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KR0101299
KAERI/TR-1833/2001
LRB
Determination of Design Parameters ofLead-Rubber Bearings by Characterization Tests
PLEASE BE AWARE THATALL OF THE MISSING PAGES IN THIS DOCUMENT
WERE ORIGINALLY BLANK
2000^ LRB
2001. 4.
Al
o ofc
I .
LRB
LRB(Lead-Rubber Bearing)
LRB
LRB
III.
bilinear JE^-i;
A]
IV.
- 111 -
- LRBi2] o l ^ 7 ^ £ - bilinear £ . 1 ^ O]AOV^^- ^. 0^4. o
- IV -
SUMMARY
I . Project Title
Determination of Design Parameters of Lead-Rubber Bearings by
Characterization Tests
I I . Purpose and Importance on the Research
A lead-rubber bearing (LRB) is commonly used as a seismic isolator
for the seismic protection of bridges. Seismic isolation systems reduce
transmitted forces to the structure by introducing sufficiently flexible
supports between the upper structure and base mat and dissipating a
significant amount of earthquake energy. In general, acceptable isolation
systems will: Remain stable for required design displacements; provide
increasing resistance with increasing displacement; not degrade under
repeated cyclic load; and have quantifiable engineering parameters.
Dynamic properties of isolation systems, which are main parameters
affecting the safety of structures, are different from isolation types and
manufacturers. The purpose of this study is to evaluate effective
stiffness and equivalent damping of the KR LRB through horizontal
shear tests and to demonstrate acceptability of proposed design
procedures and models for LRB seismic isolation systems.
III. Scope and Contents of the Research
This report includes characterization tests of LRB provided by KR
Industrial Co. and also includes evaluation of effective stiffness and
equivalent damping ratio of LRB. With test data, dynamic properties of
LRB are reviewed and design procedures proposed by KR, Japan, and
United States are compared and revised. Two bilinear models of LRB
- v -
are proposed. One is obtained from hysteresis loop, the other is based
on mechanical property data of laminated rubber and lead plug.
Comparison of analysis results with test results for a bridge
scaled-model is performed to show the applicability of proposed
bilinear models.
IV. Results of the Research and Suggestion for the Application
Based on the review and evaluation of the KR LRB design
parameters and procedures, following conclusions are drawn.
- Design parameters of LRB, effective stiffness and equivalent
damping, are significantly influenced by horizontal loading
frequency and vertical load.
- Hysteretic behavior of LRB can be idealized by a bilinear model.
The initial stiffness of the model must be determined with
accuracy.
- LRB design procedures proposed by the KR Industrial Co. may be
applicable to determine effective stiffness, but some modifications
are needed to determine equivalent damping.
- vi -
CONTENTS
SUMMARY v
Chapter 1. Introduction 1
Chapter 2. Properties of LRB 3
Section 1. General Properties 3
Section 2. Properties of the KR Bearing 11
Chapter 3. LRB Test 13
Section 1. Test Specimen • •• 13
Section 2. Test Facilities 19
Section 3. Test Procedure 19
Chapter 4. Test Results 25
Section 1. Horizontal Shear Test 25
Section 2. Post-Test Investigation of Specimen 41
Chapter 5. Comparison of LRB Parameters and Design Procedure
45
Section 1. LRB Parameters 45
Section 2. Design Procedures 48
Section 3. Modelling of Hysteresis Curve 51
Chapter 6. Conclusions 57
References 59
Appendix 1. Summary Tables of Horizontal Shear Test 61
Appendix 2. Equivalent Linear Models of LRB 79
Appendix 3. LRB Design Procedures 85
- vn -
Appendix 4. Comparison of Earthquake Behavior of Base-Isolated
Bridges with LRB 91
Appendix 5. Seismic Design Specification of Highway Bridges
99
- vm -
JL ^ •£: ill
SUMMARY v
1
3
KR ^1#£) ^ 11
LRB ^-^A|ig 13
*n 1 3
19
19
25
25
41
LRB ^ - ^ x ] ^ •£;$-*] y]iH 45
LRB ^ * 1 45
^7^]^] ti]i2. 48
57
g-*l 59
1. LRB ^ 3 | ^ i ^ : A l ^ ^2}-5. 61
- IX -
ta 2. LRB5]
3. LRB
4. LRB
5.
. ^ 79
85
7]2g- tilH 91
99
- x -
3. 2.1 <HaH<y ^ J L ^ %5,4[ Tfk'§n<T 4
S. 3.1 Al^afloj ^ja. *fl€ 13
3 3.2 LRB ^ * | 7 ] - ^ - ^ 2|7>ti0l-^ 23
3. 4.1 -rSj^r^ Aj^a 26
a 5.1 KR LRB^ 'iTfl^-^^l 45
S. 5.2 # £ - A ) i g ^ 5 . - « ^ ^ ^ - LRB ^ - ^ x ] (7>^1 ^ 1 ^ ^ : O.lHz) ••• 46
S. 5.3 ^ ^ - A ] ^ ^ 5 . « - E 1 <^^ LRB 4 ^ * 1 (7]-^l ^ 1 ^ - ^ : 0.5Hz) ••• 46
5 5.4 ^ T E H i g j i ^ f E ] <^^ LRB s -^^ l (7V^1 ^ ^ ^ r : 0.7Hz) ••• 47
a 5.5 ^ A l ^ A S J f B l <£.£- LRB s . ^^1 (7f^l ^ 1 ^ ^ : 0.8Hz) - 47
5. 5.6 £ i E H i g i i ^ . J f E i <^o. L R B S - A ^ I (7]-^l ^ 1 ^ ^ : l.OHz) ••• 48
6 5.7 ^-J l#^o]] tfl^j. ^ ^ ] A I a ] ^ 49
3 . 5.8 ^ -7>^-^«H rfltb ^^1^1 W]35L 50
a 5.9 Bilinear S ^ l ^1*}: LRB #>$*! 56
- xi -
2.1 LRB *§# 3
2.2 ^ A ] ^ ] tfl V uL^3 - g - ^ - ^ ^ 1 - ^ 5
2.3 ^ A ] * } ^ ^*V z\%3L^9\ o ^ ^ d 5
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ZL^ 2.6 ^-^-S] ^ ^ r ^ ^ 8
n ^ 2.7 LRB5] 713M ^ " ^ 9
ZL^ 2.8 LRB5] ol^^-^d 10
ZL%1 2.9 LRB5] bilinear S.^i 10
ZL^ 2.10 KR ^%JL^-^\ ^ ^ - ^ 1 ^ ^ ^ 11
2.11 KR ^-^g-^ ^ i 1 ^ ^ ^ 1^4 11
2.12 KR ^-^-^1 -8-^-^^f- ^ 1 ^ 12
3.1 lOTon LRB A ] ^ ^ O ) ^ ^ ^ ^ 14
3.2 lOTon LRB ^l^^ll^l 4 ^ > 4 plate ^7^ ]£^ 15
& 3.3 200Ton LRB A ] ^ ^ 5 ] ^ T i l i ^ 16
& 3.4 200Ton LRB ^ 1 ^ ^ ] ^ ^-t}^- plate ^ ^ ] J £ ^ 17
& 3.5 A] SH A}*i 18
^ 3.6 A ] ^ * ) 20
^ 3.7 Al^sfl x>3)- ^ ^ ^ J ^ i ^ A l ^ ^ - ^ 21
^ 3.8 ^sj7>xiHo>^:o) o^ X\7J:o}^ (7f^l ^ 1 ^ . ^ O.lHzS]
3-f) 22
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^ 4.2 O.lHzofl cfl«^ 6 1 ^ ^ - A J (F102-2) 28
% 4.3 0.5Hzofl cfl^ ^1^^-^ i (F103-2) 28
^ 4.4 0.7Hz<>fl rJftis]- o]?m*i (F106-2) 29
4.5 0.8Hz^] rfltb o l ^ ^ - ^ (F105-3) 29
4.6 l.OHzofl t f l ^ o ] ^ ^ ^ (F105-2) 30
- xn -
4.7 ^ R t ° l ] tiq-g- - f K £ # ^ ^s(- 30
4.8 ^ ^ E E ^ ] ^ ^ f ^ - i ) ^ ^SJ- 31
4.9 zfl^MrS.^ n}-€- :£<HM*13 ^ 31
4.10 OTonofl tfl^ ° 1 ^ ^ (F2001-1) 33
4.11 50Ton^Jl rfltb ° ] ^ ^ d (F2001-3) 33
ZZ.51 4.12 lOOTon^ t } ]^ o ] ^ ^ - ^ (F2001-4) 34
ZL& 4.13 150Ton^l tfl«]- o ] ^ ^ - ^ i (F2001-8) 34
ZZ.5] 4.14 200Tonofl cfl^ o ] ^ ^ . ^ (F2001-7) 35
ZL^ 4.15 < £ ^ B ^ ] x^€- -fr5l7ov^^ ^ s j - 35
] 4.16 < a ^ ^ > # ^ vc^^r ^.7|.^-^fi] ^s ) - 36
4.17 <a^-5->#^ n?-€- 4 : ^ ^ 1 1 ^ ^ ^ ^S)- 36
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ZL^ 4.20 7flo-> A>ol^-ofl n}^- ^AVclluix]^ ^ ^ . 40
ZZ.5J 4.21 Bearing ID. 101S] ^ ^ ^ r ^ 42
ZZ.e] 4.22 Bearing ID. 102^ ^ ^ ^ ^ r ^ •• 42
ZL&j 4.23 Bearing ID. 103^) ^ ^ ^ ^ ^ 43
ZZ.e] 4.24 Bearing ID. 104S) ^ ^ ^ ^ ^ 43
ZL^ 4.25 Bearing ID. 105^ ^ ^ •?• S ^ 44
ZL& 4.26 Bearing ID. 1063} ^ * | ^ ^ ^ 44
ei 5.1 -fi-317^^1 rHtt -iTllA1 y l S 49
^ 5.2 ^7>#£]«]cfl rfl^- -gTfl-i] tilS 50
5.3 o]AoVg}.s| L R B ^ ^ - ^ ^ ^ T i l ^ - ^ 51
5.4 7f^ l^£ ^ ^ i ^ r ^ ^ l - ^ tflt!: ^ - ^ ^ £ ^ ^ ^ - 54
5.5 LRB o ] ^ ^ - A l ^ 3 . ^ (F102-2) 55
- xin -
1=3} (Seismic Isolation System 3E.Tr- Base Isolation System)^:
LS.*] ZL 7 l ^
]^-1(1992^)^
7\, -5-}
[1].
711 3. 71^-1: ^ ^ ^ ^ Si«Ho> t > ^ ^ ^ 2 ] ^ ] 71 ^
ZL 7l^#
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tb
;*] «y-^.^ ^ ^s\.6\] tfl
LRB(Lead-Rubber Bearing)
lOTon fpS.£] LRB #rfc A] aflfi}- 200Ton ff-S.fi! ^ 1 3.7} $\
-a^l^-a- tal51§>S-^^ LRB
- 2 -
LRB I m
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2.1 LRB
2.
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0)5]]^ 3.711
fe 5- 2.154
2.1
(IRHD + 2)
30
35
40
45
50
55
60
65
70
75
(kgf/cm2)
9.4
12.0
15.3
18.4
22.4
33.1
45.5
59.7
74.9
95.9
(kgf/cm2)
3.1
3.8
4.6
5.5
6.5
8.3
10.8
14.0
17.6
22.6
0.93
0.89
0.85
0.80
0.73
0.64
0.57
0.54
0.53
0.52
(X104 kgf/cm2)
1.02
1.02
1.02
1.02
1.05
1.11
1.17
1.23
1.30
1.36
2 . 2 ^
-8-^°!
200-300%^
700% 3}S.<*H*|
<r G=3.5 kgf/cm2^
-71-
- 4 -
W
300
250
200
150
100
50
0
G=4.5kgf/cm2
G=3.5kgf/cm*
f
//
/
r/
fi 1
/
/
t/
' /
/
200 400 600 800
2.2
(a) 500-7X J4G = 4.5 koiycm2
2.3
350
300
<£ 250
J? 200
150
100
50
I 1 1 1
; i\ /
11
11
•j
0%
II
jIIj
100 % 200 %
1If
0 2 4 6 8 10
' d ^ ^ - r ] (mm)
(b) 500-3.75 X 26 *1 ^ *)1 (Si =33)G = 4.5 kgf/cm2
- 5 -
1*}
2.3^ •%•% 300 kgf/cm2
Si 4- O^*L#6\ 71^-7H
SI4.
SI4-
_ +301 +20 -"S, +10— 0tf - io£ -20
a-100 kgf/cm2
r- = ±200< 3iaT
*-•
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^ - 3 0
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H- - 2 0
* -30
„ -30"e +20 •
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a-rz
= 150 kgf/cm2
= ±200 9£x 3 si
•*•
-300 -200 -100 0 +100 +200 +300(mm)
o = 200kgf/cm2
r == ±200 1%X
* •
3 ®
-300 -200 -100 0' +100 +200 +300(mm)
- 2 0
- 3 0
| +20
~ 0
ts~1 0
ft--20
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_ + 3 0'e +20o
— 0
I f -20
•^-30
G •
r'-= 100 kgf/cm2
= ± . 3 IsJ
— H .—J
i-300 -200 -100 0 +100 +200 +300
£ (mm)
r == 150 kgf/cm2
El
i-—
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•r = 200 kgf/cm2
V=±300.'
. ^ — •
3L
--—
aJ
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. - ^
12
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= J - i -
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^ 2
/cm2
I
-300 -200 -100 0 +100 +200 +300(mm)
ff = 200kgf/c'm2
?="150 kgf
-300 -200 -100 0 +100 +200 +300t- (mm)
500-3.75X26 *G = 3.5 kgf/cm2
S-=iool/cm2
kgf/cm2
-300 -200 -100 0 +100 +200 +300$.¥3:12 (mm)
.=33)
- 6 -
±200% ^
fe ±300%
2.5
50- No. Si
40
g5
30
J2O
33331818
SEE
200 kgf/cm2 45.1 cm"300 37.7200 47.1300 42.2
G= 4.5 kgf /cm2
~D = 50cm52 = 5
K
2.5
- 7 -
- 8 -
000 Z 00SI 0001 OOS
§n|d 4-1 "«
"*. W///X\ i 1
t ///)L///
t wwww• ' !Y///A
%000'l
%00S
Lb
00€
WhST k-ta-|D
fe 1.30.15 kgf/mm2
330 °C
ot
Aflg. nfl
4.
bilinear
^ LRB
2.8)-§- 2.93]- ;y>g. bilinear
J iflcd
1 , •
' '
plug LR13
2.7 LRB^l 7l7lH ^
- 9 -
ffi ffi : 65 kg/cm'&--4.6, 5,-28.8
2.8 LRBSl
- 2 5 0 - 2 0 0 - 1 5 0 - 1 0 0 - 5 0 0 50 100 150 200 250 {%)
- 6 0 - 5 0 - 4 0 - 3 0 - 2 0 - 1 0 0 10 20 30 40 50 60 (cm)
2.9 LRB^ bilinear
- 10 -
KR ^1#^ ^2.10:4 2.11^ zfzj-
ZL^ 2 . 1 2 ^
12.0
§ 7.2
4.8
2.4
i
i i .
1-j- —-
i
£x Alis): :?0l: 2.9 cm
1
0 x 20 cm'
^ S ( g : 36.7 TonB ^ E : 150mm/min
10 15
Stroke (mm)
20
2.10 KR
25
10000
8000
6000
3 4000E75
2000
1/Lod
m^ ."_--5--" V -
< |,M -A3---" :
j ' • -\ f = " } ^ . | i
tv
\
\
\\
10 20 30Displacement (mm)
40
2.11 KR
- 11 -
150
120
o
60
30
II11
[• • •
Y
/r Y = 0
to.8296
5S
38
>
0^
5i
14'
I *
^365S
X
r-
) * X + 79.9 95 57 31 8
50 100 150Shear Strain (%)
200
2.12 KR
: Gr = 7.258 kgf/cm2
= 84.5 kgf/cm2
7y= 7.8%
0 = 1,083.0 kgf/cm2
1 = 58.0 kgf/cm2 (±
- 12 -
LRB ^
lOTon LRB 77h 200Ton LRB 27fl
HSJ 3.1-5 #3: ) . ^ A] ^
3. 3.
3.1
^ ^ / ^ ^ §
(Ao^>-?- plate ^ | ^ )
lOTon LRB
lOTon
150/30mm
154mm
4mmXl4# = 56mm
3mmxl3f = 39mm
030 X 142mm(7.07cm2)
200Ton LRB
200Ton
521/lOOmm
248.5mm
9.5mm X15# = 142.5mm
3mmXl4f = 42mm
0100 x 245mm(78.54cm2)
lOTon
13.71, 3.66A
9.38, 2.6801^, 200Ton LRB^
^ 20-35, ^ 50IAJ-
0}
s-*l lOTon
7.258 kg/cm2, 84.5 kg/cm2
- 13 -
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- 17 -
3.5
- 18 -
LRB ^ A ] - ^ f l 3 H ^ ^ ^ ^ ^ l * ^
>4 ] ^ ] J] l ^^ r ^^1^>ZL lOOTon
actuator 1- ^ 2 l ^ S . 2ifl(^cfl stroke: ±7511101), ^ H M K ^ - S . 1^(^
tfl stroke: ± 125mm)# * l* l^H ^ I M ) ^ ^ U " ^ = ^ - ^ ^ ^ 200Ton
actuator^ r>
roller
actuator5]-
- lOTon LRB^l
200Ton
^}ZL 10%
3.7^ lOTon LRB ^
lOTon LRB A^oflA-] ^ j > ^ ^ ^ ] g ^ ]
^ ^ - ^ ^>^-A]?J o ] x ^ A ^ Z l ^ 3.83lf
200Ton LRB
- 19 -
O
i
I
m Specimen
ffi
Reaction Floor
lOOTonActimtor
Specimen lOOTon Actuator
K.
Inaction Floor
3.6
* • —
(a) LRB
(a) LRB
3.7
- 21 -
£
150
100 -
50 -
0oo. -50to
-100 -
-150
V V V -•' i I i ; 1 M
o
i i ! i I i
I ; ! i
i"l \h\rt\\-i l i r i n i
100 200Time (sec)
\\
i i i i :I-4.
300
40
20 -
0 -o
-20 -
-40
;l :\
;i !
n- ' r - - " I - - } •
ii 1 !
' 1100 200
Time (sec)
r-h
300
3.8 °m X\7J-o]^ ( 7 ^ O.lHzS]
- 22 -
JSSI fl-3 1-21 LRB
5. 3.2 LRB
LRB ^
*™ Kr (tf/cm)
Keq (tf/cm)
«*«
cycled]
cycled
•i- T"0
j
3g 7V * '
i ..±30%
±100%^
r/ ^
# 3cycle
3cycle ^r
i-i: Q^
r
±10%
)
x) ± 20 %
±10%
)
- 23 -
lOTon ^ 200Ton LRB Il tf l^ ^ s g ^ A ^ vf]-§--§: 5. 4.
4 . S 4 H A l ^^ l ^ ( B e a r i n g ID) 101-106^ lOTon LRB
20013zf 2002^ 200Ton LRB1-
^ actuator^ ^^-$\
4.1
LRB
1. 1 ^ l^^ l ^€ ^ ^ ^ 1ZL^ 4.2^A-^«-E] ZL^ 4.6S] o | a ^ A ^ ^ . ^ 7|_^] x l ^ - ^ o.l, 0.5, 0.7,
0.8 3J l.OHzol] t f l^ lOTon LRB^ A] ^ 3 4 0 1 4 . n ^ 4.25.^-^ ^ ^ i g
^ # 200%ofl*\ Z-^&l ^5} -^^° ] ^ ^ ^ ^ yi-ir <£ ^ °M. =L^ 4.7,
4.8 ^ 4.9^
120% OJ
% ^ LRB
ZL ^ ]
- 25 -
4.1
TEST MATRIX FOR KR LEAD RUBBER BEARINGS
Filename
F101-15
F101-16
F102-1
F102-2
F103-1
F103-2
F104-1
F104-2
F105-1
F105-2
F105-3
F105-4
F106-1
F106-2
F2001-1
F2001-2
F2001-3
F2001-4
F2001-5
F2001-6
F2001-7
F2001-8
F2002-6
F2002-7
F2002-8
F2002-9
F2002-10
BearingID
101
102
103
104
105
106
2001
2002
forpndimnary
tests
VerticalLoad(Ton)
10
10
i—i
i—i
o o
10
10
10
10
10
10
10
10
1-1
1-1
o o
0
50
50
100
150
150
200
150
200
150
100
50
0
HorizontalLoading ,
Freq.(Hz)0.1
0.1
0.1
0.1
0.5
0.5
0.5
0.5
1.0
1.0
0.8
0.7
0.7
0.7
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
DurationTime(sec)
285.66
285.79
285.84
285.78
53.94
45.79
45.74
45.83
21.67
29.83
37.25
40.08
40.14
40.62
72.44
63.17
72.17
72.16
40.25
72.18
72.24
72.26
74.06
72.43
72.26
72.48
72.48
Max.Strain
200
200
200
200
150
125
125
125
100
100
100
100
100
100
50
50
50
50
50
50
50
50
50
50
50
50
50
Remarks
Strain: 25, 50, 75, 100, 125, 150, 200%
Strain: 25, 50, 75, 100, 125, 150, 200%
Strain: 25, 50, 75, 100, 125, 150, 200%
Strain: 25, 50, 75, 100, 125, 150, 200%
Strain: 25, 50, 75, 100, 125, (150)%
Strain: 25, 50, 75, 100, 125%
Strain: 25, 50, 75, 100, 125%
Strain: 25, 50, 75, 100, 125%
Strain: 10, 25, 40, 50, 75, 100%
Strain: 10, 25, 40, 50, 75, 100%
Strain: 10, 25, 40, 50, 75, 100%
Strain: 10, 25, 40, 50, 75, 100%
Strain: 10, 25, 40, 50, 75, 100%
Strain: 10, 25, 40, 50, 75, 100%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
Strain: 10, 20, 30, 40, 50%
- 26 -
-20
-80 -60 -40 -20 0 20
Displacement (mm)
(a)F103-2
40 60 80
-20
-80 -60 -40 -20 0 20
Displacement (mm)
(b)F104-2
40 60
4.1 r}€-
80
- 17 -
-30
-120 -80 -40 0 40 80Displacement (mm)
ZL^ 4.2 0.1Hz<*H tflSV ojej^-Al (F102-2)
120
-20
-80 -60 -40 -20 0 20
Displacement (mm)
n e i 4 ^ n 5H7<>I] tfl*V o l s } ^ . ;
40 60 80
(F103-2)
- 28 -
COO
-10
-20
-60 -40 -20 0 20
Displacement (mm)
40
4.4 0.7Hz<>fl (F106-2)
60
-20
-50 -40 -30 - 2 0 - 1 0 0 10 20 30 40 50
Displacement (mm)
4.5 (F105-3)
- 29 -
-20
-40 -30 -20 -10 0 10 20Displacement (mm)
4.6 1.0Hz<H] tflsv ° l ^ < d (F105-2)
30 40
£
0.8 -
0.6 -
> 0.4 -
LJJ
0.2 -
Loading rate
0.1 Hz
0.5Hz
-e 0.7HZ
-& 0.8HZ
-^ i.OHz ;
40I ' I—
80 120
Strain (%)
4.7
O-
160 200
- 30 -
1=
13
UJ
0.4
0.38
0.36
0.34
0.32
0.3
0.28
0.26
0.24
0.22
0.2
Loading rate—-€> 0.1 Hz ,
S 0.5Hz I...0.7Hz |0.8Hz | -1.0Hz |
40 80 120Strain (%)
160 200
4.8
5000
0 20
4.9
40 60 80Displacement (mm)
100 120
- 31 -
37])
2. ^ ^ 1 ^ ^ l l qg ^ £ |ZL^ 4.10^1^-r-Bl ZL^ 4.14^ o ] ^ ^ ^ ^ 2\z\ 200Ton
^ 0, 50, 100, 150
4.15, 4.16 * 4 .17^ AA &^\^Z\ 3.7)o]} cfl*V
^ i ^ o f l M ^ l ^ ^5}-!- £Al«l- ^o]rf.
4.15^- ^ 3 ] * } ^ aL7loil rcfsfA-] LRB l -fi-Jl^^ol 3.7]}
3.711
200Ton
200Ton
- 32 -
TSCOo
150 -
100 -
50 -
n
-50 -
-100 -
-150 -
/• - - £ . - • - • .
< • 1
r m s = ^ —
1
-80 -60 -40 -20 0 20 40
Displacement (mm)
ZL^ 4.10 OTon ll rfl^ ° l ^ * i (F2001-1)
60 80
-80 -60 -40 -20 0 20 40 60 80
Displacement (mm)
4.11 (F2001-3)
- 33 -
-80 -60 -40 -20 0 20 40 60
Displacement (mm)
4.12 100Ton°fl rfl^- o ] e j ^ * | (F2001-4)
80
-80 -60 -40 -20 0 20 40 60
Displacement (mm)
4.13 150Ton°fl tflSV ° l ^ * l (F2001-8)
80
- 34 -
i ' i ' r-80 -60 -40 -20 0 20 40
Displacement (mm)
H ^ 4.14 200Ton<>fl t f l ^ o ] ^ ^ - ^ (F2001-7)
60 80
7 -
6 -
E"
2 5 4
CD4 -
•%. 3 -
2 -
1 -
0 - -
\ \
10
4.15
\ \
Vertical load- O P=0Ton- B -
—e-P=50TonP=100TonP=150TonP=200TonP=200Ton
(Static)
- - B"A-
20 30Strain (%)
40 50
- 35 -
c.
XI
0.7
0.6
0.5 -
0.4 -
•= 0.3 -
0.2 -
0.1 -
0 -
A-
B "
10
4.16
G-:
—©•-
Vertical load— 0 P=O.OTon—E3 P=50Ton •— © P=1OOTon—£s P=150Ton— V P=200Ton
- P=200Ton• (Static) ;
-a1
.-- -£r-.
0-:
-o-
G
-o
20 30Strain (%)
40 50
E
o
(Dc
LU
2 0 0 0 0 - --•
15000 -
10000 -
Vertical load
I—| p—q.OTon
OTon
0 P-1 OOTonasr— P=150TonT-7 P — OOOTon
• . / /
: . . A '
V
o..••'• I D • " " ' " '
• — • ' •
/
V, • /
•' A
O
o
/ jr.
/ / '• • ' /
/
C
y
c
10 20
4.17
30 40 50Displacement (mm)
60 70
- 36 -
71S]
3. ^fl*> A>o]a.6fl Oj-S. S - ^
ZL^ 4.18, 4.19 ^ 4 .20^
o)] 71 Si ^ % ^
7]}
3.2S] LRB ^ ^ ^J7
4.18^1 A ^ B ! zisi 4.207}x] 51 1 ^ 1 - sLig Bt-1^^-^- <y-
- 37 -
Effective stiffness (kN/mm) Effective stiffness (kN/mm) Effective stiffness (kN/mm)
1
OJ0 0
1
u
H-i0 0
=^
-£-Q
fli[U
'
r|iu
4>
—*II
OXN
O
^ O
" '
CDO
ooo
jot
IIo
o oen
ooo
23
eno
00o
oo
—h||
oooXN
Stra:
ZJ
2
MO
O
O)o
ooo
100
OS)
t
•
1
• - -O
3rd cycle I
Loading cycle
Effective stiffness (kN/mm)oin
obo
w
s a i5
till"
rIIo
XN
D)ooO
120160
200
Effective stiffness (kN/mm)
Equivalent Damping (%) Equivalent Damping (%) Equivalent Damping (%)
o ois)
ots)09
oCOfs)
ow
u
VD
—hII
'oXM
trai
-Si
O
-f>-O
o
00
o
dJ|iiSL,
r|fii
J2,
Equivalent Damping (%)
pho
oK)
ofs)00
oCO w
01
IIobo
o
o
00o
oo
IIo
N
Equivalent Damping (%)
co
• • 4 =CDD .
'tr>
5000
4000 -
3000 -
2000 -
£ 1000 -•CDc
ID
EE
o••Z3
COQ .
'co
5
£
co
••oTOQ.
'coto
>0)C
111
1000
800 -
600 -
400
200 -
2000
£
c
1600 -
o 1200 -COQ .
S 800 -
* 400 -
• f
0 20 40 60 80 100 120
Displacement (mm)
(a)f=0.1Hz
Loading cycle
1st cycle
2nd cycle
3rd cycle \
4th cycle
20 40 60
Displacement (mm)
(b)f=0.5Hz
80
IOUU -
1200 -
800 -
400 -
0 -
I
Loading cycle
0 1 st cycle
E 2nd cycle \
0 3rd cycle
& 4th cycle
/
<>/r
1200Loading cycle
1st cycle
2nd cycle
3rd cycle
4th cycle
LU
10 20 30 40
Displacement (mm)
(c)f=0.7Hz
50 10 20 30 40
Displacement (mm)
(d)f=0.8Hz
50
Loading cycle1st cycle
2nd cycle
3rd cycle
4th cycle
10 20 30
Displacement(mm)
(e)f=1.0Hz
4.20 7fl§>
40
- 40 -
l 4.21^^-15] ZL^ 4.26£-
lOTon LRB^l ifl^- i&^i-i: J i < ^ 4 - H ^ 4.21s}- 4.22^
l Al^*> 3 - f o l ^ , H ^ 4.23^r 150%?}*], Z L ^ 4.24
l H ^ 4.254 4.26^r 1 0 0 % ^ l
200%?}*! A ] ^ ^ - ^4-oflfe
^-*1 Bearing ID. 101 ( n ^ 4.21)^1
3.7} tt)]^-o)]
] ^
I"
&t\-. ILZ\E.3.
- 41 -
Beariri : 101
4.21 Bearing ID. 10151
inirJDi.-: 102
• : ' ; j . : ; . . • _ • : : : • , ; _ . ; ; ; ^ ; ; . ; . - : ; . : . ; : . : ; ; - . ; : ; . ; • • . ! -4 i
4.22 Bearing ID. 102^
- 42 -
03
4.23 Bearing ID. 103^
Bearing ID : 104
4.24 Bearing ID. 104S]
- 43 -
4.25 Bearing ID. 1055]
Bearing 113 •: 106
4.26 Bearing ID. 1065]
- 44 -
LRB
LRB ^
^ lOTon LRB
PHIj- 3 #2:) oil
5.1 KR LRB^
25
50
75
100
125
150
200
(mm)
14
28
42
56
70
84
112
(kgf/cm)
618.3
403.7
332.2
296.4
275.0
260.7
194.5
(0)0.31
0.29
0.25
0.21
0.19
0.17
0.17
(kgf • cm)
2,337
5,702
9,067
12,431
15,796
19,160
25,890
2.
5.2«sflA^Jf El &
*> lOTon LRB
1^ AA 0.1, 0.5, 0.7, 0.8, l.OHz
- 45 -
5. 5.2 -£, LRB ^ : O.lHz)
7{%)
24.3
49.3
75.5
100.9
126.4
151.8
200.9
(mm)
13.6
27.6
42.3
56.5
70.8
85.0
112.5
(kgf/cm)
693.4
458.9
346.7
285.5
244.7
224.3
224.3
(/?)
0.33
0.32
0.31
0.31
0.30
0.28
0.24
(kgf • cm)
2,655
6,931
12,083
17,568
22,902
28,578
41,988
S. 5.3 ^ LRB : 0.5Hz)
7 (%) : (mm)
24.1 13.5
48.4 27.1
74.1 . 41.5
98.0 54.9
115 64.4
(kgf/cm)
673.0
520.1
397.7
316.1
285.5
(0)0.33
0.29
0.28
0.26
0.24
(kgf - cm)
2,509
6,936
11,859
15,908
17,971
- 46 -
5.4 ^ L R B m : 0.7Hz)
7{%)
9.3
24.8
40.0
49.5
72.5
86.1
(mm)
5.2
13.9
22.4
27.7
40.6
48.2
(kgf/cm)
907.5
611.8
489.5
458.9
367.1
326.3
(0)0.33
0.32
0.29
0.27
0.27
0.25
(kgf • cm)
524
2,314
4,547
5,904
10,028
11,738
3. 5.5 ^ . LRB : 0.8Hz)
r{%)
9.6
24.6
39.1
48.2
67.7
75.7
(mm)
5.4
13.8
21.9
27.0
37.9
42.4
(kgf/cm)
897.4
652.6
540.4
489.5
407.9
356.9
(/?)
0.31
0.31
0.29
0.27
0.26
0.26
(kgf • cm)
513
2,369
4,727
6,079
9,450
10,320
- 47 -
5.6 ^ LRB : l.OHz)
7{%)
9.8
23.9
37.3
45.7
61.6
(mm)
5.5
13.4
20.9
25.6
34.5
(kgf/cm)
897.4
652.6
550.6
489.5
397.7
(/?)
0.29
0.30
0.29
0.28
0.26
(kgf • cm)
497
2,231
4,364
5,529
7,682
LRB
S.
lOTon L R B ^
71- 1 0.1Hzofl
^ s . 3.2*11 >M
±20%
- 48 -
3. 5.7 -fi-xd1(%r
25
50
75
100
125
150
200
KR
618.3
403.7
332.2
296.4
275.0
260.7
194.5
673.4
426.8
345.2
302.6
276.0
257.6
233.4
(Constantinou)
673.0
458.5
386.9
351.2
329.7
315.4
297.5
(O.lHz)
693.4
458.9
346.7
285.5
244.7
224.3
224.3
o
4
in
700
600 -
500
jg 400
> 300+
200 -
100
>\
\
- c
—e—KRA Japan
—B—U.S.A.• Test
-©—• - -
- B -
- >> i
40 80 120
Strain (%)160 200
5.1
- 49 -
S. 5.8 «
25
50
75
100
125
150
200
KR
0.31
0.29
0.25
0.21
0.19
0.17
0.17
(4«)0.26
0.27
0.24
0.21
0.19
0.17
0.14
(Constantinou)
0.28
0.25
0.21
0.18
0.16
0.14
0.11
(O.lHz)
0.33
0.32
0.31
0.31
0.30
0.28
0.24
0.35
0.0580 120Strain (%)
160 200
5.2
- 50 -
5.8*1-
0^4. o] ^ - fo l l fe
14
bilinear
<c> lead-mbber combination
(b) rubber bearing only
5.3 o ] ^ - ^ . ^ LRB5]
- 51 -
5.3(a)
LRB
± (5.1)
( s - 3 )
9]
(5.4))
(5.5)-(5.7)21-
GrA
(5-5)
Ku= Kr\\
aGjGjGr
a GJGr
Qd= a, t
- 52 -
(5.4) ~ (5.7) ofl ^ A A
0.02-0.09^
Kd=Kr, #
= 10
169.65 cm2, A , = 7.07 cm2, <ry = 84.5 kgf/cm2, y y = 7 . 8 %
7.258 kgf/cm2, Go = 1,083.0 kgf/cm2, d = 58.0 kgf/cm2
^ 1 - ^ : (5.4) ~ (5.7) ofl
bilinear S.^Si\ ^ 7 } ^--^r
^ = 2 1 9 . 9 kgf/cm
^ = 1 , 5 8 8 . 1 kgf/cm
Qd= 597.4 kgf
^-^^^(character is t ic strength)
- 53 -
to
e3
(J
1000
800
600
400
200
0
-B -O.lHz0.5Hz
e 0.7Hz& 0.8Hzv l .uriz
50 100
Strain (%)
150 200
5.4
F102-2O1]
bilinear
^ bilinear
bilinear S c i
(b)),
(c))
bilinear
Bilinear LRB^ -^ ^ q (5.8)^ (5.9)^]
- 54 -
-20-60 -40 -20 0 20 40 60
Displacement (mm)
o-J
zu
10 -
-10 -
-20 -
.....J-rrtl.
1—<—i—•—i—•— — • — i — • — i — • —
(b)
-60 -40 -20 0 20 40 60Displacement (mm)
bilinear E
(c)
-60 -40 -20 0 20 40 60Displacement (mm)
bilinear
5.5 LRB (F102-2)
- 55 -
Krff =
h —
D
2 xKeffD2
bilinear
5 . 9 ^
^. 27%,
5.9 Bilinear LRB
(5.8)
(5.9)
(kgf/cm) Bilinear
Bilinear
25%
693.4
787.9
0.33
0.32
50%
458.9
503.9
0.32
0.30
75%
346.7
409.2
0.31
0.26
100%
285.5
361.9
0.31
0.23
- 56 -
a l l -
bilinear . =LB\JL
ifl-g-i-
1.
c-1 3.711
7)°]
o]
2.
A]
- 57 -
3.
3.
bilinear 3 . ^
^. bilinear
- Bilinear
- 58 -
- , 1992.1. M ^ M ^ R I I f a d l ) , ±fW^g2. 0*^^^5 i^# , %mmfw=j^An, *-^KL, 1997.
3. P.K. Freakley and A.R. Payne, Theory and Practice of Engineenng
with Rubber, Applied Science Publishers Ltd., London, p.117, 1978.
4. 0*&«#fi£i&#, &mmffiAn, ^-Att, 1995.
fe 1-21,5. JSSI &
1997.
6. I.G. Buckle, "Factors Affecting the Performance of Lead-Rubber
Energy Dissipators" , RRU Bulletin, New Zealand National Roads
Board, 157-170, 1984.
7. F. Naeim and J.M. Kelly, Design of Seismic Isolated Structures. From
Theory to Practice, John Wiley & Sons, Inc., New York, 1999.
- 59 -
1 LRB ^ S S E W S
Bearing ID : 101Vertical force : lOTon
Excitation Frequency : O.lHzData File Name : F101-16
( £ 3 : kN,mm)
7
Cycle
*«max
y
V-^ nun
Qd
Qy
Keff
Heg
WD
±25%
1
5.25
-5.00
13.82
-13.30
2.54
0.06
0.38
0.28
122.7
2
5.75
-5.36
13.90
-13.07
2.77
0.06
0.41
0.26
122.4
3
5.84
-5.52
14.16
-13.15
2.70
0.06
0.42
0.25
123.8
4
5.69
-5.62
14.05
-12.98
2.71
0.06
0.42
0.25
119.9
±50%
1
7.97
-7.17
27.78
-27.55
3.63
0.06
0.27
0.26
344.8
2
7.95
-7.48
27.95
-27.73
3.79
0.06
0.28
0.26
349.2
3
7.71
-7.38
27.79
-27.45
3.80
0.06
o:n
0.26
345.2
4
7.85
-7.72
27.89
-27.49
3.75
0.06
0.28
0.26
345.1
±75%
1
9.51
-10.38
42.09
-42.21
4.09
0.06
0.24
0.25
649.3
2
9.24
-10.20
41.78
-42.24
4.28
0.06
0.23
0.25
631.7
3
9.27
-9.87
42.07
-42.07
4.22
0.06
0.23
0.25
622.6
4
9.37
-10.24
41.79
-42.20
4.22
0.06
0.23
0.24
615.2
±100%
1
11.86
-12.62
56.73
-56.66
4.47
0.06
0.22
0.22
955.5
2
11.51
-12.28
56.64
-56.60
4.57
0.06
0.21
0.22
934.8
3
11.50
-12.32
56.39
-56.40
4.53
0.06
0.21
0.22
928.5
4
11.77
-12.29
56.33
-56.23
4.51
0.06
0.21
0.22
931.5
7 : Shear strain (%)
Qmax, Qmin : Maximum/ Minimum Shear Force (kN)
Xn,ax, Xmin : Max./Min. Horizontal Displacement (mm)
Qd : Characteristic Strength (kN)
Qy : Yield Force (kN)
Keff : Effective Stiffness (kN/mm) = K^Heq : Equivalent Viscous Damping Ratio (%)
WD : Energy Dissipation per Cycle (kN-mm) = A W
- 61 -
7
Cycle
©max
** min
y- ^ max
- ^ min
Q<
Qy
K,ff
wD
Bearing ID : 101Vertical force : lOTon
Excitation Frequency : O.lHzData File Name : F101-16
±125%
1
12.68
-13.61
71.07
71.00
4.80
0.06
0.19
0.22
1,302.0
2
12.23
-13.61
70.86
-70.85
4.92
0.06
0.18
0.22
1.281.9
3
12.31
-13.36
70.93
-70.81
4.88
0.06
0.18
0.22
1.257.6
4
12.60
-13.42
70.82
-70.58
4.85
0.06
0.18
0.22
1.274.4
±150%
1
14.01
-15.79
84.91
-85.76
5.08
0.06
0.18
0.22
1.726.8
2
14.02
-15.90
85.11
-85.85
5.21
0.06
0.18
0.21
1.703.6
3
13.82
-15.63
84.91
-85.63
5.24
0.06
0.17
0.22
1,694.8
4
13.75
-15.60
84.71
-85.22
5.22
0.06
0.17
0.22
1.693.1
(<C\Sf\ : kN,mm)
±200%
1
19.48
-21.65
112.70
-113.33
5.67
0.06
0.18
0.20
2,853.0
2
19.00
-21.30
112.67
-113.17
6.04
0.06
0.18
0.19
2.764.0
3
18.79
-20.84
112.80
-113.10
5.88
0.06
0.18
0.20
2,775.5
4
18.12
-19.93
111.72
-112.50
9.96
0.06
0.17
0.20
2.708.6
- 62 -
Bearing ID : 102Vertical Force : lOTon
Excitation Frequency : O.lHzData File Name : F102-2
( ^ : kN,mm)
7
Cycle
4? min
-^•max
y•^- min
Qd
Qy
wD
±25%
1
7.32
-8.99
13.98
-13.84
4.45
0.06
0.59
0.36
259.4
2
8.48
-9.31
13.98
-13.98
5.55
0.06
0.64
0.34
266.7
3
9.09
-9.44
13.78
-13.46
5.37
0.06
0.68
0.33
260.4
4
8.82
-9.61
14.22
-13.83
5.35
0.06
0.66
0.32
259.6
±50%
1
12.32
-13.16
27.86
-27.61
6.52
0.06
0.46
0.32
713.0
2
11.95
-13.28
27.70
-27.47
6.50
0.06
0.46
0.31
672.8
3
12.16
-12.68
27.87
-27.46
6.51
0.06
0.45
0.32
679.7
4
12.09
-12.79
27.93
-27.56
6.54
0.06
0.45
0.31
6701
±75%
1
14.46
-15.19
42.41
-42.19
7.20
0.06
0.35
0.31
1,217.2
2
13.41
-15.14
42.53
-42.19
7.22
0.06
0.34
0.31
1,183.5
3
13.63
-14.78
42.57
-42.15
7.20
0.06
0.34
0.31
1,184.9
4
13.56
-14.76
42.46
-42.01
7.29
0.06
0.34
0.32
1,183.3
±100%
i
15.46
-16.48
56.87
56.09
7.73
0.0(5
0.28
0.31
1,742.9
2 3
14.96 15.03
-15.97 i -16.00
56.841 56.761
-56.16: -56.08
7.79J 7.80
0.06: 0.06
0.27 0.28
0.31 i 0.31
1,717.1 i 1.722.8
4
14.64
-15.95
56.46
-55.67
7.83
0.06
0.27
0.32
1,700.1
7
Cycle
Qmax
Qnin
y-"-max
-"• min
Qd
Qy
Keff
Heg
wD
±125%
1
17.38
-17.73
71.44
-70.15
7.99
0.06
0.25
0.30
2.314.8
2
16.32
-17.41
71.57
-70.07
8.08
0.06
0.24
0.30
2,273.7
3
16.41
-17.56
71.58
-70.10
8.08
0.0(5
0.24
0.30
2.245.9
4
16.35
-17.46
71.09
-69.98
8.09
0.06
0.24
0.30
2.235.8
±150%
1
18.89
-19.82
86.17
-84.34
8.28
0.06
0.23
0.28
2.897.8
2
18.41
-19.25
86.20
-84.28
8.33
0.06
0.22
0.28
2.830.3
3
18.50
-19.03
86.01
-83.98
8.29
0.06
0.22
0.28
2,802.5
4
18.28
-18.77
85.59
-83.55
8.28
0.06
0.22
0.28
2,771.2
±200%
1
25.10
-25.40
113.58
-112.03
8.49
0.06
0.22
0.24
4,317.3
2
24.08
-24.86
113.40
-111.93
8.60
0.06
0.22
0.24
4,166.5
3 4
24.12; 22.89
-24.21 j -23.22
113.45 j 112.67
-111.60! -110.87
8.55] 7.12
0.06 0.06
0.22' 0.21
0.24; 0.25
4,117.6i 4.022.1
- 63 -
Bearing ID : 103Vertical Force : lOTon
Excitation Frequency : 0.5HzData File Name : F103-2
(#•$ : kN,mm)
7
Cycle
Wmax
** min
-y-**• max
y- ^ min
Qy
Keff
WD
±25%(24%)
1
5.97
-9.16
13.12
-13.45
3.13
0.06
0.57
0.34
214.7
2
7.84
-9.04
13.28
-13.56
5.14
0.06
0.63
0.34
242.6
3
8.25
-9.57
13.36
-13.55
5.25
0.06
0.66
0.33
246.0
4
8.47
-9.52
13.17
-13.46
5.37
0.0(5
0.68
0.32
240.8
±50%(48%) ;i ±75%(73%)
1
12.97
-14.74
26.99
-27.50
6.41
0.06
0.51
0.30
719.4
2
13.64
-14.52
26.86
-27.77
6.68
0.06
0.52
0.29
704.1
3
13.87
-13.95
26.67
-27.54
6.46
0.06
0.51
0.29
680.2
4
13.44
-13.72
26.83
-27.53
6.41
0.06
0.50
0.29
667.8
1
15.94
-17.78
40.43
-42.14
6.72
0.06
0.41
0.28
1.214.4
2
15.83
-17.00
40.50
-42.36
7.00
0.06
0.40
0.28
1,196.6
3
15.24
-16.69
40.66
-42.38
6.73
0.06
0.39
0.28
1.163.0
4
14.80
-16.08
40.50
-42.29
6.75
0.06
0.37
0.28
1,132.9
rCycle
** max
**min
y-™* max
y-^- min
Qd
Qy
Kg//
Hm
wD
±100%(98%)
1
17.79
-18.93
54.71
-55.24
6.80
0.06
0.33
0.26
1.641.8
2
16.97
-18.08
54.59
-55.11
6.90
0.06
0.32
0.26
1.582.0
3
16.44
-17.82
54.64
-55.24
6.83
0.06
0.31
0.26
1.560.0
4
16.43
-17.63
55.02
-55.63
6.90
0.06
0.31
0.26
1,545.5
±125%(121%)
1
18.86
-19.63
67.70
-64.02
6.70
0.06
0.29
! 0.24
1.902.1
2
17.76
-18.90
65.66
-63.70
6.156
0.06
0.28
0.24
1,814.8
3
17.61
-18.55
65.28
-63.55
6.38
0.06
0.28
0.24
1.762.4
4
17.38
-18.38
65.49
-63.57
5.74
0.06
0.28
0.24
1.725.7
- 64 -
7
Cycle
Qmax
^< min
V•**• m a x
V-"- min
0,
Bearing ID : 104Vertical Force : lOTon
Excitation Frequency : 0.5HzData File Name : F104-2
±25%(24%)
1
7.22
-8.58
13.17
-13.67
4.28
0.06
0.59
0.35
229.8
2
8.63
-8.90
13.19
-13.77
5.17
0.06
0.65
0.33
244.4
3
8.32
-8.84
13.10
-13.62
5.18
0.06
0.64
0.34
244.3
4
8.47
-9.42
13.22
-13.72
5.40
0.06
0.66
0.32
242.0
±50% (49%)
1
12.32
-14.50
27.33
-26.99
6.12
0.06
0.49
0.31
700.8
2
12.74
-14.66
27.34
-27.18
6.39
0.06
0.50
0.29
684.1
3
13.29
-15.11
27.49
-27.20
6.21
0.06
0.52
0.28
681.1
4
12.91
-14.51
27.50
-27.21
6.23
0.06
0.50
0.28
657.8
;-r| : kN,mm)
±75%(74%)
1
16.72
-18.10
41.27
-41.29
6.52
0.06
0.42
0.27
1,203.8
2
15.64
-16.54
41.43
-41.42
6.48
0.06
0.39
0.28
1,155.9
3
15.34
-16.45
41.23
-41.42
6.26
0.06
0.39
0.27
1.116.8
4
15.08
-16.74
41.52
-41.66
6.62
0.06
0.38
0.27
1,114.0
7
Cycle
Q max
*« min
-y-"• max
•"• min
Qd
Qy
Keff
WD
±100%(100%)
1
17.78
-18.89
55.72
-55.17
6.64
0.06
0.33
0.25
1.621.8
2
16.82
-18.45
55.54
-54.73
6.76
0.06
0.32
0.256
1,565.4
3
16.38
-18.35
55.53
-55.00
6.62
0.06
0.31
0.25
1.525.2
4
16.36
-17.98
55.83
-55.49
6.62
0.06
0.31
0.25
1,504.8
± 125%(124%)
1
19.60
-20.67
69.18
-65.16
6.67
0.06
0.30
0.22
1.903.9
2
18.30
-20.09
67.71
-65.46
6.36
0.06
0.29
0.23
1,835.1
3
18.12
-19.57
67.60
-65.23
6.09
0.06
0.28
0.23
1,779.4
4
17.84
-19.36
67.79
-65.21
5.48
0.06
0.28
0.22
1,731.8
- 65 -
7
Cycle
Wmax
Qmin
y•**- max
•A- min
Qd
Qy
K,f,
Hm
WD
Bearing ID : 105Vertical Force : lOTon
Excitation Frequency : l.OHzData File Name : F105-2
±10%
1
4.18
-3.94
5.17
-5.53
2.41
0.06
0.76
0.34
45.7
2
4.62
-3.82
5.15
-5.23
2.82
0.06
0.81
0.31
42.2
3
5.02
-4.59
5.38
-5.59
2.93
0.0(5
0.88
0.29
48.7
4
5.20
-4.44
5.54
-5.34
3.22
0.0(5
0.89
0.32
53.2
±25%(24%)
1
8.14
-8.22
13.03
-13.50
4.33
0.06
0.62
0.32
220.3
2
9.31
-8.07
13.47
-13.73
4.80
0.06
0.64
0.31
Z26.5
3
9.39
-7.73
13.44
-13.45
4.77
0.06
0.(54
0.30
218.8
4
9.48
-7.94
13.55
13.60
4.74
0.06
0.64
0.31
226.8
-$\ : kN,mm)
±40% (39%)
1
11.58
-11.17
21.56
-20.89
5.16
0.0(5
0.54
0.30
454.4
2
11.57
-11.10
20.98
-20.80
5.54
0.06
0.54
0.30
438.2
3 4
11.56 11.39
-10.92| -11.16
21.02
-20.77
5.50
0.0(5
0.54
21.34
-20.98
5.39
0.0(5
0.53
i
0.29 0.29
428.0 434.9
7
Cycle
Qimx
Qmin
y•<*• max
y-^- min
Qd
Qy
Keff
Hpq
wD
±50% (47%)
1
12.78
-12.54
26.3(5
-24.94
5.39
0.06
0.49
0.28
573.6
2
12.35
-12.27
25.70
-25.27
5.36
0.06
0.48
0.28
549.2
3
12.29
-12.08
25.91
-25.35
5.30
0.06
0.48
0.28
542.2
4
12.25
-12.31
26.47
25.81
5.33
0.06
0.47
0.27
538.8
±75%(72%)
1
15.43
-13.22
40.45
-32.15
4.90
0.06
0.40
0.26
833.7
2
13.51
-12.97
36.79
-33.13
5.19
0.06
0.38
0.27
783.5
3
13.51
-13.03
36.02
-32.91
4.89
0.06
0.39
0.26
753.3
4
13.42
-12.91
36.23
-33.01
4.94
0.06
0.38
0.26
731.4
- 66 -
Bearing ID : 105Vertical Force : lOTon
Excitation Frequency : 0.8HzData File Name : F105-3
( £ 3 : kN,mm)
7
Cycle
y•**- max
Y"-**• min
Qd
Qy
K-eff
WD
±10%
1
4.10
-4.12
5.34
-5.80
1.68
0.06
0.74
0.36
52.2
2
4.46
-4.19
5.11
-5.55
3.11
0.06
0.81
0.34
49.4
3
4.68
-4.86
5.13
-5.69
3.15
0.06
0.88
0.31
50.3
4
5.24
-4.99
5.31
-5.84
3.51
0.06
0.5)2
0.31
56.2
±25%(24%)
1
8.57
-8.30
13.58
-13.92
4.59
0.06
0.61
0.32
232.5
2
9.03
-8.21
13.42
-13.94
4.78
0.06
0.63
0.30
224.2
3
9.25
-8.31
13.68
-13.83
4.76
0.06
0.64
0.31
232.3
4
9.12
-8.54
13.62
-14.12
4.81
0.06
0.64
0.30
229.4
±40%
1
11.95
-11.80
22.10
-21.76
5.37
0.06
0.54
0.29
466.7
2
12.18
-11.25
21.98
-21.82
5.68
0.06
0.54
0.29
469.7
3
11.87
-11.26
22.07
-21.74
5.62
0.06
0.53
0.29
463.6
4
12.10
-11.76
22.28
-22.05
5.79
0.06
0.54
0.27
445.2
rCycle
** max
*Kmin
Y- ^ max
Y•"• min
Qd
Qy
K,ff
wD
±50%(49%)
1
12.57
-13.11
27.40
-26.42
5.90
0.06
0.48
0.28
612.5
2
13.16
-13.20
27.41
-26.61
5.59
0.06
0.49
0.27
603.4
3
12.98
-12.83
27.32
-26.72
5.53
0.06
0.48
0.27
596.1
4
13.16
-12.83
27.59
-26.87
5.92
0.06
0.48
0.26
581.8
±75%(72%)
1
17.33
-16.76
40.47
-36.89
6.01
0.06
0.44
0.24
1.010.4
2
15.14
-15.76
38.70
-37.18
5.68
0.06
0.41
0.26
943.7
3
14.98
-15.18
38.43
-37.35
5.56
0.06
0.40
0.26
926.7
4
14.70
-14.92
38.74
-37.56
5.57
0.06
0.39
0.26
915.3
±100%(88%)
1
18.01
-16.02
49.25
-40.84
5.56
0.06
0.38
0.24
1,167.9
2
15.66
-15.13
44.29
-41.02
5.54
0.06
0.36
0.25
1,037.6
3
14.60
-14.76
44.03
-40.84
5.20
0.06
0.35
0.26
1,012.0
4
14.61
-14.97
43.97
-40.90
4.30
0.06
0.35
0.25
976.1
- 67 -
7
Cycle
Qmax
Wmin
- ^ max
y•**• m i n
Qd
Qy
K«
wD
Bearing ID : 106Vertical Force : lOTon
Excitation Frequency : 0.7HzData File Name : F106-2
±10%
1 '• 2
3.58: 4.39
-4.28; -4.32
5.141 5.39
-5.22; -5.04
1.75 2.97
0.06: 0.06
0.76: 0.84
0.37 0.32
47.2 45.0
3
4.46
-4.88
5.38
-5.09
2.98
0.06
0.89
0.33
51.4
4
4.35
-4.84
5.23
-5.37
3.09
0.06
0.86
0.32
49.7
±25%
1
7.61
-7.85
14.10
-13.80
4.21
0.06
0.55
0.33
223.1
2
8.25
-8.48
14.13
-13.81
4.69
0.06
0.60
0.32
231.0
3
8.39
-8.14
14.12
-13.63
4.72
0.06
0.60
0.32
226.9
4
8.16
-8.62
14.07
-13.90
4.80
0.06
0.60
0.31
229.3
«c1% : kN,mm)
±40%
1
10.62
-12.19
22.39
-22.25
5.48
0.06
0.51
0.30
476.2
2
11.04
-11.73
22.43
-22.33
5.60
0.06
0.51
0.29
465.1
3
10.65
-11.01
22.44
-22.39
5.39
0.06
0.48
0.29
445.9
4
10.31
-11.54
22.25
-22.44
5.35
0.06
0.49
0.29
444.2
7
Cycle
*«max
*v min
y-^- max
y- ^ min
Qd
Qy
Keff
H-eq
wD
±50%
1 2
12.32 11.46
-13.15 -12.50
27.95 27.72
-27.52: -27.41
5.45 5.29
0.06 0.06
0.-16 0.44
0.27 0.29
606.8 592.0
3
12.11
-12.65
27.1*4
-27.62
5.19
0.06
0.45
0.27
579.0
4
11.93
-13.10
27.96
-27.64
5.29
0.06
0.45
0.27
580.4
±75%(74%)
1
14.87
-15.88
41.44
-39.68
5.26
0.06
0.38
0.26
1,014.9
2
13.71
-15.52
40.75
-39.84
5.37
0.06
0.36
0.27
979.7
3
13.51
-15.42
40.91
-40.22
5.66
0.06
0.36
0.27
983.4
4
13.90
-15.44
41.52
-40.86
5.91
0.06
0.36
0.26
972.7
±100%(96%)
1
17.59
-16.69
53.73
-46.92
5.92
0.06
0.34
0.24
1,298.5
2
15.14
-16.64
49.63
-46.81
5.48
0.06
0.33
0.25
1,190.5
3 4
14.37| 14.23
-16.32: -15.92
49.44: 49.40
-46.90; -46.88
4.76J 5.28
0.06 i 0.06
0.32 0.31
0.25; 0.24
1,151.1 1.110.0
- 68 -
Bearing ID : 2001Vertical Force : OTon
Excitation Frequency : 0.3HzData File Name : F2001-1
(£^:kN,mm)
7
Cycle
«tfmax
** min
y•"• max
•X- min
Qj
Qy
Keff
wD
±10%(9%)
1
12.96
-36.70
12.12
-14.87
7.90
0.68
1.84
0.14
289.6
2
15.85
-32.97
12.40
-14.28
6.99
0.68
1.83
0.14
277.6
3
15.16
-29.63
12.10
-13.85
6.79
0.68
1.73
0.14
258.4
4
16.66
-29.97
12.84
-14.09
7.00
0.68
1.73
0.14
271.5
±20%(18%)
1
41.80
-64.60
26.30
-28.91
10.52
0.68
1.93
0.15
1.391.9
2
41.82
-62.74
25.35
-29.21
10.85
0.68
1.92
0.14
1,289.1
3
39.28
-59.34
24.82
-28.29
9.85
0.68
1.86
0.14
1.137.8
4
39.91
-57.56
25.63
-27.81
9.98
0.68
1.82
0.14
1,114.1
±30%(27%)
1
62.85
-83.79
38.40
-42.24
12.59
0.68
1.82
0.14
2,589.6
2
62.42
-82.39
37.88
-42.51
13.47
0.68
1.80
0.14
2,499.3
3
61.66
-80.13
38.08
-42.00
13.18
0.68
1.77
0.13
2,357.7
4
58.82
-78.45
37.29
-41.83
12.81
0.68
1.74
0.13
2.253.7
7
Cycle
*«mMx
Qmin
y-^- max
Y- ^ min
Qd
Qy
Keff
WD
1
82.55
-101.25
52.21
-56.29
14.75
0.68
1.69
0.14
4.324.6
±40%(37%)
2 3
79.481 76.35
-98.01J -92.56
51.471 50.80
i
-56.89J -54.88
17.04J 15.40
0.68) 0.68i
1.641 1.60
0.14| 0.13
4.091.4 3.684.9
4
73.92
-92.72:
50.70
-55.30
15.07
0.68
1.57
0.13
3.580.3
1
96.67
-115.71
64.83
-69.31
17.20
0.68
1.58
0.13
5,759.8
±50%(46%)
2
92.95
-110.22
65.22
-69.00
18.27
0.68
1.51
0.13
5,589.9
3
90.70
-106.77
65.12
-68.63
17.27
0.68
1.48
0.13
5,353.5
4
86.95
-106.59
63.90
-69.05
16.43
0.68
1.46
0.13
5,150.5
- 69 -
Bearing ID : 2001Vertical Force : 50Ton
Excitation Frequency : 0.3HzData File Name : F2001-3
(t^:kN,mm)
7
Cycle
Wrrmx
Wmin
y-<*• max
y
Qd
Q>
KPff
Hpq
wD
±10%
1
53.95
-45.15
12.90
-13.82
17.07
0.68
3.71
0.22
893.6
2
55.18
-45.20
13.56
-13.07
14.58
0.68
3.77
0.19
815.4
3
53.25
-45.57
13.31
-13.31
13.07
0.68
3.71
0.18
738.6
4
54.00
-44.90
13.58
-13.04
12.71
0.68
3.72
0.17
714.1
±20%
1
73.390
-74.89
27.45
-27.28
22.33
0.68
2.71
0.21
2.677.6
2
77.16
-76.27
27.54
-27.66
25.92
0.68
2.78
0.21
2.837.0
3
77.96
-73.79
27.92
-26.85
24.63
0.68
2.77
0.21
2.673.2
4
77.71
-75.00
28.00
-27.27
23.87
0.68
2.76
0.20
2,637.6
±30%(29%)
1
100.49
-102.81
41.95
-41.47
31.55
0.68
2.44
0.20
5,443.1
2 3
102.17 102.93
i
-103.78 -103.23
41.19
-41.47
37.59
0.68
2.49
0.21
5.610.3
41.59
-41.62
36.57
0.68
2.48
0.21
5.553.1
4
102.80
-102.29
41.40
-41.32
36.29
0.68
2.48
0.20
5.397.5
7
Cycle
** max
MC min
v-**- max
y•**• min
Qd
Q,
Ke/f
Hai
WD
±40%(38%)
1
120.97
-125.57
54.48
-56.28
43.23
0.68
2.23
0.21
8.798.2
2
122.67
-126.37
54.68
-56.39
46.91
0.68
2.24
0.21
8.934.9
3
120.56
-125.36
54.02
-56.14
45.44
0.68
2.23
0.21
8.732.0
4
120.75
-123.52
54.19
-55.50
45.13
0.68
2.23
0.20
8,563.0
±50%(49%)
1
138.49
-148.77
69.14
-69.03
51.83
0.68
2.08
0.21
12.835.6
2
138.22
-144.47
68.90
-69.50
52.29
0.68
2.04
0.21
12,807 1
3
137.89
-146.15
69.05
-69.65
53.25
0.68
2.05
0.20
12.641.1
4
135.26
-146.03
68.38
-69.26
51.96
0.68
2.04
0.20
12.355.7
- 70 -
Bearing ID : 2001Vertical Force : lOOTon
Excitation Frequency : 0.3HzData File Name : F2001-4
(#-sH:kN,mm)
7
Cycle
"« max
M; min
- ^ m a x
y- " • min
0,
-KW
Hm
WD
±10%
1
75.35
-60.74
13.34
-13.49
35.89
0.68
5.07
0.30
1.705.2
75.74
-62.00
13.12
-13.71
32.42
0.68
5.13
0.27
1,584.3
3
76.22
-62.83
12.87
-13.61
30.75
0.68
5.25
0.26
1.528.9
4
79.20
-62.83
13.56
-13.48
30.69
0.68
5.25
0.26
1.560.4
±20%(19%)
1
89.34
-87.86
27.26
-28.26
48.49
0.68
3.19
0.30
4.623.6
2
90.72
-86.03
26.44
-27.52
46.57
0.68
3.28
0.30
4,432.7
3
93.69
-87.62
27.00
-27.68
45.10
0.68
3.32
0.28
4,409.1
4
93.13
-86.97
26.74
-27.21
44.74
0.68
3.34
0.28
4,296.8
±30%(29%)
1
122.45
-114.91
41.14
-41.68
56.02
0.68
2.87
0.27
8,344.6
2
120.19
-115.80
40.37
-42.29
58.19
0.68
2.86
0.27
8,311.7
3
120.39
-113.37
40.37
-41.57
57.57
0.68
2.85
0.27
8.155.7
4
121.13
-114.94
40.77
-41.77
56.72
0.68
2.86
0.27
8.139.3
7
Cycle
©max
-"• max
y-"• min
Qy
Keff
wD
±40%(39%)
1
144.49
-136.86
55.15
-56.25
65.12
0.68
2.53
0.26
12.876.5
2
138.24
-135.43
54.52
-56.33
65.01
0.68
2.47
0.27
12.602.4
o
136.90
-132.57
54.31
-55.82
63.73
0.68
2.45
0.26
12.316.5
4
135.90
-130.34
54.79
-55.56
63.03
0.68
2.41
0.27
12.225.7
±50%(49%)
1
155.17
-147.25
70.33
69.83
67.86
0.68
2.16
0.27
17.627.1
2
150.99
-140.90
70.20
-69.61
66.52
0.68
2.09
0.27
17,249.0
3
148.19
-137.79
70.13
-69.19
65.35
0.68
2.05
0.27
16,950.7
4
145.96
-137.16
70.37
-69.50
64.69
0.68
2.02
0.27
16,739.7
- 71 -
Bearing ID : 2001Vertical Force : 200Ton
Excitation Frequency : 0.3HzData File Name : F2001-7
(cV^:kN/mm)
7
Cycle
*« max
** min
V"-<*• max
y- " • min
Qd
Q,
KPff
wD
±10%
1
95.01
-53.65
13.56
-12.67
64.51
0.68
5.67
0.47
2.862.3
2
103.62
-57.42
13.57
-12.48
66.31
0.68
6.18
0.47
3,088.6
3
105.40
-60.03
13.50
-12.56
66.39
0.68
6.35
0.45
3.0(58.9
4
107.65
-61.84
13.89
-12.78
66.31
0.68
6.36
0.44
3.107.3
±20%(19%)
1
128.93
-93.40
27.44
-25.87
75.28
0.68
4.17
0.42
7.779.4
2
134.83
-100.23
27.50
-26.74
80.78
0.68
4.34
0.40
7,953.2
3
138.26
-100.52
27.37
-26.48
81.12
0.68
4.43
0.39
7,890.5
4
138.70
-102.02
27.37
-26.61
80.78
0.68
4.46
0.38
7,828.7
±30% (29%)
1
157.12
-124.76
41.60
-41.01
86.95
0.68
3.41
0.37
13,664.5
2
147.11
-108.41
40.82
-40.39
87.88
0.68
3.15
0.41
13.284.6
3
141.27
-104.81
40.60
-40.52
86.42
0.68
3.03
0.42
13,051.9
4
138.37
-108.69
40.84
-41.01
85.64
0.68
3.02
0.41
13,042.5
7
Cycle
** min
y•S*~ m a x
y-^~ min
Qd
Qs
Keff
H-eq
wD
±40%(39%)
1
147.44
-133.09
55.09
-55.03
88.90
0.68
2.55
0.39
19.001.4
2
145.56
-116.57
55.03
-54.61
88.85
0.68
2.39
0.41
18.576.6
3
144.15
-117.27
55.18
-55.09
87.83
0.68
2.37
0.41
18.421.1
4
140.01
-115.37
54.52
-54.56
87.29
0.68
2.34
0.41
18.005.9
±50%
1
168.37
-141.39
70.52
-68.67
89.60
0.68
2.23
0.36
24.553.4
2
156.78
-130.24
70.78
-68.86
88.96
0.68
2.06
0.38
23,983.5
3
152.24
-126.38
70.31
-68.43
87.59
0.68
2.01
0.39
23,502.1
4
147.43
-126.73
70.01
-68.89
86.58
0.68
1.97
0.39
23,167.0
- 72 -
Bearing ID : 2001Vertical Force : 150Ton
Excitation Frequency : 0.3HzData File Name : F2001-8
(t^:kN,mm)
7
Cycle
** max
** min
- ^ m a x
-"• min
Qd
Q,
Keff
wD
±10%(9%)
1
98.13
-59.32
12.33
-13.09
55.08
0.68
6.19
0.38
2.364.7
2
110.81
-62.21
12.35
-12.86
53.60
0.68
6.87
0.36
2,455.7
3
114.47
-6751
12.54
-13.13
53.15
0.68
7.09
0.34
2.469.0
4
116.03
-66.73
12.58
-12.59
53.08
0.S8
7.26
0.33
2,415.1
±20%(19%)
1
127.64
-99.95
26.35
-27.21
64.64
0.68
4.25
0.34
6,536.5
2
128.15
-103.ES
26.18
-26.87
66.67
0.68
4.38
0.33
6,442.8
3
127.24
-110.11
26.16
-27.07
65.79
0.68
4.46
0.32
6,411.1
4
126.91
-113.89
26.67
-27.06
65.93
0.68
4.48
0.32
6,442.0
±30% (28%)
1
144.11
-164.90
40.24
-41.06
73.23
0.68
3.80
0.29
11,420.3
2
140.75
-1(54.52
40.25
-41.08
74.59
0.68
3.75
0.29
11,246.5
3
141.88
-162.46
40.34
-40.75
73.94
0.68
3.75
0.29
11,064.2
4
141.20
-170.40
40.32
-41.33
73.28
0.63
3.82
0.28
11.030.4
7
Cycle
*« max
Qmin
y•<* max
y
Qd
Qy
Kef?
wD
±40%(38%)
1
170.(50
-195.61
54.54
-55.62
77.19
0.68
3.33
0.28
17.775.0
2
149.61
-160.69
54.32
-55.52
77.59
0.68
2.83
0.32
17.060.7
3
151.09
-15(5.75
54.75
-55.22
76.26
0.68
2.80
4
147.40
-154.86
54.44
-55.11
75.31
0.68
2.76
0.311 0.311
16.638.2 16.285.4
±50%(49%)
1
172.53
-190.33
68.98
-69.33
78.01
0.68
2.62
0.29
23,039.3
2
163.09
-175.50
69.45
-69.22
81.14
0.68
2.44
0.31
22.728.0
3
162.91
-176.91
6953
69.18
77.73
0.68
2.45
0.30
22,050.8
4
161.84
-171.88
69.45
-68.81
79.85
0.68
2.41
0.30
21.722.4
- 73 -
Bearing ID : 2002Vertical Force : 200Ton
Excitation Frequency : 0.3HzData File Name : F2002-6
Ca^:kN,mm)
7
Cycle
'K max
** min
y- ^ min
Q.v
Keff
H«t
WD
= 10% (9%)
1
57.39
-71.09
11.90
-12.25
51.53
0.68
5.32
0.41
1,986.4
2
71.67
-71.5(5
12.22
-12.10
51.05
0.68
5.89
0.39
2.138.8
3
73.29
-72.81
12.10
-12.04
51.29
0.68
6.05
0.39
2,130.9
4
75.89
-73.77
12.44
-12.09
51.43
0.68
6.10
0.38
2.183.4
±20%(18%)
1
101.65
-104.87
25.99
-26.61
80.47
0.68
3.93
0.41
7,068.9
2
97.022
-102.06
25.89
-25.94
85.22
0.68
3.84
0.43
6.957.3
3
97.38
-103.19
25.89
-26.01
84.59
0.68
3.86
0.42
6,902.6
4
99.52
-103.81
25.82
-25.78
84.12
0.68
3.94
0.42
6,861.7
±30% (29%)
1
115.67
-140.02
40.75
-41.01
92.16
0.68
a 13
0.39
12,739.2
2
107.85
-128.57
40.58
-40.71
91.94
0.68
2.91
0.41
12,377.8
3
104.85
-125.56
40.62
-40.57
87.69
0.68
2.84
0.42
12,178.2
4
102.65
-123.45
40.43
-40.50
87.68
0.68
2.79
0.42
12,145.2
7
Cycle
0mHx
^ m i i i
V-"• max
Qy
Keff
wD
= 409-0 (39%)
1
139.40
-158.86
55.16
-54.74
83.35
0.158
2.71
0.36
18.430.3
9
121.99
-142.8(5
55.08
-54.62
3 ! 41
118.81! 115.67i
-139.58; -136.03
55.42 55.27
-54.89: -54.39
84.30 82.78 ! 82.02i
0.(58
2.41
0.39
17.729.5
0.68' 0.68
2.34 2.30
0.39 0.40
17.455.4: 17.108.9
±50%(49%)
1
140.78
-162.04
69.92
-(58.94
84.00
0.68
2.18
0.36
23.612.7
2
130.01
-145.17
70.50
-69.07
84.26
0.68
1.97
0.38
23.056.9
3
126.57
-140.18
70.43
-68.96
83.42
0.68
1.91
0.39
22,702.8
4
123.15
-136.5(5
70.28
-68.49
82.82
0.(58
1.87
0.39
22,316.8
- 74 -
Bearing ID : 2002Vertical Force : 150Ton
Excitation Frequency : 0.3HzData File Name : F2002-7
(£3:kN,mm)
7
Cycle
«*max
<« min
y- " • max
Y-"• min
Qd
Qy
K-eff
WD
± 10%(8%)
1
68.97
-58.77
11.74
-12.89
40.10
0.68
5.19
0.36
1.795.1
2
68.63
-61.17
11.37
-12.89
39.68
0.68
5.35
0.36
1.760.3
3
71.83
-61.37
12.09
-12.70
39.26
0.68
5.37
0.35
1.789.6
4
70.22
-62.64
12.08
-12.84
38.67
0.68
5.33
0.34
1.786.9
±20%(18%)
1
98.35
-100.65
25.20
-27.10
60.76
0.68
3.81
0.36
5,831.4
2
96.06
-94.88
25.83
-26.22
68.04
0.68
3.67
0.37
5,732.6
3
97.31
-97.83
26.17
-26.65
67.24
0.68
3.69
0.36
5,758.2
4
96.74
-99.70
25.89
-27.15
60.67
0.68
3.70
0.34
5,525.0
±30%(28%)
1
118.69
-124.04
40.01
-42.13
69.01
0.68
2.96
0.33
10,447.2
2
113.06
-119.20
39.75
-40.89
72.10
0.68
2.88
0.34
10.110.3
3
110.25
-119.73
40.17
-40.62
76.87
0.68
2.85
0.35
10.166.7
4
107.48
-121.84
40.49
-41.49
71.18
0.68
2.80
0.34
10.055.1
7
Cycle
^ m i n
y-"- max
y-<*- min
Qd
Q,
Keff
Hen
WD
1
121.67
-145.61
55.02
-55.73
76.02
0.68
2.41
0.33
15.464.3
±40%(39%)
2
119.26
-134.72
55.57
-55.50
75.18
0.68
2.29
0.35
15.307.0
3
116.11
-132.53
54.93
-55.(3
73.33
0.68
2.25
0.35
15.006.9
4
115.01
-129.91
55.02
-55.24
72.68
0.68
2.22
0.35
14.736.0
i
1
137.57i.
-178.82
! 70.30
1 -69.50
i 76.61
! 0.68
2.26
! 0.30
j 20.764.4
±50% (49%)
2
132.60
-164.21
70.06
-69.54
76.85
0.68
2.13
0.31
20,281.0
3
128.88
-160.90
69.73
-69.52
76.24
0.68
2.08
0.32
19,962.6
4
127.60
-156.41
70.23
-69.11
74.90
0.68
2.04
0.32
19,550.9
- 75 -
Bearing ID : 2002Vertical Force : lOOTon
Excitarion Frequency : 0.3HzData File Name : F2002-8
(£:^:kN,mm)
7
Cycle
*K min
y-"• max
y-^- min
Q*
Qy
Keff
wD
±10%(9%)
1
52.89
-52.41
11.75
-13.00
31.30
0.68
4.26
0.33
1.357.2
2
57.25
-53.95
11.87
-12.93
27.67
0.68
4.49
0.30
1.316.0
3
57.60
-52.47
12.11
-12.18
26.62
0.68
4.53
0.30
1.254.9
4
58.27
-54.64
12.58
-12.65
26.32
0.68
4.48
0.29
1,287.1
±20%(18%)
1
78.46
-86.99
26.06
-26.96
38.52
0.68
3.12
0.30
4,170.0
2
82.01
-88.60
25.73
-26.18
43.65
0.68
3.29
0.29
4,082.5
3
83.48
-90.76
25.98
-26.71
41.78
0.68
3.31
0.28
4,096.9
4
83.46
-90.35
25.98
-26.74
41.15
0.68
3.30
0.28
4,045.4
±30%(29%)
1
102.49
-111.51
40.37
-41.32
52.12
0.68
2.62
0.29
7,879.5
2
101.50
-115.13
39.83
-41.77
52.67
0.68
2.66
0.28
7,846.6
3
99.85
-112.33
40.75
-40.94
52.15
0.68
2.60
0.28
7.691.4
4
98.73
-113.42
. 40.62
-41.23
52.12
0.68
2.59
0.28
7,640.2
7
Cycle
^ m a x
^ m i n
y•<*• m a x
y-"• min
Qa
Qy
Keff
wD
±40% (39%)
1
115.38
-133.27
55.27
-55.54
60.02
0.68
2.24
0.28
12.126.8
2
114.69
-128.20
55.37
-55.12
60.73
0.68
2.20
0.29
11.989.2
3
114.15
-127.01
55.32
-54.90
59.81
0.68
2.19
0.28
11.847.5
4
113.64
-125.79
55.41
-54.73
60.02
0.68
2.17
0.28
11,754.2
±50%
1
133.95
-165.04
70.75
-69.35
66.41
0.68
2.13
0.26
16.765.3
2
129.97
-162.52
70.38
-69.35
66.04
0.68
2.09
0.26
16.531.9
3
128.40
-159.38
70.47
-69.34
63.14
0.68
2.06
0.26
16.220.4
4
126.93
-154.91
70.17
-69.15
62.83
0.68
2.02
0.26
16.006.0
- 76 -
7
Cycle
** max
Omin
y-"• max
• ^ min
Q<
Qy
K,ff
wD
Bearing ID : 2002Vertical Force : 50Ton
Excitation Frequency : 0.3HzData File Name : F2002-9
±10%(8%)
1
39.98
-40.51
10.93
-13.09
16.94
0.68
3.35
0.26
801.5
2
39.19
-43.04
11.14
-13.5(5
14.99
0.68
3.33
0.24
763.6
3
39.55
-42.92
11.43
-13.56
14.51
0.68
3.30
0.24
760.8
4
38.35
-42.22
11.18
-13.27
14.28
0.68
3.30
0.23
724.7
±20% (18%)
1
62.59
-75.10
24.98
-27.14
31.14
0.(58
2.64
0.25
2,765.9
2
67.25
-76.10
25.55
-26.86
26.19
0.(18
2.74
0.23
2,694.8
3
67.67
-77.04
25.53
-27.41
25.18
0.68
2.73
0.22
2.638.9
4
67.42
-76.81
25.50
27.35
24.21
0.68
2.73
0.21
2,5(53.7
±30%(28%)
1
85.12
-98.54
40.10
-42.19
33.62
0.68
2.23
0.23
5.372.4
2 3
86.89: 87.19
-98.80, -97.73
40.151 39.98
-41.88. -41.91
35.51; 33.09
0.68' 0.(58
2.26 j 2.26
0.22 0.22
5.366.6! 5.209.3
4
86.59
-96.55
40.09
-41.50
31.51
0.68
2.25
0.22
5.128.2
7
Cycle
<*max
Qmin
- ^ m a x
Y•**• m m
Qd
Qy
Keff
wD
±40%(39%)
1
103.89
-123.67
54.92
-55.95
39.54
0.68
2.05
0.22
8.711.9
2 3
106.91: 103.53
-121.01; -119.98
54.99; 53.62
-56.11 -56.00
42.43 39.15
0.68: 0.68
2.05: 2.04
0.22 0.22
8,692.3 8.274.7
4
103.92
-117.48
54.18
-55.55
38.62
0.68
2.02
0.21
8.134.4
±50%(49%)
1
1Z2.52
-153.34
69.82
-69.95
52.43
0.68
1.97
0.21
12.424.0
2
119.79
-150.66
69.36
-70.53
51.19
0.68
1.93
0.21
12,195.4
3
117.62
-146.72
69.19
-69.68
45.10
0.68
1.90
0.20
11.684.1
4
115.99
-145.96
68.%
-69.85
43.99
0.68
1.89
0.20
11.364.8
- 77 -
7
Cycle
Qmax
** min
y- ^ max
0^
0,
Kt,f
wD
1
17.65
-28.10
11.77
-12.84
7.44
0.68
1.86
0.18
310.7
±109/
2
16.82
-28.52
11.99
-13.25
7.62
0.68
1.80
0.17
305.6
' lC\O/\
3
17.30
-27.78
12.23
-12.50
7.77
0.68
1.82
0.17
292.1
Bearing ID : 2002Vertical Force : OTon
Excitation Frequency : 0.3HzData File Name : F2002-10
4
16.60
-28.37
11.86
-12.43
7.91
0.68
1.85
0.17
283.7
±20%(17%)
1
34.01
-50.46
23.87
-26.72
8.93
0.68
1.67
0.16
1.062.4
2
33.09
-50.48
23.35
-26.76
9.94
0.68
1.67
0.15
988.5
3
32.60
-48.%
23.35
-26.36
9.99
0.68
1.64
0.15
962.8
4
32.14
-50.03
23.44
-26.80
9.67
0.68
1.64
0.15
951.1
±30% (27%)
1
52.29
-71.87
37.85
-41.41
12.51
0.68
1.57
0.15
2,326.7
2
50.74
-71.82
37.25
-41.137
12.97
0.68
1.56
0.15
2.245.8
3
50.48
-70.91
37.31
-41.02
12.80
0.68
1.55
0.15
2,179.3
4
50.74
-69.95
37.82
-40.11
12.73
0.68
1.55
0.14
2.128.8
7
Cycle
©max
^ m i n
y-^- max
y•**- min
Qd
Qy
Keff
Hpg
wD
±40%(37%)
1 2
71.45 70.94
-94.43: -93 59
52.31 51.64
-55.11 -55.45
15.17 15.79
0.68 0.68
1.54 1.54
0.14 0.14
4.024.9. 3.983.7
3 ! 4
69.38! 70.70
-92.il! -91.93
51.45 52.33
-54.54 -54.67
15.611 15.32
0.68! 0.68
1.52; 1.52
0.14: 0.14
3.847.4; 3.813.9
±50% (47%)
1
91.87
-118.19
66.82
-68.52
17.43
0.68
1.55
0.14
6,131.3
2
90.28
-117.56
66.33
-68.32
18.28
0.68
1.54
0.14
6.036.4
3
!X).O3
-115.69
66.59
-68.36
17.38
0.68
1.53
0.13
5,842.3
4
89.43
-114.97
C56.67
-68.03
16.60
0.68
1.52
0.13
5.699.6
- 78 -
American Association of State Highway and Transportation Officials
(AASHTO), California Department of Transportation (CALTRANS),
Japanese Public Works Research Institute (JPWRI), New Zealand
Ministry of Works and Development (NZMWD) §-3]
1^2.cd(equivalent linear models) A
1. LRB5} 71^12} ^ - ^
ZL^ 12]- ;g>8r bi-linear LRB^
nU£.6fl
7\
-D / -
Q
Force
^_^-J Displacement
1. bilinear
- 79 -
Q
LRBS]
- = (2)
T = 2K (3)
4Q(Z)-/).V)l j
= Fy /KL Fy =Q + K2Dy$]
TC(K2D+ Q)D
- 80 -
2Q(D-Q/9K2)TC(K2D+ Q)D
(6)
2. AASHTO A
AASHTO^
bilinear
Force
Displacement
2. LRB£] bilinear
-B-JL7J-^(effective stiffness)^ equivalent damping
m •*• in
(7)
- 81 -
area of hysteresis loop of an isolation unit2 K Ke/f di
•K Keff
ductility
hardening 1/6.5
0.
. ^=0.155}
^0.15(^-1)]
(inherent viscous damping ratio) £ofe ^7}-5.
3. CALTRANS «
CALTRANS
](effective period shift)
= 1 +o
(10)
(11)
(ion
- 82 -
IT
Ke//= {l + l n [ l +
4. JPWRI
CBUB (15)
(13)2)-
{7)o\}*\ ^o]^ AASHTO^
K0.15(0.7^-1)
- 83 -
zuBe{Q(1+uBeK2)
UBe= cBdi
0.7^
0.15(0.7^)1
(18)
5. NZMWD
NZMWD ^
^15. 1-^^>JL AASHTO
- 84 -
^m 3 LRB
1. KRB) ^ 3 ] «
9X1=
Atr
Eap Eb
=E0(l+2xSJ)
Eo:
x:
Tr:
X (#£-3 #*H) = ^ A (4)
- 85 -
K -Ky - *- r
(5)
G: H
Ke = Ky + •&.
D:
(7)
(9)
- 86 -
2.
K _4k E0(l+2xS'i) l ;
2.036
1.106
(r < 0.1)
(0.1 ^ r < 0.5)
(0.5 ^ r )
(13)
(14)
- 87 -
Kd= 0.744
Kd= 0.921
(7 < 0.5)
(7 ^ 0.5)(15)
G :
(16)
- 88 -
3.
M.C Constantinou 3.^7} Seismic Isolation of Bridges(1994) <*\) *\
(Q)
Q = ayL • Ap (17)
<ryL:
Afi:
(18)
G:
A,,
T:
= 1.1-1.6)
(19)
- 89 -
W d = A - Q (21)
(22)
- 90 -
fcd 4 LRB
l .
box, #
blocks
iz]-^r steel
^ concrete
o ooooo4.55m 2.2m
20 21
17' \ /t.P) \
2"
22
l . 0.925
23 24& _
©
25 26
29
47, \
0.925 . 1(13:
15
2 tfl #37*8=3
- 91 -
SAP 20005} Frame_S_ih3-, LRB^ Nllink.S.4: ir isolatorl^S.
load cells*!- basefe-
161.57 t/m3, 33, 3 7 ^
1 34, 36«i
82.65 t / m 3 A ^
A ^ , El Centro^l
2. oj
El Centro Mexico
B. A
channel
angle
»^(c^)
170.44
62.08
61.4
78.11
9.76
/ * ( ™A)
3.96e-4
4.61e-5
3.78e-5
1.54e-4
3.83e-7
1.36e-4
1.60e-5
3.78e-5
6.42e-6
3.83e-7
E( kN/m2)
1.999e8
1.999e8
1.999e8
1.999e8
1.999e8
7.83
7.83
7.83
7.83
7.83
0.3
0.3
0.3
0.3
0.3
S. 2
El Centro
Mexico
(kN/m)
640
660
(kN/m)
2703
3457
1 (kN/m)
285
267
4.27
5.46
- 92 -
^ 354- ^ 4 ^ sfl
Mexico*] 3JS] table motion-t-
El Centra^
3.
LRB
LRB JL^-3]
LRB ^-
^ LRB ^-
^t^r 7.258
^r 9.0 kg/cm2o]°-
0.4
¥ °-2
-0.2
-0.40 10 15
Time (sec)
3 El Centro *]
20 25
0.2
10 20
Time (sec)
30 40
4 Mexico
- 93 -
o)
- El Centro *1
7ii3|6fMs] 7}
Mexico
71-
LRB
% -5
•fl -10
10
-T5 O -
-10
.i-Ul-i- { • • - - )
-W-• { • • ! (•
10 15Time (sec)
(a)
5 El Centro
10 15Time (sec)
(b)
P^J+jl^
20
20
25
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1.1i|iV i..:'I'i'iJ.;'!^;,.!, .
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] :••ijlll;|'--i.f(|/l|j|i!
; ;
W ' l V i V - ; - - -iWll'i"'"
25
- 94 -
u
m
n
Acceleration (g)
o o
jjiu
o
o[o
9 9O is) t
- f e HL=hl
Acceleration (g)
op 9 9£> k) O K) t
nib 3
...
- -
— =
—--J
^ >
1
Displacement (mm) Displacement (mm)
p
r-t->!
J((U
H3
o
r i
o|o
Wb |
ftO
j1
_ * •
. . .
>n O
u•Jl
g
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HT
P
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00
n(tutu) (tUtU
c
t:=:
-r
.__
-
e .10
o|o
oy'x
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n
CTs
(tutu)
0.30
¥ °-15o
| 0.00
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3s
erat
i
0.
0.
30
15
0.00
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-0.30
^ ; r : ^
10
10
10 Mexico
•t-! t
20Time (sec)
(a)
20Time (sec)
(b)
tfl^
30
30
40
- 97 -
I
II
7^517}]^(A)
0.11
0.07
n % ^ ^Aj£M.^X\, Ol^^-^A], rfl^^-^A], ^-A^O^Al,
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ifl*!IIW3L
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"(m/s)
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360-760
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-
50^311-
15-50
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^^^J7}7> £
1 ^ft ^ 1 ^
(kPa)
-
50-100
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(S)
1.0
1.2
1.5
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- 100 -
4.
0.8
2.
3
2
0.8
1.0
3 (Cap Beam) a ^
1. ^ 3 ] ^
2. *> 7H
5
3
1.0
- 101 -
INIS
KAERVTR-1833/2001
LRB
(TR,
2001
lOlp. 9XM O ), a 7] 21 X 29.7cm
Oo t r
3-iHe)
LRBs) bilinear J l^- t -A ] ^
bilinear . o]
M&, LRB, o]
Bilinear JE.ri
BIBLIOGRAPHIC INFORMATION SHEET
Performing Org.Report No.
Sponsoring Org.Report No.
Standard Report No. INIS Subject Code
KAERVTR-1833/2001
Title / Subtitle Determination of Design Parameters of Lead-Rubber Bearingsby Characterization Tests
Project Managerand Department
(or Main Author)Young-Sun Choun (Integrated Safety Assessment Team)
Researcher andDepartment
In-Kil Choi (Integrated Safety Assessment Team)
Moon-Sig You (KR Industrial Co., Ltd.)
PublicationPlace
Taejon Publisher KAERI PublicationDate
2001
Page lOlp. 111. & Tab. Yes( O ), No ( ) Size 21 X 29.7cm
Note
ClassifiedOpen( O ), Restricted( ),
Class Document Report Type Technical Report
Sponsoring Org. Contract No.
Abstract (15-20 Lines)
This report includes characterization tests of LRB provided by KR IndustrialCo. and also includes evaluation of effective stiffness and equivalent dampingratio of LRB. With test data, dynamic properties of LRB are reviewed and designprocedures proposed by KR, Japan, and United States are compared and revised.Two bilinear models of LRB are proposed. One is obtained from hysteresis loop,the other is based on mechanical property data of laminated rubber and leadplug. Comparison of analysis results with test results for a bridge scaled-modelis performed to show the applicability of proposed bilinear models.
Based on the review and evaluation of the KR LRB design parameters andprocedures, following conclusions are drawn.- Design parameters of LRB, effective stiffness and equivalent damping, are
significantly influenced by horizontal loading frequency and vertical load.- Hysteretic behavior of LRB can be idealized by a bilinear model. The initial
stiffness of the model must be determined with accuracy.- LRB design procedures proposed by the KR Industrial Co. may be applicable
to determine effective stiffness, but some modifications are needed todetermine equivalent damping.
Subject Keywords(About 10 words)
Bridge, LRB, Hysteresis loop, Design parameter, Effective stiffness, Equivalentdamping, Dynamic property, Design procedure, Bilinear model
