passive energy dissipation systems - m. c. constantinou
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E E E E Ek s h d = + + +
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With MetallicYielding EDS
Without EDS
With Friction EDS
Without EDS
With Viscoelastic EDS
Without EDS
Slope Dependent on
Frequency andDeformation
Lateral Deformation Lateral Deformation
Lateral Deformation
LateralBase
Shear
LateralBas
e
Shear
LateralBas
e
Shear
Friction Force
Figure 1.1 Effect of Energy Dissipation Systems on Force-Deformation Curves of
a Structure
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Passive ControlSystem
StructureExcitation Response
Figure 1.2 Elements of a Passive Control System
Controller
Power Source
Active ControlSystem
Sensors Sensors
Excitation Structure Response
Figure 1.3 Elements of an Active Control System
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Force
Force
Displacement Displacement
Metallic YieldingDevice
Friction Device
Fo Fo
Xo Xo
Figure 2.1 Idealized Force-Displacement Loops of Hysteretic Energy Dissipation Devices
Force
Force
Displacement Displacement
F = c' xXXo o o
o
o
K = k' + c'
K'
* 2 2 2
F
Viscoelastic Solidor Fluid Device
Viscous FluidDevice
Figure 2.2 Idealized Force-Displacement Loops of Viscoelastic Energy Dissipation Devices
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Force
Force
Displacement Displacement
Dynamic
Static
Fluid RestoringForce/Damping Device
Frictional-Spring Devicewith Recentering Capability
Figure 2.3 Idealized Force-Displacement Loops of Other Energy Dissipating Devices
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F
F
F
V
V
V
V
V
Without Energy Dissipation System
With Energy Dissipation System
Energy DissipationDevice
Viscoelastic EDS
Hysteretic EDS
R
R
R
R
R
3
2
1
V = Fi
Figure 2.4 Pushover Curves and Force-Displacement Hysteresis Loops of an ElasticStructure Without and With Energy Dissipation Systems
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Figure 2.5 Pushover Curves and Force-Displacement Hysteresis Loops of a Yielding StructureHaving Proper Plastic Hinge Formation Without and With Energy Dissipation Systems
Without Energy Dissipation System
With Energy Dissipation System
Plastic Hinge
Energy DissipationDevice
Viscoelastic EDS
Hysteretic EDS
F
F
F
V
V V
V = F
3
2
1
i
R
R
R R
R
V V
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10% Added Damping
30% Added Damping
20% Added Damping
Velocity Domain (Long-Period Range)
1.0
0.8
0.6
0.4
0.2
0.00.0 0.1 0.2 0.3
Damping Ratio of Structure WithoutEnergy Dissipation System
DisplacementResponseR
atio
(ResponsewithAddedEDS/Responsew
/outEDS)
Figure 2.6 Response Reduction of Structure with Added Damping of 10, 20 or 30% ofCritical
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R
R
R R
R
F
F
F
3
2
1
Plastic Hinge
Energy DissipationDevice
Without Energy Dissipation System
With Energy Dissipation System
V = F i
V
V
V
Viscoelastic EDS
Hysteretic EDS
Figure 2.7 Pushover Curves and Force-Displacement Hysteresis Loops of a YieldingStructure Having Improper Plastic Hinge Formation Without and With Energy DissipationSystems
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F k x c x= +' ' ( ) ( )
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kk
k
W
L
4
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Figure 2.8 Definition of Relative Displacement and Angle of Inclination of Energy DissipationDevice
L 1
2
1
2mk
Tk2
i i2
i
= = K
k
j j rjj
k i ii
c
m=
1
2
2 2
2
' cos
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k
j2
j rj2
j
k
=
cos
K
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k G A
hc
G A
h
G
G
b b' ' , ' "
, "
'= = =
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4
4
3
3
2
2
1
1
0
0
0
0
0
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
Temp.= 21 C
Temp.= 32 C
o
o
k' = G' h
Ab
= 0.05
= 0.05
= 0.05
= 0.05
= 0.2
= 0.2
= 0.2
= 0.2
= 0.05
= 0.05
= 0.2
= 0.2
o
o
o
o
o
o
o
o
o
o
o
o
c' = G"Ah
b
=G'G" = c'
k'
Frequency (Hz)
LossFactor
G"(MPa)
G'(MPa
)
1.5
1.0
0.5
Figure 2.9 Properties of a Viscoelastic Solid Energy Dissipation Device
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M
m
m
k
i iki
i iki
=
2
2
V M S S k k ak ik ik k dk = =,
ki ik i
i
i iki
m S
m
=
2
=
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Table 2.1 Factor for Modification of Response
Figure 2.10 Modification of Elastic Response Spectrum for Damping Different than 5% ofCritical
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S f f S a pa= +1 22
f f11
21
2 2= = cos tan ( ) sin tan ( ) ,
Figure 2.11 Response Spectra of Maximum and Pseudo Acceleration
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W F x f d o o=4
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W c xd o= ' 2
F c x xva= sgn( )
W c x F xd v o1
o o= =+
=
+
+4 2
12
2
2
& = &
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F c
k
dF
dtc uv
bv+ =
k c
c cv v' , '( ) ( )
=
+ =
+
2
2 2 2 21 1
=
Figure 2.12 Viscous Fluid Damper Installed on Top of Chevron Brace in aStructure
Viscous Fluid Damper
C = 4 kNs/mmv
Steel Brace(A=5000 mm )2
=59o
4.30 m
3.60m L=
3.9m
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=
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Figure 2.13 Gravity and Additional Axial Load in Interior Column of 9-Story Model Structurewith Friction Energy Dissipation Devices
78in 60in 78in
2.4
2.4
3.1
4.9
5.0
4.8
4.8
4.9
1.24 k
1.24 k
1.60 k
2.54 k
2.59 k
2.48 k
2.48 k
2.54 k
W4x
13
36 in (TYP)
48 in
12.75kips
29.46kips
GravityOnly
Total
46 (TYP)o
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Figure 2.14 Illustration of Simplified Nonlinear Method of Analysis
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=
Figure 2.15 Analyzed SDOF Inelastic System with Linear Viscous Energy DissipationSystem
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= =
Table 2.2 Motions Used in Analysis and Scale Factors
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Figure 2.17 Average Damped Response Spectra of Scaled Motions
Figure 2.16 Response Spectra of Scaled Motions used in Analysis
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T D
Aeff =
2
1
2
eff
y y eff
eli
A D AD
AD
T
T=
+ +
2
Figure 2.18 Average Maximum Velocity Spectra of Scaled Motions and Pseudo-VelocitySpectra for Damping Ratio of 0.1, 0.2 and 0.5 in the Long-Period Range
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Table 2.3 Results of Analysis on Peak Displacements for System with = 0.5 secand = 0.15
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Table 2.4 Results of Analysis on Peak Displacements for System with = 1.0 secand = 0.15
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Table 2.5 Results of Analysis on Peak Displacements for System with = 0.5 secand = 0.25
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Table 2.6 Results of Analysis on Peak Displacements for System with = 1.0 sec
and = 0.25
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Table 2.7 Results of Analysis and Prediction of Simplified Method, Case ofSystem with = 1.0 sec and = 0.15
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= & &
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= = =
Figure 2.19 Average Response Spectra of Scaled Motions in the Short-Period Range andfor High Damping
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= =
Figure 2.20 Example Building
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Figure 2.21 Pushover Curves of Example Building
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Table 2.8 Modal Properties of Example Building in VariousStages of Pushover Analysis by the Modal Pattern
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Table 2.9 Modal Properties of Example Building in Various Stagesof Pushover Analysis by the Uniform Pattern
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eff
y yq A D AD
AD=
2
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= =
Figure 2.22 Overlying of Spectral Capacity Curve and Design Demand Spectrum for ResponseCalculation in Fundamental Mode, Case of Modal Pattern
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Table 2.10 Response of Example Structure for Modal Pattern of Lateral Loads
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Figu
re2.23
IllustrationofForcesActin
gonExampleStructureforModal
PatternofLateralLoadsandActio
nsinSelectedMember
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Table 2.11 Response of Example Structure for Uniform Pattern of LateralLoads
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+
Figure 2.24 Calculated First Story Shear-Drift Loops in Nonlinear Dynamic Analysis of ExampleBuilding
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Table 2.12 Comparison of Results of Nonlinear Dynamic and Simplified NonlinearMethods of Analysis
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Figure 2.25 Comparison of Distribution of Shear Force with Height in 8-story Structure with
Hysteretic and Linear Viscous Isolation Systems. Seismic Input Representative of Seismic Zone4, Soil type per 1994 UBC
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Figure 2.26 Force-Velocity Relation of Reduced-Scale Prototype Fluid Damper of San BernardinoCounty Medical Center Replacement Project
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Figure 2.27 Level 2 Bridge Design Spectra for Japan (Ground Condition 1 = Stiff Soil; GroundCondition 3 = Deep Alluvium Soil)
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Table 3.1 Passive Energy Dissipation Systems
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x t x to( ) sin=
Figure 3.1 Idealizations for Passively Damped SDOF Structures (M, K, C)
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Figure 3.3 Metallic Damper Geometries
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Figure 3.4 Stress-strain Response of Structural Steel
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F k x k x F B
Fo o
o
n
=
B k x F B
Fo
o
n
=
Figure 3.5 Force-displacement Response of X-shaped Plate Damper
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Figure 3.6 &&Ozdemir Rate-independent Model
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Figure 3.7 Two Surface Force-Displacement Model
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Table 3.2 Uniaxial Two-Surface Device Model
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Figure 3.8 Representative Friction Dampers
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t n=
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Figure 3.9 Hysteresis Loops of Limited Slip Bolted Joints
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Table 3.3 Elastic-Perfectly Plastic Device Model
Table 3.4 Hysteric Device Model with Symmetric
Bearing Stops
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Figure 3.10 Coulomb Friction Element
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( ) ( ) ( )
( )( )t G t
Gt= +'
"
=
Figure 3.11 Idealized Force-displacement Response of Viscoelastic Devices
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( ) ( ) ( ) d ( ) ( )t G t G t o
t= ++
0
( ) ( ) ( )ot
t G t d =
Figure 3.12 Typical Viscoelastic Solid Damper Configuration
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G t GG G
t te
g e
o
( )= +
+1 /
Figure 3.13 Stress Relaxation Tests at Different Strain Rates
G G G G t t e g e o o'( ) cos = + +
1
2
G G G t tg e o o" sin = +
1
2
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Figure 3.14 Comparison of Storage and Loss Moduli Between Simulation and Test
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= =
=
G G T T vs
G G T T vs
G t G T T vs t /
0 0
0 0 0
0 0 0
0
a b
log + =a b
F t k x t c t = +' '
x
kAG
cAG
''
'"
= =
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Figure 3.16 Viscoelastic Fluid Dampers
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G Ti T
i To
o
o
v* ,
=
+1
Figure 3.17 Dynamic Modulus for Polybutane Fluid
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=
F Cdx
dto=t
t
F tdF t
dtC
dx t
dto+ =
Figure 3.19 Force-displacement Response of Orificed Fluid Damper
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Figure 3.20 Comparison of Experimental and Analytically-derived Values for Orificed Fluid Damperat Room Temperature
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F F x x k x
F k x Z F x
o o
o d
= + +
+ +
1 exp sgn
sgn min
x Z x Z Z xZ xy
+ + = 2 0
Figure 3.21 Pressurized Fluid Restoring Device
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FF x xx
F x xxd
dp p
dm m
= >
+ < > + < >= < + > < >
1
< > < > =< > =&& & &
C y f g y m zy12
1 1< > = < + > < >& & &&&( )
< >&
< + > & && & < >
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=
=
= =
= =
Figure 3.32 Amplification Factor as a Function of
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opt=
+1
1
R= +1 2
opt=
+3
8 1
RA B
C Dj
j j= +
+
2 2
2 2
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< >
+
+
+
+
&&
+
+
&&
&&
+
+
&&
&& &&
&&
+
+
+
+
+
< >
+
+
< >
Table 3.5 Optimum Absorber Parameters Attached to Undamped SDOF Structure
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Table 3.6 Values of Aj
and Bj
for Various Excitations and Response Parameters
&&
&&
&
&&
&&
&&
+
&& && +
&
&&
&& &&
&&
+
&&
+
+
&&
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C a s= 2 2 2 2 2 2
1 4
D s= + 2 1 22 2 2 2
, ,xt h u+ + = 0
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u uu g h
3u
1h
v2
1 2hb
C u x 0
,t ,x ,x
2
,xxt
1/ 2
b
+ +
+
+ +
+ =
&&
&&
=
Figure 3.33 Tuned Liquid Damper Geometric Definition
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( ) ( )
( ) k1/ 2
22
2
2k 1gh
L1
1
62k 1
h
L=
Figure 3.34 Free Surface Time Histories Near Lowest Resonance
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Figure 3.35 Free Surface Time Histories Near Lowest Resonance
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Figure 3.36 Tuned Liquid Damper Surface Elevation Extrema and Base Shear Force Response
Figure 3.37 Tuned Liquid Damper Force-displacement Response
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&& & &&x Cx Kx x x p+ + + = + +g &&
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x x Cx Kx= + +&& &
$ && $ & $ $ &&x Cx Kx x p+ + = +g
$ = + $C C C= +
$K K K= +
$ $ $
$ $ $ $
$ $K 0
=o2
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i j $ =
=
01
for i j
for i j
i j $K =
=
0 for i jfor i joi
2
$ $
x y=
&& $ & &&y C y y y p+ + = + o g2
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&& $ &&y xg g= $
$ $ $C K= + 0 1
$C = + 0 12o
$
$ $ $ $C M K
=
j 1j 0
N 1 j
$
$C =2o
&& & &&y y y y p= + = +2 2 o o g
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y y y y qi i oi i oi i gi i= + = +2 2
qi= i
p
g x x C x K x x p 0t t t t t t gt t
= + + + =$ && $ & $ $ &&
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+
g x x C x
K x x p 0
t t t t t t t t
t t t t t t t t
+ + + +
+ + + +
= +
+ + =
$&& $ &
$ $ &&
g
+
( )x x x xt t t t t t t+ += + + 2
& &
& & && &&x x x xt t t t t t t+ += + +
2
( )g x K x f t t t t t t t t + + + += =
0
( )
$ $K K Ct t t t t t 2
2
t
4
t
+ + += + +
$ &&
$ $
$ $ & $ &&
f Mx p
M C x
M C x Mx
t t t t t
t t t
t t t t
t t
t
+ + +
+
+
= +
+ +
+ +
+
g
+
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K x f(n)t+ t
(n)
t t = +
K g
x(n)t t
(n)
t+ t+ =
f g x(n)t t
nt+ t+ =
( )
( ) ( )x x xn 1t t
nt t
++ += +
x xt t n
t t++
+= 1 +
x x( )1t t t+
=
K( )nt t+
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= =
&& & &&x Cx Kx f x p+ + + = +g
f =
+ +
n F n F
n F n F
n F n F
n F
1 1 2 2
2 2 3 3
j j j 1 j 1
N N
M
M
FdF
dtC
dx
dt
dx
dtj
j
j
j j+ =
0
2 1cos
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&& K x x p = +g
( ) ( )
K C K = + + + i
x f=
~ ~ ~F
i C
ix xj
jj j= +
0
2
11
cos
Bz Az f &+ =
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z
x
x
f
=
&
B
0 0
0 0
0 0
=
A
C K
0 0D 0
=
f
x p
0
0
g
=
+
&&
( )A B z 0+ =
oi i=
oi i oi= /
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Figure 4.1 Force-displacement Relationship for Elastic-Perfectly Plastic Element
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= +
m
k k
Figure 4.2 SDOF Response to 1940 El Centro (N-S Component)
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&&
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Figure 4.3 Load-displacement Response of Limited Slip Bolted Joints
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Figure 4.4 Refined Model for X-braced Friction Damper
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Figure 4.5 Experimental Hysteresis Loops for X-braced Friction Damper
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Figure 4.6 Slotted Bolted Connection
Figure 4.7 Typical Load Deformation Diagram for Slotted Bolted Connections
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Figure 4.8 Cyclic Response of Slotted Bolted Connections
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Figure 4.10 Experimental Data for EDR
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Figure 4.11 Response of Sumitomo Dampers in Nine-Story Frame for El Centro 0.712g Input
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Figure 4.12 Overall Response Comparison in Nine-story Frame for El Centro 0.712g Input
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Figure 4.13 EDR Response in Three-story Test Frame for Zacatula Ground Motion
Figure 4.14 Cumulative Energy Time History for EDR Damped Three-story Test Frame
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Figure 4.15 Numerical Results of LSB Joint for El Centro Ground Motion
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= =
Figure 4.16 Numerical Response of SDOF Structure with EDR
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= = =
Figure 4.18 Effect of Ambient Temperature on Natural Frequency and Damping Ratio
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Table 4.1 Summary of Dynamic Response Reduction Percentage under 0.12g White
Noise Excitation
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Figure 4.19 Roof Displacement Time Histories
Figure 4.20 Displacement Time History at Roof
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Table 4.2 Summary of Dynamic Response under 0.60g El Centro and HachinoheEarthquake Motions
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Figure 4.21 Response Envelopes: - - - - - -with Dampers, without Dampers
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Figure 4.23 Force-deformation Curves under 0.2g Taft Earthquake
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x = k + c x
( &
=
Figure 4.24 Contribution of Energy Terms
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ii v
i
E
E=
E Ev i i i i i= =
K K K
ii i i
i i
=+
K
K K
= +
i i i
i i
K
K K
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i i i
i i=
+
K K
i
i i
i
=
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& & =
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Figure 4.26 Damper Configurations for Three-story Structure
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Figure 4.27 Acceleration, Story Shear and Interstory Drift Profiles of 3-story Structure
Table 4.4 Properties of Three-story Structure
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Figure 4.28 Comparison of Response Profiles for Two Different Levels of the Same Earthquake
Figure 4.29 Comparison of Experimental and Analytical Results
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Figure 4.30 Displacement Response Histories
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Figure 4.31 Acceleration Response Histories
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Figure 4.32 Comparison of Forces in Structural Components at First Floor
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Figure 4.34 and as Functions of
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&&
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Figure 4.35 Large Strain Behavior of Nitinol
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Figure 4.36 Superelastic Behavior
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Figure 4.37 Torsional Bar Design
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Figure 4.38 Maximum Floor Response (0.06g El Centro)
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Figure 4.39 Maximum Floor Response (0.06g Quebec)
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Figure 5.1 Izazaga #38-40 Building, Mexico City
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Figure 5.3 Cardiology Hospital Building with Exterior Buttresses and ADAS
Damper
Figure 5.2 Brace-Damper Assembly in Izazaga #38-40 Building
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Figure 5.4 IMSS Reforma Building, Mexico City
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Figure 5.5 Brace-Damper IMSS Reforma Building Retrofit Scheme from Outside
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Table 5.1 Calculated Earthquake Response for IMSS Reforma Building
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Figure 5.7 Structural Analysis Model for Wells Fargo Bank Building
Figure 5.6 Wells Fargo Bank Building Retrofit Details
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Figure 5.8 Comparison of Computed Results for Wells Fargo Bank Building
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Figure 5.9 Pall Friction Dampers
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Figure 5.10 McConnel Library at Concordia
University in Montreal
Figure 5.11 Exposed Friction Damper in McConnel Library Galleria
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Figure 5.12 View of Canadian Space Agency Complex
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Figure 5.13 Ground Floor Plan of Main Building in Canadian Space Agency
Figure 5.14 Exterior View of Ecole Polyvalante, Sorel
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Figure 5.15 North View of Casino de Montreal
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Figure 5.16 Damper Installation in the World Trade Center, New York
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Figure 5.17 The Columbia SeaFirstBuilding, Seattle
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Figure 5.18 Plan View and Details of Wind Resisting System for ColumbiaSeaFirst Building
Figure 5.19 Damper Installation in the Columbia SeaFirst Building
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Figure 5.22 Location of VE Dampers in Santa Clara County Building
Figure 5.21 Santa Clara County Building,San Jose
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Figure 5.24 Building 116, Naval Supply Facility, San Diego
Figure 5.23 Damper Configuration in Santa Clara County Building
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Figure 5.25 Elevation and Plan of Building 116
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Figure 5.26 Damper Configuration in Building 116
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Figure 5.29 Damper-Base Isolator System Assembly for San Bernardino Medical Center
Figure 5.30 Dimensions of Viscous Fluid Damper for San Bernardino Medical Center
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Figure 5.31 Pacific Bell North Area Operations Center, Sacramento, under Construction
Figure 5.32 Damper Installation in the Pacific Bell North Area Operations Center
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Figure 5.33 Woodland Hotel, Woodland, California
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Figure 5.34 Viscous Damping Wall Locations in SUT-Building, ShizukaCity, Japan
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Figure 5.35 Water Tank TMD at Centerpoint Tower, Sydney, Australia
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Figure 5.37 TMD in Citicorp Center
Figure 5.36 Citicorp Center, New York
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Table 5.2 Tuned Mass Dampers in John Hancock Tower, Boston and Citicorp Center,New York
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Figure 5.38 Dual TMD System in John Hancock Tower, Boston
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Table 5.3 TMD and Structural Parameters, Chiba Port Tower
Figure 5.40 RMS Accelerations Without and With TMD, Chiba Port Tower
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Figure 5.41 TMD on Funade Bridge Tower, Osaka
Figure 5.42 Damped Free Vibrations Without and With TMD, Funade Bridge
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Figure 5.44 Installation of Vessels in TLD Room in Tower
Figure 5.43 TLD Vessel, Tokyo Airport Tower
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Figure 5.45 Temporal Variation of RMS Acceleration and Damping Ratio of Tower
Figure 5.46 Comparisons of RMS Acceleration Responses of TIAT with/
without TLD (x-direction, across-wind)
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B1
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Figure 7.1 A Semi-Active Mass Damper
Figure 7.2 Schematic of Semi-Active Device
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Figure 7.3 Sendagaya INTES Building
Figure 7.4 Top View of AMD
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Figure 7.6 Response Time Histories (March 29, 1993)
Figure 7.5 Elevation of AMD
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Figure 7.7 Response Fourier Spectra (March 29, 1993)
Figure 7.8 Hankyu Chayamachi Building
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Figure 7.9 Layout of HMD
-
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Figure 7.11 Principle of DUOX System
Figure 7.10 Acceleration Fourier Spectra
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Figure 7.12 Composition of DUOX System
Figure 7.13 Pendulum-type HMD
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Figure 7.14 Multistage Pendulum Mass Damper
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Figure 7.15 A Semi-Active Fluid Viscous Damper
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Figure 7.16 Experimental Values of Peak Force vs. Peak Velocity
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Figure 7.17 Test Results for Two-Stage Dampers
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Figure 7.18 Base Shear-Drift Loops for High Damping Passive Case and Base Shear ControlCase
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Figure 7.20 A Semi-active Variable Stiffness System
Figure 7.19 Comparison of Peak Response Profiles for Three-Story Structure
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Figure 7.21 KaTRI No. 21 Building
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Figure 7.22 AVS System Configuration
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Figure 7.23 AVD Device Configuration
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Figure 7.24 Schematic of a Semi-Active Fluid Damper
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Figure 7.26 Transfer Functions for a Continuous Two-Span Bridge with: (a) No Control, (b)Passive Damper, (c) Bistate Control
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Table A.1 Metallic Dampers
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Table A.2 Friction Dampers
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Table A.2 Friction Dampers (continued)
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Table A.3 Viscoelastic Dampers
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Table A.4 Viscoelastic Fluid Dampers
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Table A.4 Viscoelastic Fluid Dampers (continued)
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Table A.4 Viscoelastic Fluid Dampers (continued)
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Table A.5 Tuned Mass Dampers
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__________
Table B.1 Active and Semi-active Systems Installed in Buildings in Japan
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Table B.1 Active and Semi-active Systems Installed in Buildings in Japan (continued)
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