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