#1 212 Ketter Hall, North Campus, Buffalo, NY Fax: Tel: x 2400 Control of Structural Vibrations Lecture #4 MDOF Structures Analysis Instructor: Andrei M. Reinhorn P.Eng. D.Sc. Professor of Structural Engineering

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

#3 Navy Building in San Diego - VE Dampers

#4 Navy Building in San Diego - VE Dampers

#5

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

#7 Storied Structures with Added Damping

#8 Storied Structures with Added Damping

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

#10 Storied Structures with Added Damping

#11 Storied Structures with Added Damping

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

#13 Storied Structures with Added Damping

#14 Storied Structures with Added Damping - Equivalent Linearization

#15 Linear Approximations of Yielding Structures

#16 Uniform Distribution

#17 Code Provisions: Uniform Distribution

#18 Examples of Elastic Structures

#19

#20 Test Configurations

#21 Results in Test Structure

#22

# KIPS

#24 Code Provisions - Uniform Distribution

#25 Example of Yielding Structure

#26

#27 Code Spectrum / NEHRP 1994 FEMA 303/304

#28 Summary for Special Structures

#29 Comparison of Code vs NTH

#30 Comparison Code and NTH (cont)

#31 “Proper Inelastic Structure”

#32 “Improper Inelastic Structure”

#33 Further Challenges

#34 Further Challenges

#35