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Dynamics of Structures

Dynamics of Structures. Lecture 1 Anil K. Chopra Universidad de los Andes Bogotá, Colombia May 23, 2011. Simple System. Simple System. Free Vibration of Idealized Systems. Idealized Systems. Free Vibration. Decay of Free Vibration. Aluminum Model. Plexiglass Model. Equation of Motion.

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Dynamics of Structures

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  1. Dynamics of Structures Lecture 1 Anil K. Chopra Universidad de los Andes Bogotá, Colombia May 23, 2011

  2. Simple System Bogata, Colombia

  3. Simple System Bogata, Colombia

  4. Free Vibration of Idealized Systems Idealized Systems Free Vibration Bogata, Colombia

  5. Decay of Free Vibration Aluminum Model Plexiglass Model Bogata, Colombia

  6. Equation of Motion Single-Degree-of-Freedom System Bogata, Colombia

  7. Lateral Stiffness Bogata, Colombia

  8. Undamped Free Vibration Bogata, Colombia

  9. Natural Frequency (Period) of Vibration Bogata, Colombia

  10. Three-Story Steel Frame Building Bogata, Colombia

  11. 49-Story Steel Frame Building Period = 2.90 sec Bogata, Colombia

  12. Golden Gate Bridge Bogata, Colombia

  13. Pine Flat Dam, 400 ft high Bogata, Colombia

  14. Damped Free Vibration • Damping Ratio • Equation of Motion Bogata, Colombia

  15. Effects of Damping (<1) Bogata, Colombia

  16. Effects of Damping Bogata, Colombia

  17. Measurement of Period & Damping Bogata, Colombia

  18. Example Bogata, Colombia

  19. Vibration Generator Bogata, Colombia

  20. Vibration Generator Bogata, Colombia

  21. Measurement of Frequency & Damping Bogata, Colombia

  22. Earthquake Ground Motions Bogata, Colombia

  23. Earthquake Ground Motions Bogata, Colombia

  24. Ground Acceleration, Velocity & Displacement Bogata, Colombia

  25. Equation of Motion Bogata, Colombia

  26. Structural Response Depends on Tn and  Bogata, Colombia

  27. Structural Deformation & Forces • Equivalent Static Forces • Pseudo-Acceleration • Internal Forces by Static Analysis Bogata, Colombia

  28. Earthquake Response Spectrum • Peak Response • Plot of for fixed damping Bogata, Colombia

  29. Deformation Response Spectrum Bogata, Colombia

  30. Pseudo Velocity Response Spectrum Plot of V v’s Tn • 2 3 Tn, sec Bogata, Colombia

  31. Pseudo Acceleration Response Spectrum Plot of A v’s Tn Peak Force Bogata, Colombia

  32. Combined D-V-A Spectrum Bogata, Colombia

  33. Combined D-V-A Spectrum  = 0, 2, 5, 10, and 20% Bogata, Colombia

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

  35. Deformation Response Spectrum  = 0, 2, 5, 10, and 20% Bogata, Colombia

  36. Peak Response from Spectrum Internal forces by statics Bogata, Colombia

  37. Example Bogata, Colombia

  38. Example Bogata, Colombia

  39. Example Bogata, Colombia

  40. Response Spectrum and Peak Ground Accleration, Velocity, and Displacement Bogata, Colombia

  41. Ground Acceleration, Velocity & Displacement Bogata, Colombia

  42. Response Spectrum Plotted on Normalized Scales Bogata, Colombia

  43. Mean Response Spectrum & Design Spectrum Bogata, Colombia

  44. Construction of Elastic Design Spectrum Bogata, Colombia

  45. Amplification Factors N. M. Newmark and W. J. Hall, Earthquake Spectra and Design, EERI, Berkeley, CA, 1982, pp. 35, and 36. Bogata, Colombia

  46. Construction of Design Spectrum, 84th Percentile,  = 5% Bogata, Colombia

  47. Elastic Design Spectrum, 84th Percentile,  = 5% Bogata, Colombia

  48. Elastic Design Spectrum,  = 1, 2, 5, 10, 20% Bogata, Colombia

  49. Elastic Design Spectrum,  = 1, 2, 5, 10, 20% Bogata, Colombia

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