1. #1 212 Ketter Hall, North Campus, Buffalo, NY 14260 www.civil.buffalo.edu Fax: 716 645 3733 Tel: 716 645 2114 x 2400 Control of Structural Vibrations Lecture #4 MDOF Structures Analysis Instructor: Andrei M. Reinhorn P.Eng. D.Sc. Professor of Structural Engineering

2. #2 Review Review of MDOF response using ortho-normalized modes

3. #3 Navy Building in San Diego - VE Dampers

4. #4 Navy Building in San Diego - VE Dampers

5. #5

6. #6 Code and Standards Formulations for Storied Structures with Added Damping

7. #7 Storied Structures with Added Damping

8. #8 Storied Structures with Added Damping

9. #9 Storied Structures with Added Damping Formulation using non-normalized modes:

10. #10 Storied Structures with Added Damping

11. #11 Storied Structures with Added Damping

12. #12 Storied Structures with Added Damping SPECIAL CASE - WIDELY USED

13. #13 Storied Structures with Added Damping

14. #14 Storied Structures with Added Damping - Equivalent Linearization

15. #15 Linear Approximations of Yielding Structures

16. #16 Uniform Distribution

17. #17 Code Provisions: Uniform Distribution

18. #18 Examples of Elastic Structures

19. #19

20. #20 Test Configurations

21. #21 Results in Test Structure

22. #22

23. #23 8.5 KIPS

24. #24 Code Provisions - Uniform Distribution

25. #25 Example of Yielding Structure

26. #26

27. #27 Code Spectrum / NEHRP 1994 FEMA 303/304

28. #28 Summary for Special Structures

29. #29 Comparison of Code vs NTH

30. #30 Comparison Code and NTH (cont)

31. #31 “Proper Inelastic Structure”

32. #32 “Improper Inelastic Structure”

33. #33 Further Challenges

34. #34 Further Challenges

35. #35