1_Dynamics+of+Structures_12.7.2010

Dynamics of Structures Lecture 1

Anil K. Chopra Electricity Generating Authority of Thailand Bangkok, Thailand December 7-8, 2010 EGAT Thailand

Bangkok, Thailand

1

Simple System

EGAT Thailand

Bangkok, Thailand

2

Simple System

EGAT Thailand

Bangkok, Thailand

3

Free Vibration of Idealized Systems

Idealized Systems

EGAT Thailand

Free Vibration

Bangkok, Thailand

4

Decay of Free Vibration Aluminum Model

Plexiglass Model

EGAT Thailand

Bangkok, Thailand

5

Equation of Motion

f1  fD  fS  0

mu  cu  ku  mug  t  Single-Degree-of-Freedom System EGAT Thailand

Bangkok, Thailand

6

Lateral Stiffness 3EI k 3 h

96 EIc k 7 h3 EI b  EIc EGAT Thailand

Bangkok, Thailand

7

Undamped Free Vibration mu  ku  0 u  t   u  0  cos nt 

u 0

n

sin nt

k n  m

EGAT Thailand

Bangkok, Thailand

8

Natural Frequency (Period) of Vibration k n  m Tn 

2

n

n fn  2

EGAT Thailand

Bangkok, Thailand

rads/sec sec

cps (Hz)

9

Three-Story Steel Frame Building

EGAT Thailand

Bangkok, Thailand

Direction

Period, sec

Long

0.63

Short

0.74

Torsion

0.46

10

Sixty-Story Steel Frame Building

Period = 2.90 sec

EGAT Thailand

Bangkok, Thailand

11

Golden Gate Bridge

EGAT Thailand

Bangkok, Thailand

Direction

Period, sec

Transverse

18.2

Vertical

10.9

Longitudinal

3.8

Torsional

4.4

12

Pine Flat Dam, 400 ft high

EGAT Thailand

Water Depth, ft

Period, sec

310

0.288

345

0.306

Bangkok, Thailand

13

Damped Free Vibration 

Equation of Motion



Damping Ratio

mu  cu  ku  0

c c    2mn ccr

u  2nu  n2u  0

EGAT Thailand

Bangkok, Thailand

14

Effects of Damping (