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ECIV 724 A Dynamics of Structures

ECIV 724 A Dynamics of Structures. Instructor: Dr. Dimitris C. Rizos 300 Main St. Dept. of Civil and Environmental Engineering (803) 777-6166 rizos@engr.sc.edu. Earth Layers. The Main Earth Layers are: Core Lower Mantle Upper Mantle Crust. Earth Layers.

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ECIV 724 A Dynamics of Structures

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  1. ECIV 724 A Dynamics of Structures Instructor: Dr. Dimitris C. Rizos 300 Main St. Dept. of Civil and Environmental Engineering (803) 777-6166 rizos@engr.sc.edu

  2. Earth Layers • The Main Earth Layers are: • Core • Lower Mantle • Upper Mantle • Crust

  3. Earth Layers

  4. Theory of Tectonic Plates

  5. Theory of Tectonic Plates

  6. Fault Types

  7. St. Andreas Fault Location: Carrizo Plain area, San Luis Obispo County, California. Surface Rupture Right-Lateral Strike-Slip Faults Photo credit: R.E. Wallace, U.S. Geological Survey.

  8. El Progresso, Guatemala February 4, 1976 Plastic Deformation Saturated unconsolidated deposits left-lateral strike-slip fault

  9. Dickey, Idaho horizontal offset ~2 m Fault scarp

  10. Earthquake of February 4, 1976, Guatemala

  11. offset 2.6 m San Francisco, April 18, 1906 Guatemala February 4, 1976

  12. Wave Types

  13. Wave Types

  14. Ground Motion • External excitation in the form of • Ground Displacements • Ground Velocities • Ground Accelerations • Typical Duration 20-100 sec

  15. Ground Motion Ground Motion has 3 Components N-S, E-W and Vertical Horizontal components are of major interest (excessive shear forces) Vertical component has been traditionally ignored, but may be important.

  16. Intstrumentation Strong Motion Accelerograph A transducer: SDOF highly damped (60-70%) Known k, m (fn ~ 25 Hz) Sampling Rate: 1/100, 1/50 sec (10,000 sampling points)

  17. LIQUEFACTION-DIFFERENTIAL SETTLEMENTS Niigata, Japan.June 16, 1964, 7.4

  18. GROUND DEFORMATION-DIFFERENTIAL SETTLING Earthquake of July 29, 1967, Caracas, Venezuela.

  19. GROUND SHAKING Before Huaraz, Peru May 31, 1970, 7.8R After

  20. San Fernando Mexico City

  21. Collapsed Cypress section of Interstate 880 the 1989 Loma Prieta (California)

  22. Northridge 1994 Parking garage at California State University

  23. Damaged Kobe waterfront (1995)

  24. Office Buildings, Kobe 1995

  25. Kobe 1995 Collapsed first and second stories

  26. Collapse of Freeway in 1989 Loma Prieta, CA Earthquake (7.1R)

  27. Structural Response Assumed to be Independent of Ground Motion True for most cases when Soil-Structure Interaction is not an issue

  28. EARTHQUAKE ANALYSIS SDF SYSTEMS A SDF system is subjected to a ground motion ug(t). The deformation response u(t) is to be calculated.

  29. EARTHQUAKE ANALYSIS EQUIVALENT STATIC FORCE fs(t) is the force which must be applied statically in order to create a displacement u(t).

  30. REPONSE SPECTRA A response spectrum is a plot of maximum response (e.g. displacement, velocity, acceleration) of SDF systems to a given ground acceleration versus systems parameters (Tn , ). A response spectrum is calculated numerically using time integration methods for many values of parameters (Tn, ).

  31. REPONSE SPECTRA Example : Deformation response spectrum for El Centro earthquake

  32. Deformation, pseudo-velocityandpseudoacceleration response spectra can be defined and ploted on the same graphs n : natural circular frequency of the SDF system.

  33. COMBINED D-V-A SPECTRUM

  34. RESPONSE SPECTRUM CHARCTERISTICS Tn < 0.03 s : rigid system no deformation u(t) ≈ 0  D ≈ 0

  35. RESPONSE SPECTRUM CHARCTERISTICS Tn > 15 s : flexible system no total displacement u(t) = ug(t)  D = ugo

  36. RESPONSE SPECTRUM CHARCTERISTICS

  37. Example

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