Earthquakes and Structures

  • 제8권5호
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  • Pages.1055-1067
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  • 2015
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  • 2092-7614(pISSN)
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  • 2092-7622(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Earthquake response spectra estimation of bilinear hysteretic systems using random-vibration theory method

  • 투고 : 2014.06.11
  • 심사 : 2014.11.05
  • 발행 : 2015.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

A theoretical procedure to estimate spectral displacement of a hysteretic oscillator with bilinear stiffness excited by band-limited excitation is presented. The stochastic method of ground-motion simulation is combined with the random vibration theory to compute linear and nonlinear structural response. The response is obtained by computing the root-mean-square oscillator response using dissipation energy balancing by integrating over all energy levels of system weighting with the stationary probability density of the energy. The results are presented in a convenient form, and the accuracy of the procedure is assessed by comparison with results obtained with the time-domain method using the recorded data. The model shows little or no bias at the structural period of engineering interest.

키워드

참고문헌

  1. Abrahamson, N.A., Somerville, P.G. and Cornell, C.A. (1990), "Uncertainty in numerical strong motion predictions", Proceedings of the Fourth U.S. National Conference on Earthquake Engineering, Palm Springs, California.
  2. Atkinson, G.M. (1993), "Earthquake source spectra in Eastern North America", Bull. Seismol. Soc. Am., 83(6), 1778-1798.
  3. Atkinson, G.M. and Boore, D.M. (1998), "Evaluation of models for earth-quake source spectra in eastern North America", Bull. Seismol. Soc. Am., 88(4), 917-934.
  4. Atkinson, G.M. and Silva, W. (1997), "An empirical study of earthquake source spectra for California earthquakes", Bull. Seismol. Soc. Am., 87(1), 97-113.
  5. Atkinson, G.M. and Silva, W. (2000), "Stochastic modeling of California ground motions", Bull. Seismol. Soc. Am., 90(2), 255-274. https://doi.org/10.1785/0119990064
  6. Beresnev, I.A. and Atkinson, G.M. (1998), "Stochastic finite-fault modeling of ground motions from the 1994 Northridge, California, earth-quake, I. Validation on rock sites", Bull. Seismol. Soc. Am., 88(6), 1392-1401.
  7. Beresnev, I. and Atkinson, G. (1999), "Generic finite-fault model for ground motion prediction in eastern North America", Bull. Seismol. Soc. Am., 89(3), 608-625.
  8. Boatwright, J. and Choy, G.L. (1992), "Acceleration source spectra anticipated for large earthquakes in northeastern North America", Bull. Seismol. Soc. Am., 82(2), 660-682.
  9. Boore, D.M. (1983), "Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra", Bull. Seismol. Soc. Am., 73(6A), 1865-1894.
  10. Boore, D.M. (2003), "Prediction of ground motion using the stochastic method", Pure Appl. Geophys., 160, 635-676. https://doi.org/10.1007/PL00012553
  11. Boore, D.M. (2009), "Comparing stochastic point-source and finite-source ground-motion simulations", SMSIM and EXSIM, Bull. Seismol. Soc. Am., 99(6), 3202-3216. https://doi.org/10.1785/0120090056
  12. Boore, D.M. and Atkinson, G.M. (1987), "Stochastic prediction of ground motion and spectral response parameters at hard-rock sites in eastern North America", Bull. Seismol. Soc. Am., 77(2), 440-467.
  13. Boore, D.M. and Joyner, W.B. (1984), "A note on the use of random vibration theory to predict peak amplitudes of transient signals", Bull. Seism. Soc. Am., 74(5), 2035-2039.
  14. Boore, D.M. and Joyner, W.B. (1997), "Site amplification for generic rock sites", Bull. Seismol. Soc. Am., 87(2), 327-341.
  15. Boore, D.M. and Thompson, E.M. (2012), "Empirical improvements for estimating earthquake response spectra with random-vibration theory", Bull. Seismol. Soc. Am., 102(2), 761-772. https://doi.org/10.1785/0120110244
  16. Borzi, B., Calvi, G.M. ,Elnashai, A.S., Faccioli, E. and Bommer, J.J. (2011),"Inelastic spectra for displacement-based seismic design", Soil Dyn. Earthq. Eng., 21(1), 47-61. https://doi.org/10.1016/S0267-7261(00)00075-0
  17. Bozorgnia, Y., Hachem, M.M. and Campbell, K.W. (2010), "Ground motion prediction equation ("Attenuation Relationship") for inelastic response spectra", Earthq. Spectra, 26(1), 1-23. https://doi.org/10.1193/1.3281182
  18. Brune, J.N. (1970), "Tectonic stress and the spectra of seismic shear waves from earthquakes", J. Geophys. Res., 75(26), 4997-5009. https://doi.org/10.1029/JB075i026p04997
  19. Brune, J. (1971), "Correction: Tectonic stress and the spectra of seismic shear waves", J. Geophys. Res., 76, 5002. https://doi.org/10.1029/JB076i020p05002
  20. Cai, G.Q. and Lin, Y.K. (1988), "A new approximate solution technique for randomly excited nonlinear oscillators", Int. J. Nonlin. Mech., 23(5), 409-420. https://doi.org/10.1016/0020-7462(88)90038-8
  21. Cai, G.Q. and Lin, Y.K. (1990), "On randomly excited hysteretic structures", J. Appl. Mech., 57(2), 442-448. https://doi.org/10.1115/1.2892009
  22. Caughey, T.K. (1971), Nonlinear theory of random vibrations: Advances in applied mechanics, New York, Academic Press.
  23. Chang, S.W., Bray, J.D. and Seed, R.B. (1996), "Engineering implications of ground motions from the Northridge Earthquake", Bull. Seismol. Soc. Am., 86(1B), 270-288.
  24. Hanks, T.C. and McGuire, R.K. (1981), "The character of high-frequency strong ground motion", Bull. Seismol. Soc. Am., 71(6), 2071-2095.
  25. Hudson, D.E. (1962), "Some problems in the application of spectrum techniques to strong-motion earthquake analysis", Bull. Seismol. Soc. Am., 52(2), 417-430.
  26. Kanai, K. (1957), "Semiempirical formula for the seismic characteristics of the ground motion", Bull. Earthq. Res. Inst., University of Tokyo, 35(2), 308-325.
  27. Kanamori, H. (1977), "The energy release in great earthquakes", J. Geophys. Res., 82(B20), 2981-2987. https://doi.org/10.1029/JB082i020p02981
  28. Koliopulos, P.K. and Nichol, E.A. (1994), "Comparative performance of equivalent linearization techniques for inelastic seismic design", Eng. Struct., 16(1), 5-10. https://doi.org/10.1016/0141-0296(94)90099-X
  29. Kuwamura, H., Kirinot, Y. and Akiyama, H. (1994), "Prediction of earthquake energy input from smoothed Fourier amplitude spectrum", Earthq. Eng. Struct. Dyn., 23(10), 1125-1137. https://doi.org/10.1002/eqe.4290231007
  30. Lee, V.W. and Trifunac, M.D. (2010), "Should average shear wave velocity in the top 30 m of soil be the only local site parameter used to describe seismic amplification?", Soil Dyn. Earthq. Eng., 30(11), 1250-1258. https://doi.org/10.1016/j.soildyn.2010.05.007
  31. Lin, Y.K. and Cai, G.Q. (2004), Probabilistic Structural Dynamics: Advanced Theory and Applications, McGraw-Hill, New York.
  32. Liu, L. and Pezeshk, S. (1999), "An improvement on the estimation of pseudoresponse spectral velocity using RVT method", Bull. Seismol. Soc. Am., 89(5), 1384-1389.
  33. Lutes, L.D. (1970), "Approximate techniques for treating random vibrating of hysteretic systems", J. Acoustic. Soc. Am., 48(1), 299-306. https://doi.org/10.1121/1.1912128
  34. Miranda, E. (2000), "Inelastic displacement ratios for structures on firm sites", J. Struct. Eng., 126(10), 1150-1159. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:10(1150)
  35. Moustafa, A., Ueno, K. and Takewak, I. (2010), "Critical earthquake loads for SDOF inelastic structures considering evolution of seismic waves", Earthq. Struct., 1(2), 147-162. https://doi.org/10.12989/eas.2010.1.2.147
  36. Motazedian, D. and Atkinson, G.M. (2005), "Stochastic finite-fault modeling based on a dynamic corner frequency", Bull. Seismol. Soc. Am., 95(3), 995-1010. https://doi.org/10.1785/0120030207
  37. Raoof, M., Herrmann, R. and Malagnini, L. (1999), "Attenuation and excitation of three component ground motion in southern California", Bull. Seism. Soc. Am., 89(4), 888-902.
  38. Roberts, J.B. and Spanos, P.D. (1990), Random Vibration and Statistical Linearization, Wiley, Chichester.
  39. Rudinger, F. and Krenk, S. (2003), "Spectral density of oscillator with bilinear stiffness and white noise excitation", Prob. Eng. Mech., 18(3), 215-222. https://doi.org/10.1016/S0266-8920(03)00015-8
  40. Ruiz-Garcia, J. and Miranda, E. (2003), "Inelastic displacement ratios for evaluation of existing structures", Earthq. Eng. Struct. Dyn., 32(8), 1237-1258. https://doi.org/10.1002/eqe.271
  41. Suzuki, Y. and Minai, R. (1988), "Application of stochastic differential equations to seismic reliability analysis of hysteretic structures", Prob. Eng. Mech., 3, 43-52. https://doi.org/10.1016/0266-8920(88)90007-0
  42. Tajimi, H. (1960), "A statistical method of determining the maximum response of a building structure during an earthquake", 2nd World Cpnference on Earthquake Engineering, Tokyo.
  43. Takewaki, I. (2001), "Resonance and criticality measure of ground motions via probabilistic critical excitation method", Soil Dyn. Earthq. Eng., 21(8), 645-659. https://doi.org/10.1016/S0267-7261(01)00046-X
  44. Takewaki, I. (2002a), "Seismic critical excitation method for robust design: a review", J. Struct. Eng., 128(5), 665-672. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:5(665)
  45. Takewaki, I. (2002b), "Critical excitation for elastic-plastic structures via statistical equivalent linearization", Prob. Eng. Mech., 17(1), 73-84. https://doi.org/10.1016/S0266-8920(01)00030-3
  46. Takewaki, I. (2005), "Resonance and criticality measure of ground motions via probabilistic critical excitation method", Soil Dyn. Earthq. Eng., 21(8), 645-659. https://doi.org/10.1016/S0267-7261(01)00046-X
  47. Takewaki, I. (2006), "Probabilistic critical excitation method for earthquake energy input rate", J. Eng. Mech., 132(9), 990-1000. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:9(990)
  48. Toro, G.R., Abrahamson, N.A. and Schneider, J.F. (1997), "Model of strong ground motions from earthquakes in central and eastern North America: best estimates and uncertainties", Seismol. Res. Lett., 68(1), 41-57. https://doi.org/10.1785/gssrl.68.1.41
  49. Yamamoto, K., Fujita K. and Takewaki I. (2011), "Instantaneous earthquake input energy and sensitivity in base-isolated building", Struct. Des. Tall Spec. Build., 20(6), 631-648. https://doi.org/10.1002/tal.539
  50. Yazdani, A. and Eftekhari, S.N. (2012), "Variance decomposition of the seismic response of structures", Scientia Iranica, 19(1), 84-90. https://doi.org/10.1016/j.scient.2011.12.003
  51. Yazdani, A. and Takada, T. (2011), "Probabilistic study of the effect of the influence of ground motion variables on the response spectra", Struct. Eng. Mech., 39, 877-893. https://doi.org/10.12989/sem.2011.39.6.877

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