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Earthquake Dynamics of Structures. Anil K. Chopra DSI: Devlet Su Isleri Ankara, Turkey October 13, 2011. Simple System. Simple System. Free Vibration of Idealized Systems. Idealized Systems. Free Vibration. Decay of Free Vibration. Aluminum Model. Plexiglass Model.
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Earthquake Dynamics of Structures Anil K. Chopra DSI: Devlet Su Isleri Ankara, Turkey October 13, 2011
Free Vibration of Idealized Systems Idealized Systems Free Vibration
Decay of Free Vibration Aluminum Model Plexiglass Model
49-Story Steel Frame Building Period = 2.90 sec
Effects of Damping Bogata, Colombia
Earthquake Response Spectrum • Peak Response • Plot of for fixed damping
Pseudo-Acceleration Response Spectrum = 0, 2, 5, 10, and 20%
Peak Response from Spectrum Internal forces by statics
Pseudo-Acceleration Response Spectrum = 0, 2, 5, 10, and 20%
Eigenvalue Problem • N solutions such that • Eigenvalues and Eigenvectors • Natural period of vibration, • Natural mode of vibration,
Frequency Response Curve Acceleration Frequency
Response History Analysis: Example Modal and total responses
Modal Response Spectrum Analysis (RSA) • Peak response estimated directly from response or design spectrum • Peak modal responses • Modal combination rule
Analysis of Finite Element Systems • RHA and RSA procedures valid • Extend methods to include dam-water-foundation rock interaction effects