design procedures of response spectrum method …...response spectrum method and time history...

Taiki Saito, Professor Shugo Takano, Graduate Student

Toyohashi University of Technology

Design Procedures of Response Spectrum Method and Time History Analysis of

Seismic Isolation Buildings in Japan

Design procedures of response spectrum method and time history analysis

Building height

Soil profile

Response spectrum method Time history analysis

Less than 60m More than 60m

Type 1 or 2

Type 3 or 2 which hasPossibility of liquefaction

Evaluation committee(approved by Ministry)

Building permission

Index

1. Introduction for target building 2. Response spectrum method (RSM)3. Time history analysis (THA)

Building Introduction part 1: Outlook of the building

FIGURE.1 Target Building

Story Height Horizontal stiffness (kN/mm)(mm) X direction Y direction

7 3000 951 32436 3000 2407 35535 3000 1242 59574 3000 1336 79503 3000 1457 101832 3000 1544 129661 3000 2005 12814

Purpose CondominiumTotal floor areas(m2) 1950Maximum height(m) 23.6Sort of building Reinforced concrete

Structure type X axis RC flameY axis RC flame +RC wall

Basement Cast in place concrete

Story Height(mm) Weight(kN)7 3000 44106 3000 41655 3000 41654 3000 41653 3000 42142 3000 42141 3000 4214i 1700 5292

Material (N/mm2)

Steel bar Main bar 345Stirrup 295

Concrete 24

Table1: Building detail

Table2:Building height and weight

Table4:Materials strength of the building

Building Introduction part 2: Characteristic of the building

Table3:Building stiffness

Building Introduction part 3: Elevation plan

FIGURE.2 Elevation Plan of the building

Building Introduction part 4: Plan of the building

FIGURE.3

X1 X2 X3 X4 X5 X6

Y1

Y2

X1 X2 X3 X4 X5 X6

Y1

Y2LRB650(I1)

LRB650(I1)

LRB650(I1)

LRB650(I1)

LRB700(I2)

LRB700(I2)

LRB700(I2) LRB700(I2)

LRB700(I2) LRB700(I2)

C1 C1

C1 C1

C1 C1

C1 C1

C1 C1

C1 C1

W1 W1 W1 W1 W1 W1

Standard floor plan Isolators level

Lead plug Natural rubber Steel plate

Coveringrubber

Flange

LRB

LRBφ650 4

LRBφ700 8

Story Beam

6,7

Symbol G1 G2Main bar

(up) 4-D25 6-D25

Main bar (below) 3-D25 4-D25

Stirrup D13-@200 D13-@200

h*b

700*350 700*3504,5


(up) 5-D25 7-D25


Stirrup D13-@200 D13-@200

h*b

750*400 750*400

2,3


(up) 5-D25 8-D25


Stirrup D13-@200 D13-@200

h*b

800*400 800*400

1


(up) 7-D25 10-D25


Stirrup D13-@200 D13-@200

h*b

1300*500 1300*500

Member information of the building: BEAM

Table5: Detail of the Beam

Story Column

5,6,7

Symbol C1Main bar 10-D25Stirrup D13-@100

h*b

700*7503,4


h*b

700*750 1,2


h*b

750*750

Member information of the building: COLUMN

Table6: Detail of the Columns

Story Wall W1

All

Thickness(mm) 200Reinforcement 2-D13@200

Story Slab

All

Thickness(mm) 220

Reinforcement D13@100

Member information of the building: WALL and SLABS

Table7: Detail of the Walls

Table8: Detail of the Slabs

Index

1. Introduction for target building 2. Response spectrum method (RSM)3. Time history analysis (THA)

Isolation device

Input seismic force

Response calculation

Design criteriamδd > δresponse

Super and sub structures

YES

NO

1: Design limit deformation of isolators2: Damping factor(h) and acceleration reduction factor(Fh)3: Time period(Ts)

1: Surface soil amplification factor(Gs)2: Seismic hazard zoning factor(Z)

RSM: Design for the seismic isolation level

RSM: How to design seismic force on the building

Seismic force on the building can calculate by formula (1) and (2)

FIGURE.4 Design method of calculation for seismic force

S0: Acceleration response spectrum at the engineering bedrock (h=0.05)Fh: Reduction factor due to dampingGs: Surface soil amplification factorZ: Seismic zoning factorα： factor considering variation of material (>= 1.2)

aQ S M

1.1responseQM

0a h hS S F G Z

RSM: Seismic isolation device (1)

Seismic isolation system LRBφ650(I1) LRBφ700(I2)Diameter (mm) 650 700

Thickness of rubber layer (mm) 10 12Hr(mm): Effective height of rubber 159.6 (4.2×38 layers) 162 (4.5×36 layers)

S1: Primary shape factor 38.7 38.9S2: Secondary shape factor 4.1 4.3

K1(kN/m): Initial stiffness 10,695 12,217K2(kN/m): Secondary stiffness 823 940

Qy(kN): Yielding strength 122.7 140.9δy(m): Yielding deformation 0.0115 0.0115

Table9: Detail of the Seismic Isolation Device

Lead plug Natural rubberSteel plate

Rubber covering

Flange

122.7kN

10695kN/m

1.15cm

823kN/m140.9kN

12217kN/m

1.15cm

940kN/m

RSM: Seismic isolation device (2)

Seismic isolation system LRBφ650(I1) LRBφ700(I2)σ0(N/mm2):Basic vertical strength 30 36

1/3(σ0) (N/mm2) 10 12γ (%) : Horizontal limit strain 342.27 353.62

δu(mm):Horizontal limit deformation 546 573β:Coefficient due to device 0.8

mδd(mm):Limit design deformation 437 459

010203040506070

0 100 200 300 400 500

σ(N

/mm

2 )

γ(%)

010203040506070

0 100 200 300 400 500

σ(N

/mm

2 )

γ(%)

FIGURE.4 LRBΦ650 FIGURE.5 LRBΦ700

Table9: Detail of the Seismic Isolation Device

σ0σ0

(1/3)σ0(1/3)σ0

γγ

RSM: Factors calculation part ①: Equivalent damping factor Damping factor of the building can be calculated by formula (3) to (7)

‐8000

‐6000

‐4000

‐2000

0

2000

4000

6000

8000

‐60 ‐40 ‐20 0 20 40 60Q(kN)

δ(cm)

FIGURE.6 Hysteresis loop

0.84

WhW

Equivalent damping factor

1.51 10hF

h

Reduction factor of response spectrum WW

0.84

WhW

12 m dW Q 4 'W Q

' 1 1Q Q

1 1/ /

1 1 1 1m d y

y y y

Q K Q K

0.8 2 1 10.8 14 1 1

WhW

m d y

2 1/K K

1K

2K

y

'Q

RSM： Factors calculation part ②: Acceleration response spectrum

0

200

400

600

800

1000

0 1 2 3 4 5

gal(c

m/s

2 )

T(s)

Acceleration response spectrum can be calculated by equation below

FIGURE.7 Acceleration response spectrum

(cm/s2)0

320 30 0.16800 0.16 0.64

512 / 0.64

s s

s

s s

T TS T

T T

RSM： Factors calculation part ③: Time period of the building

Acceleration response spectrum can be calculated by equation below

FIGURE.8 Building mass

2sMTK

M Super mass

‐8000

‐6000

‐4000

‐2000

0

2000

4000

6000

8000

‐60 ‐40 ‐20 0 20 40 60Q(kN)

δ(cm)

437mm

6158kN K=14093kN/m

M=3555kNs2/m Ts = 3.16 s

RSM: Factors calculation part ④: Surface soil amplification factor

Soil profile type (Gs)

Definition Describe

1 T=0.4 Solid soil2 T=0.6 Moderate3 T=0.8 Soft soil

1

1.5

2

2.5

3

0 1 2 3 4 5

Gs

T(s)

Soil profile type 1

Soil profile type 2

Soil profile type 3

Table10: Soil profile type definition

FIGURE.9 Soil profile type

Soil condition at construction site

RSM: Factors calculation part ⑤: Seismic hazard zoning factor

FIGURE.9 Soil profile type

This value is taken for design

RSM: Summary of design factors

0

200

400

600

800

1000

1200

1400

0 1 2 3 4 5Sa

(gal

(cm

/s2 )

)

T(s)

0

200

400

600

800

1000

1200

1400

0 10 20 30 40 50 60

Sa(g

al(c

m/s

2 ))

Sd(cm)

FIGURE.10 Sa-T curve

FIGURE.11 Sa-Sd curve

2 2 2/ / (2 )d a aS S S T

RSM: Capacity spectrum method part ①: Introduction

FIGURE.12: Procedures for capacity spectrum method

1.Reduce acceleration spectrum

2.Change the slope based on μ

3.Connect the cross-point→1.

4.Find performance point

μ=3

μ=2

μ=1

μ=4

D(μ=1)

D(μ=2)

D(μ=3)

D(μ=4)

RSM: Capacity spectrum method part ②: Result

0

200

400

600

800

1000

0 5 10 15 20 25 30 35

S a(g

al(c

m/s

2 ))

Sd(cm)

0

30

60

90

120

150

0 5 10 15 20 25 30 35

S a(g

al(c

m/s

2 ))

Sd(cm)

Requirement :Result : 437 291 (mm)Judge : OK

Design for the superstructure

FIGURE.13: Result of the Capacity spectrum method

m d responceδ δ

291response mm

RSM: Design of superstructure: Design procedures

Story drift

Seismic isolation layer

Clearance space

1: Design coefficient of story force 2: Calculate seismic shear force 3: Calculate seismic force at seismic isolators device

Device check

1: Eccentricity of the seismic isolation interface<0.032: Shear coefficient of dampers>0.03

1: σLmax<1/3𝜎02: σs1<2/3𝜎03: σs2<𝜎04: σs3>0

1: 1.25・δresponse2: 0.2(m)+δresponse3: 0.6(m)+1 or 2 (using path in basement

RSM: Seismic isolation layer : Eccentricity ratio (Rex,ey)

1. Center of gravity

2. Center of rigidity

3. Eccentricity distance

4. Rotation stiffness

5. Elastic radius

𝑋∑ 𝑋 · 𝑁

∑ 𝑁

𝑌∑ 𝑌 · 𝑁

∑ 𝑁

𝑋∑ 𝑋 · 𝐾

∑ 𝐾

𝑌∑ 𝑌 · 𝐾

∑ 𝐾

𝑒 𝑌 𝑌𝑒 𝑋 𝑋

𝐾 𝐾 · 𝑌 𝑌 𝐾 · 𝑋 𝑋

𝑟𝐾

∑ 𝐾

𝑟𝐾

∑ 𝐾

𝑅𝑒𝑟

𝑅𝑒𝑟

Eccentricity ratio

𝑅0.10710.41 0.01

𝑅0.28710.41 0.027

(Xg, Yg)= (13607, 5787)

(Xk, Yk)= (13500, 5500)

FIGURE.14: Center of the gravity and rigidity Less than 0.03→OK

RSM: Shear force at isolation layer

Qe: Shear force at rubber

Qh Shear force at damper (lead plug)

＋＝

D

F

D

F F

D

eQ hQ

1eQ K

hQ yield load

0.823 291( ) 4 0.94 291( ) 8 3146ekN kNQ mm mm kNmm mm

+ = ( )

122.7( ) 4 140.9( ) 8 1618( )hQ kN kN kN + =

LRBφ650 LRBφ700

27

Lead plug

RSM: Seismic isolation layer : Shear coefficient of dampers(μ)

Over 0.03→OK

1618 0.046 0.033555 9.8

hQM g

RSM: Story drift : Shear coefficient of superstructure(Cri)

1 211 3i i

i

TAT

i h eri

A Q QCM g

1

2

3

4

5

6

7

0 2000 4000 6000st

ory

(F)

Qi(kN)

γ： factor considering the variation of material (>=1.3)T： The natural period of superstructure with fixed base(0.02+0.01α)H

RSM: Story drift

1

2

3

4

5

6

7

0 0.001 0.002 0.003 0.004

Stor

y(F)

Max drift

1/300X directionY direction

Both directions are not over 1/300→OK

FIGURE.14: Procedures to calculate story drift

1

2

3

4

5

6

7

0 5000 10000 15000

stor

y(F

)

stifness(kN/mm)

X directionY direction

1

2

3

4

5

6

7

0 2000 4000 6000

stor

y(F

)

Qi(kN)Shear force on each floors Horizontal stiffness of each directions Story drift of each directions

Step ①: Calculate shear force on each floor depend on CriStep ②: Estimate horizontal stiffness of the building by frame

analysisStep ③: Shear force divide by stiffness → Max drift

② ③

RSM: Device check ①:Long-term load

𝜎13 · 𝜎

(N/mm2) 1(LRB650) 2(LRB700) 3(LRB700) 4(LRB700) 5(LRB700) 6(LRB650)Load 6.81 10.12 8.79 8.79 10.12 7.23

criteria < 10 < 12 < 12 < 12 < 12 < 10Judge OK OK OK OK OK OKLoad 6.78 8.8 7.64 7.64 8.8 7.23

criteria < 10 < 12 < 12 < 12 < 12 < 10Judge OK OK OK OK OK OK

Table12: Result of device check

RSM: Device check ②: Long-term load + seismic force

𝜎 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑠𝑒𝑖𝑠𝑚𝑖𝑐 𝑓𝑜𝑟𝑐𝑒

𝜎 ·σ0


Criteria < 20 < 24 < 24 < 24 < 20 > 20Judge OK OK OK OK OK OKLoad 7.54 9.66 8.50 8.50 9.66 7.99

Criteria < 20 < 24 < 24 < 24 < 20 > 20Judge OK OK OK OK OK OK


RSM: Device check ③:1.3・Long-term load + seismic force

𝜎 1.3 · 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑠𝑒𝑖𝑠𝑚𝑖𝑐 𝑓𝑜𝑟𝑐𝑒

𝜎 𝜎


Design < 30 < 36 < 36 < 36 < 36 < 30Criteria OK OK OK OK OK OK

Load 9.57 12.30 10.80 10.80 12.30 10.16 Criteria < 30 < 36 < 36 < 36 < 36 < 30

Judge OK OK OK OK OK OK


RSM: Device check ④:0.7・Long-term load - seismic force

𝜎 0.7 · 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑠𝑒𝑖𝑠𝑚𝑖𝑐 𝑓𝑜𝑟𝑐𝑒

𝜎 0


Criteria > 0 > 0 > 0 > 0 > 0 > 0Judge OK OK OK OK OK OKLoad 3.99 5.30 4.48 4.48 5.30 4.30

Criteria > 0 > 0 > 0 > 0 > 0 > 0Judge OK OK OK OK OK OK


RSM: Clearance space

1) 1.25 · 𝛿2) 0.2 m 𝛿3) 0.6 m 1 or 2 In case of using to path

1) 1.25 · 𝛿 1.25 ∗ 0.291 𝑚 0.364 𝑚2) 0.2 m 𝛿 0.2 𝑚 0.291 𝑚 0.491 𝑚

Compare 1) and 2) and bigger value must be taken. In case of using path at seismic isolation layer, it should plus 0.6(m)

In the result, clearance space must secure more than 0.491(m).

Index

1. Introduction for target building 2. Response spectrum method (RSM) 3. Time history analysis (THA)

Design procedures of time history analysis

Confirm final condition Of the target building

Vertical direction input artificial earthquake

Response calculation

Design criteriamδd > δresponse

Variationof isolation device

Horizontal direction input artificial earthquake

Seismic isolation

YES

NO

If necessary

THA: Variation of isolation device

Isolators Character of restoring force Condition

Variation FactorVariation RatioProduct

variation Temperature Dependency Aging

Laminated Rubber with Lead Plug

Secondary Stiffness K2Upper Limit 10% 6% 11% 27%Lower Limit -10% -5% 0% -15%

Section Load QdUpper Limit 10% 23% 0% 33%Lower Limit -10% -21% 0% -31%

Table16: Variation of Isolation Device

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 5 10 15 20 25 30 35 40

Q(k

N)

δ(cm)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 5 10 15 20 25 30 35 40

Q(k

N)

δ(cm)

Standard x axis

Upper limit x axis

Lower limit x axis

Standard y axis

Lower limit y axis

Upper limit y axis

FIGURE.15: Capacity curve which considered variation of Isolation device

THA: Generate artificial earthquake ground motions in horizontal direction

-600

-400

-200

0

200

400

600

0 10 20 30 40 50 60

acc.

(cm

/s2 )

T(S)

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10

Sa(c

m/s

2 )

T(s)

Sa(el centro)Sa(target)

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10

Sa(cm/s

2 )

T(s)

Sa(Kobe EW)

Sa(target)

-600

-400

-200

0

200

400

600

0 10 20 30 40 50 60Sa(c

m/s

2 )

T(s)-600

-400

-200

0

200

400

600

0 10 20 30 40 50 60

Sa(c

m/s

2)

T(s)

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10

Sa(c

m/s

2)

T(s)

Sa(tohoku EW)

Sa(target)

El centro NS Kobe EW Tohoku EW

Input horizontal direction earthquake

THA: Building model

STERA_3D model

Isolators setting Input earthquake① Create building model based on information

② Select type of isolators

③ set behavior of isolators

④ Input earthquake

THA: Result of maximum response value in X direction from input horizontal earthquake(El Centro , Kobe , Tohoku)

1234567

0 10 20 30 40 50

Stor

y(F)

δ(cm)

tohokukobeel centro

1234567

0 2000 4000 6000

Stor

y(F)

Q(kN)

tohokukobeel centro

1234567

0 100 200 300St

ory(

F)Acceleration(cm/s2)

tohokukobeel centro

m d responceδ δ

437( )m d mmδOK

Lower limit of variation Upper limit of variation Upper limit of variation

Max response of X direction

mδd

THA: Result of maximum response value in Y direction from input horizontal earthquake(El Centro , Kobe , Tohoku)

1234567

0 10 20 30 40 50

Stor

y(F)

δ(cm)

tohokukobeel centro

1234567

0 100 200 300 400St

ory(

F)Acceleration(cm/s2)

tohoku

kobe

el centro

1234567

0 2000 4000 6000

Stor

y(F)

Q(kN)

tohoku

kobe

el centro

m d responceδ δ

437( )m d mmδOK

Lower limit of variation Upper limit of variation Upper limit of variation

Max response of Y direction

mδd

design procedures of response spectrum method …...response spectrum method and time history...

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