LNG / - -

Guidelines of Designing Lead Rubber Bearing for
a Cable-Stayed Bridge to Control Seismic Response
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:
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2003
Oct. 11. 2003

‘ ’.
Structural Dynamics & Vibration Control Lab., KAIST
Contents
Introduction
Backgrounds
short-span bridges.
base isolator
Introduction
Backgrounds
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. .
Structural Dynamics & Vibration Control Lab., KAIST
Long span bridge such as cable-stayed bridges
- Flexible : long period modes and natural seismic isolation
- Small structural damping
of isolation system directly to cable-stayed bridges.
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, .
Structural Dynamics & Vibration Control Lab., KAIST
Objective
for cable-stayed bridge.

Ali . .
Structural Dynamics & Vibration Control Lab., KAIST
Design Parameters of LRB
Flexibility of rubber : period shift
Plastic behavior of lead : energy dissipation
Design Procedure of LRB
forces and displacements.
procedure.
1 bi-linear , , .
LRB , .
Structural Dynamics & Vibration Control Lab., KAIST
The design parameters of LRB are chosen that design index
(DI) is minimized or unchanged (less than 0.05) for variation
of design parameters.
Proposed Design Procedure
i = 1 ~ 5
considered.
: shear and moment at deck level at towers
: deck displacement (longitudinal direction)

.
5 1 .
.
5 , , .
Structural Dynamics & Vibration Control Lab., KAIST
Design procedure
- Step 1
- Step 2
: and are assumed.
: use selected and assume .
- Step 5

…
Bridge Model
Fig. 2 Bill Emerson Memorial Bridge (Benchmark cable-stayed bridge model)
Benchmark cable-stayed bridges (Dyke et al. 2003)
Numerical Examples
142.7 m
350.6 m
142.7 m

.

Dyke 2 128 .
Structural Dynamics & Vibration Control Lab., KAIST
Finite element evaluation model
128 cable elements, 579 nodes
- Stiffness matrix : nonlinear static analysis corresponding
to the deformed stated of bridge with dead loads
- Damping matrix : 3 % of critical damping to each mode
- Control devices : longitudinal direction between the deck
and piers
multi-excitation
….. .
, 3% .
LRB , .
Structural Dynamics & Vibration Control Lab., KAIST
Design Earthquakes
- The PGA of El Centro earthquake
: scaled to the design PGA of cable-stayed bridges (0.36 g’s.)
Fig. 3 Design Earthquake (Scaled El Centro)

.
, PGA 0.36g scaling.
3 PSD.
102.unknown
96.unknown
Kanai-Tajimi artificial earthquake
- Stationary Kanai-Tajimi filter
- Power spectral density
: constant power spectral intensity.
- = 37.3 rad/s, = 0.3 (Spencer et al.)
2,3 PSD Kanai-Tajimi . Spencer .
Structural Dynamics & Vibration Control Lab., KAIST
Properties of LRB
Table 1. Properties of LRB
* : Pier 1,4 - 1557.18 (tf), Pier 2,3 - 5383 (tf) ** : Max. of DI =5
Need the stiffer rubber and bigger lead core size than
general buildings and short-span bridges.
The plastic behavior of lead core of LRB is important to
reduce the seismic response for cable-stayed bridge.
DI**
1.4W* (tf/m)
0.13W (tf)
.
Bouc-Wen .
W .
, . , , .
Structural Dynamics & Vibration Control Lab., KAIST
El Centro : 1940, Imperial Valley, 0.348 g’s
Mexico City : 1985, Galeta de Campos, 0.143 g’s
Gebze : 1999, Turkey Gebze, 0.265 g’s
Fig. 4 Time-history of input earthquakes
Performance of Designed LRB
.
El Centro, Mexico City, Gebze 3 . 4 .
273.unknown
275.unknown
J1 : Max. base shear
J3 : Max. base mom.
J5 : Max. cable deviation
J6 : Max. deck displacement
J7 : Norm base shear
J9 : Norm base mom.
level
El Centro .
Naeim-Kelly .
, ……… . .
LRB I LRB II , . 2 , . , .
Chart1
J1
J1
J1
J1
J2
J2
J2
J2
J3
J3
J3
J3
J4
J4
J4
J4
J5
J5
J5
J5
J6
J6
J6
J6
J7
J7
J7
J7
J8
J8
J8
J8
J9
J9
J9
J9
J10
J10
J10
J10
J11
J11
J11
J11
J1 : Max. base shear
J3 : Max. base mom.
J5 : Max. cable deviation
J6 : Max. deck displacement
J7 : Norm base shear
J9 : Norm base mom.
level
*** : Naeim-Kelly Method ( Teff = 1.5 sec )
**** : Naeim-Kelly Method ( Teff = 2.0 sec )
. . N-K I . LRB I LRB I , .
Chart3
J1
J1
J1
J1
J2
J2
J2
J2
J3
J3
J3
J3
J4
J4
J4
J4
J5
J5
J5
J5
J6
J6
J6
J6
J7
J7
J7
J7
J8
J8
J8
J8
J9
J9
J9
J9
J10
J10
J10
J10
J11
J11
J11
J11
Evaluation criteria under Gebze earthquake
J1 : Max. base shear
J3 : Max. base mom.
J5 : Max. cable deviation
J6 : Max. deck displacement
J7 : Norm base shear
J9 : Norm base mom.
level
Gebze .
Gebze . Gebze , El Centro . N-K II .
Chart4
J1
J1
J1
J1
J2
J2
J2
J2
J3
J3
J3
J3
J4
J4
J4
J4
J5
J5
J5
J5
J6
J6
J6
J6
J7
J7
J7
J7
J8
J8
J8
J8
J9
J9
J9
J9
J10
J10
J10
J10
J11
J11
J11
J11
Table 2. Maximum evaluation criteria for three historical earthquake
The performance of designed LRB is good for several
historical earthquakes.
Evaluation Criteria
LRB I
LRB II
N-K I
N-K II
1.0938
1.1134
1.1027
1.4220
0.6145
0.6718
0.6484
1.0271
0.8423
0.8610
0.9673
1.4240
0.5262
0.5409
0.6389
1.2043
.
.
, LRB N-K I N-K II Base shear base moment , deck level shear moment , . N-K II .
.
Structural Dynamics & Vibration Control Lab., KAIST
Design Properties of LRB for Earthquake Frequency
The behavior of structure is affected by not only PGA but also
the dominant frequency of earthquake.
The PGA of earthquakes : 0.36g’s
Fig. 8 Power Spectral Density of input earthquakes
, .
, .
.
PGA PGA 0,36g . 0.5, 1.5 .2.0 .
335.unknown
355.unknown
351.unknown
Properties of LRB
and of LRB
: Low frequency flexible LRB.
Frequency
3 .
, .
.
Structural Dynamics & Vibration Control Lab., KAIST
The guidelines and procedure of designing LRB for
seismically excited cable-stayed bridge are investigated.
The cable-stayed bridge is needed stiffer rubber and
bigger lead core size than general structures.
The plastic behavior of lead core of LRB is important
to reduce the seismic response of cable-stayed bridge.
Conclusions
.
.
, . , .
Structural Dynamics & Vibration Control Lab., KAIST
The performance of designed LRB is good for several
historical earthquakes.
flexible LRB is needed.
.
, , PGA .
Structural Dynamics & Vibration Control Lab., KAIST
Thank you for your attention!!
This research is supported by the National Research Lab.
Grant (No.: 2000-N-NL-01-C-251) in Korea.
Acknowledgments
Previous Application of LRB for cable-stayed bridge
Ali and Abdel-Ghaffar
Wesolowsky and Wilson
- Effective period of LRB
Design Procedure of LRB for General Structures
The natural period of general building and continuous
bridge is 0.3 sec ~ 0.6 sec.
The main design aim for these structures is shifting the
natural period of these structures.
The stiffness of LRB is designed that the natural period of
structure or effective period of isolator is 1.4 sec ~ 2.0 sec.
The characteristic strength of LRB is recommended to use
five percent of weight carried by LRB to obtain additional
damping effect. (Ghobarah, A. and Ali, H. M., 1988)
Structural Dynamics & Vibration Control Lab., KAIST
Design Procedure (N-K Method)
of isolator is established.
where, M is the structural mass assigned to the isolator
3. The effective damping ( ).
Structural Dynamics & Vibration Control Lab., KAIST
5. Shear strength ( )
6. Post-yield stiffness ( )
7. Yield displacement ( )
LRB Model (Bouc-Wen Model)
: Linear stiffness of LRB
: Yielding displacement of lead
hysteretic curve
Evaluation Criteria
Table 1 Evaluation criteria (Control/Uncontrolled)
Scaled El Centro
RMS J1
J2
RMS J2
J3
RMS J3
J4
RMS J4
J6
Performance of Designed LRB
* : Scaled El Centro earthquake ** : Kanai – Tajimi artificial earthquake
LRB I*
LRB II**
Table 4. Performance of Designed LRB (El Centro)
* : Scaled El Centro ** : Kanai – Tajimi Artificial Earthquake
*** : Naeim and Kelly
0.8764
0.8716
0.9505
0.3593
0.3532
0.4796
0.7439
0.7428
0.8378
0.4038
0.4069
0.4732
Table 5. Performance of Designed LRB (Mexico City)
* : Scaled El Centro ** : Kanai – Tajimi Artificial Earthquake
*** : Naeim and Kelly
1.0938
1.1134
1.1027
0.3961
0.3991
0.3659
0.8197
0.8610
0.7770
0.5088
0.5145
0.4875
Table 6. Performance of Designed LRB (Gebze)
* : Scaled El Centro ** : Kanai – Tajimi Artificial Earthquake
*** : Naeim and Kelly
1.0251
1.1190
1.0543
0.6145
0.6718
0.6484
0.8423
0.8583
0.9673
0.5262
0.5409
0.6389