Statistical Study of Ductility Factors for Elastic Perfectly Plastic SDOF Systems

탄소성 단자유도 구조물에 대한 연성계수의 통계적 분석

  • Published : 2003.04.01


This paper present a summary of the results of statistical study of the ductility factor which is key component of response modification factor(R). To compute the ductility factor, a group of 1,860 ground motions recorded from various earthquake was considered. Based on the local site conditions at the recording station, ground motions were classified into four groups according to average shear wave velocity. Inleastic spectrum were computed for elastic perfectly plastic SDOF systems undergoing different level of inelastic deformation and period. Ductility factors were calculated by deviding elastic response spectrum by inelastic response spectrum. The influence f displacement ductility ratio, site condition, magnitude and epicentral distance on ductility factors were studied. The coefficient of variation was computed to evaluated the dispersion of ductility factors as the defined ratio of the standard deviation to the mean.


response modification factor;ductility factor;displacement ductility ratio;site condition


  1. ATC, “Structural response modification factors,” ATC Report 19, Redwood City, 1995, p. 64.
  2. Rodriguez-Marek, A., Bray, J. D., and Abrahamson, N., “Characterization of site response general site categories,” PEER Report 1999/03, University of California, Berkeley, 1999, p. 252.
  3. Lee, H. H. and Han, S. W., “Evaluation of inelastic demand for elasto perfectly plastic and bilinear model,” Journal of Architectural Institute of Korea, Vol. 16, No. 9, 2000, pp. 27-34.
  4. Nassar, A. A. and Krawinkler, H., “Seismic demands for SDOF and MDOF systems,” John A. Blume Earthquake Engineering Center, Report No. 95, Stanford University, California, 1991, p. 204.
  5. Newmark, N. M. and Hall, W. J., “Earthquake spectra and design,” Earthquake Engineering Research Institute, Berkeley, 1982, p. 488.
  6. Hachem, M. M., BISPEC Version 1.1.2, University of California, Berkeley, 2000.
  7. Bertero, V. V., Anderson, J. C., Krawinkler, H., and Miranda, E., “Design guidelines for ductility and drift limits,” Earthquake Engineering Research Center Report, Report No. UCB/EERC 91-15, UC at Berkely, California, 1991. 7, p. 146.
  8. ATC, “A critical review of current approaches to earthquake-resistant design,” ATC Report 34, Redwood City, 1995, p. 94.
  9. Miranda, E. and Bertero, V. V., “Evaluation of strength reduction factors for earthquake resistant design,” Earthquake Spectra, Earthquake Engineering Research Institute, Vol. 10, No. 2, 1994, pp. 357-379.
  10. Korea National Housing Corporation, “Evaluation of the response modification factor(R) for wall-typed apartment building structures,” Korea National Housing Corporation, 1998. 12, p. 302.
  11. Lee, H. H., “Hysteretic characteristics of inelastic demand spectra,” Journal of Architectural Institute of Korea, Vol. 18, No. 9, 2002, pp. 77-84.
  12. Kang, C. K. and Choi, B. J., “Empirical estimation of ductility factors for elasto-plastic SDOF systems in alluvium sites,” The 2nd International Symposium on Steel Structures, 2002, pp. 533-542.
  13. Mahin, S. A. and Lin, J., “Construction of inelastic response spectra for single-degree-of-freedom systems: Computer program and applications,” UCB/EERC-83/17, Earthquake Engineering Research Center, University of California, Berkeley, 1983. 6, p. 87.
  14. Chopra, A. K, Dynamics of Structures, Theory and Applications to Earthquake Engineering, Prentice-Hall, 1995, p. 729.
  15. Borzi, B. and Elnashai, A. S., “Refined force reduction factors for seismic design,” Engineering Structures, Vol. 22, 2000, pp. 1244-1260.
  16. Miranda, E., “Evaluation of site-dependent strength reduction factors,” Journal of Structural Engineering, ASCE, Vol. 119, No. 12, 1993, pp. 3503-3519.
  17. Lam, N., Wilson, J., and Hutchinson, G., “The ductility reduction factor in the seismic design of buildings,” Journal of Earthquake Engineering and Structural Dynamics, Vol. 27, 1998, pp. 749-769.<749::AID-EQE761>3.0.CO;2-L
  18. Tiwari, A. K. and Gupta, V. K., “Scaling of ductility and damage-based strength reduction factors for horizontal motions,“ Journal of Earthquake Engineering and Structural Dynamics, Vol. 29, 2000, pp. 969-987.<969::AID-EQE948>3.0.CO;2-N