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 Core Lower Mantle Lower Mantle Upper Mantle Upper Mantle Crust Crust

3. Earth Layers

4. Theory of Tectonic Plates

6. Fault Types

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

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

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

10. Earthquake of February 4, 1976, Guatemala

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

12. 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 Horizontal components are of major interest (excessive shear forces) Ground Motion has 3 Components N-S, E-W and Vertical 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 (f n ~ 25 Hz) Sampling Rate: 1/100, 1/50 sec (10,000 sampling points)

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

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

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

21. San FernandoMexico City

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

23. Northridge 1994 Parking garage at California State University

24. Damaged Kobe waterfront (1995)

25. Office Buildings, Kobe 1995

26. Kobe 1995 Collapsed first and second stories

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

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

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

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

31. 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 (T n,  ). A response spectrum is calculated numerically using time integration methods for many values of parameters (T n,  ).

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

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

34. COMBINED D-V-A SPECTRUM

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

36. RESPONSE SPECTRUM CHARCTERISTICS T n > 15 s : flexible system no total displacement u(t) = u g (t)  D = u go

37. RESPONSE SPECTRUM CHARCTERISTICS

38. Example