x
TABLES OF CONTENTS
CHAPTER
1
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF SYMBOLS
xv
LIST OF APPENDICES
xvii
INTRODUCTION
1.1
Research Background
2
1.2
Problems Statement
3
1.3
Objectives
4
1.4
Scope of work
5
1.5
Organization of Report
5
xi
2
LITERATURE REVIEW
2.0
General
7
2.1
Behavior of cantilever tower
8
2.2
Tuned Mass Damper (TMD)
10
2.3
Single and multiple tuned mass damper
14
2.4
Pendulum Tuned Mass Damper (PTMD)
16
2.4.1
Characteristic of PTMD
16
2.4.2
Performance of Pendulum Damper
18
2.5
Structure with Pendulum Tuned Mass
Damper
3
21
THEORETICAL BACKGROUND
4
3.1
Model of tower
31
3.2
Model of tower and pendulum
38
3.2.1
Lagrange’s Equation
41
3.3
Pendulum Tuned Mass Damper (PTMD)
42
METHODOLOGY
4.1
General
45
4.2
Modeling by SAP2000 version 14.2
46
4.3
Material Properties
49
4.4
Pendulum tuned mass damper
50
4.5
Analysis
52
4.5.1
Free vibration analysis
53
4.5.2
Response Spectrum Analysis
54
4.6
Flow Chart
55
xii
5
6
RESULTS AND DISCUSSION
5.1
Introduction
57
5.2
Member Size and Section Properties
58
5.3
Time History Analysis
61
5.4
Response Spectrum Analysis
62
5.5
Model Signage
63
5.6
Modeling of the Tower and Pendulum
Tuned Mass Damper
64
5.7
Free Vibration Analysis
67
5.8
Axial Forces
70
5.9
Shear Force
72
5.10
Bending Moments
75
5.11
Stresses
78
5.12
Story Drift
84
CONCLUSION AND RECOMMENDATION
6.1
Overview
87
6.2
Conclusions
88
6.3
Recommendation
90
REFERENCES
92
Appendices A- E
94
xiii
LIST OF TABLES
TABLE NO.
TITLE
PAGE
Table 5.1
Member size for level 1 until 19
58
Table 5.2
Member size for level 20 until 23
59
Table 5.3
Loading combination component
59
Table 5.4
Axial force at tower head at various
earthquakes ground motions
Table 5.5
Shear force at tower head at various
earthquakes ground motions
Table 5.6
79
Stress, S22 at tower shaft at various
earthquake ground motions
Table 5.9
75
Stress, S11 at tower shaft at various
earthquake ground motions
Table 5.8
73
Bending moment at tower head at various
earthquakes ground motions
Table 5.7
70
81
Story drift at top of tower at various
earthquake ground motions
84
xiv
LIST OF FIGURES
FIGURES NO.
FIGURES
Figure 2.1
One degree of freedom system fitted with TMD
Figure 2.2
Effective damping and relative movement of
TMD mass ratio of 0.02 (Kwok K.C.S. et al. 1995)
Figure 2.3
12
13
Simple pendulum tuned mass damper
(Yamazaki et al.)
Figure 2.4
PAGE
17
Maximum displacement of the top of the chimney
equipped with a pendulum with respect to
the pendulum mass (sinusoidal excitation)
(R. Jankowski et al. 2003)
Figure 2.5
Simple pendulum tuned mass damper
(Yamazaki et al.)
Figure 2.6
19
21
Water tank TMD at Sydney Tower
(Kwok K.C.S. et al. 1995).
22
Figure 2.7
TMD at Chifley Tower (Kwok K.C.S. et al. 1995).
23
Figure 2.8
TMD at Chifley Tower (Kwok K.C.S. et al. 1995).
24
Figure 2.9
Crystal Tower Osaka pendulum tuned mass damper
layout (Crystal Tower. Takemaka Corporation.
Figure 2.10
Ice storage tank- Crystal Tower
25
xv
(Courtesy of Takemaka Corporation.)
Figure 2.11
Citicorp Center New York tuned mass damper
(Kwok K.C.S. et al. 1995)
Figure 2.12
27
Multistage pendulum tuned mass damper
(Kwok K.C.S. et al. 1995).
Figure 2.13
26
29
Pendulum tuned mass damper in Taipei 101
(Haskett T. et al.).
30
Figure 3.1
Overall view of the chimney
33
Figure 3.2
One degree of freedom model of chimney
33
Figure 3.3
Maximum accelerations with varying E and ξ
at height ha under action Ca
Figure 3.4
Maximum accelerations with varying E and ξ
at height ha under action Cb
Figure 3.5
37
Two degree of freedom model of the chimney with
a pendulum damper
Figure 3.6
36
39
Geometry of the spherical PTMD coupled with
a translational main structure.
40
Figure 3.7
A simple pendulum tuned mass damper
43
Figure 3.8
Compound Pendulum
44
Figure 4.1
The side elevation drawing of the structure.
47
Figure 4.2
The modeling of the tower using SAP2000.
48
Figure 4.3
The modeling of the pendulum tuned mass damper.
51
Figure 4.4
The sequence in SAP2000
55
Figure 5.1
Side elevation air traffic control tower at KLIA2
60
Figure 5.2
The El- Centro earthquake 1940 data
61
Figure 5.3
Design response spectrum configurations
xvi
(from 2006 IBC)
62
Figure 5.4
Elements indications at tower head
63
Figure 5.5
Element indications at tower shaft
64
Figure 5.6
Model of air traffic control tower without
PTMD in SAP2000
Figure 5.7
65
Model of pendulum tuned mass damper (PTMD)
with simple structure
66
Figure 5.8
Model of KLIA2 with 2 PTMD
66
Figure 5.9
Model of KLIA2 with 4 PTMD
67
Figure 5.10
First mode shape of KLIA2 with
natural period 2.9s
Figure 5.11
Second mode shape of KLIA2 with
natural period 2.32s
Figure 5.12
77
Graph of bending moment percentage reduction
for response spectrum analysis
Figure 5.18
74
Graph of bending moment percentage reduction
for time history analysis
Figure 5.17
74
Graph of shear force percentage reduction for
response spectrum analysis
Figure 5.16
71
Graph of shear force percentage reduction for
time history analysis
Figure 5.15
71
Graph of axial force percentage reduction for
response spectrum analysis
Figure 5.14
69
Graph of axial force percentage reduction for
time history analysis
Figure 5.13
68
77
Graph of stress, S11 percentage reduction for
time history analysis
80
xvii
Figure 5.19
Graph of stress, S11 percentage reduction
for response spectrum analysis
Figure 5.20
Graph of stress, S22 percentage reduction for
time history analysis
Figure 5.21
Figure 5.23
82
Graph of stress, S22 percentage reduction
for response spectrum analysis
Figure 5.22
80
83
Graph of story drift percentage reduction for
time history analysis
85
Graph of story drift percentage reduction for
response spectrum analysis
86
xviii
LIST OF SYSMBOLS
φ
-
Amplitudes
ρ
-
Mass density
ζ (x-h)
-
Direct function
ω
-
rth eigenfrequency
C
-
Damping matrix
c1
-
Damping capacity of main system
c2
-
Damping capacity of tuned mass damper
C1
-
Damping coefficient
fbi
-
Frequencies
G
-
Acceleration of gravity
k1
-
Stiffness of main system
k2
-
Stiffness of tuned mass damper
K1
-
Stiffness coefficient
K
-
Stiffness matrix
L
-
Pendulum length
m1
-
Mass of main system
m2
-
Mass of tuned mass damper
xix
M
-
Total mass of the chimney
mtot.
-
Total mass of the tower
m1
-
m2 mass of the equivalent oscillator
M2
-
Pendulum mass
M
-
Diagonal mass matrix;
qr
-
Generalized coordinates
Qr
-
Generalized force
t
-
Time
T
-
Tension cable
x1
-
x1 (t) = response of main system
x2
-
x2 (t) = response of tuned mass damper
x1 (t)
-
Horizontal displacement
-
Acceleration
ẋ
-
Velocity
x
-
Relative displacement with time;
-
Ground acceleration
g
xx
LIST OF APPENDICES
APPENDIX
TITLE
A
Manual Calculation
B
Floor plan of Air traffic Control tower
for level 1 until 19
C
97
98
Side elevation of Air traffic Control tower
for tower shaft
E
94
Floor plan of Air traffic Control tower
for level 20 to 23
D
PAGE
99
Side elevation of Air traffic Control tower
for tower head
100