Earthquake Response Spectrum Analysis

Earthquake Response Spectrum Analysis - CE 573 Structural...

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Unformatted text preview: CE 573: Structural Dynamics Earthquake Response Spectrum Analysis: SDOF Case • Recall: Spectral Displacement and Response Spectrum [ ] ( ) ( ) 1 ( ) ( ) sin ( ) max ( ) , , , ( ) . t t d d d d x t F e t d S x t S m c k F m ξω τ τ ω τ τ ω − − = − ⇒ ≡ = ∫ t • Earthquake Response Spectra 2 EOM: ( ) ( ) 2 ( ). eff g g mu cu ku F t mu t u u u u t ξω ω + + = = − ⇔ + + = − ¡¡ ¡ ¡¡ ¡¡ ¡ ¡¡ [ ] [ ] ( ) [ ] [ ] ( ) ( ) ( ) ( ) ( ) 1 1 ( ) ( ) sin ( ) ( ) sin ( ) max ( ) , , . ( ) ( ) cos ( ) ( ) sin ( ) ( ) cos ( t t t t g d g d d d g t t t t t g d g g d d u t u e t d u e t d S u t S u u t u e t d u e t d u e t ξω τ ξω τ ξω τ ξω τ ξω τ τ ω τ τ τ ω τ τ ω ω ω ξ ξω τ ω τ τ τ ω τ τ τ ω τ ω − − − − − − − − − − − = − ≈ − ⇒ ≡ = = − − + − ≈ − ∫ ∫ ∫ ∫ ¡¡ ¡¡ ¡¡ ¡ ¡¡ ¡¡ ¡¡ [ ] ( ) ( ) [ ] [ ] [ ] ( ) 2 2 ( ) ( ) ( ) ) max ( ) , , ....
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Earthquake Response Spectrum Analysis - CE 573 Structural...

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