Effect of Demand Spectrums on the Accuracy of Capacity Spectrum Method

요구곡선 산정방법에 따른 능력스펙트럼법의 유효성 평가 및 비교

  • Published : 2004.06.01


While transforming the inelastic system into the equivalent elastic one gives an advantage of simpler analysis, the actual inelastic behavior of the system is hardly modeled in the capacity spectrum method (CSM). Therefore, the accuracy of CSM depends on the precise estimation of equivalent period and damping ratio as well as the modification of the elastic response spectrum and the corresponding demand spectrum. In this paper, the effect of demand spectrums on the accuracy of CSM is evaluated. First, the response reduction factors provided in ATC-40 and Euro Code are evaluated. Numerical analysis results indicated that the acceleration responses obtained using the factor of Euro Code are closer to the actual response than those obtained using the factors of ATC-40. Next, the accuracy of CSM is evaluated constructing the demand spectrum using the absolute acceleration responses and pseudo acceleration responses. The results obtained using the absolute acceleration responses were found to be generally larger than those obtained using the pseudo ones. Since CSM often underestimates the response, the use of absolute acceleration response gives the response relatively closer to the exact ones. However, the difference becomes negligible as the hardening ratio and the yield strength ratio become larger.


  1. Applied Technology Council, 'Seismic evaluation and retrofit of concrete buildings,' Report ATC-40, Applied Technology Council, Redwood City, California, 1996
  2. Federal Emergency Management Agency, 'NEHRP guidelines for the seismic rehabilitation of buildings,' Reports FEMA-273 (Guidelines) and 274 (Commentary), Federal Emergency Management Agency, Washington, DC, 1997
  3. Rosenblueth, E. and Herrera, I., 'On a kind of hysteretic damping,' Journal of Engineering Mechanics Division ASCE, 1964, Vol. 90, pp. 37-48
  4. Miranda, E. and Ruiz-Garcia, J., 'Evaluation of approximate methods to estimate maximum inelastic displacement demands,' Earthquake Engineering and Structural Dynamics, 2001, Vol. 31, pp. 561-582
  5. 김홍진, 민경원, 이상현, 박민규, '최대 비탄성 변위 응답예측을 위한 기존 능력 스펙트럼법들의 유효성 평가 및 비교', 한국지진공학회 논문집, 제8권 제2호, 2004, pp. 33-44
  6. Lin, Y-Y. and Chang, K-C, 'An improved capacity spectrum method for ATC-40,' Earthquake Engineering and Structural Dynamics, 2003, Vol. 32, pp. 2013-2025
  7. Newmark, N. M. and Hall, W. J., Earthquake spectra and design, Monograph Ser, Earthquake Engineering Research Institute, Oakland, California, 1982
  8. Chopra, A. K., Dynamics of structures, Prentice-Hall, Englewood Cliffs, N. J., 1995
  9. Sadek, F., Mohraz, B., and Riley, M. A., 'Linear procedures for structures with velocity-dependent dampers,' Journal of Structural Engineering ASCE, 2000, Vol. 126, No. 8, pp. 887-895
  10. Whittaker, A, Constantinou, M., and Tsopelas, P., 'Displacement estimates for performance-based seismic design,' Journal of Structural Engineering ASCE, 1998, Vol. 124, No. 8, pp. 905-912
  11. Tsopelas, P., Constantinou, M. C., Kircher, C. A., and Whittaker, A. S., 'Evaluation of simplified methods of analysis for yielding structures,' Technical Report NCEER-97-0012, National Center for Earthquake Engineering Research, State University of New York at Buffalo, 1997
  12. Eurocode 8, Design provisions for earthquake resistance of structures, Part 1-1: General rules and rules for buildingseismic actions and general requirements for structures, ENV, 1998, CEN
  13. Chopra, A. K., and Gael, R. K., 'Evaluation of NSP to estimate seismic deformation: SDF systems,' Journal of Structural Engineering ASCE, 2000, Vol. 126(4), pp. 482-490