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1-degree of freedom Oscillator : Elastic Response Spectra

1-degree of freedom Oscillator : Elastic Response Spectra. The Elastic System. D. m. k , ξ. D. μ. θ C. m. D. R. μ. m. β. M. F. F. μ m g. m g ( μ cos β – sin β ). – θ C. θ C. θ. D. D. – μ m g. – m g ( μ cos β + sin β ).

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1-degree of freedom Oscillator : Elastic Response Spectra

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  1. 1-degree of freedom Oscillator : Elastic Response Spectra

  2. The Elastic System D m k , ξ

  3. D μ θC m D R μ m β M F F μ m g mg (μ cosβ –sinβ) –θC θC θ D D –μ m g –mg (μ cosβ +sinβ) Fundamental Inelastic Analogues

  4. The Elastic System D m k , ξ

  5. m k 2.0 SA : g 1.0 0.0 T : sec 0.0 0.4 0.8 1.2 RESPONSE SPECTRUM CONCEPT

  6. DESIGN SPECTRUM m x SA SA 2.5 .PGA T, z ( 1 / T ) a PGA T NATURAL PERIOD : s T = 0.1 x No. of floors (sec)

  7. 0.8 PGA 0.4 Ground Acceleration : g 0.0 -0.4 Time t : sec -0.8 0 5 10 15 20 25 2.5 2.0 1.5 SA : g 1.0 PGA 0.5 Period T : sec 0.0 0 1 2 3 4 5 Earthquake Motion: Takatori – Kobe (1995)

  8. Earthquake Motion: Takatori record Kobe (1995) Pseudo-Spectral Parameters SD SV»PSV = wx SD SA»PSA = w2x SD w= 2 p / T = 2 p f

  9. RECORDED MOTIONS(Christchurch Hospital) New Zealand Μ 7.1 – 4 Sept 2010 A : g 0.15 g t : s 0.36 g Μ 6.3– 22 Febr 2011 A : g t : s Μ 6.0– 13 June 2011 A : g 0.19 g t : s

  10. RECORDED MOTIONS – CHHC componentS89W SA : g T : s

  11. 2.5 2.0 1.5 Kobe SA : g 1.0 0.5 New York Period T : sec 0.0 0 1 2 3 4 5 Earthquake Motions: Nahanni vs. Kobe

  12. RECORDED MOTIONS Lyttelton Port Company (LPCC) – N10W Μ 7.1 – 4 Sept 2010 A : g 0.34 g t : s Μ 6.3 – 22 Feb 2011 A : g 0.78 g t : s Μ 6.0 – 13 June 2011 A : g 0.59 g t : s

  13. RECORDED MOTIONS – LPCC componentN10W SA : g T : s

  14. RECORDED MOTIONS Heathcote Valley School (HVSC) – S26W Μ 7.1 – 4 Sept 2010 0.55 g A : g t : s Μ 6.3 – 22 Feb 2011 A : g 1.42 g t : s Μ 6.0 – 13 June 2011 0.66 g A : g t : s

  15. RECORDED MOTIONS – HVSC componentS26W SA : g T : s

  16. 0.2 PGA 0.1 Ground Acceleration : g 0.0 -0.1 Time t : sec -0.2 0 5 10 15 20 1.0 0.6 SA : g 0.2 Period T : sec 0.0 0 1 2 3 4 5 NYC Earthquake Motion: Nahanni (1985)

  17. 0.98g Α : g 1.86g Α : g t : s Christchurch 2011Mw = 6.0 SA : g

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