Earthquake Engineering and Engineering Vibration

, Volume 18, Issue 1, pp 171–185 | Cite as

Seismic reliability assessment of a steel moment-resisting frame with two different ductility levels using a cloud analysis approach

  • Seyed Bahram Beheshti AvalEmail author
  • Amir Masoumi Verki


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..


cloud analysis (CA) multiple-strip analysis (MSA) incremental dynamic analysis (IDA) synthetic ground motions 


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  1. 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.Google Scholar
  2. 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.Google Scholar
  3. 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 (ATC 58), Redwood City, California.Google Scholar
  4. 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.Google Scholar
  5. Azarbakht A and Dolšek 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.CrossRefGoogle Scholar
  6. 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.CrossRefGoogle Scholar
  7. 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.Google Scholar
  8. Baker JW (2008), “An Introduction to Probabilistic Seismic Hazard Analysis (PSHA),” White Paper, Stanford Edu., Version 1.3, 72 pp, October 1St.Google Scholar
  9. 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.CrossRefGoogle Scholar
  10. 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: CrossRefGoogle Scholar
  11. Cosic M, Folić R and Folić B (2014), “Seismic Performances of the Structures at Variation of Artificial Accelerograms,” GRAĐEVINAR, 66(9): 787–800.Google Scholar
  12. 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 Report 2004/05, Pacific Earthquake Engineering Research (PEER) Center, University of California Berkeley, CA: 39–52.Google Scholar
  13. 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.CrossRefGoogle Scholar
  14. 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.Google Scholar
  15. 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.Google Scholar
  16. 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.Google Scholar
  17. 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.CrossRefGoogle Scholar
  18. Ellingwood B (1990), “Validation Studies of Seismic PRAs,” Nuclear Engineering and Design, 132(2): 189–196.CrossRefGoogle Scholar
  19. 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: CrossRefGoogle Scholar
  20. 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.Google Scholar
  21. 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: CrossRefGoogle Scholar
  22. Federal Emergency Management Agency (FEMA, 2009), Quantification of Building Seismic Performance Factors (FEMA-P695), Washington, D.C.Google Scholar
  23. Federal Emergency Management Agency (FEMA, 2003), NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures (FEMA 450), Washington, D.C.Google Scholar
  24. Federal Emergency Management Agency (FEMA, 2000), Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings (FEMA 350), Washington, D.C.Google Scholar
  25. Gutenberg B and Richter CF (1954), Seismicity of the Earth and Associated Phenomena, Princeton University Press, Princeton, New Jersey.Google Scholar
  26. Ghodrati Amiri G, Mahdavian A and Manouchehri Dana F (2007), “Attenuation Relationships for Iran,” Journal of Earthquake Engineering, 11(4): 469–492.CrossRefGoogle Scholar
  27. Gasparini DA and Vanmarcke EH (1976), “Simulated Earthquake Motions Compatible with Prescribed Response Spectra,” Publication No. R76-4, Massachusetts Institute of Technology, Cambridge.Google Scholar
  28. Gentle JE (2005), Random Number Generation and Monte Carlo Methods (Statistics and Computing), 2nd ed., New York, USA. Springer Science and Business Media, Inc.Google Scholar
  29. 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.CrossRefGoogle Scholar
  30. 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.Google Scholar
  31. Jalayer F (2003), “Direct Probabilistic Seismic Analysis: Implementing Non-Linear Dynamic Assessments,” PhD Thesis, Dept. of Civil and Environmental Engr., Stanford University.Google Scholar
  32. Jalayer F and Cornell CA (2009), “Alternative Non-Linear Demand Estimation Methods for Probability-Based Seismic Assessments,” Earthquake Engineering and Structural Dynamics, 38(8): 951–972.CrossRefGoogle Scholar
  33. 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.CrossRefGoogle Scholar
  34. Jalayer F, Franchin P and Pinto PE (2007), “A Scalar Decision Variable for Seismic Reliability Analysis of RC Frames,” Special Issue of Earthquake Engineering and Structural Dynamics on Structural Reliability, 36(13): 2050–2079.Google Scholar
  35. 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.Google Scholar
  36. Katsanos E, Sextos AG, and Manolis GD (2010), “Selection of Earthquake Ground Motion Records,” Soil Dynamics and Earthquake Engineering, 40(4): 157–169.CrossRefGoogle Scholar
  37. 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.CrossRefGoogle Scholar
  38. 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.Google Scholar
  39. 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.CrossRefGoogle Scholar
  40. Mazzoni S, McKenna F, Scott MH and Fenves GL (2006), OpenSees Command Language Manual, Pacific Earthquake Engineering Research (PEER) Center, California, Berkeley.Google Scholar
  41. 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.Google Scholar
  42. 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.Google Scholar
  43. 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.CrossRefGoogle Scholar
  44. 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.CrossRefGoogle Scholar
  45. 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.CrossRefGoogle Scholar
  46. Raghunandan M and Liel LB (2013), “Effect of Ground Motion Duration on Earthquake-Induced Structural Collapse,” Structural Safety, 41: 119–133.CrossRefGoogle Scholar
  47. 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.CrossRefGoogle Scholar
  48. Rezaeian S and Der Kiureghian A (2010), “Stimulation of Ground Motions for Specified Earthquake and Site Characteristics,” Earthquake Engineering & Structural Dynamics, 39: 1155–1180.Google Scholar
  49. Shinozuka M, Feng M, Lee J and Naganuma T (2000), “Statistical Analysis of Fragility Curves,” Journal of Engineering Mechanics, ASCE, 126(12): 1224–1231.CrossRefGoogle Scholar
  50. Shome N, Cornell CA, Bazzurro P and Carballo JE (1998), “Earthquakes Records and Nonlinear Responses,” Earthquake Spectra, 14(3): 469–500.CrossRefGoogle Scholar
  51. 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.Google Scholar
  52. Stefano D and Pintucchi B (2010), “Predicting Torsion-Induced Lateral Displacements for Pushover Analysis: Influence of Torsional System Characteristics,” Earthquake Engineering & Structural Dynamics, 39(12): 1369–1394.Google Scholar
  53. 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.CrossRefGoogle Scholar
  54. 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.CrossRefGoogle Scholar
  55. 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.Google Scholar
  56. Vamvatsikos D and Cornell CA (2002), “Incremental Dynamic Analysis,” Earthquake Engineering and Structural Dynamics, 31(3): 491–514.CrossRefGoogle Scholar
  57. Vamvatsikos D and Cornell CA (2005), “Developing Efficient Scalar and Vector Intensity Measures for IDA Capacity Estimation by Incorporating Elastic Spectral Shape Information,” Earthquake Engineering and Structural Dynamics, 34(13): 1–22.CrossRefGoogle Scholar
  58. Vamvatsikos D (2007), “SPO2IDA Software for Short, Moderate and Long Periods,” Report, Scholar
  59. Vejdani-Noghreiyan HR and Shooshtari A (2008), “Comparison of Exact IDA and Approximate MPABased IDA for Reinforced Concrete Frames,” Proceedings of 14th WCEE, Beijing, China.Google Scholar
  60. Vamvatsikos D (2012), “Accurate Application and Higher-Order Solutions of the SAC/FEMA Probabilistic Format for Performance Assessment,” 15 WCEE, LISBOA.Google Scholar
  61. 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.Google Scholar

Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Seyed Bahram Beheshti Aval
    • 1
    Email author
  • Amir Masoumi Verki
    • 1
  1. 1.Department of Civil EngineeringK. N. Toosi University of TechnologyTehranIran

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