Passive Energy Dissipation Systems - M. C. Constantinou

8/12/2019 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


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


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



Plastic Hinge


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




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 2.6 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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Date post:	03-Jun-2018
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Passive Energy Dissipation Systems - M. C. Constantinou

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