability,New York,NY,USA.
Lee K and Foutch DA(2002),“Seismic Performance Evaluation of Pre-Northridge Steel Frame Buildings with Brittle Connections,”Journal of Structural Engineering,ASCE,128(4):546-555.
Mazzoni S,McKenna F,Scott MH and Fenves GL(2006),OpenSees Command Language Manual,Pacific Earthquake Engineering Research(PEER)Center,California,Berkeley.
McGuire RK and Arabasz WJ(1990),“An Introduction to Probabilistic Seismic Hazard Analysis,in Geotechnical and Environmental Geophysics,”Society of Exploration Geophysicists,Tulsa,1:333-353.
Merz H and Cornell CA(1973),“Seismic Risk Analysis Based on a Quadratic Magnitude-Frequency Law,”Bulletin of the Seismological Society of America,63(6):1999-2006.
Mezgebo MG and Lui EM(2017),“A New Methodology for Energy-Based Seismic Design of Steel Moment Frames,”Earthquake Engineering&Engineering Vibration,16(1):131-152,DOI:10.1007/s11803-017-0373-1.
Mousavi M,Ghafory-Ashtiany M and Azarbakht A(2011),“A New Indicator of Elastic Spectral Shape for the Reliable Selection of Ground Motion Records,”Earthquake Engineering&Structural Dynamics,40(12):1403-1416.
Pisarenko V,Sornette D and Rodkin MV(2010),“Distribution of Maximum Earthquake Magnitudes in Future Time Intervals,”Application to the Seismicity of Japan(1923-2007),Earth Planets Space,62:567-578.
Raghunandan M and Liel LB(2013),“Effect of Ground Motion Duration on Earthquake-Induced Structural Collapse,”Structural Safety,41:119-133.
Rathje E,Farai F,Russell S and Bray JD(2004),“Empirical Relationships for Frequency Content Parameters of Earthquake Ground Motions,”Earthquake Spectra,20(1):119-144.
Rezaeian S and Der Kiureghian A(2010),“Stimulation of Ground Motions for Specified Earthquake and Site Characteristics,”Earthquake Engineering&Structural Dynamics,39:1155-1180.
Shinozuka M,Feng M,Lee J and Naganuma T(2000),“Statistical Analysis of Fragility Curves,”Journal of Engineering Mechanics,ASCE,126(12):1224-1231.
Shome N,Cornell CA,Bazzurro P and Carballo JE(1998),“Earthquakes Records and Nonlinear Responses,”Earthquake Spectra,14(3):469-500.
Shome N and Cornell CA(1999),“Probabilistic Seismic Demand Analysis of Nonlinear Structures,”Reliability of Marine Structures,Deptartment of Civil and Environmental Engineering,Stanford University.
Stefano D and Pintucchi B(2010),“Predicting TorsionInduced Lateral Displacements for Pushover Analysis:Influence of Torsional System Characteristics,”Earthquake Engineering&Structural Dynamics,39(12):1369-1394.
Sullivan TJ,Welch DP and Calvi GM(2014),“Simplified Seismic Performance Assessment and Implications for Seismic Design,”Earthquake Engineering&Engineering Vibration,13(1):95-122,DOI:10.1007/s11803-014-0242-0.
Tafakori E,Pourzeynali S and Estekanchi HE(2017),
“Probabilistic Seismic Loss Estimation via Endurance Time Method,”Earthquake Engineering&Engineering Vibration,16(1):233-245,DOI:10.1007/s11803-017-0379-8.
Taflampas I,Maniatakis CH and Spyrakos CC(2008),"Estimation of Input Seismic Energy by Means of a New Definition of Strong Motion Duration,”14th World Conference on Earthquake Engineering,Beijing,China Report No.S10-065:12-17.
Vamvatsikos D and Cornell CA(2002),“Incremental Dynamic Analysis,”Earthquake Engineering and Structural Dynamics,31(3):491-514.
Vamvatsikos D and Cornell CA(2005),“Developing Efficient Scalar and Vector Intensity Measures for IDACapacity Estimation by Incorporating Elastic Spectral Shape Information,”Earthquake Engineering and Structural Dynamics,34(13):1-22.
Vamvatsikos D(2007),“SPO2IDA Software for Short,Moderate and Long Periods,”Report,http://blume.stanford.edu/pdffiles/Tech%20Reports/TR151_spo2idaallt.xls.
Vejdani-Noghreiyan HR and Shooshtari A(2008),“Comparison of Exact IDA and Approximate MPA-Based IDA for Reinforced Concrete Frames,”Proceedings of 14th WCEE,Beijing,China.
Vamvatsikos D(2012),“Accurate Application and Higher-Order Solutions of the SAC/FEMA Probabilistic Format for Performance Assessment,"15 WCEE,LISBOA.
Zareian F,Krawinkler H,Ibarra L and Lignos D(2010),“Basic Concept and Performance Measures in Prediction of Collapse of Buildings under Earthquake Ground Motions,”The Structural Design of Tall and Special Buildings Journal,19(1-2):167-181,DOI:10.1002/tal.546.