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
Symbol G1 G2Main bar
(up) 5-D25 7-D25
Main bar (below) 3-D25 4-D25
Stirrup D13-@200 D13-@200
h*b
750*400 750*400
2,3
Symbol G1 G2Main bar
(up) 5-D25 8-D25
Main bar (below) 4-D25 6-D25
Stirrup D13-@200 D13-@200
h*b
800*400 800*400
1
Symbol G1 G2Main bar
(up) 7-D25 10-D25
Main bar (below) 5-D25 7-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
Symbol C1Main bar 12-D25Stirrup D13-@100
h*b
700*750 1,2
Symbol C1Main bar 12-D25Stirrup D13-@100
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
(N/mm2) 1(LRB650) 2(LRB700) 3(LRB700) 4(LRB700) 5(LRB700) 6(LRB650)Load 7.57 10.98 9.65 9.65 10.98 7.99
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
Table13: Result of device check
RSM: Device check ③:1.3・Long-term load + seismic force
𝜎 1.3 · 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑠𝑒𝑖𝑠𝑚𝑖𝑐 𝑓𝑜𝑟𝑐𝑒
𝜎 𝜎
(N/mm2) 1(LRB650) 2(LRB700) 3(LRB700) 4(LRB700) 5(LRB700) 6(LRB650)Load 9.61 14.02 12.29 12.29 14.02 10.16
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
Table14: Result of device check
RSM: Device check ④:0.7・Long-term load - seismic force
𝜎 0.7 · 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑠𝑒𝑖𝑠𝑚𝑖𝑐 𝑓𝑜𝑟𝑐𝑒
𝜎 0
(N/mm2) 1(LRB650) 2(LRB700) 3(LRB700) 4(LRB700) 5(LRB700) 6(LRB650)Load 4.01 6.22 5.29 5.29 6.22 4.30
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
Table15: Result of device check
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