Journal of the Earthquake Engineering Society of Korea (한국지진공학회논문집)

Earthquake Engineering Society of Korea (한국지진공학회)
권호 표지
DOI QR코드

DOI QR Code

Dynamic Instability of Strength-Limited Bilinear SDF Systems

강도한계 이선형 단자유도 시스템의 동적 불안정

  • Published : 2008.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

This study investigates the dynamic instability of strength-limited bilinear single degree of freedom (SDF) systems under seismic excitation. The strength-limited bilinear hysteretic model best replicates the hysteretic behavior of the steel moment resisting frames. To estimate the dynamic instability of SDF systems, the collapse strength ratio is used, which is the yield-strength reduction factor when collapse occurs. Statistical studies are carried out to estimate median collapse strength ratios and those dispersions of strength-limited bilinear SDF systems with given natural periods, hardening stiffness ratios, post-capping stiffness ratios, ductility and damping ratios ranging from 2 to 20% subjected to 240 earthquake ground motions recorded on stiff soil sites. Equations to calculate median and standard deviation of collapse strength ratios in strength-limited bilinear SDF systems are obtained through nonlinear regression analysis. By using the proposed equations, this study estimated the probabilistic distribution of collapse strength ratios, and compared this with the exact values from which the accuracy of the proposed equations was verified.

강도한계 이선형 단자유도 시스템의 지진 하중 하에서의 동적 불안정에 대해 연구하였다. 강도한계 이선형 이력 모델은 철골 모멘트 골조의 이력거동을 가장 잘 모사한다. 단자유도 시스템의 동적 불안정을 판단하기 위해 붕괴 강도비를 사용하였고, 이것은 붕괴가 일어날 때의 항복강도 저감계수이다. 단단한 지반에서 측정된 240개의 지진을 이용하고 고유주기, 강성 경화 기울기, 음강성 기울기, 연성 그리고 $2{\sim}20%$의 감쇠비를 변수로 하여 강도한계 이선형 단자유도 시스템의 붕괴 강도비의 평균과 편차 값들을 구할 수 있도록 통계 분석을 하였다. 비선형 회귀분석을 통해 강도한계 이선형 단자유도 시스템의 붕괴 강도비의 평균과 표준편차를 계산할 수 있는 식을 구하였다. 제안한 식을 이용하여 붕괴 강도비의 확률적 분포를 구하였고, 실제 값과 비교하여 제안한 식의 정확성을 입증하였다.

Keywords

References

  1. Jennings, P. C. and Husid, R. "Collapse of yielding structures during earthquakes." J. Eng. Mech. Div. (ASCE), Vol. 94, No. 5, 1968, pp. 1045-1065
  2. Bernal, D. "Amplification factors for inelastic dynamic P-delta effects in earthquake analysis." Earthquake Eng. Struct. Dyn., Vol. 15, No. 5, 1987, pp. 635-651 https://doi.org/10.1002/eqe.4290150508
  3. MacRae, G. A. "P-delta effects on single-degree-of-freedom structures in earthquakes." Earthquake Spectra, Vol. 10, No. 3, 1994, pp. 539-568 https://doi.org/10.1193/1.1585788
  4. Bernal, D. "Instability of buildings subjected to earthquakes." J.Struct. Eng., Vol. 118, No. 8, 1992, pp. 2239-2260 https://doi.org/10.1061/(ASCE)0733-9445(1992)118:8(2239)
  5. Miranda, E. and Akkar, D. "Dynamic instability of simple structural systems." J. Struct. Eng. (ASCE), Vol. 129, No. 12, 2003, pp. 1722-1726 https://doi.org/10.1061/(ASCE)0733-9445(2003)129:12(1722)
  6. Ibarra, L. F., Medina, R. A., and Krawinkler, H. "Hysteretic models that incorporate strength and stiffness deterioration." Earthquake Eng. Struct. Dyn., Vol. 34, No. 12, 2005, pp. 1489-1511 https://doi.org/10.1002/eqe.495
  7. Han, S. W. and Chopra, A. K. "Approximate incremental dynamic analysis using the modal pushover analysis procedure." Earthquake Eng. Struct. Dyn., Vol. 135, 2006, pp. 1853-1873
  8. Bernal, D. "Instability of buildings during seismic response." Engineering Structures, Vol. 20, No. 4-6, 1998, pp. 496-502 https://doi.org/10.1016/S0141-0296(97)00037-0
  9. Vamvatisikos, D and Cornell, C. A. "Direct estimation of seismic demand and capacity of multi-degree of freedom systems through incremental dynamic analysis of single degree of freedom approximation." Journal of Structural Engineering (ASCE), Vol. 131, No. 4, 2005, pp. 589-599 https://doi.org/10.1061/(ASCE)0733-9445(2005)131:4(589)
  10. Chopra, A. K., Dynamics of Structures: Theory and Applications to Earthquake Engineering (3rd edn). Prentice-Hall: New Jersey, 2007
  11. Ibarra, L. F. "Global collapse of frame structures under seismic excitations." Ph.D. Thesis, Dept. of Civil Engineering, Stanford University, Stanford, CA, 2003
  12. Ruiz-Garcia, J. and Miranda, E., Performance-based assessment of existing structures accounting for residual displacement. Report No-153, John A. Blume Earthquake Engineering Center, Stanford University, Stanford, CA, 2005
  13. Akai, T. J. Applied numerical methods for engineers. Wiley: Toronto, 1994