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Earthquake Dynamics of Structures

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

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  1. Earthquake Dynamics of Structures Anil K. Chopra DSI: Devlet Su Isleri Ankara, Turkey October 13, 2011

  2. Simple System

  3. Simple System

  4. Free Vibration of Idealized Systems Idealized Systems Free Vibration

  5. Decay of Free Vibration Aluminum Model Plexiglass Model

  6. Natural Frequency (Period) of Vibration

  7. Three-Story Steel Frame Building

  8. 49-Story Steel Frame Building Period = 2.90 sec

  9. Golden Gate Bridge

  10. Pine Flat Dam, 400 ft high

  11. Effects of Damping (<1)

  12. Effects of Damping Bogata, Colombia

  13. Earthquake Ground Motions

  14. Earthquake Ground Motions

  15. Ground Acceleration, Velocity & Displacement

  16. Equation of Motion

  17. Structural Response Depends on Tn and 

  18. Earthquake Response Spectrum • Peak Response • Plot of for fixed damping

  19. Pseudo-Acceleration Response Spectrum  = 0, 2, 5, 10, and 20%

  20. Peak Response from Spectrum Internal forces by statics

  21. Pseudo-Acceleration Response Spectrum  = 0, 2, 5, 10, and 20%

  22. Elastic Design Spectrum,  = 1, 2, 5, 10, 20%

  23. Multi-Degree-of-Freedom (MDF) System

  24. Multi-Degree-of-Freedom (MDF) System

  25. MDF System

  26. Natural Frequency (Period) of Vibration 26

  27. Free Vibration: Mode 1

  28. Free Vibration: Mode 2

  29. Eigenvalue Problem • N solutions such that • Eigenvalues and Eigenvectors • Natural period of vibration, • Natural mode of vibration,

  30. Example: 5-Story Shear Frame

  31. Vibration Periods and Modes

  32. Vibration Periods and Modes

  33. Folsom Dam, California

  34. Vibration Generator

  35. Frequency Response Curve Acceleration Frequency

  36. Frequencies and Damping Ratios

  37. Response History Analysis: Example Modal and total responses

  38. Elastic Design Spectrum,  = 1, 2, 5, 10, 20%

  39. Modal Response Spectrum Analysis (RSA) • Peak response estimated directly from response or design spectrum • Peak modal responses • Modal combination rule

  40. Finite Element System

  41. Analysis of Finite Element Systems • RHA and RSA procedures valid • Extend methods to include dam-water-foundation rock interaction effects

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