Master’s Thesissdvc.kaist.ac.kr/article/dissertation/2004_lsj_ms.pdf · 2008-03-05 · A thesis submitted to the faculty of the Korea Advanced Institute of Science and Technology

석사학위논문

Masterrsquos Thesis

지진 하중을 받는 사장교를 위한

수동 제어 장치의 설계 Design of Passive Control System

for Seismically Excited Cable-Stayed Bridges

이 성 진 (李聖振 Lee Sung Jin) 건설 및 환경공학과

Department of Civil and Environmental Engineering

한 국 과 학 기 술 원 Korea Advanced Institute of Science and Technology

2004


수동 제어 장치의 설계

Design of Passive Control System




Advisor Professor In-Won Lee

by

Sung-Jin Lee

Department of Civil and Environmental Engineering Korea Advanced Institute of Science and Technology

A thesis submitted to the faculty of the Korea Advanced Institute of Science and Technology in partial fulfillment of the requirements for the degree of Master of Engineering in the Department of Civil and Environmental Engineering

Daejeon Korea 2003 12 22 Approved by __________________ Professor In-Won Lee Major Advisor



이 성 진

위 논문은 한국과학기술원 석사학위논문으로 학위논문 심사위원회에서 심사 통과하였음

2003 년 12 월 22 일

심사 위원장 이 인 원 (인)

심 사 위 원 윤 정 방 (인)

심 사 위 원 김 진 근 (인)

i

MCE

20023430

ABSTRACT

In this dissertation the design procedure and guidelines of lead rubber bearing

(LRB) are proposed and the effectiveness of designed LRB is investigated for seismically

excited cable-stayed bridges Furthermore additional control device ie viscous damper

(VD) is considered to improve the control performances

The LRB is widely used for the seismic isolation system to control responses of

buildings and short-span bridges under earthquakes because these provide structural

support base isolation damping and restoring forces in a single unit The most important

feature of the seismic isolation system for short-span bridges and buildings is lengthening

the natural period of structures However the seismic characteristics of long-span bridges

such as cable-stayed bridges are different from those of short-span bridges and buildings

and these bridges have very complex behavior in which the vertical translational and

torsional motions are often strongly coupled For these reasons it is conceptually

unacceptable for long-span bridges to use directly the recommended design procedure

and guidelines of LRB for short-span bridges and buildings Therefore new design

approach and guidelines are required to design LRB for cable-stayed bridges

Considering important responses of cable-stayed bridges the design index (DI) is

proposed to design LRB The proper LRB is selected when proposed DI is minimized or

converged for variation of properties of LRB The design results show that the damping

and energy dissipation effect of LRB are more important than the shift of the natural

이 성 진 Lee Sung Jin Design of Passive Control System for Seismically

Excited Cable-Stayed Bridges 지진 하중을 받는 사장교를 위한 수동

제어 장치의 설계 Department of Civil and Environmental Engineering

2003 55p Advisor Professor Lee In Won Text in English

ii

period of structures for cable-stayed bridges And the control performance of designed

LRB is also verified

The sensitivity analyses of properties of LRB are conducted for different

characteristics of input earthquakes The performance of designed LRB is not changed

significantly for different characteristic of input earthquakes and thus the robustness of

designed LRB is verified for different characteristics of earthquakes

Finally the VD is employed to obtain the additional reduction of seismic responses

because there are some responses that are not controlled sufficiently by only LRB

Additional VD can reduce the some responses such as shear at deck level of towers and

deck displacement without loss of control effects of LRB These results show that the

seismic responses of cable-stayed bridges can be controlled sufficiently by appropriate

designed passive control devices

iii

TABLE OF CONTENTS

ABSTRACT i

TABLE OF CONTENTS iii

LIST OF TABLES v

LIST OF FIGURES vi

CHAPTER 1 INTRODUCTION 1

11 Backgrounds 1

12 Literature Review 3

13 Objectives and Scopes 4

CHAPTER 2 PROPOSED DESIGN PROCEDURE OF LRB 6

21 LRB 6

211 Design Parameters of LRB 6

212 LRB Model 8

22 Proposed Design Procedure 10

CHAPTER 3 NUMERICAL EXAMPLE 13 31 Bridge Model 13

32 Design and Seismic Performance of LRB 15

321 Design Earthquake Excitations 15

322 Design of LRB 17

323 Control Performance of Designed LRB 24

33 Effect of Characteristics of Earthquakes 36

331 Effect of Frequency Contents of Earthquakes 36

iv

332 Effect of PGA of Earthquakes 40

34 VD for Additional Passive Control System 45

341 Design of VD 45

342 Control Performance of Designed LRB with VD 47

CHAPTER 4 CONCLUSIONS 49

SUMMARY (IN KOREAN) 51

REFERENCES 53

ACKNOWLEDGEMENTS

CURRICULUM VITAE

v

LIST OF TABLES 31 Design properties of LRB 24

32 Controlled responses of bridge for design earthquakes 25

33 Designed properties of LRB (Wesolowsky and Wilson-WW bearing) 27

34 Uncontrolled maximum responses for performance criteria 29

35 Performance of designed LRB under El Centro earthquake 29

36 Performance of designed LRB under Mexico City earthquake 30

37 Performance of designed LRB under Gebze earthquake 30

38 Designed properties of LRB for different frequency contents 37

39 Performance of LRB for different frequency contents under scaled El Centro

earthquake 38

310 Performance of LRB for different frequency contents under scaled Mexico City

earthquake 39

311 Performance of LRB for different frequency contents under scaled Gebze

earthquake 39

312 Design properties of LRB for different PGA 40

313 Performance of LRB for different PGA of earthquake under 10 scaled

El Centro earthquake 42



315 Performance of LRB for different PGA of earthquake under 036 grsquos scaled

artificial random excitation 43


Artificial random excitation 43

317 Additional reduction of responses with LRB and VD 48

vi

LIST OF FIGURES

21 Schematic of LRB 7

22 Hysteretic curve of LRB 7

31 Schematic of the Bill Emersion Memorial Bridge 13

32 Design earthquake excitation (Scaled El Centro earthquake) 15

33 Design earthquake excitation (Artificial random excitation) 16

34 Deck weight supported by LRB 17

35 Sensitivity of responses and DI under scaled El Centro earthquake (1st iteration)

20

36 Sensitivity of responses and DI under scaled El Centro earthquake (2nd iteration)

21

37 Sensitivity of responses and DI under artificial random excitation (1st iteration)

22

38 Sensitivity of responses and DI under artificial random excitation (2nd iteration)

23

39 Time history of three earthquakes 25

310 Time history responses of cable-stayed bridge under El Centro earthquake 31

311 Time history responses of cable-stayed bridge under Mexico City earthquake 32

312 Time history responses of cable-stayed bridge under Gebze earthquake 33

313 Restoring force of LRB under three earthquakes 35

314 Power spectral density of three earthquakes 36

315 Design of VD 46

1

CHAPTER 1

INTRODUCTION

11 Backgrounds

The bridge structures tend to be constructed in longer and slender form as the

analysis and design technology are advanced in civil structures high-strengthhigh-

quality materials are developed and people hope to construct beautiful bridges Therefore

the construction and research of long-span bridges such as cable-stayed and suspension

bridges have become a popular and challenging problem in civil engineering fields

However these long-span bridges have the flexibility of their cable-superstructure system

and low structural damping For these reasons excessive internal forces and vibrations

may be induced in these structures by the dynamic loads such as strong winds and

earthquakes These large internal forces and vibrations may induce direct damages as

well as fatigue fractures of structures Furthermore these may deteriorate the safety and

serviceability of bridges Therefore it is very important to control these responses of

long-span bridges and thus to improve the safety and serviceability of these bridges under

severe dynamic loads

Many seismic design methods and construction technology have been developed and

investigated over the years to reduce seismic responses of buildings bridges and

potentially vulnerable structures Among the several seismic design methods the seismic

isolation technique is widely used recently in many parts of the world The concept of the

seismic isolation technique is shifting the fundamental period of the structure to outrange

of period containing large seismic energy of earthquake ground motions by separating

Chapter 1 Introduction 2

superstructure and substructure and reducing the transmission of earthquake forces and

energy into the superstructure However the seismic isolation technique allows relatively

large displacements of structures under earthquakes Therefore it is necessary to provide

supplemental damping to reduce these excessive displacements


buildings and short-span bridges under earthquakes because this bearing not only

provides structural support by vertical stiffness but also is excellent to shift the natural

period of structures by flexibility of rubber and to dissipate the earthquake energy by

plastic behavior of central lead core

The most important design feature of the seismic isolation system is lengthening the

natural period of structures Therefore design period of structures or isolators is specified

in the first and then the appropriate properties of isolators are determined in the general

design of seismic isolation system

However most long-span bridges such as cable-stayed bridges have longer period

modes than short-span bridges due to their flexibility Therefore these bridges tend to

have a degree of the natural seismic isolation Furthermore these bridges have a lower

structural damping than general short-span bridges and exhibit very complex behavior in

which the vertical translational and torsional motions are often strongly coupled For

these reasons it is conceptually unacceptable for long-span bridges to use directly the

recommended design procedure and guidelines of LRB for short-span bridges and

buildings Therefore new design approach and guidelines are required to design LRB

because seismic characteristics of cable-stayed bridges are different from those of short-

span bridges and buildings The energy dissipation and damping effect of LRB are more

important than the shift of the natural period of structures in the cable-stayed bridges

which are different from buildings and short-span bridges


12 Literature Review

The LRB was invented by W H Robinson in 1975 and has been applied to the

seismic isolation system of bridge structures in New Zealand since 1978 [2] The LRB is

excellent to shift the natural period of structures and to dissipate the earthquake energy

Furthermore this bearing offers a simple method of passive control and is relatively easy

and inexpensive to manufacture For these reasons the LRB has been widely investigated

and used for the seismic isolation system to reduce responses of buildings and short-span

bridges in many areas of the world

Many studies have been conducted for LRB in buildings [345] as well as short to

medium span highway bridges [67] and some design guidelines are suggested for

highway bridges [6] And procedures involved in analysis and design of seismic isolation

systems such as LRB are provided by Naeim and Kelly [10]

The comprehensive study of effectiveness of LRB for cable-stayed bridges is

investigated in recently Ali and Abdel-Ghaffar [1] investigated the effectiveness of

rubber bearing and LRB and they showed that earthquake-induced forces and vibrations

could be reduced by proper choice of properties and locations of these bearings This

reduction is obtained by the energy dissipation of central lead core in LRB and the

acceptable shear strength of LRB is recommended for seismically excited cable-stayed

bridges However the recommended value by Ali and Abdel-Ghaffar do not consider

characteristics of earthquake motions Park et al [89] presented the effectiveness of

hybrid control system based on LRB which is designed by recommended procedure of

Ali and Abdel-Ghaffar [1]

However there are few studies on procedures and guidelines to design LRB for

cable-stayed bridges Wesolowsky and Wilson [10] used a seismic isolation design

approach described by Naeim and Kelly [11] to control seismically excited cable-stayed

bridges with LRB This method applied for building structures begins with the


specification of the effective period and design displacement of isolators in the first and

then iterate several steps to obtain design properties of isolators using the geometric

characteristics of bearings However the effective stiffness and damping usually depend

on the deformation of LRB Therefore the estimation of design displacement of bearing

is very important and is required the iterative works Generally the design displacement

is obtained by the response spectrum analysis that is an approximation approach in the

design method of bearing described by Naeim and Kelly [11] However it is difficult to

get the response spectrum since the behavior of cable-stayed bridges is very complex

compared with that of buildings and short-span bridges Therefore the time-history

analysis is required to obtain more appropriate results

13 Objectives and Scopes

The purpose of this study is to suggest the design procedure and guidelines for LRB

and to investigate the effectiveness of LRB to control seismic responses of cable-stayed

bridges Furthermore additional passive control device (ie viscous dampers) is

employed to improve the control performance

First the design index (DI) and procedure of LRB for seismically excited cable-

stayed bridges are proposed Important responses of cable-stayed bridge are reflected in

proposed DI The appropriate properties of LRB are selected when the proposed DI value

is minimized or converged for variation of properties of design parameters In the design

procedure important three parameters of LRB (ie elastic and plastic stiffness shear

strength of central lead core) are considered for design parameters The control

performance of designed LRB is compared with that of LRB designed by Wesolowsky

and Wilson approach [10] to verify the effectiveness of the proposed design method


Second the sensitivity analyses of properties of LRB are conducted for different

characteristics of input earthquakes to verify the robustness of proposed design procedure

In this study peak ground acceleration (PGA) and dominant frequency of earthquakes are

considered since the behavior of the seismic isolation system is governed by not only

PGA but also frequency contents of earthquakes

Finally additional passive control system (VD) is designed and this damper is

employed in cable-stayed bridge to obtain the additional reduction of seismic responses

of bridge since some responses (ie shear at deck shear of the towers and deck

displacement) are not sufficiently controlled by only LRB

6

CHAPTER 2

PROPOSED DESIGN PROCEDURE OF LRB

21 LRB

211 Design Parameters of LRB

Typical earthquake accelerations have dominant periods of about 01 ~ 10 sec and

the general buildings and continuous bridges have fundamental period about 03 ~ 06 sec

[23] The basic concept of the seismic isolation system is lengthening the fundamental

period of the structures to outrange of period containing the large seismic energy of

earthquake motion by flexibility of isolators and dissipating the earthquake energy by

supplemental damping

Because the LRB offers a simple method of passive control and are relatively easy

and inexpensive to manufacture this bearing is widely employed for the seismic isolation

system for buildings and short-span bridges The LRB is composed of an elastomeric

bearing and a central lead plug as shown in figure 21 Therefore this bearing provides

structural support horizontal flexibility damping and restoring forces in a single unit

The force-displacement hysteresis curve of this bearing (elastic-plastic behavior) is

shown in figure 22 For weak winds and braking forces the LRB remains stiff due to the

central lead core However for strong winds and earthquakes this behaves like rubber

bearing because the central lead core is yielded In this figure Ke Kp and Keff are elastic

plastic and effective stiffness of LRB respectively Qy is shear strength of central lead

core Fy and Fu are yielding and ultimate strength of LRB Xy and Xd are yielding

displacement of central lead core and design displacement of LRB respectively

Chapter 2 Proposed Design Procedure of LRB 7

Rubber

Lead Core Steel Lamination

Figure 21 Schematic of LRB

Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke

Figure 22 Hysteretic curve of LRB

The LRB shifts the natural period of structures by flexibility of rubber and dissipates

the earthquake energy by plastic behavior of central lead core Therefore it is important

to combine the flexibility of rubber and size of central lead core appropriately to reduce

seismic forces and displacements of structures In other words the elastic and plastic

stiffness of LRB and the shear strength of central lead core are important design

parameters to design this bearing for the seismic isolation design

In the design of LRB for buildings and short-span bridges the main purpose is to

shift the natural period of structures to longer one Therefore the effective stiffness of


LRB and design displacement at a target period are specified in the first Then the proper

elastic plastic stiffness and shear strength of LRB are determined using the geometric

characteristics of hysteric curve of LRB through several iteration steps [1011] Generally

the 5 of bridge weight carried by LRB is recommended as the shear strength of central

lead core to obtain additional damping effect of LRB in buildings and highway bridges

[6]

However most long-span bridges such as cable-stayed bridges tend to have a degree

of natural seismic isolation and have lower structural damping than general short-span

bridges Furthermore the structural behavior of these bridges is very complex Therefore

increase of damping effect is expected to be important issue to design the LRB for cable-

stayed bridges In other words the damping and energy dissipation effect of LRB may be

more important than the shift of the natural period of structures in the cable-stayed

bridges which are different from buildings and short-span bridges For these reasons the

design parameters related to these of LRB may be important for cable-stayed bridges

212 LRB Model The nonlinear behavior of LRB is described by Bouc-Wen model [1213] which is a

nonlinear differential equation This model represents the bilinear hysteric behavior

sufficiently The restoring force of LRB is formulated as equation (1) that is composed of

linear and nonlinear terms as

zXXXX yrrr eeLRB KααKf )(1)( minus+=amp (1)

where α are the elastic stiffness and the ratio of plastic-elastic stiffness of LRB rX

and rXamp are the relative displacements and velocities of nodes at which bearings are

installed respectively z are the yield displacement of central lead core and the


dimensionless hysteretic component satisfying the following nonlinear first order

differential equation formulated as equation (2)

)(1 n1n zXzzXXX

z rrry

ampampampamp βγ minusminus=minus

iA (2)

where Ai γ β and n are dimensionless constants that affect the hysteretic behavior of

model Ai = n =1 and γ=β=05 are usually used to describe the bilinear curve of LRB and

these values are adopted in this study

Finally the equation describing the forces produced by LRB is formulated as

equation (3)

LRBftimes= LRBLRB GF (3)

where GLRB is the gain matrix to account for number and location of LRB


22 Proposed Design Procedure

The objective of seismic isolation system such as LRB is to reduce the seismic

responses and keep the safety of structures Therefore it is a main purpose to design the

LRB that important seismic responses of cable-stayed bridges are minimized Because the

appropriate combination of flexibility and shear strength of LRB is important to reduce

responses of bridges it is essential to design the proper elastic-plastic stiffness and shear

strength of LRB

The proposed design procedure of LRB is based on the sensitivity analysis of

proposed DI for variation of properties of design parameters (ie Ke Kp and Qy) In this

study the DI is suggested considering five responses defined important issues related to

earthquake responses and behavior of cable-stayed bridges [14] as shown in equation (4)

These responses are base shear and overturning moment at tower supports (R1 and R3)

shear and bending moment at deck level of towers (R2 and R4) and longitudinal deck

displacement (R5) For variation of design parameters the DI and responses are obtained

In the sensitivity analysis controlled responses are normalized by the maximum response

of each response And then these controlled responses are normalized by the maximum

response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)

where Ri is i-th response and Rimax is maximum i-th response for variation of properties of

design parameters

The appropriate design properties of LRB are selected when the DI is minimized or

converged In other words the LRB is designed when five important responses are

minimized or converged The convergence condition is shown in equation (5)


ε)(le

minus +

j

1jj

DIDIDI (5)

where DIj and DIj+1 is j-th and j+1-th DI value for variation of properties of design

parameter In this study the tolerance (ε) is selected as 001 considering computational

efficiency However designerrsquos judgment and experience are required in the choice of

this value

Using the proposed DI the design procedure of LRB for seismically excited cable-

stayed bridges is proposed as follows

Step 1 Choice of design input excitation (eg historical or artificial earthquakes)

Step 2 The proper Kp satisfied proposed design condition is selected for variation of

Kp (Qy and Ke Kp are assumed as recommended value)

Step 3 With Kp obtained in step 2 the proper Qy is selected for variation of Qy (Ke

Kp is assumed as recommended value)

Step 4 With Kp and Qy obtained in step 2 and 3 the proper Ke Kp is selected for

variation of Ke Kp

Step 5 Iterate step 2 3 and 4 until the designed properties of LRB are unchanged

Generally responses of structures tend to be more sensitive to variation of Qy and Kp

than to variations of Ke [2] therefore it is usually reasonable to select Qy and Kp ahead of

Ke to design LRB In this study Kp is determined in the first During the sensitivity

analysis of Kp properties of the other design parameters are assumed to generally

recommended value The Qy is used to 9 of deck weight carried by LRB recommended


by Ali and Abdel-Ghaffar [1] And the Ke Kp of LRB is assumed to 10 [21]

After the proper Kp of LRB is selected Qy is obtained using the determined Kp and

assumed Ke Kp of LRB (10) Finally with the determined Kp and Qy of LRB the Ke Kp of

LRB is selected Generally design properties of LRB are obtained by second or third

iteration because responses and DI are not changed significantly as design parameters are

varied This is why assumed properties of LRB in the first step are sufficiently reasonable

values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model

The bridge model used in this study is the benchmark cable-stayed bridge model

shown in figure 31 Dyke et al [15] developed the benchmark cable-stayed bridge model

and this model is three-dimensional linearized evaluation model that represents the

complex behavior of the full-scaled benchmark cable-stayed bridge This bridge was

developed to investigate the effectiveness of various control devices and strategies under

the coordination of the ASCE Task Committee on Benchmark Control Problems This

bridge is composed of two towers 128 cables and additional fourteen piers in the

approach bridge from the Illinois side It have a total length of 12058 m and total width

of 293 m The main span is 3506 m and the side spans are the 1427 m in length

Figure 31 Schematic of the Bill Emersion Memorial Bridge [15]

Chapter 3 Numerical Example 14

In the uncontrolled bridge the sixteen shock transmission devices are employed in

the connection between the tower and the deck These devices are installed to allow for

expansion of deck due to temperature changes However these devices are extremely stiff

under severe dynamic loads and thus behavior like rigid link

The bridge model resulting from the finite element method has total of 579 nodes

420 rigid links 162 beam elements 134 nodal masses and 128 cable elements The

stiffness matrices used in this linear bridge model are those of the structure determined

through a nonlinear static analysis corresponding to the deformed state of the bridge with

dead loads [16] Then static condensation model reduction scheme is applied to the full

model of the bridge to obtain a 419-DOF (degree of freedom) reduced-order model The

damping matrices are developed by assigning 3 of critical damping to each mode

which is consistent with assumptions made during the design of bridge

Because the bridge is assumed to be attached to bedrock the soil-structure

interaction is neglected The seismic responses of bridge model are solved by the

incremental equations of motion using the Newmark-β method [17] one of the popular

direct integration methods in combination with the pseudo force method [17]

A detailed description of benchmark control problem for cable-stayed bridges

including the bridges model and evaluation criteria can be found in Dyke et al [15]


32 Design and Seismic Performance of LRB

321 Design Earthquake Excitations In the design of LRB using the proposed procedure input excitations are selected in

the first However the choice of critical design ground excitations for structures is not an

easy task Several possible ground motions should be considered based on the earthquake

history of the site statistical data and other geological evidence In this study one

historical and one artificial earthquake are used as the design earthquakes for numerical

design example

The first design earthquake is historical El Centro earthquake (the North-South

component recorded at the Imperial Valley Irrigation District substation in El Centro

California during the Imperial Valley California earthquake of May 18 1940) El Centro

earthquake has the general energy distribution and is widely used for studies of seismic

hazards The original peak ground acceleration (PGA) of 0348 grsquos is scaled to 0360 grsquos

which is design PGA of Emerson Memorial Bridge Figure 32 shows the time history and

power spectral density of scaled El Centro earthquake

0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty

a) Time history b) Power spectral density

Figure 32 Design earthquake excitation (Scaled El Centro earthquake)


The second design earthquake is artificial random excitation that is stationary

random process with a spectral density function defined by the Kanai-Tajimi spectrum

[18] stated as equations (6) and (7)

222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)

where gζ and ωg are dominant damping coefficient and frequency in the site area and

S0 is the power spectral intensity respectively In this study gζ =03 and ωg =373 rads

are used to generate the artificial random excitation [19] The time history and power

spectral density of artificial random excitation are shown in figure 33 The PGA of

earthquake is also scaled to 036 grsquos

0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

a) Time-history b) Power spectral density

Figure 33 Design earthquake excitation (Artificial random excitation)


In the design of LRB these design ground motions are applied in the longitudinal

direction of bridge and act at simultaneously at all supports

322 Design of LRB The LRB for cable-stayed bridge is designed by using the proposed design

procedure stated in chapter 22 The LRB is employed between the deck and pierbent

connection of bridge in longitudinal direction as shown in figure 31

In the design of LRB Kp of LRB is selected in the first and it is varied from 03W

Where W is deck weight supported by LRB and the value of W is shown in figure 34 Ali

and Abdel-Ghaffar [20] adopted the approach that properties of parameters are taken as a

portion of the superstructure weight supported by bearings The W is considered as the

lumped mass since the behavior of bridges is generally governed by the motions of

longitudinal direction And in the first design step the other properties of LRB are

assumed to conventionally recommended values Qy is assumed to 009W recommended

by Ali and Abdel-Ghaffar [1] and Ke Kp is assumed to 10 [21]

Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck

Pier 2 Pier 3 Pier 4

Figure 34 Deck weight supported by LRB (Lumped mass)

After Kp of LRB is obtained Qy and Ke Kp of LRB are designed in order At this

time Qy and Ke Kp of LRB are varied from 003W and from 5 The proposed DI is

computed by considering five important responses of cable-stayed bridge [14] The peak

and norm responses of the bridge are reflected in DI for scaled El Centro earthquake and

artificial random excitation respectively


The properties of LRB are selected by proposed procedure and the tolerance (ε) is

selected to 001 considering economical efficiency The first and second design iteration

of LRB sensitivity of DI and responses for variation of design properties of LRB are

shown as figure from 35 to 38 for design earthquakes

Even though cable-stayed bridge is originally flexible structure and possess a natural

seismic isolation seismic responses of bridge can be reduced by installing the proper

LRB In general the base shear and moment at towers and bending moment at deck level

of towers are significantly reduced as the base isolation system is adopted However the

negative effect such as large displacement and shear at deck level of towers may be

induced by unsuitable properties of LRB The base shear and moment at towers are

always less than those of uncontrolled system in all properties of LRB and less sensitive

However the deck displacement is more sensitive to the variation of properties of LRB

than the other responses Therefore the deck displacement shear and moment at deck

level of towers are recommended as target responses to design LRB for cable-stayed

bridges

Generally as the properties of LRB are larger responses of cable-stayed bridge are

reduced However some responses and DI are increased or not reduced when excess

properties of each parameter are employed In other words there is not improvement of

seismic reduction in the excess stiffness and shear strength of LRB As the Kp and Qy are

increased the responses and reduction rates of responses are decreased Variation of

responses and DI for Ke Kp is generally less sensitive than the other design parameters

Therefore Kp and Qy are important parameters that may influence the behavior of cable-

stayed bridges among the design parameters because the plastic behavior and energy

dissipation of LRB is more important than the elastic behavior for seismically excited

cable-stayed bridges In the other hands the Ke Kp of LRB is not important parameter

relatively to design LRB Therefore Ke Kp of LRB is recommended to use the general

value (Ke Kp=9~11) and it is not necessary to consider seriously in the design of LRB for


seismically excited cable-stayed bridges Furthermore the peak and norm responses for

the scaled El Centro earthquake and the artificial random excitation varied with a similar

trend for each design parameters


03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index

a) Kp (Qy=009W Ke Kp =10)

003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index

Base shearDeck shearBase momDeck momDeck dispDesign Index

b) Qy (Kp=08W Ke Kp =10)

5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index

c) Ke Kp (Kp=08W Qy=011W)

Figure 35 Sensitivity of responses and DI under scaled El Centro earthquake (1st iteration)


03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


Figure 36 Sensitivity of responses and DI under scaled El Centro earthquake (2nd iteration)


03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index


Figure 37 Sensitivity of responses and DI under artificial random excitation (1st iteration)


03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index



Figure 38 Sensitivity of responses and DI under artificial random excitation (2nd iteration)


Parameter

Through the proposed design procedure appropriate properties of LRB for cable-

stayed bridges are obtained for two design earthquakes In the design of LRB design

properties of LRB are obtained by second or third iteration The design result is shown in

table 31 The LRB I and II are designed for the scaled El Centro earthquake and artificial

random excitation respectively

Table 31 Designed properties of LRB

Kp (tfm) Qy (tf) Ke Kp LRB I 14W 013W 10 LRB II 12W 009W 11

The determined Kp and Qy for cable-stayed bridge are generally larger values than

those for general buildings and short-span bridges For example the Qy obtained by

proposed procedure is larger than those for general buildings and short-span bridges (ie

005W) Therefore the LRB used in seismically excited cable-stayed bridges requires

stiffer rubber and bigger central lead core size than that in general buildings and short-

span bridges In other words the damping and energy dissipation effect of LRB are more

important than the shift of the natural period of structures for seismically excited cable-

stayed bridges

323 Control Performance of Designed LRB The controlled responses and reduction rates of cable-stayed bridges are shown in

table 32 for design earthquakes The controlled responses are normalized maximum

uncontrolled responses in several parts This shows that the use of LRB offers a potential

advantage for the seismic design of cable-stayed bridge Specially the base shear and

moment at towers and bending moment at the deck level of towers are appropriately

reduced in the bridges installed LRB However the shear at deck level of towers is not

reduced efficiently compared with the other responses The peak responses under scaled

LRB


El Centro earthquake and the norm responses under artificial random excitation show

similar reduction trends in the cable-stayed bridge with LRB I and II

Table 32 Controlled responses of bridge for design earthquakes

Responses LRB I LRB II R1 base shear at towers (kN) 165times104 (0327) 217times103 (0545) R2 shear at deck level of towers (kN) 450times103 (0932) 526times102 (0836) R3 base mom at towers (kNm) 319times105 (0300) 369times104 (0448) R4 mom at deck level of towers (kNm) 868times104 (0381) 120times104 (0675) R5 longitudinal deck displacement (m) 989times10-2 (0980) 119times10-2 (1415) ( ) Controlled responseUncontrolled responses

The control performance under other historical earthquakes is investigated to verify

the effectiveness of LRB designed by proposed method Three historical earthquakes

provided in the benchmark problems are considered in this study i) 1940 El Centro NS

recorded at Imperial Valley (0348grsquos) ii) 1985 Mexico City recorded at Galeta de

Campos (0143grsquos) iii) 1999 Turkey Gebze NS recorded at Kocaeli (0265grsquos) The time

history of three earthquakes is shown in figure 39

0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )

a) El Centro earthquake b) Mexico City earthquake c) Gebze earthquake

Figure 39 Time history of three earthquakes


The performance of cable-stayed bridge with LRB I and II is verified by adopting

eleven evaluation criteria provided in benchmark problem [15] The first six evaluation

criteria consider the ability of the controller to reduce peak responses

=max

ob

biti

GebzeMexicoCityElCentro F

)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti

GebzeMexicoCityElCentro M

)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti

GebzeMexicoCityElCentro T

T)t(TmaxJ max5

=ob

bi

ti

GebzeMexicoCityElCentro x

)t(xmaxJ max6

(8-13)

where )t(Fbi is the base shear at the ith tower maxobF is the maximum uncontrolled

base shear )t(Fdi is the shear at deck level in the ith tower maxodF is the maximum

uncontrolled shear at deck level of towers )t(M bi is the base moment at the ith towers

maxobM is the maximum uncontrolled moment at the base shear of the towers )t(M di is

the moment at the deck level in the ith tower maxodM is the maximum uncontrolled

moment at the deck level of towers oiT is the nominal pretension in the ith cable aiT is

the actual tension in the cable and obx is the maximum of the uncontrolled deck

response at these locations

The second five evaluation criteria consider normed (ie RMS) responses over the

entire simulation time as follows

=)t(F

)t(FmaxJ

ob

bii

GebzeMexicoCityElCentromax7

=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)


where )t(Fob is the maximum RMS uncontrolled base shear of towers )t(Fod

is the maximum RMS uncontrolled shear at the deck level of towers )t(M ob is the

maximum RMS uncontrolled overturning moment of towers )t(M od is the maximum

RMS uncontrolled moment at the deck level of towers The normed value of the

responses denoted sdot is defined as

(19)

where tf is defined as the time required for the response to attenuate

To compare the results The LRB is designed using method that Wesolowsky and

Wilson [10] are presented for cable-stayed bridges This design procedure is based on

Naeim and Kelly approach [11] that specify a design displacement and period in the first

Wesolowsky and Wilson specify the effective period of isolator considering the average

maximum deck displacement (∆) and base shear (S) of the non-isolated bridge for several

earthquakes In this study the maximum displacement (Xd) and ultimate strength (Fu) of

isolators are specified to 2∆ and 025S respectively The responses under six earthquakes

are considered (El Centro Mexico City Gebze Northridge Kobe earthquake and

artificial random excitation used in chapter 32) to obtain the average maximum deck

displacement and base shear of the non-isolated bridge The properties of designed LRB

are shown in table 33

Table 33 Designed properties of LRB (Wesolowsky and Wilson-WW bearing)

Kp (tfm) Qy (tf) Ke Kp 0627W 0075W 10

The uncontrolled maximum responses under three earthquakes for performance

int sdot=sdotft

f

dtt 0

2)(1


criteria are shown in table 34 and the simulation results are shown in tables from 35 to

37 and the time history of responses considered in DI are shown in figure from 310 to

312 for three historical earthquakes

The result shows that most responses of cable-stayed bridge are reduced sufficiently

by proper LRB For example the base shear and moment at towers and moment at deck

level of towers are remarkably diminished compared with uncontrolled system And the

deck displacement of LRB I is smaller than that of LRB II However the shear at deck

level of towers and deck displacement of LRB I and II are not be reduced sufficiently

Nevertheless these responses are generally smaller than those of WW bearing

For El Centro earthquake all controlled responses are smaller than uncontrolled

responses except the deck displacement of LRB II The LRB designed by proposed

method shows a better performance than that by Wesolowsky and Wilson method For

example the shear at deck level of towers is reduced about 133 (LRB I) and 92

(LRB II) the deck displacement is reduced about 376 (LRB I) and 163 (LRB II)

compared with WW bearing For Mexico City earthquake however LRB I and II are not

efficient compared with WW bearing except the deck displacement This is why the WW

bearing is designed more flexible than LRB I and II Therefore the plastic behavior of

LRB is not adequately occurred in the LRB I and II because the Mexico City earthquake is

relatively small earthquake (figure 313) Nevertheless the seismic performance of

designed LRB is sufficiently good compared with uncontrolled system For Gebze

earthquake the performance of LRB designed by proposed method is also acceptable and

better than that of WW bearing The shear at the deck level of towers and deck

displacement increase a little compared with uncontrolled responses Nevertheless these

responses did not increase seriously compared with those of WW bearing The deck

displacement of WW bearing is a little large (about 17cm) because this LRB is designed

more flexible than LRB I and LRB II

These results show that seismic responses of cable-stayed bridge can be reduced


sufficiently by only proper LRB However the deck displacement for two earthquakes is

relatively larger than that of uncontrolled system Nevertheless the increased deck

displacement (under 10cm) is still less than the allowable displacement that the deck will

be disintegrated from its end connections (30cm [14])

Table 34 Uncontrolled maximum responses for performance criteria

Evaluation Criteria El Centro Mexico City Gebze

Max base shear at towers (kN) 4878times104 1118times104 3085times104

Max shear at deck level of towers (kN) 4671times103 1525times103 3150times103 Max base mom at towers (kNm) 1027times106 1982times105 6978times105 Max mom at deck level of towers (kNm) 2205times105 8670times104 1093times105 Max longitudinal deck displacement (m) 9758times10-2 2432times10-2 7192times10-2 Norm base shear at towers (kN) 5265times103 1474times103 2609times103 Norm shear at deck level of towers (kN) 4561times102 1889times102 2312times102 Norm base mom at towers (kNm) 1163times105 3147times104 5779times104 Norm mom at deck level of towers (kNm) 2013times104 6931times103 9507times103

Table 35 Performance of designed LRB under El Centro earthquake

Evaluation Criteria LRB I LRB II WW bearing

J1 max base shear at towers 03194 03116 03311 J2 max shear at deck level of towers 08821 09247 10179 J3 max base mom at towers 03024 02931 03003 J4 max mom at deck level of towers 03621 04797 06047 J5 max deviation of cable-tension 01506 01673 01898 J6 max longitudinal deck displacement 08760 11764 14048 J7 norm base shear at towers 02577 02397 02347 J8 norm shear at deck level of towers 07505 08134 09829 J9 norm base mom at towers 02756 02540 02532 J10 norm mom at deck level of towers 04007 04722 05855 J11 norm deviation of cable tension 00164 00144 00176


Table 36 Performance of designed LRB under Mexico City earthquake



Table 37 Performance of designed LRB under Gebze earthquake




0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

a) Base shear at towers

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

b) Shear at deck level of towers

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl

c) Base moment at towers

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

d) Moment at deck level of towers

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)

e) Deck displacement

Figure 310 Time history responses of cable-stayed bridge under El Centro earthquake

LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)


Figure 311 Time history responses of cable-stayed bridge under Mexico City earthquake

LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)


Figure 312 Time history responses of cable-stayed bridge under Gebze earthquake

LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


The restoring force of LRB installed at pier 2 is shown in figure from 313 The

control forces and energy dissipation of LRB are sufficiently occured in El Centro and

Gebze earthquake However in the Mexico City earthquake those of LRB are relatively

smaller than those of LRB in El Centro and Gebze earthquake This is why the plastic

behavior of LRB is not adequately occurred in designed LRB because this earthquake is

relatively small Nevertheless proper restoring forces are generated during this

earthquake and seismic responses of cable-stayed bridge are reduced

-10 -5 0 5 10Deformation (cm)

-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)

a) Restoring force of LRB under El Centro Earthquake


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)

b) Restoring force of LRB under Mexico City Earthquake (continuded)

LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)

c) Restoring force of LRB under Gebze Earthquake

Figure 313 Restoring force of LRB under three earthquakes

Results in this chapter indicate that seismic responses of cable-stayed bridges are

controlled sufficiently by only appropriate LRB And the LRB used in seismically excited

cable-stayed bridges requires stiffer rubber and bigger central lead core size than that in

general buildings and short-span bridges due to its flexibility and low structural damping

In other words the damping and energy dissipation effect of LRB is more important than

the shift of the natural period of structures for seismically excited cable-stayed bridges

LRB I LRB II


33 Effect of Characteristics of Earthquakes

331 Effect of Frequency Contents of Earthquakes The earthquakes are characterized by PGA frequency contents and duration of

earthquakes Therefore in the design of seismic isolator such as LRB the PGA as well as

the frequency contents of earthquakes may be important parameter and the performance

of isolator is affected by these characteristics of earthquakes The characteristics of

earthquakes may be estimated by the earthquake history statistical and geological data of

site However different earthquakes that not considered in design of seismic isolation

system may be excited in the design structures

In this chapter LRB is designed using proposed design procedure for several

earthquakes which have the different frequency contents to investigate the effect of

frequency contents of earthquakes Furthermore the variation of performance of designed

LRB is investigated to verify the robustness of designed LRB for different frequency

contents of earthquakes Three earthquakes used in chapter 323 are considered as design

earthquakes and the PGA of three earthquakes is scaled to 036 grsquos in order to exclude the

effect of the PGA of earthquakes The power spectral density of earthquakes is shown in

figure 314

0 5 10 15Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty

a) Scaled El Centro b) Scaled Mexico City c) Scaled Gebze

Figure 314 Power spectral density of three earthquakes


Table 38 shows properties of LRB designed by the proposed design method under

different design earthquakes The LRBEL LRBME and LRBGE are designed under scaled El

Centro Mexico City and Gebze earthquake respectively

Table 38 Designed properties of LRB for different frequency contents

Frequency (Hz) Kp (tfm) Qy (tf) Ke Kp LRBEL 15 14W 013W 10 LRBME 05 11W 012W 11 LRBGE 20 14W 016W 9

As can be seen in Table 38 Kp and Qy are more sensitive to the frequency contents

of earthquake than Ke Kp of LRB For Mexico City earthquake the earthquake energy is

concentrated in low frequency (about 05Hz) the flexible LRB is required In other words

the flexible Kp and small Qy are necessary to Mexico City earthquake On the other hands

for El Centro and Gebze earthquake the earthquake energy is concentrated in relatively

high frequency (about 15Hz and 20Hz) the stiff LRB is required compared with that for

Mexico City earthquake This indicates that as the frequency contents of earthquake are

concentrated in higher range stiffer LRB is needed However the Ke Kp of LRB is not

changed seriously by the frequency contents of earthquakes

Because the seismic isolation system such as LRB may have inadaptability to the

uncertainty of earthquake the performance of designed LRB is verified for the other

earthquakes which have different frequency contents The performance and variation of

performance of designed LRB are shown in table from 39 to 311 under the other

earthquakes that have different frequency contents Generally responses of cable-stayed

bridge with LRB designed by proposed design procedure are not varied seriously for

different design earthquakes However the deck displacement is more sensitive than the

other responses For example in table 310 the deck displacement of bridge with LRBME

is increased about 462(about 156cm) Nevertheless the control performance of


designed LRB using target design earthquake is not varied significantly if other

earthquakes that have different frequency contents are excited to cable-stayed bridge

Table 39 Performance of LRB for different frequency contents

under scaled El Centro earthquake

Evaluation Criteria LRBEL LRBME LRBGE

J1 max base shear at towers 0327(0) 0331(12) 0326(-03) J2 max shear at deck level of towers 0932(0) 0949(18) 0916(-17) J3 max base mom at towers 0301(0) 0298(-10) 0314(43) J4 max mom at deck level of towers 0381(0) 0415(89) 0389(21) J5 max deviation of cable-tension 0163(0) 0175(74) 0154(-55) J6 max longitudinal deck displacement 0980(0) 1077(99) 0989(09) J7 norm base shear at towers 0261(0) 0255(-23) 0275(54) J8 norm shear at deck level of towers 0800(0) 0830(38) 0808(10) J9 norm base mom at towers 0279(0) 0271(-29) 0299(72) J10 norm mom at deck level of towers 0389(0) 0426(95) 0382(-18) J11 norm deviation of cable tension 0016(0) 0015(-63) 0017(63) ( ) Variation of performance()



under scaled Mexico City earthquake

Evaluation Criteria LRBME LRBEL LRBGE

J1 max base shear at towers 0573(0) 0594(37) 0616(75) J2 max shear at deck level of towers 1070(0) 1066(-04) 1081(10) J3 max base mom at towers 0628(0) 0563(-104) 0587(-65) J4 max mom at deck level of towers 0417(0) 0398(-46) 0387(-72) J5 max deviation of cable-tension 0119(0) 0123(34) 0134(123) J6 max longitudinal deck displacement 1917(0) 1607(-162) 1601(-165) J7 norm base shear at towers 0465(0) 0469(09) 0484(41) J8 norm shear at deck level of towers 0801(0) 0771(-37) 0759(-52) J9 norm base mom at towers 0460(0) 0466(13) 0482(48) J10 norm mom at deck level of towers 0542(0) 0501(-76) 0499(-79) J11 norm deviation of cable tension 0014(0) 0016(114) 0017(214) ( ) Variation of performance()


under scaled Gebze earthquake (ControlUncontrol)

Evaluation Criteria LRBGE LRBEL LRBME

J1 max base shear at towers 0372(0) 0398(70) 0414(113) J2 max shear at deck level of towers 0960(0) 1028(71) 1073(118) J3 max base mom at towers 0376(0) 0415(104) 0425(130) J4 max mom at deck level of towers 0583(0) 0638(94) 0684(173) J5 max deviation of cable-tension 0104(0) 0122(173) 0142(365) J6 max longitudinal deck displacement 1097(0) 1314(198) 1604(462) J7 norm base shear at towers 0338(0) 0333(-15) 0335(-09) J8 norm shear at deck level of towers 0844(0) 0872(33) 0975(155) J9 norm base mom at towers 0374(0) 0373(-03) 0381(19) J10 norm mom at deck level of towers 0535(0) 0560(47) 0651(217) J11 norm deviation of cable tension 0011(0) 0010(-91) 0011(0) ( ) Variation of performance()


332 Effect of PGA of Earthquakes In this chapter the effect of PGA of earthquakes is investigated to design LRB The

LRB is designed using proposed design procedure for several earthquakes which have

different PGA

The El Centro earthquake and the artificial random excitation are employed as

design earthquakes In the El Centro earthquake the PGA of earthquake is scaled to one

and a half of original PGA (0348grsquos and 0174grsquos) The PGA is scaled to 036grsquos and

018grsquos in the artificial random excitation case

Table 312 shows the design results of LRB under different PGA of earthquake The

LRB10EL and LRB05El are designed under 10 and 05-scaled El Centro earthquake and the

LRBAI and LRBAII are designed under 036 grsquos and 018 grsquos scaled-artificial random

excitation respectively

Table 312 Designed properties of LRB for different PGA

PGA (grsquos) Kp (tfm) Qy (tf) Ke Kp LRB10EL 0348 14W 013W 9 LRB05El 0174 10W 008W 8 LRBAI 0360 12W 009W 11 LRBAII 0180 13W 006W 12

The design result shows that the shear strength of central lead core is depend on the

PGA of two design earthquakes That is as the PGA of earthquakes increases the larger

Qy of LRB is required and thus the larger energy dissipation capacity is necessary

However Kp of LRB is depended or not on the PGA of earthquake and Ke Kp of LRB is

not sensitive to this earthquake characteristic

The variation of performance of each designed LRB is simulated for other

earthquakes which have different PGA of earthquake and results are shown in table from

313 to 316


When the relatively weak earthquake is applied to bridges with LRB designed by

strong earthquakes the control effect of LRB is reduced in responses related to base of

towers (ie base shear and moment of towers) On the other hand that of LRB increases

in responses related to deck level of towers (ie shear and moment at deck level of towers

and deck displacement) This is why LRB designed under strong earthquakes have

relatively large shear strength therefore the plastic behavior of central lead core is not

happened sufficiently and thus the effect of base isolation is not generated sufficiently In

this reason responses related to base of towers increase On the other hands the control

effect of LRB decreases in responses related to deck level of tower because designed

LRB is relatively flexible

Performance of designed LRB is not varied seriously for different PGA of

earthquakes However the deck displacement and deviation of cable tension relatively

increase by this earthquake characteristic For example in table 313 the effect of

LRB05EL for deck displacement is worsened about 443 (about 128 cm) under 10-

scaled El Centro earthquake and that of LRBAII for deck displacement is did about 614

(117cm) under 036 grsquos scaled artificial random excitation And that for deviation of

cable tension is also worsened However the increased deck displacement is still less than

the allowable displacement (30 cm [14]) and the deviation of cable tension in the cable is

remaining within allowable value [15]


Table 313 Performance of LRB for different PGA of earthquakes

under 10 scaled El Centro earthquake

Evaluation Criteria LRB10EL LRB05EL

J1 max base shear at towers 0318(0) 0312(-17) J2 max shear at deck level of towers 0887(0) 0996(123) J3 max base mom at towers 0304(0) 0300(-12) J4 max mom at deck level of towers 0365(0) 0551(511) J5 max deviation of cable-tension 0148(0) 0175(181) J6 max longitudinal deck displacement 0907(0) 1309(443) J7 norm base shear at towers 0259(0) 0238(-80) J8 norm shear at deck level of towers 0762(0) 0908(191) J9 norm base mom at towers 0278(0) 0254(-86) J10 norm mom at deck level of towers 0399(0) 0512(284) J11 norm deviation of cable tension 0015(0) 0015(-64) ( ) Variation of performance ()




J1 max base shear at towers 0303(0) 0347(147) J2 max shear at deck level of towers 0913(0) 0810(-113) J3 max base mom at towers 0303(0) 0368(216) J4 max mom at deck level of towers 0398(0) 0360(-96) J5 max deviation of cable-tension 0072(0) 0076(66) J6 max longitudinal deck displacement 1129(0) 0977(-135) J7 norm base shear at towers 0278(0) 0325(172) J8 norm shear at deck level of towers 0846(0) 0777(-82) J9 norm base mom at towers 0307(0) 0360(174) J10 norm mom at deck level of towers 0414(0) 0396(-42) J11 norm deviation of cable tension 0068(0) 0012(806) ( ) Variation of performance ()



under 036grsquos scaled artificial random excitation

Evaluation Criteria LRBAI LRBAII

J1 max base shear at towers 0662(0) 0660(-02) J2 max shear at deck level of towers 0785(0) 0780(-06) J3 max base mom at towers 0518(0) 0575(111) J4 max mom at deck level of towers 0678(0) 0601(-113) J5 max deviation of cable-tension 0098(0) 0063(-358) J6 max longitudinal deck displacement 1929(0) 1170(-393) J7 norm base shear at towers 0545(0) 0595(94) J8 norm shear at deck level of towers 0836(0) 0856(24) J9 norm base mom at towers 0448(0) 0524(168) J10 norm mom at deck level of towers 0676(0) 0674(-03) J11 norm deviation of cable tension 1369(0) 0008(-380) ( ) Variation of performance ()



Evaluation Criteria LRBAII LRBAI

J1 max base shear at towers 0638(0) 0657(30) J2 max shear at deck level of towers 0776(0) 0770(-079) J3 max base mom at towers 0534(0) 0545(20) J4 max mom at deck level of towers 0651(0) 0723(111) J5 max deviation of cable-tension 0059(0) 0099(689) J6 max longitudinal deck displacement 1389(0) 2240(614) J7 norm base shear at towers 0555(0) 0522(-60) J8 norm shear at deck level of towers 0826(0) 0823(-04) J9 norm base mom at towers 0465(0) 0438(-58) J10 norm mom at deck level of towers 0656(0) 0691(54) J11 norm deviation of cable tension 0074(0) 0013(804) ( ) Variation of performance ()


These results in this chapter show that the appropriate properties and performance of

LRB are affected by the characteristics of earthquakes However most of responses

except deck displacement and the deviation of cable tension the performance of LRB

designed by proposed procedure is not varied significantly for characteristics of input

earthquakes Furthermore even though these two responses are varied for different

characteristics of earthquake these are also remaining allowable range


34 VD for Additional Passive Control System

341 Design of VD Using the proposed design procedure the LRB is designed for seismically excited

cable-stayed bridges and the effectiveness of designed LRB is verified in chapters 32

and 33 The most responses of a seismically excited cable-stayed bridge are controlled

sufficiently using the designed LRB However some responses (ie shear at the deck

levels of towers and deck displacement) are similar or larger than those of uncontrolled

system Even though these responses may not be problem for safety and serviceability of

bridges the reduction of responses is required

It is hard to reduce these two responses adopting only LRB without increase of the

other responses as seen in figure from 35 to 38 Moreover if the LRB is inordinately

stiff the yield of central lead core is not happened and thus the energy dissipation effect

of plastic behavior of LRB is not expected Therefore in this chapter other passive

control system is employed to obtain the additional reduction of seismic responses of

cable-stayed bridge Because the energy dissipation of control devices are more important

than the period shift of structure for cable-stayed bridge the VD is considered as

additional passive control device and installed between the deck and pier connection of

bridge in longitudinal direction

In this study the capacity of VD is considered as 1000 kN and maximum velocity of

these devices is assumed to 1ms which is identical velocity requirement of active device

in the benchmark control problem The restoring force of VD is modeled as equation (19)

mVD VF C= (19)

where C is damping coefficient and m is velocity exponent m=03~19 is usually used in

most steel structure for seismic protection [22] In this study m=10 is used (ie linear


dampers)

In the design of VD only two responses (ie shear at the deck levels of towers and

deck displacement) are considered In addition the constraint condition stated as equation

(20) is applied That is the variation of the other three responses can not be increased

over 10 of originally controlled responses

11LRB

VDLRBResponse le

+ (20)

In the first four dampers are employed to tower and deck connection (pier 2 3) and

the variation of responses are obtained by time history analysis Next other four dampers

are employed to bent 1 and pier 4 And dampers are installed until two target responses

are increased or converged or the constraint condition is not satisfied

The results are shown figure 315 The number of dampers is selected 16 since the

variation of base shear at towers under Gebze earthquake is not satisfied the constraint

condition However the shear at the deck level of towers and deck displacement is more

reduced as the VD is applied to cable-stayed bridge and the shear at deck level of towers

is more reduced when dampers are employed in pier 2 and 3 than in bent 1 and pier 4

0 4 8 12 16 20Number of dampers

-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)

a) The variation of responses under El Centro earthquake (continuded)



-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()

Base shearDeck shearBase momDeck momDeck disp

b) The variation of responses under Mexico City earthquake


-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)

c) The variation of responses under Gebze earthquake

Figure 315 Design of VD

342 Control Performance of Designed LRB with VD The selected VD is applied to cable-stayed bridges with designed LRB to obtain

additional reduction of responses which are not reduced sufficiently in the LRB installed

bridge The result is shown in table 317 Most of responses of cable-stayed bridge more

decrease as the VD is added to LRB Reduction of shear at the deck level of towers and

deck displacement is larger than that of the other responses However the deviation of

cable-tension is increased a little as the VD is added to LRB Nevertheless this is

remaining within a recommended range of allowable values [15]

This result shows that the seismic responses of cable-stayed bridges can be


adequately controlled by only passive control system

Table 317 Additional reduction of responses with LRB and VD

(LRB I+VD LRB I)

Evaluation Criteria El Centro Mexico City Gebze J1 max base shear at towers 0998 0906 1093 J2 max shear at deck level of towers 0804 0809 0881 J3 max base mom at towers 0989 0877 0976 J4 max mom at deck level of towers 0819 0878 0834 J5 max deviation of cable-tension 1094 0973 1194 J6 max longitudinal deck displacement 0865 0649 0786 J7 norm base shear at towers 0946 0882 0941 J8 norm shear at deck level of towers 0877 0837 0896 J9 norm base mom at towers 0955 0865 0936 J10 norm mom at deck level of towers 0991 0899 0929 J11 norm deviation of cable tension 1082 0881 0916

49

CHAPTER 4

CONCLUSIONS

In this study the design procedure and guidelines for LRB are proposed for

seismically excited cable-stayed bridges and the effect of LRB designed by proposed

procedure is investigated Conclusions of this study are summarized as follows

First from the design result of LRB several design feature of LRB in cable-stayed

bridges are identified The LRB used in cable-stayed bridges requires stiffer rubber and

bigger central lead core size than that in general buildings and short-span bridges due to

their flexibility and low structural damping In other words the damping and energy

dissipation effect of LRB is more important than the shift of the natural period of

structures for seismically excited cable-stayed bridges As the properties of LRB are

larger the responses of cable-stayed bridge are reduced However there is not

improvement of performance of LRB in the excess stiffness and shear strength of LRB

Among the design parameters of LRB plastic stiffness and shear strength of central lead

core are important design parameters because the plastic behavior and energy dissipation

of LRB is more important than the elastic behavior for seismically excited cable-stayed

bridges Furthermore the seismic responses of cable-stayed bridges can be reduced

sufficiently by only LRB designed with proposed procedure

Second proper properties and performance of LRB are affected by the

characteristics of earthquakes (ie frequency contents and PGA of earthquake) As the

frequency contents of earthquake are concentrated in higher range stiffer LRB is

necessary and as the PGA of earthquake increases the larger shear strength of LRB is

required However the ratio of elastic-plastic stiffness of LRB is not sensitive to these

Chapter 4 Conclusions 50

characteristics of earthquakes Most of responses except deck displacement and the

deviation of cable tension the performance of LRB designed by proposed procedure is

not changed significantly for different characteristic of earthquakes However these two

responses are also remaining allowable range though the performance of designed LRB is

worsened

Third the most responses of cable-stayed bridge are controlled sufficiently using the

designed LRB However some responses (ie shear at deck level of towers and deck

displacement) are similar or larger than those of uncontrolled system Even though these

responses may not be problem for bridges these responses are more reduced by

additional damping devices such as viscous damper

Finally the seismic responses of cable-stayed bridges are adequately controlled by

only appropriated design passive control system

요 약 문

지진 하중을 받는 사장교를 위한 수동 제어 장치의 설계

본 논문에서는 지진 하중을 받는 사장교를 위한 납고무 받침의 설계 방

법 및 기준을 제안하였고 제안된 방법에 의해 설계된 납고무 받침의 면진

성능을 확인하였다 또한 사장교의 면진 성능 향상을 위해서 추가적인 수동

제어 장치로서 점성댐퍼를 적용하였다

납고무 받침은 구조물의 수직하중 지지기능 지진 격리 효과 감쇠 효과

및 복원력을 하나의 장치로 얻을 수 있어서 단경간 교량이나 건축 구조물의

면진 장치로 널리 이용되어 왔다 이런 구조물의 면진 설계 시 가장 중요한

목적은 구조물의 고유주기를 이동시키는 것이다 하지만 사장교와 같은 장

대 교량의 동적 특징은 일반 단경간 교량이나 건축 구조물과는 다르며 또한

이런 장대 교량은 비교적 복잡한 거동을 보인다 따라서 단경간 교량이나

건축 구조물에서 사용되는 납고무 받침의 설계 방법이나 기준을 사장교와

같은 장대 교량에 바로 적용하는 것은 힘들다

본 연구에서는 사장교의 동적 거동에서 중요하게 생각하는 응답을 고려

하여 납고무 받침의 설계 지수를 제안하였다 납고무 받침은 물성치의 변화

에 따라 제안된 설계 지수가 최소가 되거나 수렴할 때의 물성치 값을 선택

하여 설계하였다 제안된 방법에 의한 설계 결과 지진 하중을 받는 사장교

에 적합한 납고무 받침은 구조물의 고유주기 이동보다는 지진 에너지 소산

기능이 더 중요함을 확인하였다 또한 설계된 납고무 받침의 면진 성능 또한

검증하였고 제안된 방법에 의해 설계된 납고무 받침의 면진 성능이 우수함

을 확인하였다

제안된 설계 방법에 의해 지진 하중의 특성에 따라 납고무 받침을 설계

하여 그 특성을 분석하였다 또한 이때 설계된 납고무 받침에 대하여 지진

하중의 특징에 따른 면진 성능의 강인성을 조사 하였다 설계된 납고무 받침

은 면진 성능은 다른 특성을 가지는 지진하중에서도 크게 변하지 않음을 확

인하였다

마지막으로 추가적인 지진응답의 감소를 위해 점성댐퍼를 납고무 받침이

설치된 사장교에 적용하였다 이는 사장교의 경우 면진 장치에 의한 구조물

의 고유 주기 이동보다는 지진 에너지 소산 기능이 더 중요하게 요구 되기

때문이다 점성댐퍼를 추가적으로 설치할 경우 납고무 받침만으로 충분히

제어하지 못했던 응답이 더욱 감소하였다 이는 지진 하중을 받는 사자요에

서 적절히 설계된 수동제어 장치만으로도 충분히 제어 성능을 확보 할 수

있음을 보여 주는 것이다

53

REFERENCE

[1] H M Ali and A M Abdel-Ghaffar ldquoSeismic Passive Control of Cable-Stayed

Bridgesrdquo Shock and Vibration Vol2 No4 pp259-272 1995

[2] R I Skinner W H Robinson and G H McVerry An Introduction to Seismic

Isolation John Wiley and Sons 1993

[3] M C Griffith I D Aiken and J M Kelly ldquoDisplacement Control and Uplift

Restraint for Base Isolated Structuresrdquo Journal of Structural Engineering Vol116

pp1135-1148 1990

[4] J M Kelly ldquoBase Isolation Linear Theory and Designrdquo Earthquake Spectra

EERI Vol6 No2 pp223-244 1990

[5] S Nagarjaiah A M Robinson and M C Constantinou ldquoNonlinear Dynamics

Analysis of 3-D Base-Isolated Structuresrdquo Journal of Structural Engineering

ASCE Vol117 No7 pp2035-2054 1991

[6] A Gobarah and H M Ali ldquoSeismic Performance of Highway Bridgesrdquo Journal

of Engineering Structures Vol10 pp157-166 1988

[7] I G Buckle and R L Mayes ldquoThe Application of Seismic Isolation to Bridgesrdquo

Proceeding of the ASCE Structural Congress Seismic Engineering Research and

Practice pp633-642 1990

[8] K S Park H J Jung and I W Lee ldquoHybrid Control Strategy for Seismic

Protection of a Benchmark Cable-Stayed Bridgerdquo Engineering Structures Vol25

pp405-417 2003

[9] K S Park H J Jung B F Spencer Jr and I W Lee ldquoHybrid Control System for

Seismic Protection of a Phase II Benchmark Cable-Stayed Bridgerdquo Journal of

Structural Control Vol27 pp231-247 2003

Reference 54

[10] M J Wesolowsky and J C Wilson ldquoSeismic Isolation of Cable-Stayed Bridges for

Near-Filed Ground Motionsrdquo Earthquake Engineering and Structural Dynamics

Vol32 pp2107-2126 2003

[11] F Naeim and J M Kelly Design of Seismic Isolated Structures-from Theory to

Practice John Willey and Sons 1999

[12] R Bouc ldquoForced Vibration of Mechanical System with Hysteresisrdquo Proceedings

of the 4th Conference on Nonlinear Oscillation 1967

[13] Y K Wen ldquoMethod for Random Vibration of Inelastic Structuresrdquo Journal of

Applied Mechanicals Division Vol42 No2 pp39-52 1989

[14] G Turan ldquoActive Control of a Cable-Stayed Bridge against Earthquake

Excitationsrdquo Thesis for the Degree of Doctoral of Philosophy in Civil Engineering

in University of Illinois at Urbana Champaign 2001

[15] S J Dyke J M Caicedo G Turan L A Bergman and S Haque ldquoPhase I

Benchmark Control Problems for Seismic Response of Cable-Stayed Bridgesrdquo

Journal of Structural Engineering Vol29 No7 pp857-872 2003

[16] J Wilson and W Gravelle ldquoModeling of a Cable-Stayed Bridge for Dynamic

Analysisrdquo Earthquake Engineering and Structural Dynamics Vol20 pp707-721

1991

[17] A K Chopra Dynamics of Structures- Theory and Application to Earthquake

Engineering 2nd Edition Prentice Hall 2001

[18] F R Rofooei A Mobarake and G Ahmadi ldquoGeneration of Artificial Records with

a Nonstationary Kanai-Tajimi Modelrdquo Engineering Structures Vol23 pp827-837

2001

[19] B F Spencer Jr S J Dyke and H S Depskar ldquoBenchmark Problems in Structural

Control part I-active tendon systemrdquo Earthquake Engineering and Structural

Dynamics Special Issue on Benchmark Problems Vol27 No11 pp1127-1137

Reference 55

1998

[20] H M Ali A M Abdel-Ghaffar ldquoModeling of Rubber and Lead Passive-Control

Bearings for Seismic Analysisrdquo Journal of Structural Engineering Vol121

pp1134-1144 1995

[21] W H Robinson ldquoLead Rubber Hysteretic Bearings Suitable for Protecting

Structures during Earthquakesrdquo Earthquake Engineering and Structural Dynamics

Vol10 pp593-604 1982

[22] D Lee and P Taylor ldquoViscous Damper Development and Future Trendsrdquo The

Structural Design and Tall Buildings Vol10 pp311-320 2001

[23] 이철희 구봉근 전규식 이병진 ldquo납 면진받침을 이용한 교량의 면진설

계rdquo 한국지진공학회 1999년도 춘계학술대회 논문집 pp161-168 1999

[24] 박규식 정형조 B F Spencer Jr 이인원 ldquo수동 능동 반능동 및 복합 시

스템을 이용한 사장교의 지진응답 제어rdquo 한국지진공학회 논문집 제 7권

제 1호 pp17-29








by

Sung-Jin Lee






이 성 진


2003 년 12 월 22 일




i

MCE

20023430

ABSTRACT
























ii













iii

TABLE OF CONTENTS

ABSTRACT i


LIST OF TABLES v

LIST OF FIGURES vi


11 Backgrounds 1




21 LRB 6


212 LRB Model 8









iv



341 Design of VD 45




REFERENCES 53

ACKNOWLEDGEMENTS

CURRICULUM VITAE

v










earthquake 38


earthquake 39


earthquake 39











vi

LIST OF FIGURES








20


21


22


23







315 Design of VD 46

1

CHAPTER 1

INTRODUCTION

11 Backgrounds











































































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29




by

Sung-Jin Lee






이 성 진


2003 년 12 월 22 일




i

MCE

20023430

ABSTRACT
























ii













iii

TABLE OF CONTENTS

ABSTRACT i


LIST OF TABLES v

LIST OF FIGURES vi


11 Backgrounds 1




21 LRB 6


212 LRB Model 8









iv



341 Design of VD 45




REFERENCES 53

ACKNOWLEDGEMENTS

CURRICULUM VITAE

v










earthquake 38


earthquake 39


earthquake 39











vi

LIST OF FIGURES








20


21


22


23







315 Design of VD 46

1

CHAPTER 1

INTRODUCTION

11 Backgrounds











































































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29



이 성 진


2003 년 12 월 22 일




i

MCE

20023430

ABSTRACT
























ii













iii

TABLE OF CONTENTS

ABSTRACT i


LIST OF TABLES v

LIST OF FIGURES vi


11 Backgrounds 1




21 LRB 6


212 LRB Model 8









iv



341 Design of VD 45




REFERENCES 53

ACKNOWLEDGEMENTS

CURRICULUM VITAE

v










earthquake 38


earthquake 39


earthquake 39











vi

LIST OF FIGURES








20


21


22


23







315 Design of VD 46

1

CHAPTER 1

INTRODUCTION

11 Backgrounds











































































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

i

MCE

20023430

ABSTRACT
























ii













iii

TABLE OF CONTENTS

ABSTRACT i


LIST OF TABLES v

LIST OF FIGURES vi


11 Backgrounds 1




21 LRB 6


212 LRB Model 8









iv



341 Design of VD 45




REFERENCES 53

ACKNOWLEDGEMENTS

CURRICULUM VITAE

v










earthquake 38


earthquake 39


earthquake 39











vi

LIST OF FIGURES








20


21


22


23







315 Design of VD 46

1

CHAPTER 1

INTRODUCTION

11 Backgrounds











































































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

ii













iii

TABLE OF CONTENTS

ABSTRACT i


LIST OF TABLES v

LIST OF FIGURES vi


11 Backgrounds 1




21 LRB 6


212 LRB Model 8









iv



341 Design of VD 45




REFERENCES 53

ACKNOWLEDGEMENTS

CURRICULUM VITAE

v










earthquake 38


earthquake 39


earthquake 39











vi

LIST OF FIGURES








20


21


22


23







315 Design of VD 46

1

CHAPTER 1

INTRODUCTION

11 Backgrounds











































































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

iii

TABLE OF CONTENTS

ABSTRACT i


LIST OF TABLES v

LIST OF FIGURES vi


11 Backgrounds 1




21 LRB 6


212 LRB Model 8









iv



341 Design of VD 45




REFERENCES 53

ACKNOWLEDGEMENTS

CURRICULUM VITAE

v










earthquake 38


earthquake 39


earthquake 39











vi

LIST OF FIGURES








20


21


22


23







315 Design of VD 46

1

CHAPTER 1

INTRODUCTION

11 Backgrounds











































































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

iv



341 Design of VD 45




REFERENCES 53

ACKNOWLEDGEMENTS

CURRICULUM VITAE

v










earthquake 38


earthquake 39


earthquake 39











vi

LIST OF FIGURES








20


21


22


23







315 Design of VD 46

1

CHAPTER 1

INTRODUCTION

11 Backgrounds











































































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

v










earthquake 38


earthquake 39


earthquake 39











vi

LIST OF FIGURES








20


21


22


23







315 Design of VD 46

1

CHAPTER 1

INTRODUCTION

11 Backgrounds











































































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

vi

LIST OF FIGURES








20


21


22


23







315 Design of VD 46

1

CHAPTER 1

INTRODUCTION

11 Backgrounds











































































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

1

CHAPTER 1

INTRODUCTION

11 Backgrounds











































































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29
























































































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29






























































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29



































6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29











6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

6

CHAPTER 2


21 LRB





















Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


Rubber



Fy

Fu

Qy

Kp

Keff

Xy Xd

Ke
















[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29







[6]




















)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29




)(1 n1n zXzzXXX

z rrry


iA (2)





equation (3)










strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29








strength of LRB










response

sum=

=5

1i maxi

i

RR

DI i=1hellip5 (4)


design parameters





ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


ε)(le

minus +

j

1jj

DIDIDI (5)




this value









variation of Ke Kp














values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29








values

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

13

CHAPTER 3

NUMERICAL EXAMPLE

31 Bridge Model





































design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29



























design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29








design example








0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15

Frequency (Hz)

0

2

4

6

8

10

Pow

er sp

ectr

al d

ensi

ty







222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29





222

22

)(4])(1[])(41[

)(ggg

ggSωωζωω

ωωζω

+minus

+= S0 (6)

S0)14(

0302 +

=gg

g

ζπωζ (7)






0 10 20 30 40 50Time (sec)

-4

-2

0

2

4

Acc

eler

atio

n (m

s2 )

0 5 10 15 20

Frequency (Hz)

0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty

















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29















Pier 1 (Bent 1)

26400 KN

26400 KN26400 KN

26400 KN

7638 KN

7638 KN

7638 KN

7638 KN

Deck























bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29
















bridges


















03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29






03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


03 04 05 06 07 08 09KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11 12KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


03 04 05 06 07 08 09 10 11KpW

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 01 011 012 013QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index



5 6 7 8 9 10KeKp

00

02

04

06

08

10

12

14

16

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index



5 6 7 8 9 10 11KeKp

00

05

10

15

20

25

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design index




03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


03 04 05 06 07 08 09 10 11 12KpW

00

05

10

15

20

25

30

35

Eva

luat

ion

crite

ria

25

30

35

40

45

50

Design

index


003 004 005 006 007 008 009 010 011QyW

00

05

10

15

20

25

30

Eval

uatio

n cr

iteri

a

25

30

35

40

45

50

Design

index





Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


Parameter















stayed bridges








LRB












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29












0 25 50 75 100Time (sec)

-4

-2

0

2

4

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-2

-1

0

1

2

Acce

lera

tion

(ms

2 )

0 25 50 75 100Time (sec)

-3

-15

0

15

3

Acce

lera

tion

(ms

2 )







=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29





=max

ob

biti


)t(FmaxJ max1

=max

od

diti


)t(FmaxJ max2

=maxob

biti


)t(MmaxJ max3

=maxod

diti


)t(MmaxJ max4

minus

=oi

oiai

ti


T)t(TmaxJ max5

=ob

bi

ti


)t(xmaxJ max6

(8-13)











=)t(F

)t(FmaxJ

ob

bii


=)t(F

)t(FmaxJ

od

dii


=)t(M

)t(MmaxJ

ob

bii


=)t(M

)t(MmaxJ

od

dii


minus

=oi

oiai

i


T)t(TmaxJ max11

(14-18)







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29







(19)
















int sdot=sdotft

f

dtt 0

2)(1

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

















































0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29





















0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29









0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Bas

e sh

ear

at to

wer

s (times

104

kN)


0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)

0 20 40 60 80 100Time (sec)

-50

-25

00

25

50

Shea

r at

dec

k le

vel o

f tow

ers (times1

03 k

N)


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e m

omen

t at t

ower

s (times1

06 k

N m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Base

mom

ent a

t tow

ers

(times10

6 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)

0 20 40 60 80 100Time (sec)

-24

-16

-08

00

08

16

24

Mom

ent a

t dec

k le

vel o

f tow

ers (times1

05 k

N m

)


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Dec

k di

spla

cem

ent (times1

0-2

m)

0 20 40 60 80 100Time (sec)

-12

-8

-4

0

4

8

12

Dec

k di

spla

cem

ent (times1

0-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Bas

e sh

ear

at to

wer

s (10

4 K

N)


0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-2

-1

0

1

2

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)


0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Base

mom

ent a

t tow

ers (

105

kN m

)

UncontrolControl

0 20 40 60 80 100Time (sec)

-20

-10

00

10

20

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)

0 20 40 60 80 100Time (sec)

-90

-60

-30

00

30

60

90

Mom

ent a

t dec

k le

vel o

f tow

ers (

104 kN

m)


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-40

-20

00

20

40

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)

0 20 40 60 80 100Time (sec)

-30

-20

-10

00

10

20

30

Bas

e sh

ear

at to

wer

s (10

4 kN

)


0 20 40 60 80 100Time (sec)

-3

-2

-1

0

1

2

3

Shea

r at

dec

k le

vel o

f tow

ers (

103

kN)

0 20 40 60 80 100Time (sec)

-36

-24

-12

0

12

24

36

Shea

r at

dec

k le

vel o

f tow

ers

(10

3 kN

)


0 20 40 60 80 100Time (sec)

-70

-35

00

35

70

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl

0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Bas

e m

omen

t at t

ower

s (10

5 kN

m)

UncontrolControl


0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)

0 20 40 60 80 100Time (sec)

-12

-08

-04

00

04

08

12

Mom

ent a

t dec

k le

vel o

f tow

ers (

105 kN

m)


0 20 40 60 80 100Time (sec)

-80

-40

00

40

80

Dec

k di

spla

cem

ent (

10-2

m)

0 20 40 60 80 100Time (sec)

-120

-80

-40

00

40

80

120

Dec

k di

spla

cem

ent (

10-2

m)



LRB I

LRB I

LRB I

LRB I

LRB I

LRB II

LRB II

LRB II

LRB II

LRB II










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29










-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)


-8000

-4000

0

4000

8000

Res

tori

ng fo

rce

(kN

)



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


LRB I LRB II

LRB I LRB II



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29



-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)


-6000

-4000

-2000

0

2000

4000

6000

Res

tori

ng fo

rce

(kN

)









LRB I LRB II

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

















figure 314


0

2

4

6

8

10

Pow

er sp

ectr

al d

ensit

y


0

10

20

30

40

Pow

er sp

ectr

al d

ensi

ty


0

4

8

12

16

Pow

er sp

ectr

al d

ensi

ty














































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29












































different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29




















different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29













different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29




different PGA


















313 to 316



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29



































































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29















































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29






































mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29





























mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29






















mVD VF C= (19)




dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29


dampers)





11LRB

VDLRBResponse le

+ (20)











-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)




-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29



-400

-300

-200

-100

00

100

200

300

400V

aria

tion

of r

espo

nse

()




-400

-300

-200

-100

00

100

200

300

400

Var

iatio

n of

res

pons

e (

)














(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29




(LRB I+VD LRB I)


49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

49

CHAPTER 4

CONCLUSIONS



























worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29






worsened








요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

요 약 문





















을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

을 확인하였다





인하였다








53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

53

REFERENCE







pp1135-1148 1990


EERI Vol6 No2 pp223-244 1990



ASCE Vol117 No7 pp2035-2054 1991








pp405-417 2003




Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

Reference 54



Vol32 pp2107-2126 2003















1991





2001




Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

Reference 55

1998



pp1134-1144 1995



Vol10 pp593-604 1982







제 1호 pp17-29

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Master’s Thesissdvc.kaist.ac.kr/article/dissertation/2004_lsj_ms.pdf · 2008-03-05 · A thesis submitted to the faculty of the Korea Advanced Institute of Science and Technology