1 structural dynamics & vibration control lab., kaist 사장교의 면진 성능 향상을...

1 1Structural Dynamics & Vibration Control Lab., KAIST

사장교의 면진 성능 향상을 위한 납고무 받침의 설계 기준 제안

Guidelines of Designing L.R.B. for

a Cable-Stayed Bridge to Reduce Seismic Responses

사장교의 면진 성능 향상을 위한 납고무 받침의 설계 기준 제안

Guidelines of Designing L.R.B. for

a Cable-Stayed Bridge to Reduce Seismic Responses

이 성진 : 한국과학기술원 건설 및 환경공학과 석사과정

박 규식 : 한국과학기술원 건설 및 환경공학과 박사과정

이 종헌 : 경일대학교 토목공학과 교수

이 인원 : 한국과학기술원 건설 및 환경공학과 교수

이 성진 : 한국과학기술원 건설 및 환경공학과 석사과정

박 규식 : 한국과학기술원 건설 및 환경공학과 박사과정

이 종헌 : 경일대학교 토목공학과 교수

이 인원 : 한국과학기술원 건설 및 환경공학과 교수

(Oct. 24. ~ 25., 2003)2003년도


Backgrounds

Introduction

Lead Rubber Bearing (LRB) for base isolation system

Design of base isolation system for building and short span

bridges.

- Design natural period of structure or effective period of

base isolator

Long span bridge such as cable-stayed bridges

- Flexible : long period modes and natural seismic isolation

- Small structural damping


Objective

it is difficult to apply this procedure and guidelines of isolation

system directly to cable-stayed bridges.

Suggest the design procedure and guidelines of LRB for seismically

excited cable-stayed bridge.


pK

eK

yQ

yX dX

effK

yF

uF , : elastic & plastic stiffness

: effective stiffness

: characteristic shear strength

, : yield and ultimate strength

, : yield and ultimate displacement

eK pK

yQ

effK

yF uF

yX dX

Fig. 1 Behavior and design parameters of LRB

Determine the , , to minimize the earthquake forces and displacements.

eK pK yQ

Design Procedure of LRB

Design Parameters of LRB


The design parameters of LRB

- design index (DI) is minimized or unchanged (less than 1%

of maximum DI) for variation of design parameters.

Proposed Design Procedure

5

1maxi i

i

J

JDI i = 1 ~ 5 )1(

- Five important responses of cable-stayed bridge

: base shear and moment at towers

: shear and moment at deck level at towers

: deck displacement (longitudinal direction)


Design procedure

- Step 1

: design earthquake (history or artificial earthquake)

- Step 2

: appropriate is selected for variation of .

: and are assumed.

- Step 3


: use selected and assume .

- Step 4


- Step 5

: iterate step 2 ~ 4 until parameters remain unchanged.

pK pK

yQeK

yQ

eKyQ

pK

pe KK / pe KK /


Numerical Examples

Bridge Model

Fig. 2 Bill Emerson Memorial Bridge (Benchmark cable-stayed bridge model)

Benchmark cable-stayed bridges (Dyke et al. 2003)

142.7 m 350.6 m 142.7 m

gx


Design Earthquakes

Scaled El Centro earthquake (1940) - 0.36 g’s ( design PGA )

0 5 10 15Frequency(H z)

0

2

4

6

8

10

Pow

er S

pect

ral D

ensi

ty

Power Spectral Density

0 50 100 150 200tim e (sec)

- 4

- 2

0

2

4

Acc

ela

tion(

m/s

^2)

Tim e-Acceleration G raph

Fig. 3 Design Earthquake (Scaled El Centro)

Artificial earthquake ( Stationary Kanai-Tajimi filter )

0222

22

)(4])(1[

])(41[( SS

gg

g

)2(

- = 37.3 rad/s, = 0.3 (Spencer et al.)g g

220 )14(

03.0gS

gg

g

)3(


Properties of Designed LRB

DI**

LRB I (Scaled El Centro)

1.4W* (tf/m) 0.13W (tf) 11 3.334

LRB II (Kanai – Tajimi) 1.5W (tf/m) 0.12W (tf) 12 4.175

pK yQ pe KK /

Table 1. Properties of Designed 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.


Performance of Designed LRB Evaluation Criteria for Benchmark Cable-stayed Bridge

Max. base shear at towers

Max. shear at deck level

Max. base moment at towers

Max. moment at deck level

Max. cable deviation

Max. deck displacement at abutment

Normed base shear at towers

Normed shear at deck level

Normed base moment at towers

Normed moment at deck level

Normed cable deviation

Max control force

Max device stroke

1J

2J

3J

4J

5J

6J

7J

8J

9J

10J

11J

12J

13J

Table 2. Evaluation criteria


El Centro : 1940, Imperial Valley, 0.348 g’s

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Cont

rol/U

ncont

rol

J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 J 9 J 10 J 11 J 12 J 13

Evaluation Criteria

LRB ILRB II

Park et al.N-K

0 1 0 2 0 3 0 4 0 5 0-3

-2

-1

0

1

2

3

4

Acc

eler

atio

n (m

/s2 ) El Centro

LRB I : Scaled El Centro LRB II : Kana-Tajimi Artificial Earthquake

Park et al. : “ 납고무 받침의 비선형성을 고려한 벤치마크 사장교의 복합제어” ,

한국지진공학회논문집 , Vol. 3, No. 4, pp. 51-63

N-K : Naeim-Kelly Method ( Teff = 1.5 sec )


Mexico City : 1985, Galeta de Campos, 0.143 g’s

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Cont

rol/U

ncont

rol

J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 J 9 J 10 J 11 J 12 J 13

Evaluation Criteria

0 1 0 2 0 3 0 4 0 5 0T im e (sec )

- 2

- 1

0

1

2

M exico C ity


Gebze : 1999, Turkey Gebze, 0.265 g’s

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Cont

rol/U

ncont

rol

J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 J 9 J 10 J 11 J 12 J 13

Evaluation Criteria

3.829 2.100

0 1 0 2 0 3 0 4 0 5 0-2

-1

0

1

2

3

G ebze


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


0

10

20

30

40

Pow

er S

pect

ral D

ensi

ty

Scaled M exico C ity (0 .5H z)


0

2

4

6

8

10

Pow

er S

pect

ral D

ensi

ty

Scaled E l C entro (1 .5 H z)


0

4

8

12

16

Pow

er S

pect

ral D

ensi

ty

Scaled Gebze (2 .0H z)

Fig. 7 Power Spectral Density of input earthquakes


Properties of LRB

Frequency

Scaled Mexico City 0.5 Hz 0.9W (tf/m) 0.15W (tf) 10

Scaled El Centro 1.5 Hz 1.4W (tf/m) 0.13W (tf) 11

Scaled Gebze 2.0 Hz 1.5W (tf/m) 0.16W (tf) 9

pK yQpe KK /

Table 3. Properties of LRB for earthquake frequency

- and of LRB

: affected by dominant frequency of earthquake.

- Low frequency : Need the more flexible LRB.

- and of LRB

: not related to dominant frequency of earthquake.

pK eK

yQpe KK /


Conclusions

The guidelines and procedure of designing LRB for seismically

excited cable-stayed bridge are researched.

The stiffer rubber and bigger lead core size is needed for cable

-stayed bridge than general structures.

The plastic behavior of lead core of LRB is important to reduce

the seismic response of cable-stayed bridge.

The performance of designed LRB is good for several historical

earthquakes.

As the dominant frequency of earthquake is low, the flexible

LRB is needed.


Thank you for your attention!!

Acknowledgments

This research is supported by the National Research Lab. Grant (No.: 2000-N-NL-01-C-251) in Korea.

1 structural dynamics & vibration control lab., kaist 사장교의 면진 성능 향상을...

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