Introduction of the Structural Calculation Method for Seismically-Isolated … · 2020. 3. 24. ·...
Transcript of Introduction of the Structural Calculation Method for Seismically-Isolated … · 2020. 3. 24. ·...
1
Introduction of the Structural Calculation Method
for Seismically-Isolated Building in Japan
with a Calculation Example by ELM
by the Committee of Foreign Affairs JSSI March 2020
Abstract The seismic isolation system is a structurally applicable construction method for newly constructed buildings and for existing buildings through retrofitting Many seismically isolated buildings have sprung up in Japan totaling approximately 9000 at present Condominiums account for 40 of that and retrofitting accounts for approximately 4
Notification No 2009 ldquoCalculation Method for Seismically Isolated Buildingsrdquo 1) was issued in 2000 with Equivalent linearized method Time history response analysis method was common before 2000 and popular now The number of buildings by equivalent linearized method is gradually increasing and is 10 of all these buildings This paper shows the calculation procedure by equivalent linearized method Important matters for calculation are explained with a flow-chart while showing an example of a building with seismic isolation Abbreviation SI Seismically Isolated Seismic Isolation SE Structural Engineer ELM Equivalent Linearized Method THAM Time History response Analysis Method LRB Laminated Rubber Bearing SLD SLiDer with elastomer SD Steel Damper MLIT Ministry of Land Infrastructure Transportation and tourism Contents 1 Introduction 2 Calculation procedure 21 Applicability of ELM 22 Structural calculation procedure for SI buildings 23 Synopsis of ELM 24 Other important matters for SI buildings 3 Example of a seven-story RC building 31 Building model 32 Selection of devices for SI 33 Arrangement of devices in SI layer 331 Eccentricity ratio of SI layer 332 Total yield strength 333 Period of the isolation system considering only the stiffness of LRBs 34 Setting of acceleration spectrum on the surface of the site 35 Calculation of response displacement and shear-force of the SI layer 36 Calculation of shear-force of superstructure and substructure 361 SI layer 362 Superstructure 363 Story drift of super-structure and vertical load changes on isolator devices 364 Substructure 37 Evaluation of response values of SI layer from wind load 38 Confirmation of safety of devices for vertical load 39 Securing safety of connections of devices to structures 310 Confirmation of satisfaction of stipulations on SI system 4 Reference
2
1 Introduction In Japan the most recent building code provisions took effect in 2000 Procedures and practices for conducting SI buildings are introduced
Generally a two-stage code for calculation method was introduced in the Building Standard Law of Japan as shown in Table 1 The two stages are usually defined as damage limitation (Level 1 approximately a 50-year return period) and life-safety limitation (Level 2 approximately a 500-year return period) In the damage-limitation stage the structural safety performance must be preserved in the considered earthquake In the life safety-limitation stage the building should not collapse in order to assure the safety of human lives The performance target can be classified into three parts superstructure SI layer and substructure as shown in Table 1
In the Japanese code a 5 damping spectral-acceleration at bed-rock site is defined The site spectrum is obtained by considering the soil amplification factor which is dependent on the soil profile THAM is the most popular method in Japan while ELM can only be used in stipulated conditions which are building height of less than sixty meters on soil condition where there is no possibility of liquefaction and by SI system on the base
Subsequently a typical 7-story reinforced concrete building isolated with a combination of LRBs SLDs and SDs is calculated to demonstrate the practice
Table 1 Performance target of SI buildings2)
Frequency of External Disturbance
Rarely occurring event Extremely rarely occurring event
Superstructure
horizontal strength
elastic elastic limited
story drift angle lt1500 lt1300
SI layer isolator lt100-150
lt150-250 tensile stresslt1Nmm2
within stable stress and deformation relation
damper standard deformation design limit deformation
Substructure
horizontal strength
elastic elastic
story drift angle 11000 1500
Shear strain of LRB
3
2 Calculation procedure 21 Applicability of ELM In Figure 1 is shown the choice of the calculation route following the Japanese code The ELM is used at limited conditions shown in Table 2 for buildings that are less than 60m high that have SI layer located above the ground and that have first or second class ground classification etc
The THAM is possible for all buildings as follows Following Table 2 the applicability of the ELM is checked over as follows (Section22 23)
Figure 1 Choice of the calculation route
Table 2 Applicability of the ELM
Limitation on ground class Ⅰ Ⅱ
Maximum height of superstructure 60m
Location of devices Base only
Maximum mass-stiffness center eccentricity 3
Tension in isolator Not allowed
Yield strength gt 003W
Period range of Te T2 gt 25s
Structural calculation for SI buildings
Confirmation by a building official
Less than 60m
Location of SI layer
Building height
Within building
First class and second class ground
without possibility of liquefaction
Above the ground or on the top
of the basement
Ground classification
T H A M
More than 60m
Calculation Methods
Second class with possibility of liquefaction
or third class
Approval by MLIT
E L M
4
22 Structural calculation procedure for SI buildings Generally the ELM can be illustrated as follows The base shear force is obtained from the spectral acceleration and weight as shown in Equation (1)
e
eaeh
K
TSThFM )()(=
11=r (1)
rr =
es KQ = where design displacement of the isolation system
M total weight of the building Fh(hTe) response reduction factor h effective damping Sa(Te)(g) site response acceleration considering site soil conditions Ke effective stiffness of the isolation system r the maximum design displacement used to determine the clearance coefficient related to the eccentricity of the isolation system safety factor related to variation of properties with temperature ageing or products
tolerances discrepancy introduced in the Japanese code Qs shear force in the base of the superstructure
In general the five percent-damped spectral acceleration Sa(T) is given by Equation (2)
)()()( 0 TSTGZTS sa = (2) where
Z the seismic hazard zone factor Gs(T) a soil amplification factor dependent on the soil profile S0(T) the design spectral acceleration at engineering bedrock (Vsgt400ms) defined in Equation (3) which is shown in Figure 1 for Level 2 input
+
=
TT
T
TT
smS
640125
64016008
1603023
)( 20 (3)
The site amplification coefficient Gs(T) is defined in Figure 32 based on different site classes However in the engineering practice the Gs(T) is usually calculated iteratively based on the investigated Vs or N values and types for the soil profile rather than directly using the coefficients defined in the code The zone coefficient Z is divided into four levels as 10 09 08 and 07(Okinawa only) within Japan
12
10
08
06
04
02
00
Sp
ectr
al a
ccel
erat
ion
(m
s2)
Period (s)016 064 T (s)
512T
Figure 1 Design spectral acceleration at the engineering bedrock (Vsgt400ms)
5
The response reduction factor Fh (hTe) is defined in Equation (4) by using the effective viscous damping of a fluid damper hv and a hysteretic damper hd which is decreased to 80 percent of the effective damping for a combined viscous-hysteretic system
40)80(101
51
++= h
dvh F
hhF (4)
To use ELM calculation model must appropriately evaluate one mass for superstructure and characteristics of isolation devices at supposed response range Modeling of isolation devices must appropriately evaluate stiffness and damping characteristics based on the test data by manufacturer
The convergence procedure of the ELM is shown in Figure 2 The procedure is summarized as follows
bullAssume a displacement of the isolation system DD0 () bullCalculate the effective stiffness Ke and effective damping e(h) of the isolation system assuming a bi-linear model for the isolation system bullCalculate the equivalent period Te of the isolation system bullCalculate the corresponding response reduction factor Fh(hT e) and the spectral acceleration Sa(Te) bullCalculate a new isolation system displacement DD() using Equation (1) bullRepeat the above steps until DD() converges
Hysteresis loop
2nd
1st
3rd
Q
DD D
QISO
K1stK2nd
K3rd
DD0
Figure 2 Illustration of the convergence procedure for the ELM 23 Synopsis of ELM Step by step procedure to use ELM is summarized as follows 1 Assumption for sections of frame members of the building
The item is done by SE using the method that are similar to conventional buildings 2 Selection of devices for SI
Devices for SI are selected from those approved by MLIT and their performance is checked to determine which are allowable compressive capacity horizontal stiffness ultimate deformation capacity etc
3 Arrangement of devices in SI layer The item is the arrangement of devices which must have an eccentricity-ratio in SI layer of 3 or less
4 Setting of acceleration spectrum on the surface of the site The setting of acceleration spectrum on the surface of the site is necessary for achieving displacement and shear force of SI layer Therefore soil property conditions on the site should be checked The soil amplification factor Gs(T) is usually calculated iteratively based on the investigated Vs or N values and types for the soil profile
6
5 Calculation of response displacement and shear-force of the SI layer The item is calculation of response displacement and shear-force of the SI layer on the above spectrum with damping factor by using the design limit deformation based on the design limit period
6 Calculation of shear-force of superstructure and substructure The above shear-force is distributed to each story of the superstructure by using the distribution rule
7 Evaluation of response values of SI layer from wind load The item is evaluation of response values of SI layer for wind load on the restoring force-displacement curve of SI layer to confirm safety against extremely rare-occurring strong winds
8 Confirmation of safety of devices for vertical load The eighth item is confirmation of safety of devices against vertical load during earthquakes Stress must be below allowable stress against vertical loads including up and down acceleration of 30 of a building own-weight No minus stress is allowable for bearings
9 Securing safety of connections of devices to structures Securing of safety of connection of devices to structures such as footings capitals girders and columns is important to make use of the performance of devices
10 Confirmation of satisfaction of stipulations on SI system Finally SI system must satisfy stipulations which are as follows bullClearance (space moat gap) is required to secure displacement which includes response value and certain safety-margin value as below
No passerby 10 cm General 20 cm Passerby 80 cm
bullMovement of SI building must be maintained in heavy snow falls bullExchange of devices or checking devices must be possible bullA notice-board or an indicator for ldquo this building is seismically isolatedrdquo is required
24 Other important matters for SI buildings In addition to the above the following items are important matters for SI buildings bullArchitectural Planning (a) Planning of Isolation Layer
Architectural details in or in the vicinity of the isolation layer must be planned so as not to cause injury to humans or damage architectural members considering that the isolation layer deforms significantly during earthquakes
(b) Fire Resistive Covering and Performance of Isolators The isolators must support superstructure without losing supporting capacity of vertical loads subjected to fires expected to happen in or in the vicinity of the isolation layer
Fire resistive covering must protect isolators until fire ends It must follow the expected deformation of isolators without covering materials falling off
bullPlanning of Equipment System Equipment in the vicinity of the isolation layer must be planned in order for their functions to be
maintained during earthquakes considering large displacement at the isolation layer bullConstruction SE must inform the constructor of design-demand requirements at construction stage Also
construction supervisor must supervise the suggested construction planning and the undertaken construction to provide expected performance as a SI building
bullMaintenance Building owner must properly maintain own building after completion SE must draw up
maintenance plans and inform the owner so that the required SI performance is maintained during the buildingrsquos lifetime
7
3 Example of a seven-story RC building Synopsis of ELM described in section 23 will be used to calculate the seven-story building 31 Building model The outline of the building is shown below The elevation span-direction and longitudinal-direction draws are shown in Figure 31 Typical plan is shown in Figure 32
Principal use Condominium
Total floor area 1470m2
Maximum eaves height 220m
Classification of
structure Reinforced concrete structure
Structural type X(lateral) direction Moment frames
Y(longitudinal) direction Moment frames
with bearing walls
Ground classification Second class (Tg=034s)
Foundation Direct
1
38
03
00
30
03
00
30
03
00
32
0
2
3
4
5
6
7
8
500 500
38
03
00
30
03
00
30
03
00
32
0
X2X1 X3 X4Y1 Y2
700700 700
Figure 31 The elevation span-direction and longitudinal-direction draws
Figure 32 Typical plan of the building
X1 X4
Y1
Y2
8
The story mass and horizontal stiffness of both X Y direction of the building are summarized in Table 31 The fundamental periods of the fixed-base model are Tx = 0682s and Ty = 0258s The vertical loads of each column on isolation devices are summarized in Table 32
Table 31 Story mass and the horizontal stiffness of the building
Horizontal stiffness
(kNmm)
Height(m) Weight
(kN)
X Y
7 320 2854 325 1144
6 300 3328 449 2168
5 300 3293 488 2845
4 300 3331 560 3449
3 300 3379 635 4191
2 300 3390 720 5363
1 380 4220 778 10690
SI 150 4461
Total 28256
Table 32 Vertical loads on isolation devices (kN)
X1 X2 X3 X4
Y2 4363 5161 4659 2975
Y1 2539 3767 3728 2504
32 Selection of devices for SI Figure 34 shows the layout of isolation devices for the building A combination of LRBs (RB80 RB80S) SLDs (SC60 SC70) and SDs are selected to give a demonstration of the calculation procedure The sketch of the used isolation devices is shown in Figure 33
Figure 33 Sketch of the isolation devices
(from left LRB SLD SD)
The characteristics of each device are shown in Table 33 The design displacement limit δs at the isolation interface is determined as the minimum value of the design displacement limit md for all components of the isolation system The design displacement limit md for each device is obtained by multiplying the safety factor β by the ultimate deformation u for each device The value of the safety factor β is based on empirical knowledge resulting from experimental data obtained in
Steel Damper Rod
9
Japan A typical example of determining md for a LRB and SLD is shown in Figure 34 This Figure shows that the bearing must be designed within the limits of vertical stress horizontal displacement and limitation by buckling of bearing In Figure 34 ultimate deformation u is derived from 13 of ultimate vertical design strength Fc For typical devices safety factors are given as follows
=08 for elastomeric isolator =09 for sliding bearing and rotating ball bearing =10 for damper and restorer Table 33 Characteristics of isolation devices
Name of device LRB3) SLD SD
Type name RB80S RB80 SC60 SC70 SD-U
G of rubber Nmm2 039 039 078 078
Diameter mm 800 800 600 700 45
Rubber Thickness mm 6 6 5 5
Number of sheet of rubber 33 30 4 4
Total thickness of rubber mm 198 180 20 20
S1 317 317 29 335
S2 40 44 30 35
Unloading stiffness K1 kNmm 099 109 11 15 76
Post yielding stiffness K2 kNmm 099 109 0 0 0128
Friction Factor - - 0011 0011 -
Yield load Qy kN - - 412 540 184
Vertical Stiffness kNmm 2480 2730 10600 14400 -
Tensile Strength kN 501 501 0 0 -
Allowable Stress Nmm2 10 10 17 17
Allowable Load kN 3748 4910 0
Ultimate compressive
strength cr Nmm2 45 49 57 57 -
Fc Nmm2 41 41 51 51
ultimate deformation u m 0679 0617 055 055 065
safety factor 08 08 09 09 10
design displacement limit
md m 0543 0494 0495 0495 065
10
Figure 34 Design displacement limits for a LRB and SLD
Ultimate compressive strength
Vertical design strength
≦ 09 cr
Design limit
Ultimate compressive strength
Fc
Vertical design strength
≦ 09 cr
Fc 3
Design limit
cr
09 cr
Displacement
u md
LRB
SLD
Displacement
u md
Fc 3
Fc
cr
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
2
1 Introduction In Japan the most recent building code provisions took effect in 2000 Procedures and practices for conducting SI buildings are introduced
Generally a two-stage code for calculation method was introduced in the Building Standard Law of Japan as shown in Table 1 The two stages are usually defined as damage limitation (Level 1 approximately a 50-year return period) and life-safety limitation (Level 2 approximately a 500-year return period) In the damage-limitation stage the structural safety performance must be preserved in the considered earthquake In the life safety-limitation stage the building should not collapse in order to assure the safety of human lives The performance target can be classified into three parts superstructure SI layer and substructure as shown in Table 1
In the Japanese code a 5 damping spectral-acceleration at bed-rock site is defined The site spectrum is obtained by considering the soil amplification factor which is dependent on the soil profile THAM is the most popular method in Japan while ELM can only be used in stipulated conditions which are building height of less than sixty meters on soil condition where there is no possibility of liquefaction and by SI system on the base
Subsequently a typical 7-story reinforced concrete building isolated with a combination of LRBs SLDs and SDs is calculated to demonstrate the practice
Table 1 Performance target of SI buildings2)
Frequency of External Disturbance
Rarely occurring event Extremely rarely occurring event
Superstructure
horizontal strength
elastic elastic limited
story drift angle lt1500 lt1300
SI layer isolator lt100-150
lt150-250 tensile stresslt1Nmm2
within stable stress and deformation relation
damper standard deformation design limit deformation
Substructure
horizontal strength
elastic elastic
story drift angle 11000 1500
Shear strain of LRB
3
2 Calculation procedure 21 Applicability of ELM In Figure 1 is shown the choice of the calculation route following the Japanese code The ELM is used at limited conditions shown in Table 2 for buildings that are less than 60m high that have SI layer located above the ground and that have first or second class ground classification etc
The THAM is possible for all buildings as follows Following Table 2 the applicability of the ELM is checked over as follows (Section22 23)
Figure 1 Choice of the calculation route
Table 2 Applicability of the ELM
Limitation on ground class Ⅰ Ⅱ
Maximum height of superstructure 60m
Location of devices Base only
Maximum mass-stiffness center eccentricity 3
Tension in isolator Not allowed
Yield strength gt 003W
Period range of Te T2 gt 25s
Structural calculation for SI buildings
Confirmation by a building official
Less than 60m
Location of SI layer
Building height
Within building
First class and second class ground
without possibility of liquefaction
Above the ground or on the top
of the basement
Ground classification
T H A M
More than 60m
Calculation Methods
Second class with possibility of liquefaction
or third class
Approval by MLIT
E L M
4
22 Structural calculation procedure for SI buildings Generally the ELM can be illustrated as follows The base shear force is obtained from the spectral acceleration and weight as shown in Equation (1)
e
eaeh
K
TSThFM )()(=
11=r (1)
rr =
es KQ = where design displacement of the isolation system
M total weight of the building Fh(hTe) response reduction factor h effective damping Sa(Te)(g) site response acceleration considering site soil conditions Ke effective stiffness of the isolation system r the maximum design displacement used to determine the clearance coefficient related to the eccentricity of the isolation system safety factor related to variation of properties with temperature ageing or products
tolerances discrepancy introduced in the Japanese code Qs shear force in the base of the superstructure
In general the five percent-damped spectral acceleration Sa(T) is given by Equation (2)
)()()( 0 TSTGZTS sa = (2) where
Z the seismic hazard zone factor Gs(T) a soil amplification factor dependent on the soil profile S0(T) the design spectral acceleration at engineering bedrock (Vsgt400ms) defined in Equation (3) which is shown in Figure 1 for Level 2 input
+
=
TT
T
TT
smS
640125
64016008
1603023
)( 20 (3)
The site amplification coefficient Gs(T) is defined in Figure 32 based on different site classes However in the engineering practice the Gs(T) is usually calculated iteratively based on the investigated Vs or N values and types for the soil profile rather than directly using the coefficients defined in the code The zone coefficient Z is divided into four levels as 10 09 08 and 07(Okinawa only) within Japan
12
10
08
06
04
02
00
Sp
ectr
al a
ccel
erat
ion
(m
s2)
Period (s)016 064 T (s)
512T
Figure 1 Design spectral acceleration at the engineering bedrock (Vsgt400ms)
5
The response reduction factor Fh (hTe) is defined in Equation (4) by using the effective viscous damping of a fluid damper hv and a hysteretic damper hd which is decreased to 80 percent of the effective damping for a combined viscous-hysteretic system
40)80(101
51
++= h
dvh F
hhF (4)
To use ELM calculation model must appropriately evaluate one mass for superstructure and characteristics of isolation devices at supposed response range Modeling of isolation devices must appropriately evaluate stiffness and damping characteristics based on the test data by manufacturer
The convergence procedure of the ELM is shown in Figure 2 The procedure is summarized as follows
bullAssume a displacement of the isolation system DD0 () bullCalculate the effective stiffness Ke and effective damping e(h) of the isolation system assuming a bi-linear model for the isolation system bullCalculate the equivalent period Te of the isolation system bullCalculate the corresponding response reduction factor Fh(hT e) and the spectral acceleration Sa(Te) bullCalculate a new isolation system displacement DD() using Equation (1) bullRepeat the above steps until DD() converges
Hysteresis loop
2nd
1st
3rd
Q
DD D
QISO
K1stK2nd
K3rd
DD0
Figure 2 Illustration of the convergence procedure for the ELM 23 Synopsis of ELM Step by step procedure to use ELM is summarized as follows 1 Assumption for sections of frame members of the building
The item is done by SE using the method that are similar to conventional buildings 2 Selection of devices for SI
Devices for SI are selected from those approved by MLIT and their performance is checked to determine which are allowable compressive capacity horizontal stiffness ultimate deformation capacity etc
3 Arrangement of devices in SI layer The item is the arrangement of devices which must have an eccentricity-ratio in SI layer of 3 or less
4 Setting of acceleration spectrum on the surface of the site The setting of acceleration spectrum on the surface of the site is necessary for achieving displacement and shear force of SI layer Therefore soil property conditions on the site should be checked The soil amplification factor Gs(T) is usually calculated iteratively based on the investigated Vs or N values and types for the soil profile
6
5 Calculation of response displacement and shear-force of the SI layer The item is calculation of response displacement and shear-force of the SI layer on the above spectrum with damping factor by using the design limit deformation based on the design limit period
6 Calculation of shear-force of superstructure and substructure The above shear-force is distributed to each story of the superstructure by using the distribution rule
7 Evaluation of response values of SI layer from wind load The item is evaluation of response values of SI layer for wind load on the restoring force-displacement curve of SI layer to confirm safety against extremely rare-occurring strong winds
8 Confirmation of safety of devices for vertical load The eighth item is confirmation of safety of devices against vertical load during earthquakes Stress must be below allowable stress against vertical loads including up and down acceleration of 30 of a building own-weight No minus stress is allowable for bearings
9 Securing safety of connections of devices to structures Securing of safety of connection of devices to structures such as footings capitals girders and columns is important to make use of the performance of devices
10 Confirmation of satisfaction of stipulations on SI system Finally SI system must satisfy stipulations which are as follows bullClearance (space moat gap) is required to secure displacement which includes response value and certain safety-margin value as below
No passerby 10 cm General 20 cm Passerby 80 cm
bullMovement of SI building must be maintained in heavy snow falls bullExchange of devices or checking devices must be possible bullA notice-board or an indicator for ldquo this building is seismically isolatedrdquo is required
24 Other important matters for SI buildings In addition to the above the following items are important matters for SI buildings bullArchitectural Planning (a) Planning of Isolation Layer
Architectural details in or in the vicinity of the isolation layer must be planned so as not to cause injury to humans or damage architectural members considering that the isolation layer deforms significantly during earthquakes
(b) Fire Resistive Covering and Performance of Isolators The isolators must support superstructure without losing supporting capacity of vertical loads subjected to fires expected to happen in or in the vicinity of the isolation layer
Fire resistive covering must protect isolators until fire ends It must follow the expected deformation of isolators without covering materials falling off
bullPlanning of Equipment System Equipment in the vicinity of the isolation layer must be planned in order for their functions to be
maintained during earthquakes considering large displacement at the isolation layer bullConstruction SE must inform the constructor of design-demand requirements at construction stage Also
construction supervisor must supervise the suggested construction planning and the undertaken construction to provide expected performance as a SI building
bullMaintenance Building owner must properly maintain own building after completion SE must draw up
maintenance plans and inform the owner so that the required SI performance is maintained during the buildingrsquos lifetime
7
3 Example of a seven-story RC building Synopsis of ELM described in section 23 will be used to calculate the seven-story building 31 Building model The outline of the building is shown below The elevation span-direction and longitudinal-direction draws are shown in Figure 31 Typical plan is shown in Figure 32
Principal use Condominium
Total floor area 1470m2
Maximum eaves height 220m
Classification of
structure Reinforced concrete structure
Structural type X(lateral) direction Moment frames
Y(longitudinal) direction Moment frames
with bearing walls
Ground classification Second class (Tg=034s)
Foundation Direct
1
38
03
00
30
03
00
30
03
00
32
0
2
3
4
5
6
7
8
500 500
38
03
00
30
03
00
30
03
00
32
0
X2X1 X3 X4Y1 Y2
700700 700
Figure 31 The elevation span-direction and longitudinal-direction draws
Figure 32 Typical plan of the building
X1 X4
Y1
Y2
8
The story mass and horizontal stiffness of both X Y direction of the building are summarized in Table 31 The fundamental periods of the fixed-base model are Tx = 0682s and Ty = 0258s The vertical loads of each column on isolation devices are summarized in Table 32
Table 31 Story mass and the horizontal stiffness of the building
Horizontal stiffness
(kNmm)
Height(m) Weight
(kN)
X Y
7 320 2854 325 1144
6 300 3328 449 2168
5 300 3293 488 2845
4 300 3331 560 3449
3 300 3379 635 4191
2 300 3390 720 5363
1 380 4220 778 10690
SI 150 4461
Total 28256
Table 32 Vertical loads on isolation devices (kN)
X1 X2 X3 X4
Y2 4363 5161 4659 2975
Y1 2539 3767 3728 2504
32 Selection of devices for SI Figure 34 shows the layout of isolation devices for the building A combination of LRBs (RB80 RB80S) SLDs (SC60 SC70) and SDs are selected to give a demonstration of the calculation procedure The sketch of the used isolation devices is shown in Figure 33
Figure 33 Sketch of the isolation devices
(from left LRB SLD SD)
The characteristics of each device are shown in Table 33 The design displacement limit δs at the isolation interface is determined as the minimum value of the design displacement limit md for all components of the isolation system The design displacement limit md for each device is obtained by multiplying the safety factor β by the ultimate deformation u for each device The value of the safety factor β is based on empirical knowledge resulting from experimental data obtained in
Steel Damper Rod
9
Japan A typical example of determining md for a LRB and SLD is shown in Figure 34 This Figure shows that the bearing must be designed within the limits of vertical stress horizontal displacement and limitation by buckling of bearing In Figure 34 ultimate deformation u is derived from 13 of ultimate vertical design strength Fc For typical devices safety factors are given as follows
=08 for elastomeric isolator =09 for sliding bearing and rotating ball bearing =10 for damper and restorer Table 33 Characteristics of isolation devices
Name of device LRB3) SLD SD
Type name RB80S RB80 SC60 SC70 SD-U
G of rubber Nmm2 039 039 078 078
Diameter mm 800 800 600 700 45
Rubber Thickness mm 6 6 5 5
Number of sheet of rubber 33 30 4 4
Total thickness of rubber mm 198 180 20 20
S1 317 317 29 335
S2 40 44 30 35
Unloading stiffness K1 kNmm 099 109 11 15 76
Post yielding stiffness K2 kNmm 099 109 0 0 0128
Friction Factor - - 0011 0011 -
Yield load Qy kN - - 412 540 184
Vertical Stiffness kNmm 2480 2730 10600 14400 -
Tensile Strength kN 501 501 0 0 -
Allowable Stress Nmm2 10 10 17 17
Allowable Load kN 3748 4910 0
Ultimate compressive
strength cr Nmm2 45 49 57 57 -
Fc Nmm2 41 41 51 51
ultimate deformation u m 0679 0617 055 055 065
safety factor 08 08 09 09 10
design displacement limit
md m 0543 0494 0495 0495 065
10
Figure 34 Design displacement limits for a LRB and SLD
Ultimate compressive strength
Vertical design strength
≦ 09 cr
Design limit
Ultimate compressive strength
Fc
Vertical design strength
≦ 09 cr
Fc 3
Design limit
cr
09 cr
Displacement
u md
LRB
SLD
Displacement
u md
Fc 3
Fc
cr
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
3
2 Calculation procedure 21 Applicability of ELM In Figure 1 is shown the choice of the calculation route following the Japanese code The ELM is used at limited conditions shown in Table 2 for buildings that are less than 60m high that have SI layer located above the ground and that have first or second class ground classification etc
The THAM is possible for all buildings as follows Following Table 2 the applicability of the ELM is checked over as follows (Section22 23)
Figure 1 Choice of the calculation route
Table 2 Applicability of the ELM
Limitation on ground class Ⅰ Ⅱ
Maximum height of superstructure 60m
Location of devices Base only
Maximum mass-stiffness center eccentricity 3
Tension in isolator Not allowed
Yield strength gt 003W
Period range of Te T2 gt 25s
Structural calculation for SI buildings
Confirmation by a building official
Less than 60m
Location of SI layer
Building height
Within building
First class and second class ground
without possibility of liquefaction
Above the ground or on the top
of the basement
Ground classification
T H A M
More than 60m
Calculation Methods
Second class with possibility of liquefaction
or third class
Approval by MLIT
E L M
4
22 Structural calculation procedure for SI buildings Generally the ELM can be illustrated as follows The base shear force is obtained from the spectral acceleration and weight as shown in Equation (1)
e
eaeh
K
TSThFM )()(=
11=r (1)
rr =
es KQ = where design displacement of the isolation system
M total weight of the building Fh(hTe) response reduction factor h effective damping Sa(Te)(g) site response acceleration considering site soil conditions Ke effective stiffness of the isolation system r the maximum design displacement used to determine the clearance coefficient related to the eccentricity of the isolation system safety factor related to variation of properties with temperature ageing or products
tolerances discrepancy introduced in the Japanese code Qs shear force in the base of the superstructure
In general the five percent-damped spectral acceleration Sa(T) is given by Equation (2)
)()()( 0 TSTGZTS sa = (2) where
Z the seismic hazard zone factor Gs(T) a soil amplification factor dependent on the soil profile S0(T) the design spectral acceleration at engineering bedrock (Vsgt400ms) defined in Equation (3) which is shown in Figure 1 for Level 2 input
+
=
TT
T
TT
smS
640125
64016008
1603023
)( 20 (3)
The site amplification coefficient Gs(T) is defined in Figure 32 based on different site classes However in the engineering practice the Gs(T) is usually calculated iteratively based on the investigated Vs or N values and types for the soil profile rather than directly using the coefficients defined in the code The zone coefficient Z is divided into four levels as 10 09 08 and 07(Okinawa only) within Japan
12
10
08
06
04
02
00
Sp
ectr
al a
ccel
erat
ion
(m
s2)
Period (s)016 064 T (s)
512T
Figure 1 Design spectral acceleration at the engineering bedrock (Vsgt400ms)
5
The response reduction factor Fh (hTe) is defined in Equation (4) by using the effective viscous damping of a fluid damper hv and a hysteretic damper hd which is decreased to 80 percent of the effective damping for a combined viscous-hysteretic system
40)80(101
51
++= h
dvh F
hhF (4)
To use ELM calculation model must appropriately evaluate one mass for superstructure and characteristics of isolation devices at supposed response range Modeling of isolation devices must appropriately evaluate stiffness and damping characteristics based on the test data by manufacturer
The convergence procedure of the ELM is shown in Figure 2 The procedure is summarized as follows
bullAssume a displacement of the isolation system DD0 () bullCalculate the effective stiffness Ke and effective damping e(h) of the isolation system assuming a bi-linear model for the isolation system bullCalculate the equivalent period Te of the isolation system bullCalculate the corresponding response reduction factor Fh(hT e) and the spectral acceleration Sa(Te) bullCalculate a new isolation system displacement DD() using Equation (1) bullRepeat the above steps until DD() converges
Hysteresis loop
2nd
1st
3rd
Q
DD D
QISO
K1stK2nd
K3rd
DD0
Figure 2 Illustration of the convergence procedure for the ELM 23 Synopsis of ELM Step by step procedure to use ELM is summarized as follows 1 Assumption for sections of frame members of the building
The item is done by SE using the method that are similar to conventional buildings 2 Selection of devices for SI
Devices for SI are selected from those approved by MLIT and their performance is checked to determine which are allowable compressive capacity horizontal stiffness ultimate deformation capacity etc
3 Arrangement of devices in SI layer The item is the arrangement of devices which must have an eccentricity-ratio in SI layer of 3 or less
4 Setting of acceleration spectrum on the surface of the site The setting of acceleration spectrum on the surface of the site is necessary for achieving displacement and shear force of SI layer Therefore soil property conditions on the site should be checked The soil amplification factor Gs(T) is usually calculated iteratively based on the investigated Vs or N values and types for the soil profile
6
5 Calculation of response displacement and shear-force of the SI layer The item is calculation of response displacement and shear-force of the SI layer on the above spectrum with damping factor by using the design limit deformation based on the design limit period
6 Calculation of shear-force of superstructure and substructure The above shear-force is distributed to each story of the superstructure by using the distribution rule
7 Evaluation of response values of SI layer from wind load The item is evaluation of response values of SI layer for wind load on the restoring force-displacement curve of SI layer to confirm safety against extremely rare-occurring strong winds
8 Confirmation of safety of devices for vertical load The eighth item is confirmation of safety of devices against vertical load during earthquakes Stress must be below allowable stress against vertical loads including up and down acceleration of 30 of a building own-weight No minus stress is allowable for bearings
9 Securing safety of connections of devices to structures Securing of safety of connection of devices to structures such as footings capitals girders and columns is important to make use of the performance of devices
10 Confirmation of satisfaction of stipulations on SI system Finally SI system must satisfy stipulations which are as follows bullClearance (space moat gap) is required to secure displacement which includes response value and certain safety-margin value as below
No passerby 10 cm General 20 cm Passerby 80 cm
bullMovement of SI building must be maintained in heavy snow falls bullExchange of devices or checking devices must be possible bullA notice-board or an indicator for ldquo this building is seismically isolatedrdquo is required
24 Other important matters for SI buildings In addition to the above the following items are important matters for SI buildings bullArchitectural Planning (a) Planning of Isolation Layer
Architectural details in or in the vicinity of the isolation layer must be planned so as not to cause injury to humans or damage architectural members considering that the isolation layer deforms significantly during earthquakes
(b) Fire Resistive Covering and Performance of Isolators The isolators must support superstructure without losing supporting capacity of vertical loads subjected to fires expected to happen in or in the vicinity of the isolation layer
Fire resistive covering must protect isolators until fire ends It must follow the expected deformation of isolators without covering materials falling off
bullPlanning of Equipment System Equipment in the vicinity of the isolation layer must be planned in order for their functions to be
maintained during earthquakes considering large displacement at the isolation layer bullConstruction SE must inform the constructor of design-demand requirements at construction stage Also
construction supervisor must supervise the suggested construction planning and the undertaken construction to provide expected performance as a SI building
bullMaintenance Building owner must properly maintain own building after completion SE must draw up
maintenance plans and inform the owner so that the required SI performance is maintained during the buildingrsquos lifetime
7
3 Example of a seven-story RC building Synopsis of ELM described in section 23 will be used to calculate the seven-story building 31 Building model The outline of the building is shown below The elevation span-direction and longitudinal-direction draws are shown in Figure 31 Typical plan is shown in Figure 32
Principal use Condominium
Total floor area 1470m2
Maximum eaves height 220m
Classification of
structure Reinforced concrete structure
Structural type X(lateral) direction Moment frames
Y(longitudinal) direction Moment frames
with bearing walls
Ground classification Second class (Tg=034s)
Foundation Direct
1
38
03
00
30
03
00
30
03
00
32
0
2
3
4
5
6
7
8
500 500
38
03
00
30
03
00
30
03
00
32
0
X2X1 X3 X4Y1 Y2
700700 700
Figure 31 The elevation span-direction and longitudinal-direction draws
Figure 32 Typical plan of the building
X1 X4
Y1
Y2
8
The story mass and horizontal stiffness of both X Y direction of the building are summarized in Table 31 The fundamental periods of the fixed-base model are Tx = 0682s and Ty = 0258s The vertical loads of each column on isolation devices are summarized in Table 32
Table 31 Story mass and the horizontal stiffness of the building
Horizontal stiffness
(kNmm)
Height(m) Weight
(kN)
X Y
7 320 2854 325 1144
6 300 3328 449 2168
5 300 3293 488 2845
4 300 3331 560 3449
3 300 3379 635 4191
2 300 3390 720 5363
1 380 4220 778 10690
SI 150 4461
Total 28256
Table 32 Vertical loads on isolation devices (kN)
X1 X2 X3 X4
Y2 4363 5161 4659 2975
Y1 2539 3767 3728 2504
32 Selection of devices for SI Figure 34 shows the layout of isolation devices for the building A combination of LRBs (RB80 RB80S) SLDs (SC60 SC70) and SDs are selected to give a demonstration of the calculation procedure The sketch of the used isolation devices is shown in Figure 33
Figure 33 Sketch of the isolation devices
(from left LRB SLD SD)
The characteristics of each device are shown in Table 33 The design displacement limit δs at the isolation interface is determined as the minimum value of the design displacement limit md for all components of the isolation system The design displacement limit md for each device is obtained by multiplying the safety factor β by the ultimate deformation u for each device The value of the safety factor β is based on empirical knowledge resulting from experimental data obtained in
Steel Damper Rod
9
Japan A typical example of determining md for a LRB and SLD is shown in Figure 34 This Figure shows that the bearing must be designed within the limits of vertical stress horizontal displacement and limitation by buckling of bearing In Figure 34 ultimate deformation u is derived from 13 of ultimate vertical design strength Fc For typical devices safety factors are given as follows
=08 for elastomeric isolator =09 for sliding bearing and rotating ball bearing =10 for damper and restorer Table 33 Characteristics of isolation devices
Name of device LRB3) SLD SD
Type name RB80S RB80 SC60 SC70 SD-U
G of rubber Nmm2 039 039 078 078
Diameter mm 800 800 600 700 45
Rubber Thickness mm 6 6 5 5
Number of sheet of rubber 33 30 4 4
Total thickness of rubber mm 198 180 20 20
S1 317 317 29 335
S2 40 44 30 35
Unloading stiffness K1 kNmm 099 109 11 15 76
Post yielding stiffness K2 kNmm 099 109 0 0 0128
Friction Factor - - 0011 0011 -
Yield load Qy kN - - 412 540 184
Vertical Stiffness kNmm 2480 2730 10600 14400 -
Tensile Strength kN 501 501 0 0 -
Allowable Stress Nmm2 10 10 17 17
Allowable Load kN 3748 4910 0
Ultimate compressive
strength cr Nmm2 45 49 57 57 -
Fc Nmm2 41 41 51 51
ultimate deformation u m 0679 0617 055 055 065
safety factor 08 08 09 09 10
design displacement limit
md m 0543 0494 0495 0495 065
10
Figure 34 Design displacement limits for a LRB and SLD
Ultimate compressive strength
Vertical design strength
≦ 09 cr
Design limit
Ultimate compressive strength
Fc
Vertical design strength
≦ 09 cr
Fc 3
Design limit
cr
09 cr
Displacement
u md
LRB
SLD
Displacement
u md
Fc 3
Fc
cr
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
4
22 Structural calculation procedure for SI buildings Generally the ELM can be illustrated as follows The base shear force is obtained from the spectral acceleration and weight as shown in Equation (1)
e
eaeh
K
TSThFM )()(=
11=r (1)
rr =
es KQ = where design displacement of the isolation system
M total weight of the building Fh(hTe) response reduction factor h effective damping Sa(Te)(g) site response acceleration considering site soil conditions Ke effective stiffness of the isolation system r the maximum design displacement used to determine the clearance coefficient related to the eccentricity of the isolation system safety factor related to variation of properties with temperature ageing or products
tolerances discrepancy introduced in the Japanese code Qs shear force in the base of the superstructure
In general the five percent-damped spectral acceleration Sa(T) is given by Equation (2)
)()()( 0 TSTGZTS sa = (2) where
Z the seismic hazard zone factor Gs(T) a soil amplification factor dependent on the soil profile S0(T) the design spectral acceleration at engineering bedrock (Vsgt400ms) defined in Equation (3) which is shown in Figure 1 for Level 2 input
+
=
TT
T
TT
smS
640125
64016008
1603023
)( 20 (3)
The site amplification coefficient Gs(T) is defined in Figure 32 based on different site classes However in the engineering practice the Gs(T) is usually calculated iteratively based on the investigated Vs or N values and types for the soil profile rather than directly using the coefficients defined in the code The zone coefficient Z is divided into four levels as 10 09 08 and 07(Okinawa only) within Japan
12
10
08
06
04
02
00
Sp
ectr
al a
ccel
erat
ion
(m
s2)
Period (s)016 064 T (s)
512T
Figure 1 Design spectral acceleration at the engineering bedrock (Vsgt400ms)
5
The response reduction factor Fh (hTe) is defined in Equation (4) by using the effective viscous damping of a fluid damper hv and a hysteretic damper hd which is decreased to 80 percent of the effective damping for a combined viscous-hysteretic system
40)80(101
51
++= h
dvh F
hhF (4)
To use ELM calculation model must appropriately evaluate one mass for superstructure and characteristics of isolation devices at supposed response range Modeling of isolation devices must appropriately evaluate stiffness and damping characteristics based on the test data by manufacturer
The convergence procedure of the ELM is shown in Figure 2 The procedure is summarized as follows
bullAssume a displacement of the isolation system DD0 () bullCalculate the effective stiffness Ke and effective damping e(h) of the isolation system assuming a bi-linear model for the isolation system bullCalculate the equivalent period Te of the isolation system bullCalculate the corresponding response reduction factor Fh(hT e) and the spectral acceleration Sa(Te) bullCalculate a new isolation system displacement DD() using Equation (1) bullRepeat the above steps until DD() converges
Hysteresis loop
2nd
1st
3rd
Q
DD D
QISO
K1stK2nd
K3rd
DD0
Figure 2 Illustration of the convergence procedure for the ELM 23 Synopsis of ELM Step by step procedure to use ELM is summarized as follows 1 Assumption for sections of frame members of the building
The item is done by SE using the method that are similar to conventional buildings 2 Selection of devices for SI
Devices for SI are selected from those approved by MLIT and their performance is checked to determine which are allowable compressive capacity horizontal stiffness ultimate deformation capacity etc
3 Arrangement of devices in SI layer The item is the arrangement of devices which must have an eccentricity-ratio in SI layer of 3 or less
4 Setting of acceleration spectrum on the surface of the site The setting of acceleration spectrum on the surface of the site is necessary for achieving displacement and shear force of SI layer Therefore soil property conditions on the site should be checked The soil amplification factor Gs(T) is usually calculated iteratively based on the investigated Vs or N values and types for the soil profile
6
5 Calculation of response displacement and shear-force of the SI layer The item is calculation of response displacement and shear-force of the SI layer on the above spectrum with damping factor by using the design limit deformation based on the design limit period
6 Calculation of shear-force of superstructure and substructure The above shear-force is distributed to each story of the superstructure by using the distribution rule
7 Evaluation of response values of SI layer from wind load The item is evaluation of response values of SI layer for wind load on the restoring force-displacement curve of SI layer to confirm safety against extremely rare-occurring strong winds
8 Confirmation of safety of devices for vertical load The eighth item is confirmation of safety of devices against vertical load during earthquakes Stress must be below allowable stress against vertical loads including up and down acceleration of 30 of a building own-weight No minus stress is allowable for bearings
9 Securing safety of connections of devices to structures Securing of safety of connection of devices to structures such as footings capitals girders and columns is important to make use of the performance of devices
10 Confirmation of satisfaction of stipulations on SI system Finally SI system must satisfy stipulations which are as follows bullClearance (space moat gap) is required to secure displacement which includes response value and certain safety-margin value as below
No passerby 10 cm General 20 cm Passerby 80 cm
bullMovement of SI building must be maintained in heavy snow falls bullExchange of devices or checking devices must be possible bullA notice-board or an indicator for ldquo this building is seismically isolatedrdquo is required
24 Other important matters for SI buildings In addition to the above the following items are important matters for SI buildings bullArchitectural Planning (a) Planning of Isolation Layer
Architectural details in or in the vicinity of the isolation layer must be planned so as not to cause injury to humans or damage architectural members considering that the isolation layer deforms significantly during earthquakes
(b) Fire Resistive Covering and Performance of Isolators The isolators must support superstructure without losing supporting capacity of vertical loads subjected to fires expected to happen in or in the vicinity of the isolation layer
Fire resistive covering must protect isolators until fire ends It must follow the expected deformation of isolators without covering materials falling off
bullPlanning of Equipment System Equipment in the vicinity of the isolation layer must be planned in order for their functions to be
maintained during earthquakes considering large displacement at the isolation layer bullConstruction SE must inform the constructor of design-demand requirements at construction stage Also
construction supervisor must supervise the suggested construction planning and the undertaken construction to provide expected performance as a SI building
bullMaintenance Building owner must properly maintain own building after completion SE must draw up
maintenance plans and inform the owner so that the required SI performance is maintained during the buildingrsquos lifetime
7
3 Example of a seven-story RC building Synopsis of ELM described in section 23 will be used to calculate the seven-story building 31 Building model The outline of the building is shown below The elevation span-direction and longitudinal-direction draws are shown in Figure 31 Typical plan is shown in Figure 32
Principal use Condominium
Total floor area 1470m2
Maximum eaves height 220m
Classification of
structure Reinforced concrete structure
Structural type X(lateral) direction Moment frames
Y(longitudinal) direction Moment frames
with bearing walls
Ground classification Second class (Tg=034s)
Foundation Direct
1
38
03
00
30
03
00
30
03
00
32
0
2
3
4
5
6
7
8
500 500
38
03
00
30
03
00
30
03
00
32
0
X2X1 X3 X4Y1 Y2
700700 700
Figure 31 The elevation span-direction and longitudinal-direction draws
Figure 32 Typical plan of the building
X1 X4
Y1
Y2
8
The story mass and horizontal stiffness of both X Y direction of the building are summarized in Table 31 The fundamental periods of the fixed-base model are Tx = 0682s and Ty = 0258s The vertical loads of each column on isolation devices are summarized in Table 32
Table 31 Story mass and the horizontal stiffness of the building
Horizontal stiffness
(kNmm)
Height(m) Weight
(kN)
X Y
7 320 2854 325 1144
6 300 3328 449 2168
5 300 3293 488 2845
4 300 3331 560 3449
3 300 3379 635 4191
2 300 3390 720 5363
1 380 4220 778 10690
SI 150 4461
Total 28256
Table 32 Vertical loads on isolation devices (kN)
X1 X2 X3 X4
Y2 4363 5161 4659 2975
Y1 2539 3767 3728 2504
32 Selection of devices for SI Figure 34 shows the layout of isolation devices for the building A combination of LRBs (RB80 RB80S) SLDs (SC60 SC70) and SDs are selected to give a demonstration of the calculation procedure The sketch of the used isolation devices is shown in Figure 33
Figure 33 Sketch of the isolation devices
(from left LRB SLD SD)
The characteristics of each device are shown in Table 33 The design displacement limit δs at the isolation interface is determined as the minimum value of the design displacement limit md for all components of the isolation system The design displacement limit md for each device is obtained by multiplying the safety factor β by the ultimate deformation u for each device The value of the safety factor β is based on empirical knowledge resulting from experimental data obtained in
Steel Damper Rod
9
Japan A typical example of determining md for a LRB and SLD is shown in Figure 34 This Figure shows that the bearing must be designed within the limits of vertical stress horizontal displacement and limitation by buckling of bearing In Figure 34 ultimate deformation u is derived from 13 of ultimate vertical design strength Fc For typical devices safety factors are given as follows
=08 for elastomeric isolator =09 for sliding bearing and rotating ball bearing =10 for damper and restorer Table 33 Characteristics of isolation devices
Name of device LRB3) SLD SD
Type name RB80S RB80 SC60 SC70 SD-U
G of rubber Nmm2 039 039 078 078
Diameter mm 800 800 600 700 45
Rubber Thickness mm 6 6 5 5
Number of sheet of rubber 33 30 4 4
Total thickness of rubber mm 198 180 20 20
S1 317 317 29 335
S2 40 44 30 35
Unloading stiffness K1 kNmm 099 109 11 15 76
Post yielding stiffness K2 kNmm 099 109 0 0 0128
Friction Factor - - 0011 0011 -
Yield load Qy kN - - 412 540 184
Vertical Stiffness kNmm 2480 2730 10600 14400 -
Tensile Strength kN 501 501 0 0 -
Allowable Stress Nmm2 10 10 17 17
Allowable Load kN 3748 4910 0
Ultimate compressive
strength cr Nmm2 45 49 57 57 -
Fc Nmm2 41 41 51 51
ultimate deformation u m 0679 0617 055 055 065
safety factor 08 08 09 09 10
design displacement limit
md m 0543 0494 0495 0495 065
10
Figure 34 Design displacement limits for a LRB and SLD
Ultimate compressive strength
Vertical design strength
≦ 09 cr
Design limit
Ultimate compressive strength
Fc
Vertical design strength
≦ 09 cr
Fc 3
Design limit
cr
09 cr
Displacement
u md
LRB
SLD
Displacement
u md
Fc 3
Fc
cr
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
5
The response reduction factor Fh (hTe) is defined in Equation (4) by using the effective viscous damping of a fluid damper hv and a hysteretic damper hd which is decreased to 80 percent of the effective damping for a combined viscous-hysteretic system
40)80(101
51
++= h
dvh F
hhF (4)
To use ELM calculation model must appropriately evaluate one mass for superstructure and characteristics of isolation devices at supposed response range Modeling of isolation devices must appropriately evaluate stiffness and damping characteristics based on the test data by manufacturer
The convergence procedure of the ELM is shown in Figure 2 The procedure is summarized as follows
bullAssume a displacement of the isolation system DD0 () bullCalculate the effective stiffness Ke and effective damping e(h) of the isolation system assuming a bi-linear model for the isolation system bullCalculate the equivalent period Te of the isolation system bullCalculate the corresponding response reduction factor Fh(hT e) and the spectral acceleration Sa(Te) bullCalculate a new isolation system displacement DD() using Equation (1) bullRepeat the above steps until DD() converges
Hysteresis loop
2nd
1st
3rd
Q
DD D
QISO
K1stK2nd
K3rd
DD0
Figure 2 Illustration of the convergence procedure for the ELM 23 Synopsis of ELM Step by step procedure to use ELM is summarized as follows 1 Assumption for sections of frame members of the building
The item is done by SE using the method that are similar to conventional buildings 2 Selection of devices for SI
Devices for SI are selected from those approved by MLIT and their performance is checked to determine which are allowable compressive capacity horizontal stiffness ultimate deformation capacity etc
3 Arrangement of devices in SI layer The item is the arrangement of devices which must have an eccentricity-ratio in SI layer of 3 or less
4 Setting of acceleration spectrum on the surface of the site The setting of acceleration spectrum on the surface of the site is necessary for achieving displacement and shear force of SI layer Therefore soil property conditions on the site should be checked The soil amplification factor Gs(T) is usually calculated iteratively based on the investigated Vs or N values and types for the soil profile
6
5 Calculation of response displacement and shear-force of the SI layer The item is calculation of response displacement and shear-force of the SI layer on the above spectrum with damping factor by using the design limit deformation based on the design limit period
6 Calculation of shear-force of superstructure and substructure The above shear-force is distributed to each story of the superstructure by using the distribution rule
7 Evaluation of response values of SI layer from wind load The item is evaluation of response values of SI layer for wind load on the restoring force-displacement curve of SI layer to confirm safety against extremely rare-occurring strong winds
8 Confirmation of safety of devices for vertical load The eighth item is confirmation of safety of devices against vertical load during earthquakes Stress must be below allowable stress against vertical loads including up and down acceleration of 30 of a building own-weight No minus stress is allowable for bearings
9 Securing safety of connections of devices to structures Securing of safety of connection of devices to structures such as footings capitals girders and columns is important to make use of the performance of devices
10 Confirmation of satisfaction of stipulations on SI system Finally SI system must satisfy stipulations which are as follows bullClearance (space moat gap) is required to secure displacement which includes response value and certain safety-margin value as below
No passerby 10 cm General 20 cm Passerby 80 cm
bullMovement of SI building must be maintained in heavy snow falls bullExchange of devices or checking devices must be possible bullA notice-board or an indicator for ldquo this building is seismically isolatedrdquo is required
24 Other important matters for SI buildings In addition to the above the following items are important matters for SI buildings bullArchitectural Planning (a) Planning of Isolation Layer
Architectural details in or in the vicinity of the isolation layer must be planned so as not to cause injury to humans or damage architectural members considering that the isolation layer deforms significantly during earthquakes
(b) Fire Resistive Covering and Performance of Isolators The isolators must support superstructure without losing supporting capacity of vertical loads subjected to fires expected to happen in or in the vicinity of the isolation layer
Fire resistive covering must protect isolators until fire ends It must follow the expected deformation of isolators without covering materials falling off
bullPlanning of Equipment System Equipment in the vicinity of the isolation layer must be planned in order for their functions to be
maintained during earthquakes considering large displacement at the isolation layer bullConstruction SE must inform the constructor of design-demand requirements at construction stage Also
construction supervisor must supervise the suggested construction planning and the undertaken construction to provide expected performance as a SI building
bullMaintenance Building owner must properly maintain own building after completion SE must draw up
maintenance plans and inform the owner so that the required SI performance is maintained during the buildingrsquos lifetime
7
3 Example of a seven-story RC building Synopsis of ELM described in section 23 will be used to calculate the seven-story building 31 Building model The outline of the building is shown below The elevation span-direction and longitudinal-direction draws are shown in Figure 31 Typical plan is shown in Figure 32
Principal use Condominium
Total floor area 1470m2
Maximum eaves height 220m
Classification of
structure Reinforced concrete structure
Structural type X(lateral) direction Moment frames
Y(longitudinal) direction Moment frames
with bearing walls
Ground classification Second class (Tg=034s)
Foundation Direct
1
38
03
00
30
03
00
30
03
00
32
0
2
3
4
5
6
7
8
500 500
38
03
00
30
03
00
30
03
00
32
0
X2X1 X3 X4Y1 Y2
700700 700
Figure 31 The elevation span-direction and longitudinal-direction draws
Figure 32 Typical plan of the building
X1 X4
Y1
Y2
8
The story mass and horizontal stiffness of both X Y direction of the building are summarized in Table 31 The fundamental periods of the fixed-base model are Tx = 0682s and Ty = 0258s The vertical loads of each column on isolation devices are summarized in Table 32
Table 31 Story mass and the horizontal stiffness of the building
Horizontal stiffness
(kNmm)
Height(m) Weight
(kN)
X Y
7 320 2854 325 1144
6 300 3328 449 2168
5 300 3293 488 2845
4 300 3331 560 3449
3 300 3379 635 4191
2 300 3390 720 5363
1 380 4220 778 10690
SI 150 4461
Total 28256
Table 32 Vertical loads on isolation devices (kN)
X1 X2 X3 X4
Y2 4363 5161 4659 2975
Y1 2539 3767 3728 2504
32 Selection of devices for SI Figure 34 shows the layout of isolation devices for the building A combination of LRBs (RB80 RB80S) SLDs (SC60 SC70) and SDs are selected to give a demonstration of the calculation procedure The sketch of the used isolation devices is shown in Figure 33
Figure 33 Sketch of the isolation devices
(from left LRB SLD SD)
The characteristics of each device are shown in Table 33 The design displacement limit δs at the isolation interface is determined as the minimum value of the design displacement limit md for all components of the isolation system The design displacement limit md for each device is obtained by multiplying the safety factor β by the ultimate deformation u for each device The value of the safety factor β is based on empirical knowledge resulting from experimental data obtained in
Steel Damper Rod
9
Japan A typical example of determining md for a LRB and SLD is shown in Figure 34 This Figure shows that the bearing must be designed within the limits of vertical stress horizontal displacement and limitation by buckling of bearing In Figure 34 ultimate deformation u is derived from 13 of ultimate vertical design strength Fc For typical devices safety factors are given as follows
=08 for elastomeric isolator =09 for sliding bearing and rotating ball bearing =10 for damper and restorer Table 33 Characteristics of isolation devices
Name of device LRB3) SLD SD
Type name RB80S RB80 SC60 SC70 SD-U
G of rubber Nmm2 039 039 078 078
Diameter mm 800 800 600 700 45
Rubber Thickness mm 6 6 5 5
Number of sheet of rubber 33 30 4 4
Total thickness of rubber mm 198 180 20 20
S1 317 317 29 335
S2 40 44 30 35
Unloading stiffness K1 kNmm 099 109 11 15 76
Post yielding stiffness K2 kNmm 099 109 0 0 0128
Friction Factor - - 0011 0011 -
Yield load Qy kN - - 412 540 184
Vertical Stiffness kNmm 2480 2730 10600 14400 -
Tensile Strength kN 501 501 0 0 -
Allowable Stress Nmm2 10 10 17 17
Allowable Load kN 3748 4910 0
Ultimate compressive
strength cr Nmm2 45 49 57 57 -
Fc Nmm2 41 41 51 51
ultimate deformation u m 0679 0617 055 055 065
safety factor 08 08 09 09 10
design displacement limit
md m 0543 0494 0495 0495 065
10
Figure 34 Design displacement limits for a LRB and SLD
Ultimate compressive strength
Vertical design strength
≦ 09 cr
Design limit
Ultimate compressive strength
Fc
Vertical design strength
≦ 09 cr
Fc 3
Design limit
cr
09 cr
Displacement
u md
LRB
SLD
Displacement
u md
Fc 3
Fc
cr
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
6
5 Calculation of response displacement and shear-force of the SI layer The item is calculation of response displacement and shear-force of the SI layer on the above spectrum with damping factor by using the design limit deformation based on the design limit period
6 Calculation of shear-force of superstructure and substructure The above shear-force is distributed to each story of the superstructure by using the distribution rule
7 Evaluation of response values of SI layer from wind load The item is evaluation of response values of SI layer for wind load on the restoring force-displacement curve of SI layer to confirm safety against extremely rare-occurring strong winds
8 Confirmation of safety of devices for vertical load The eighth item is confirmation of safety of devices against vertical load during earthquakes Stress must be below allowable stress against vertical loads including up and down acceleration of 30 of a building own-weight No minus stress is allowable for bearings
9 Securing safety of connections of devices to structures Securing of safety of connection of devices to structures such as footings capitals girders and columns is important to make use of the performance of devices
10 Confirmation of satisfaction of stipulations on SI system Finally SI system must satisfy stipulations which are as follows bullClearance (space moat gap) is required to secure displacement which includes response value and certain safety-margin value as below
No passerby 10 cm General 20 cm Passerby 80 cm
bullMovement of SI building must be maintained in heavy snow falls bullExchange of devices or checking devices must be possible bullA notice-board or an indicator for ldquo this building is seismically isolatedrdquo is required
24 Other important matters for SI buildings In addition to the above the following items are important matters for SI buildings bullArchitectural Planning (a) Planning of Isolation Layer
Architectural details in or in the vicinity of the isolation layer must be planned so as not to cause injury to humans or damage architectural members considering that the isolation layer deforms significantly during earthquakes
(b) Fire Resistive Covering and Performance of Isolators The isolators must support superstructure without losing supporting capacity of vertical loads subjected to fires expected to happen in or in the vicinity of the isolation layer
Fire resistive covering must protect isolators until fire ends It must follow the expected deformation of isolators without covering materials falling off
bullPlanning of Equipment System Equipment in the vicinity of the isolation layer must be planned in order for their functions to be
maintained during earthquakes considering large displacement at the isolation layer bullConstruction SE must inform the constructor of design-demand requirements at construction stage Also
construction supervisor must supervise the suggested construction planning and the undertaken construction to provide expected performance as a SI building
bullMaintenance Building owner must properly maintain own building after completion SE must draw up
maintenance plans and inform the owner so that the required SI performance is maintained during the buildingrsquos lifetime
7
3 Example of a seven-story RC building Synopsis of ELM described in section 23 will be used to calculate the seven-story building 31 Building model The outline of the building is shown below The elevation span-direction and longitudinal-direction draws are shown in Figure 31 Typical plan is shown in Figure 32
Principal use Condominium
Total floor area 1470m2
Maximum eaves height 220m
Classification of
structure Reinforced concrete structure
Structural type X(lateral) direction Moment frames
Y(longitudinal) direction Moment frames
with bearing walls
Ground classification Second class (Tg=034s)
Foundation Direct
1
38
03
00
30
03
00
30
03
00
32
0
2
3
4
5
6
7
8
500 500
38
03
00
30
03
00
30
03
00
32
0
X2X1 X3 X4Y1 Y2
700700 700
Figure 31 The elevation span-direction and longitudinal-direction draws
Figure 32 Typical plan of the building
X1 X4
Y1
Y2
8
The story mass and horizontal stiffness of both X Y direction of the building are summarized in Table 31 The fundamental periods of the fixed-base model are Tx = 0682s and Ty = 0258s The vertical loads of each column on isolation devices are summarized in Table 32
Table 31 Story mass and the horizontal stiffness of the building
Horizontal stiffness
(kNmm)
Height(m) Weight
(kN)
X Y
7 320 2854 325 1144
6 300 3328 449 2168
5 300 3293 488 2845
4 300 3331 560 3449
3 300 3379 635 4191
2 300 3390 720 5363
1 380 4220 778 10690
SI 150 4461
Total 28256
Table 32 Vertical loads on isolation devices (kN)
X1 X2 X3 X4
Y2 4363 5161 4659 2975
Y1 2539 3767 3728 2504
32 Selection of devices for SI Figure 34 shows the layout of isolation devices for the building A combination of LRBs (RB80 RB80S) SLDs (SC60 SC70) and SDs are selected to give a demonstration of the calculation procedure The sketch of the used isolation devices is shown in Figure 33
Figure 33 Sketch of the isolation devices
(from left LRB SLD SD)
The characteristics of each device are shown in Table 33 The design displacement limit δs at the isolation interface is determined as the minimum value of the design displacement limit md for all components of the isolation system The design displacement limit md for each device is obtained by multiplying the safety factor β by the ultimate deformation u for each device The value of the safety factor β is based on empirical knowledge resulting from experimental data obtained in
Steel Damper Rod
9
Japan A typical example of determining md for a LRB and SLD is shown in Figure 34 This Figure shows that the bearing must be designed within the limits of vertical stress horizontal displacement and limitation by buckling of bearing In Figure 34 ultimate deformation u is derived from 13 of ultimate vertical design strength Fc For typical devices safety factors are given as follows
=08 for elastomeric isolator =09 for sliding bearing and rotating ball bearing =10 for damper and restorer Table 33 Characteristics of isolation devices
Name of device LRB3) SLD SD
Type name RB80S RB80 SC60 SC70 SD-U
G of rubber Nmm2 039 039 078 078
Diameter mm 800 800 600 700 45
Rubber Thickness mm 6 6 5 5
Number of sheet of rubber 33 30 4 4
Total thickness of rubber mm 198 180 20 20
S1 317 317 29 335
S2 40 44 30 35
Unloading stiffness K1 kNmm 099 109 11 15 76
Post yielding stiffness K2 kNmm 099 109 0 0 0128
Friction Factor - - 0011 0011 -
Yield load Qy kN - - 412 540 184
Vertical Stiffness kNmm 2480 2730 10600 14400 -
Tensile Strength kN 501 501 0 0 -
Allowable Stress Nmm2 10 10 17 17
Allowable Load kN 3748 4910 0
Ultimate compressive
strength cr Nmm2 45 49 57 57 -
Fc Nmm2 41 41 51 51
ultimate deformation u m 0679 0617 055 055 065
safety factor 08 08 09 09 10
design displacement limit
md m 0543 0494 0495 0495 065
10
Figure 34 Design displacement limits for a LRB and SLD
Ultimate compressive strength
Vertical design strength
≦ 09 cr
Design limit
Ultimate compressive strength
Fc
Vertical design strength
≦ 09 cr
Fc 3
Design limit
cr
09 cr
Displacement
u md
LRB
SLD
Displacement
u md
Fc 3
Fc
cr
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
7
3 Example of a seven-story RC building Synopsis of ELM described in section 23 will be used to calculate the seven-story building 31 Building model The outline of the building is shown below The elevation span-direction and longitudinal-direction draws are shown in Figure 31 Typical plan is shown in Figure 32
Principal use Condominium
Total floor area 1470m2
Maximum eaves height 220m
Classification of
structure Reinforced concrete structure
Structural type X(lateral) direction Moment frames
Y(longitudinal) direction Moment frames
with bearing walls
Ground classification Second class (Tg=034s)
Foundation Direct
1
38
03
00
30
03
00
30
03
00
32
0
2
3
4
5
6
7
8
500 500
38
03
00
30
03
00
30
03
00
32
0
X2X1 X3 X4Y1 Y2
700700 700
Figure 31 The elevation span-direction and longitudinal-direction draws
Figure 32 Typical plan of the building
X1 X4
Y1
Y2
8
The story mass and horizontal stiffness of both X Y direction of the building are summarized in Table 31 The fundamental periods of the fixed-base model are Tx = 0682s and Ty = 0258s The vertical loads of each column on isolation devices are summarized in Table 32
Table 31 Story mass and the horizontal stiffness of the building
Horizontal stiffness
(kNmm)
Height(m) Weight
(kN)
X Y
7 320 2854 325 1144
6 300 3328 449 2168
5 300 3293 488 2845
4 300 3331 560 3449
3 300 3379 635 4191
2 300 3390 720 5363
1 380 4220 778 10690
SI 150 4461
Total 28256
Table 32 Vertical loads on isolation devices (kN)
X1 X2 X3 X4
Y2 4363 5161 4659 2975
Y1 2539 3767 3728 2504
32 Selection of devices for SI Figure 34 shows the layout of isolation devices for the building A combination of LRBs (RB80 RB80S) SLDs (SC60 SC70) and SDs are selected to give a demonstration of the calculation procedure The sketch of the used isolation devices is shown in Figure 33
Figure 33 Sketch of the isolation devices
(from left LRB SLD SD)
The characteristics of each device are shown in Table 33 The design displacement limit δs at the isolation interface is determined as the minimum value of the design displacement limit md for all components of the isolation system The design displacement limit md for each device is obtained by multiplying the safety factor β by the ultimate deformation u for each device The value of the safety factor β is based on empirical knowledge resulting from experimental data obtained in
Steel Damper Rod
9
Japan A typical example of determining md for a LRB and SLD is shown in Figure 34 This Figure shows that the bearing must be designed within the limits of vertical stress horizontal displacement and limitation by buckling of bearing In Figure 34 ultimate deformation u is derived from 13 of ultimate vertical design strength Fc For typical devices safety factors are given as follows
=08 for elastomeric isolator =09 for sliding bearing and rotating ball bearing =10 for damper and restorer Table 33 Characteristics of isolation devices
Name of device LRB3) SLD SD
Type name RB80S RB80 SC60 SC70 SD-U
G of rubber Nmm2 039 039 078 078
Diameter mm 800 800 600 700 45
Rubber Thickness mm 6 6 5 5
Number of sheet of rubber 33 30 4 4
Total thickness of rubber mm 198 180 20 20
S1 317 317 29 335
S2 40 44 30 35
Unloading stiffness K1 kNmm 099 109 11 15 76
Post yielding stiffness K2 kNmm 099 109 0 0 0128
Friction Factor - - 0011 0011 -
Yield load Qy kN - - 412 540 184
Vertical Stiffness kNmm 2480 2730 10600 14400 -
Tensile Strength kN 501 501 0 0 -
Allowable Stress Nmm2 10 10 17 17
Allowable Load kN 3748 4910 0
Ultimate compressive
strength cr Nmm2 45 49 57 57 -
Fc Nmm2 41 41 51 51
ultimate deformation u m 0679 0617 055 055 065
safety factor 08 08 09 09 10
design displacement limit
md m 0543 0494 0495 0495 065
10
Figure 34 Design displacement limits for a LRB and SLD
Ultimate compressive strength
Vertical design strength
≦ 09 cr
Design limit
Ultimate compressive strength
Fc
Vertical design strength
≦ 09 cr
Fc 3
Design limit
cr
09 cr
Displacement
u md
LRB
SLD
Displacement
u md
Fc 3
Fc
cr
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
8
The story mass and horizontal stiffness of both X Y direction of the building are summarized in Table 31 The fundamental periods of the fixed-base model are Tx = 0682s and Ty = 0258s The vertical loads of each column on isolation devices are summarized in Table 32
Table 31 Story mass and the horizontal stiffness of the building
Horizontal stiffness
(kNmm)
Height(m) Weight
(kN)
X Y
7 320 2854 325 1144
6 300 3328 449 2168
5 300 3293 488 2845
4 300 3331 560 3449
3 300 3379 635 4191
2 300 3390 720 5363
1 380 4220 778 10690
SI 150 4461
Total 28256
Table 32 Vertical loads on isolation devices (kN)
X1 X2 X3 X4
Y2 4363 5161 4659 2975
Y1 2539 3767 3728 2504
32 Selection of devices for SI Figure 34 shows the layout of isolation devices for the building A combination of LRBs (RB80 RB80S) SLDs (SC60 SC70) and SDs are selected to give a demonstration of the calculation procedure The sketch of the used isolation devices is shown in Figure 33
Figure 33 Sketch of the isolation devices
(from left LRB SLD SD)
The characteristics of each device are shown in Table 33 The design displacement limit δs at the isolation interface is determined as the minimum value of the design displacement limit md for all components of the isolation system The design displacement limit md for each device is obtained by multiplying the safety factor β by the ultimate deformation u for each device The value of the safety factor β is based on empirical knowledge resulting from experimental data obtained in
Steel Damper Rod
9
Japan A typical example of determining md for a LRB and SLD is shown in Figure 34 This Figure shows that the bearing must be designed within the limits of vertical stress horizontal displacement and limitation by buckling of bearing In Figure 34 ultimate deformation u is derived from 13 of ultimate vertical design strength Fc For typical devices safety factors are given as follows
=08 for elastomeric isolator =09 for sliding bearing and rotating ball bearing =10 for damper and restorer Table 33 Characteristics of isolation devices
Name of device LRB3) SLD SD
Type name RB80S RB80 SC60 SC70 SD-U
G of rubber Nmm2 039 039 078 078
Diameter mm 800 800 600 700 45
Rubber Thickness mm 6 6 5 5
Number of sheet of rubber 33 30 4 4
Total thickness of rubber mm 198 180 20 20
S1 317 317 29 335
S2 40 44 30 35
Unloading stiffness K1 kNmm 099 109 11 15 76
Post yielding stiffness K2 kNmm 099 109 0 0 0128
Friction Factor - - 0011 0011 -
Yield load Qy kN - - 412 540 184
Vertical Stiffness kNmm 2480 2730 10600 14400 -
Tensile Strength kN 501 501 0 0 -
Allowable Stress Nmm2 10 10 17 17
Allowable Load kN 3748 4910 0
Ultimate compressive
strength cr Nmm2 45 49 57 57 -
Fc Nmm2 41 41 51 51
ultimate deformation u m 0679 0617 055 055 065
safety factor 08 08 09 09 10
design displacement limit
md m 0543 0494 0495 0495 065
10
Figure 34 Design displacement limits for a LRB and SLD
Ultimate compressive strength
Vertical design strength
≦ 09 cr
Design limit
Ultimate compressive strength
Fc
Vertical design strength
≦ 09 cr
Fc 3
Design limit
cr
09 cr
Displacement
u md
LRB
SLD
Displacement
u md
Fc 3
Fc
cr
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
9
Japan A typical example of determining md for a LRB and SLD is shown in Figure 34 This Figure shows that the bearing must be designed within the limits of vertical stress horizontal displacement and limitation by buckling of bearing In Figure 34 ultimate deformation u is derived from 13 of ultimate vertical design strength Fc For typical devices safety factors are given as follows
=08 for elastomeric isolator =09 for sliding bearing and rotating ball bearing =10 for damper and restorer Table 33 Characteristics of isolation devices
Name of device LRB3) SLD SD
Type name RB80S RB80 SC60 SC70 SD-U
G of rubber Nmm2 039 039 078 078
Diameter mm 800 800 600 700 45
Rubber Thickness mm 6 6 5 5
Number of sheet of rubber 33 30 4 4
Total thickness of rubber mm 198 180 20 20
S1 317 317 29 335
S2 40 44 30 35
Unloading stiffness K1 kNmm 099 109 11 15 76
Post yielding stiffness K2 kNmm 099 109 0 0 0128
Friction Factor - - 0011 0011 -
Yield load Qy kN - - 412 540 184
Vertical Stiffness kNmm 2480 2730 10600 14400 -
Tensile Strength kN 501 501 0 0 -
Allowable Stress Nmm2 10 10 17 17
Allowable Load kN 3748 4910 0
Ultimate compressive
strength cr Nmm2 45 49 57 57 -
Fc Nmm2 41 41 51 51
ultimate deformation u m 0679 0617 055 055 065
safety factor 08 08 09 09 10
design displacement limit
md m 0543 0494 0495 0495 065
10
Figure 34 Design displacement limits for a LRB and SLD
Ultimate compressive strength
Vertical design strength
≦ 09 cr
Design limit
Ultimate compressive strength
Fc
Vertical design strength
≦ 09 cr
Fc 3
Design limit
cr
09 cr
Displacement
u md
LRB
SLD
Displacement
u md
Fc 3
Fc
cr
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
10
Figure 34 Design displacement limits for a LRB and SLD
Ultimate compressive strength
Vertical design strength
≦ 09 cr
Design limit
Ultimate compressive strength
Fc
Vertical design strength
≦ 09 cr
Fc 3
Design limit
cr
09 cr
Displacement
u md
LRB
SLD
Displacement
u md
Fc 3
Fc
cr
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
11
33 Arrangement of devices in SI layer To make the gravity center and stiffness center close the bearings are located under every column and the total yield force of the dampers is set to 39 of the weight of the superstructure to give good performance The arrangement of isolation devices in SI layer is shown in Figure 35
Dimensions and characteristics of the isolation devices are shown in Table 33 The characteristics of the building are summarized in Table 34 These devices were selected to support the vertical stress caused by the superstructure almost at the allowable pressure of each device
Plot plan of devices
SD SD
SD SDRB80S
RB80SRB80S SC60SC60
RB80 SC70SC70
-2000
0
2000
4000
6000
8000
10000
12000
-4000 0 4000 8000 12000 16000 20000 24000
X (mm)
Y( m
m)
Figure 35 Arrangement of isolation devices in SI layer
Table 34 Characteristics of the building
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
331 Eccentricity ratio of SI layer
The maximum eccentricity ratio of SI layer under displacement of 500mm is 245 which should be less than 3 In Table 35 eccentricity ratios of SI layer at each displacement are summarized The maximum eccentricity ratio = 245lt3 helliphelliphelliphellipOK
Table 35 Eccentricity ratio of SI layer at each displacement
δ(mm) 50 100 200 300 400 500
Shear strain () 25 51 101 152 202 253
Eccentricity X(mm) -35 14 71 104 126 141
Y(mm) 146 37 -91 -166 -216 -252
Eccentricity ratio X() 168 040 094 167 213 245
Y() 040 015 073 104 124 138
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
12
332 Total yield strength
The total yield strength of SI layer should be larger than 3 of the total weight upon the SI layer If we assume each footing has a weight of 50kN the check procedure is as follows
Qy=0011(5161+4659+3767+3728)+1844=926 kN
W=28256+Footing weight=28256+508=28656 kN
QyW=926528656=0032 gt 003 helliphelliphelliphellipOK
333 Period of the isolation system considering only the stiffness of LRBs
Period of the isolation system considering only the stiffness of laminated rubber bearings should be longer than 25 sec
0254572
8928656143222 ===
tK
MT gt25s helliphelliphelliphellipOK
34 Setting of acceleration spectrum on the surface of the site The acceleration spectrum on the surface of the site can be obtained by Equation (2) The design spectral acceleration at engineering bedrock (Vsgt400ms) S0(T) defined in Equation (3) which is shown in Figure 1 for Level 2 input The site amplification factor Gs is calculated based on the soil properties above engineering bedrock either by the simplified method according to the soil classification of first to third or by the precise method calculated by using the wave propagation procedure considering the non-linearity of the soil profile
In Figure 36 are shown Site amplification coefficients for the three kind site classes In this study the precise method is used In Table 36 is shown soil profile used in this study The bottom of the base is at GL-40m After several convergence calculations the ground surface acceleration spectrum was obtained and shown in Figure 37
30
25
20
15
10
05
00
Gs(
T)
543210
Period (s)
Site class 1
Site class 2 Site class 3
Figure 36 Site amplification coefficients for the three kind site classes (in Japan)
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
13
Table 36 Soil profile used for this study
Layer Soil property Depth(m) N values VS (ms) (tm3)
1 Clay 00 3 150 193
2 Clay 55 10 210 193
3 Clay 85 6 210 193
4 Sand 115 7 320 195
5 Sand 150 11 360 195
6 Sand 185 11 360 195
7 Sand 215 13 360 195
8 Sand 245 50 360 195
9 Clay 268 17 360 195
10 Sand 285 40 270 200
Bed Gravel 305 60 460 200
00
20
40
60
80
100
120
140
160
180
200
00 10 20 30 40 50
T(sec)
Res
onse
acc
eler
atio
n s
pec
trum
(ms
2)
Engineering bedrock
Ground surface by Gs
Figure 37 The ground surface acceleration spectrum
35 Calculation of response displacement and shear-force of the SI layer The SI layer in the ELM method is modeled as a normal bilinear model The constants used for the building shown in section 31-34 are summarized in Table 37 Following the convergence procedure shown in Figure 2 the response displacement of the SI layer is obtained from the ground surface acceleration spectrum shown in Figure 37 and SI characteristics shown in Table 37 In Table 37 the iteration processes are shown too
= m = = m r = r design displacement limit md
are safety factors related with temperature dependent stiffness changes and property dispersions in manufacturing of devices is used to check the response displacement to be less than design displacement limit md and secure the isolation gap is used to gain safety for both super-structure and sub-structure One may use = =13 defined in the building code or calculates the by considering the characteristics changes of the SI layer As shown in Table 38 the characteristics changes include the changes to Plus side (hardness) and Minus side (softening) In Table 39 the response results by the standard Plus change and Minus change are shown
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
14
Table 37 Iterative calculations to determine design displacement
Constants used in calculations
M 29223 kNmiddots2m K1 86460 kNm
Qy 926 kN K2 4572 kNm
Iterative Calculations Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Converged
(m) e
eaeh
K
TSThFM )()( 0416 0412 0408 0404 0400 0396
Ke (kNm)
2KQy + 6468 6500 6538 6572 6612 6649
hd 0179 0181 0184 0185 0188 0190
Fh )80(101
51
dv hh ++ 0617 0613 0608 0604 0600 0595
TD (s) eK
M2 4223 4213 4201 4190 4177 4165
)( ea TS TGs 125 0920 0916 0912 0908 0904 0900
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
15
Table 38 Characteristics changes to Plus side (hardness) and Minus side (softening)
Parameters Standard + Changes - Changes
LRB
ΣnK1(kNm) 4060 32 5359 -18 3329
Stiffness K1 Aging () 10 0
Temperature () 7 -3
Dispersion () 15 -15
SLD
ΣnK1(kNm) 52000 57 81640 -34 34320
ΣQy(kN) 190 15 2190 -25 1428
Stiffness K1 Aging () 20 0
Temperature () 7 -4
Dispersion () 20 -20
Vertical load () 10 -10
Yield load Qy Aging () 0
0
Temperature () 0 0
Dispersion () 20 -20
Vertical load () 15 15
Repetition () -20 -20
SD
ΣnK1(kNm) 30400 15 34960 -15 25840
ΣnK2(kNm) 512 0 512 0 512
ΣnQy(kN) 736 13 832 -14 640
Stiffness K1 Aging () 0 0
Temperature () 0 0
Dispersion () 15 -15
Stiffness K2 Aging () 0 0
Temperature () 0 0
Dispersion () 0 0
Yield load Qy Aging () 0
0
Temperature () 1 -2
Dispersion () 15 -10
Total
ΣnK1(kNm) 86460 +41 121959 -27 63489
ΣnK2(kNm) 4572 +28 5871 -17 3790
ΣnQy(kN) 926 +13 1051 -15 783
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
16
Table 39 Response results for standard Plus change and Minus change parameters
Parameters standard + changes - changes
Unloading stiffness K1 (kNm) 86460 121959 63489
Post yield stiffness K2 (kNm) 4572 5871 3841 Yield load Qy (kN) 926 1051 833
Amplification factor of acceleration Gs 1230 1230 1230
Equivalent viscous damping factor hd 0152 0151 0152
Reduction ratio Fh 0595 0598 0595
Shear-force of SI layer Q (kN) 2631 2991 2363
Standard displacement δ (m) 0396 0350 0440
Response displacement of SI layer δr (m) 0435 0386 0485
Max horizontal clearance
(No passerby +01) (m) 0585
Max horizontal clearance
(General +02) (m) 0685
Max horizontal clearance
(Passerby +08) (m) 1285
Shear-force of hysteretic dampers Qh (kN) 1117 1218
Shear-force of isolators and
restorers Qe (kN)
1606 1878
Seismic force subjected to SI layer Qiso (kN) 2723 3096
Coefficient of shear-force of SI layer Cr1 0095 0108
Coefficient shear-force of superstructure Cri 0099 0112
Safety factor 114
Shear force ratio for dampers gt=003 μ 0039
Tangent stiffness at standard displacement Kt (kNm) 4572
Tangent Period Ttgt=25 Tt (s) 5023
36 Calculation of shear-force of superstructure and substructure
The response results are summarized in Table 39 The detailed procedure is as follows
361 SI layer
Mg
QQA
QQQ
QQQA
Mg
QQQQQQC ehi
evh
evhivvehehri
+=
++
++++++=
)()(2)(22
3067)()(2)(22 =+=++++= ehvvehehiso QQQQQQQQQ
The calculated Ai and Cri are summarized in Table 310
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
17
362 Superstructure
The response shear force is shown in Table 310 and Figure 38 comparing with the design shear force
Table 310 Response results of super-structure and design values
Height Weight Ai Cri Qi OTM
Design
Coef Cix
Cri Qi OTM
m kN kN kNm Cix kN kNm
7 320 2854 2155 0159 454 1452 0240 1510 685 2192
6 300 3328 1728 0140 866 4050 0220 1570 1360 6272
5 300 3293 1528 0131 1243 7780 0200 1524 1895 11957
4 300 3331 1392 0125 1603 12590 0180 1438 2305 18872
3 300 3379 1284 0120 1949 18438 0160 1328 2590 26641
2 300 3390 1193 0116 2279 25275 0140 1203 2741 34863
1 380 4220 1094 0112 2666 35405 0130 1160 3093 46617
SI 150 4461 1008 0108 3058 39993 0108 1109 3091 --
0
1
2
3
4
5
6
7
8
000 010 020 030 040
Shear-force coefficient Ci
Sto
ry
0
1
2
3
4
5
6
7
8
0 25000 50000Mt (kNm)
Figure 38 Comparison with calculated and design values of Ci and OTM 363 Story drift of super-structure and vertical load changes on isolator devices The story drift of super-structure and vertical load changes on isolator devices due to the horizontal earthquake load are obtained by applying the earthquake force shown in Table 310 horizontally to the super-structure statically In Figure 39 is shown the analytical model The base at each isolator device can be modeled as fixed or supported by a spring with the value of vertical stiffness
The design shear force is used to give safety other than calculated Qi The drift angle in all floors of the super-structure must be less than 1300 demanded by the building code The vertical load changes are used to check the maximum and minimum pressure on each isolator device shown in section 38
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
18
Figure 39 The analytical model to calculate drift angle and vertical load changes
364 Substructure The foundation is assumed at depth 4m underground The shear force of the sub-structure can be obtained by following step
Qsub=Qiso+2 k Wb=3091+20096000=4147 kN k seismic intensity for sub-structure k=01(1-H40)=009 Wb weight of the foundation Wb =6000 kN
37 Evaluation of response values of SI layer from wind load The wind load is confirmed by two levels where the return period is 50 and 500 years respectively The response is related with the geometry of the building and wind velocity In Figure 310 is shown the response displacement of the SI layer Not to let the SI layer has large deformation even during extreme wind is necessary In Figure 311 is shown the comparison between two levelrsquos wind loads and design shear force Since this building is small the design shear force is large enough
0
500
1000
1500
2000
0 50 100 150 200
Displacement (mm)
Sh
ear-
forc
e (
kN
)
Figure 310 Response against wind load on the force-displacement curve of SI layer
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000
Story shear-force Qwi Qei
Sto
ry
Figure 311 Comparison between two levelrsquos wind loads and design shear force
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
19
38 Confirmation of safety of devices for vertical load The vertical load changes on isolator devices due to the horizontal earthquake load were calculated at section 363 A vertical earthquake load of 03g is also applied to check maximum and minimum pressure on each isolator device The maximum response displacement of 0476m due to Minus change is used
Maximum pressure WD13 + Vseis Minimum pressure WD07 - Vseis
WD vertical loads on isolation devices shown in Table 32 Vseis vertical load changes calculated at section 363
In Table 311 is shown an example of the maximum and minimum pressure check on the RB80 In Figure 312 are shown two cases of vertical load for isolator devices Case 1 shows permanent load at displacement zero Case 2 shows the above maximum and minimum pressure on each isolator device
Table 311 Maximum and minimum pressure check on the RB80
Devices Vertical
load Seismic load (Vseis) WD13 + Vseis WD07 - Vseis
Isolator WD
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
X
(kN)
Y
(kN)
RB80 4363 1135 736 6807 6408 1919 2318
RB80S stress-strain curve
σc=45
Fc
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain()
Com
p stress(N
m
m2)
RB80 stress-strain curve
σc=49
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500
Lateral strain ()
SC60 stress-displacement curve
σc=57
09σc
Fc vetical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Co
mp
st
ress
(N
mm
2)
SC70 stress-displacement curve
σc=57
09σcFc vertical
standard
strength
13Fc
23Fc
0
10
20
30
40
50
60
0 100 200 300 400 500 600
Lateral displacement (mm)
Figure 312 Comparison between response and limit of isolator devices
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018
20
39 Securing safety of connections of devices to structures
The footings and beams must be strong enough to ensure the isolator or damper devices work normally during an earthquake To design those structure elements and the connection plates or anchor plates the extreme deformation of the SI layer is assumed
The connection part is acted with a shear force and large moment as shown in Figure 313 and calculated by following equations The maximum shear force and moment check on the RB80 is shown in Table 312 Fixing bolts and anchor stud bars etc should be calculated using these values too
Nd = WD13 + Vseis
δ = δr Qd = Qy + K2δ M = Mv+tMd = 12 Ndδ + Qd(ht+12 h)
Moment due to the P-Δ effect Moment by shear force
Figure 313 Moment acting on the footings and beams
Table 312 Maximum shear force and moment check on the RB80
Nd δ Qd Mv h ht tMd M (kN) (m) (kN) (kN m) (m) (m) (kN m) (kN m)
RB80 6807 0490 534 1668 05 07 641 2309
310 Confirmation of satisfaction of stipulations on SI system The clearance around the SI building should be maintained As shown in Table 39 the maximum response displacement of SI layer is 0490m Then the clearance for inspection should be 0685m the clearance for passerby should be 1285m 4 Reference 1) MLIT etc 2000 The Notification and Commentary on the Structural Calculation Procedures
for Building with Seismic Isolation ndash2000ndash (in Japanese) 2) M Higashino S Okamoto 2006 Response Control and Seismic Isolation of Buildings Taylor amp
Francis 3) ISO 22762 Elastomeric seismic-protection isolators 2018