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Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 1
SEISMIC PROTECTIVE SYSTEMS: SEISMIC ISOLATION
Developed by:Michael D. Symans, PhDRensselaer Polytechnic Institute
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 2
Major Objectives
• Illustrate why use of seismic isolation systems may be beneficial
• Provide overview of types of seismic isolation systems available
• Describe behavior, modeling, and analysis of structures with seismic isolation systems
• Review building code requirements
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 3
OutlineSeismic Base Isolation
– Configuration and Qualitative Behavior of Isolated Building
– Objectives of Seismic Isolation Systems
– Effects of Base Isolation on Seismic Response
– Implications of Soil Conditions
– Applicability and Example Applications of Isolation Systems
– Description and Mathematical Modeling of SeismicIsolation Bearings• Elastomeric Bearings• Sliding Bearings
– Modeling of Seismic Isolation Bearings in Computer Software
– Code Provisions for Base Isolation
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 4
Configuration of Building Structure with Base Isolation System
Passive DamperIsolation Bearing
BaseIsolationSystem
Sup
erst
ruct
ure Basemat
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 5
Three-Dimensional View of BuildingStructure with Base Isolation System
SlidingBearing
ElastomericBearing
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 6
Installed Seismic Isolation Bearings
ElastomericBearing
Sliding Bearing
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 7
Behavior of Building Structurewith Base Isolation System
Base-Isolated StructureConventional Structure
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 8
Objectives of Seismic Isolation Systems
• Enhance performance of structures atall hazard levels by:
Minimizing interruption of use of facility(e.g., Immediate Occupancy Performance Level)
Reducing damaging deformations in structural and nonstructural components
Reducing acceleration response to minimize contents-related damage
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 9
Characteristics of Well-DesignedSeismic Isolation Systems
• Flexibility to increase period of vibration and thus reduce force response
• Energy dissipation to control the isolation system displacement
• Rigidity under low load levels such as wind and minor earthquakes
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20
Spectral Displacement, Inches
Pseu
doac
cele
ratio
n, g
T=.50 T=1.0
T=1.5
T=2.0
T=3.0
T=4.0
5% Damping
10%
20%
30%40%
Effect of Seismic Isolation (ADRS Perspective)
Decreased Shear ForceIncreased Displacement
Pse
udo-
Spe
ctra
l Acc
eler
atio
n, g
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 11
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20
Spectral Displacement, Inches
Pseu
doac
cele
ratio
n, g
T=.50 T=1.0
T=1.5
T=2.0
T=3.0
T=4.0
5% Damping
10%
20%
30%40%
Effect of Seismic Isolation with Supplemental Dampers (ADRS Perspective)
Decreased Shear ForceSlightly Increased Displ.
Pse
udo-
Spe
ctra
l Acc
eler
atio
n, g
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 12
Increase Period of Vibration of Structureto Reduce Base Shear
Bas
e Sh
ear
Period
WithoutIsolation
T1 T2
WithIsolation
Increasing Damping
Effect of Seismic Isolation(Acceleration Response Spectrum Perspective)
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 13
Increase of period increases displacementdemand (now concentrated at base)
Dis
plac
emen
t
Period
WithoutIsolation
T1 T2
WithIsolation
Increasing Damping
Effect of Seismic Isolation(Displacement Response Spectrum Perspective)
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 14
Bas
e Sh
ear
Period
Soft Soil
Stiff Soil
Effect of Soil Conditions onIsolated Structure Response
WithoutIsolation
T1 T2
WithIsolation
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 15
Applicability of Base Isolation Systems
MOST EFFECTIVE- Structure on Stiff Soil- Structure with Low Fundamental Period (Low-Rise Building)
LEAST EFFECTIVE- Structure on Soft Soil- Structure with High Fundamental Period (High-Rise Building)
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 16
First Implementation of Seismic Isolation
Foothill Community Law and Justice Center,Rancho Cucamonga, CA
- Application to new building in 1985- 12 miles from San Andreas fault- Four stories + basement + penthouse- Steel braced frame- Weight = 29,300 kips- 98 High damping elastomeric bearings- 2 sec fundamental lateral period- 0.1 sec vertical period- +/- 16 inches displacement capacity- Damping ratio = 10 to 20% (dependent on shear strain)
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 17
Application of Seismic Isolation to Retrofit ProjectsMotivating Factors:
- Historical Building Preservation(minimize modification/destruction of building)
- Maintain Functionality(building remains operational after earthquake)
- Design Economy(seismic isolation may be most economic solution)
- Investment Protection(long-term economic loss reduced)
- Content Protection(Value of contents may be greater than structure)
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 18
Example of Seismic Isolation Retrofit
U.S. Court of Appeals,San Francisco, CA- Original construction started in 1905- Significant historical and architectural value
- Four stories + basement- Steel-framed superstructure- Weight = 120,000 kips- Granite exterior & marble, plaster,
and hardwood interior- Damaged in 1989 Loma Prieta EQ- Seismic retrofit in 1994- 256 Sliding bearings (FPS)- Displacement capacity = +/-14 in.
Isolation Bearing
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 19
Types of Seismic Isolation Bearings
Elastomeric Bearings- Low-Damping Natural or Synthetic Rubber Bearing- High-Damping Natural Rubber Bearing- Lead-Rubber Bearing (Low damping natural rubber with lead core)
Sliding Bearings- Flat Sliding Bearing- Spherical Sliding Bearing
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 20
Geometry of Elastomeric Bearings
Major Components:- Rubber Layers: Provide lateral flexibility- Steel Shims: Provide vertical stiffness to support building weight
while limiting lateral bulging of rubber- Lead plug: Provides source of energy dissipation
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 21
Low Damping Natural or Synthetic Rubber Bearings
Linear behavior in shear for shear strains up to and exceeding 100%.
Damping ratio = 2 to 3%
Advantages: - Simple to manufacture- Easy to model- Response not strongly sensitive to rate of loading, history of loading, temperature, and aging.
Disadvantage:Need supplemental damping system
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 22
High-Damping Natural Rubber Bearings• Maximum shear strain = 200 to 350%
• Damping increased by adding extrafinecarbon black, oils or resins, and other proprietary fillers
• Damping ratio = 10 to 20% at shear strains of 100%
• Shear modulus = 50 to 200 psi
• Effective Stiffness and Damping depend on:- Elastomer and fillers- Contact pressure- Velocity of loading- Load history (scragging)- Temperature
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 23
Lead-Rubber Bearings• Invented in 1975 in New Zealand and
used extensively in New Zealand, Japan, and the United States.
• Low damping rubber combined with central lead core
• Shear modulus = 85 to 100 psi at 100%shear strain
• Maximum shear strain = 125 to 200% (since max. shear strain is typically less than 200%, variations in properties are not as significant as for high-damping rubber bearings)
• Solid lead cylinder is press-fitted into centralhole of elastomeric bearing
• Lead yield stress = 1500 psi(results in high initial stiffness)
• Yield stress reduces with repeated cyclingdue to temperature rise
• Hysteretic response is strongly displacement-dependent
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 24
Elastomeric Bearing Hysteresis Loops
ShearForce Displacement
AxialForce
Shea
r For
ce
Displacement
Lead-Rubber Bearing
Low DampingRubber BearingHigh Damping
Rubber Bearing
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 25
Shear Deformation of Elastomeric Bearing
- Bearing Manufactured by Scougal Rubber Corporation.- Test Performed at SUNY Buffalo.- Shear strain shown is approximately 100%.
DeformedShape
LoadCell
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 26
25.4 cm (10 in.)
1.3 m (4.3 ft)
Full-Scale Bearing Prior to Dynamic Testing
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 27
Testing of Full-Scale Elastomeric Bearing at UC San Diego- Compressive load = 4000 kips- 400% Shear Strain [1.0 m (40 in.) lateral displacement]- Video shown at 16 x actual speed of 1.0 in/sec
Cyclic Testing of Elastomeric Bearing
Bearing Manufactured byDynamic Isolation Systems Inc.
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 28
Note: Damping force 90o out of phase with elastic force.
P t P t P t( ) sin( ) cos( ) cos( )sin( )= +0 0ω δ ω δ
Loading Frequency
PhaseAngle(Lag)
-1500
-1000
-500
0
500
1000
1500
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
TIME, SECONDS
FOR
CE,
KIP
S
ELASTIC FORCEDAMPING FORCETOTAL FORCE
)tsin(u)t(u ω= 0 Imposed Motion
Assumed Form of Total Force
ωδ
Harmonic Behavior of Elastomeric Bearing
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 29
)cos(uPK
0
0S δ= )sin(
uPK
0
0L δ=
)t(uC)t(uK)t(P S &+=
ωLKC = ⎟⎟
⎠
⎞⎜⎜⎝
⎛= −
0
1sinPPZδ
Storage Stiffness Loss Stiffness Damping Coeff. Phase Angle
oLZ uKP =
( )δξ tan21
=
Shea
r For
ce, P
Displacement, u
ZP
ou
oP
SK
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 30
rS t
A'GK =r
L tA''GK =
)t(uC)t(uK)t(P S &+=
ωLKC = ⎟⎟
⎠
⎞⎜⎜⎝
⎛= −
0
1sinττδ Z
Storage Stiffness Loss Stiffness Damping Coeff. Phase Angle
( ) ( ) ωγγτ /tGtG)t( &′′+′=
Loss Factor
( )δηξ tan21
2==
Damping Ratio
Shea
r Str
ess
Shear Strain
Zτ
oγ
oτ
G ′
( )( ) ( )δωωη tan
GG
=′′′
=
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 31
-3 -2 -1 0 1 2 3Bearing Deformation (cm)
-8
-6
-4
-2
0
2
4
6
8
Bear
ing
Forc
e (k
N)
Experimental Hysteresis Loops of Low Damping Rubber Bearing
Low Damping Rubber Bearing- Reduced scale bearing for ¼-scale building frame- Diameter and height approx. 5 in. - Prototype fundamental period of building = 1.6 sec
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 32
Shear Storage Modulus of High-Damping Natural RubberSh
ear S
tora
ge M
odul
us (p
si)
Shear Strain (%)0 100 200 300
300
200
0
100 Increasing Frequency
Increasing Pressure
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 33
Effective Damping Ratio of High-Damping Natural RubberEf
fect
ive
Dam
ping
Rat
io (%
)
Shear Strain (%)0 100 200 300
20
15
0
10
Increasing Frequency
Increasing Pressure
5
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 34
Linear Mathematical Model forNatural and Synthetic Rubber Bearings
( ) ( ) ( )tuctuktP effeff &+=
= Effective stiffness at design displacement
= Effective damping coefficientassociated with design displacement
effk
effc
Shea
r For
ce, P
Displacement, u
u
effCP
effK
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 35
Equivalent Linear Properties from IdealizedBilinear Hysteresis Loop
DQK
DFkeff +== α
S
Deff W4
Wπ
ξ =
2effS DK
21W =
( )( )KDQD
DDQ2 Yeff απξ
+−
=( )YD DDQ4W −=
If Q >> DY, then: QD4WD ≈
DFkeff =
Forc
e
Displacement
Q
D
D−
F
K
KαyF
YD
effK
Area = DW
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 36
Refined Nonlinear Mathematical Model forNatural and Synthetic Rubber Bearings
( ) ( ) ( ) ( )tZP1tuuP
tP yy
y αα −+=
0uZuZZuZu 1y =−++ −
&&&& θβγ ηη
= Post-to-pre yielding stiffness ratio
= Yield force
= Yield displacement
= Evolutionary variable
= Calibration constants
α
yP
yu
Z
θηβγ ,,,
Shea
r For
ce, P
Displacement, u
Shear Force in Bearing
Evolutionary Equation
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 37
Spherical Sliding Bearing:Friction Pendulum System (FPS)
Stainless Steel Concave Surface
Concave Plate
Articulated Slider With
PTFE Coating
Concave Plate and Sliderfor FPS Bridge Bearing- Seismic retrofit of Benicia-Martinez Bridge,
San Francisco, CA- 7.5 to 13 ft diameters- Displ. Capacity of 13 ft bearings = +/- 4.3 ft
Housing Plate With PTFE
Coating Above Slider
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 38
Free-Body Diagram of Top Plate and
Slider Under Imposed Lateral
Force F
WF
Ff
θθ
cosF
tanWF f+=
Nθ
θ
Mathematical Model of FrictionPendulum System Bearings
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 39
Radius of Curvature of FPS Bearings
+R
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 40
θθ
cosF
tanWF f+=
1...!2
1cos
...!3
sin
2
3
≈+−=
≈+−=
θθ
θθθθ
For u < 0.2R, is small (2% error in u)
θθ θcosRR
θsinR
θ RR
θR
Mathematical Model of FrictionPendulum System Bearings
u
Ru
≈θ
( )usgnNF f &μ=
( )usgnWuRWF &μ+=
Wcos
WN ≈=θ
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 41
1...!2
1cos
...!3
sin
2
3
≈+−=
≈+−=
θθ
θθθθ
Vertical Displacement of FPS Bearings
Ru
≈θ
θ θcosRR
θsinR
uv
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛−=−= −
Rusincos1R)cos1(Rv 1θ
R2u
2Rv
22≈≈
θ
θ RR
θR
.)in(v
.)in(u
0
1
0 105
0.5
T = 2.75 sec
Note: Vertical frequency is twicethat of lateral frequency
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 42
Note: Bearing will not recenter if
( ) fr FFusgnWuRWF +=+= &μ
Components of FPS Bearing Lateral Force
F
u
rF
u
Slope = R
W
fF
u
Wμ
Wμ−
+ =u&+u&−
)Ru(FF fr μ<<For large T, and thus large R, this can be a concern.
u&
( )usgn &
-1
1
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 43
FuR
W
WFf μ=Rigid Model withStrain Hardening
( )usgnWuRWF &μ+=
Mechanical Model of Friction Pendulum System Bearings
F
u
u&
( )usgn &
-1
1
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 44
D
F F
u
F
u
F
u
Time
F
u
Hysteretic Behavior of FrictionPendulum System Bearings
( )usgnWuRWF &μ+=
gR2T π=
FreeVibrationPeriod
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 45
Forc
e, F
Displacement, u
fF
D
F
RW effK
Area =DW
Idealized FPS Bearing Hysteresis Loop
ShearForce Displacement
AxialForce
( )usgnWuR
WF &μ+=
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 46
-5 -4 -3 -2 -1 0 1 2 3 4 5-10
-8
-6
-4
-2
0
2
4
6
8
10
Bear
ing
Forc
e (k
N)
Bearing Displacement (cm)
Actual FPS Bearing Hysteresis Loop
FPS Bearing- Reduced-scale bearing for ¼-scale building frame- R = 18.6 in; D = 11 in.; H = 2.5 in. (reduced scale)- Prototype fundamental period of building = 2.75 sec (R = 74.4 in. = 6.2 ft)
Stick-Slip
Stick-Slip
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 47
Velocity-Dependence of Coefficient of Friction
( ) ( )uaexpminmaxmax &−−−= μμμμ- Shear strength of PTFE depends on rate of loading.
ActualVelocity-Dependence
μ
u&
minμ
maxμ
ApproximateVelocity-Dependence
μ
u&
minμ
maxμsμ
Coulomb Model
( )usgnWuRWF &μ+=
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 48
Pressure-Dependence of Coefficient of Friction
Pressure- and Velocity-Dependence
dμ
u&
Equal Increments of Increasing Pressure, p
⎟⎟⎠
⎞⎜⎜⎝
⎛++=
WP
gu1
AWp sv&&
TypicallyNeglected
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 49
Pressure-Dependence of Coefficient of Friction( ) ( )uaexpminmaxmax &−−−= μμμμ
0.15
0.00
0.05
0.10
50250Bearing Pressure (ksi)
Coe
ffici
ent o
f Fric
tion
minμ
Figure is based on studies of PTFE-based self-lubricating composites used in FPS bearings.
)ptanh(maxomaxmax αμΔμμ −=maxμΔ
omaxμ
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 50
( ) ( ) ( )tWZtuRWtF μ+=
Viscoplasticity Model
0uZuZZuZY 1 =−++ −&&&& γβα ηη
Z
u&
Refined Model of FPS Bearing Behavior
( ) ( )uaexpminmaxmax &−−−= μμμμCoefficient of Friction
( ) ( ) ( )usgnWtuRWtF &μ+=
u&
( )usgn &
-1
1
Evolutionary Equation
1
-1
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 51
Evaluation of Dynamic Behaviorof Base-Isolated Structures
• Isolation Systems are Almost Always Nonlinear and Often Strongly Nonlinear
• Equivalent Linear Static Analysis Using Effective Bearing Properties is CommonlyUtilized for Preliminary Design
• Final Design Should be Performed UsingNonlinear Dynamic Response History Analysis
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 52
F
uKeff
K
Equivalent Linear Properties of FPS Isolation Bearings
( ) ( ) ( )usgnWtuRWtF &μ+=
uW
RW
uFKeff
μ+==
Area = Ed
( ) ( )uRR2
uK5.04Wu4
E4E
2effs
deff +
===μπμ
πμ
πξ
Effective (Secant) Stiffness at Displacement u
Effective Damping Ratioat Displacement u
Effective linear properties are displacement-dependent. Therefore, design using effective linear properties is an iterative process.
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 53
Seismic Analysis using Nonlinearand Equivalent Linear Models
( ) ( ) ( )usgnWtuRWtF &μ+=
uW
RWKeff
μ+=
( )uRR2
eff +=
μπμξ
Nonlinear Model
Linear Model
F
u
F
u
F
uRW
ueffK
effC
effneff effm2C ξω=
( ) ( ) ( )tuCtuKtF effeff &+=
F
WFf μ=
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 54
-2 -1.5 -1 -0.5 0 0.5 1 1.5-4000
-2000
0
2000
4000
-2 -1.5 -1 -0.5 0 0.5 1 1.5-4000
-2000
0
2000
4000
Forc
e (lb
)
Displacement (in)
Example: Seismic Response UsingNonlinear and Linear Models
maxeff u
WRWK μ
+=
Slope = RW
W2μ
Slope =
maxu
Nonlinear.in65.1umax =
lb069,2Fmax =
Linear.in68.1umax =
lb261,2Fmax =maxu
maxF
maxF
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 55
Flat Sliding Bearings
• Flat Bearings:
• Bearings do NOT increase natural period of structure;Rather they limit the shear force transferred into thesuperstructure
• Requires supplemental self-centering mechanismto prevent permanent isolation system displacement
• Not commonly used in building structures
( ) ( ) ( )usgnWtuRWtF &μ+=
∞→R ( ) ( )usgnWtF &μ=∴
For Spherical Bearings:
F
u
Wμ
Wμ−
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 56
Examples of Computer Software forAnalysis of Base-Isolated Structures
• ETABSLinear and nonlinear analysis of buildings
• SAP2000General purpose linear and nonlinear analysis
• DRAIN-2DTwo-dimensional nonlinear analysis
• 3D-BASIS Analysis of base-isolated buildings
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 57
Simplified Evaluation of Dynamic Behaviorof Base-Isolated Structures
Fixed-Base
Base-Isolated
Mode 1(T = Tf)
Mode 1(T = TI1)
Mode 2(T = TI2)
Eigenproblem AnalysisResults:
TI1 >> Tf
TI1 >> TI2
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 58
Modeling Isolation Bearings Using the SAP2000 NLLINK Element
Displacement, D2Fo
rce,
F2
ISOLATOR1 Property – Biaxial Hysteretic Isolator
Displacement, D3
Forc
e, F
3
1
23
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 59
22y22222 ZF)1(DkF ββ −+=
⎩⎨⎧ >
=otherwise
0ZDif0
1a 22
2
&
Coupled Plasticity Equations
33y33333 ZF)1(DkF ββ −+=
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎦
⎤⎢⎣
⎡
−−−−
=⎭⎬⎫
⎩⎨⎧
33y
3
22y
2
233322
323222
3
2
DFk
DFk
Za1ZZaZZaZa1
ZZ
&
&
&
&
Shear Force Along EachOrthogonal Direction
Coupled EvolutionaryEquations
⎩⎨⎧ >
=otherwise
0ZDif0
1a 33
3
&
1ZZ 23
22 ≤+
1ZZ 23
22 =+
Range ofEvolutionaryVariables
Defines Yield Surface
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 60
Modeling Isolation Bearings Using the SAP2000 NLLINK Element
ISOLATOR2 Property – Biaxial Friction Pendulum Isolator
1
23
Forc
e, F
2
Displacement, D2
Forc
e, F
3
Displacement, D3
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 61
Mechanical Model of FPS Bearing in SAP2000
ISOLATOR2 Property – Biaxial Friction Pendulum Isolator
Forc
e, F
Displacement, DSpherical Slider
D(t)
F(t)
Hookean Spring Sliding Friction Element
P
P
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 62
⎩⎨⎧ <
==otherwise
0Dif0
DkPF 111
1
Forces in Biaxial FPS Isolator
( ) rv2min2max2max2 e−−−= μμμμ
Axial Force:+ = Comp.- = Tension
Friction Coefficients
23
22 DDv && +=
Resultant Velocity
P
D1
2222
2 ZPDRPF μ+=
Shear Force Along EachOrthogonal Direction
3333
3 ZPDRPF μ+=
( ) rv3min3max3max3 e−−−= μμμμ
2
233
222
vDrDrr&& +
=
Effective Inverse Velocity
k1
For FPS Bearing,R2 = R3
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 63
Forces in Biaxial FPS Isolator
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎦
⎤⎢⎣
⎡
−−−−
=⎭⎬⎫
⎩⎨⎧
33
3
22
2
233322
323222
3
2
DPk
DPk
Za1ZZaZZaZa1
ZZ
&
&
&
&
μ
μ Coupled EvolutionaryEquations
⎩⎨⎧ >
=otherwise
0ZDif0
1a 22
2
&
⎩⎨⎧ >
=otherwise
0ZDif0
1a 33
3
&
1ZZ 23
22 ≤+
1ZZ 23
22 =+
Range ofEvolutionaryVariables
Defines Yield Surface
32 k,k Elastic Shear Stiffnesses (stiffness prior to sliding)
Note: Flat Bearings: Set R = 0 for both directions (restoring forces will be set equal to zero).
Cylindrical Bearings: Set R = 0 for one direction.
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 64
Historical Development of Code Provisions for Base Isolated Structures
• Late 1980’s: BSB (Building Safety Board of California)“An Acceptable Method for Design and Review of Hospital Buildings
Utilizing Base Isolation”
• 1986 SEAONC “Tentative Seismic Isolation Design Requirements”- Yellow book [emphasized equivalent lateral force (static) design]
• 1990 SEAOC “Recommended Lateral Force Requirements and Commentary”- Blue Book- Appendix 1L: “Tentative General Requirements for the Design and
Construction of Seismic-Isolated Structures”
•1991 and 1994 Uniform Building Code- Appendix entitled: “Earthquake Regulations for Seismic-Isolated Structures”- Nearly identical to 1990 SEAOC Blue Book
• 1994 NERHP Recommended Provisions for Seismic Regulations forNew Buildings (FEMA 222A – Provisions; FEMA 223A - Commentary)
- Section 2.6: Provisions for Seismically Isolated Structures- Based on 1994 UBC but modified for strength design and national applicability
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 65
Historical Development of Code Provisions for Base Isolated Structures
• 1996 SEAOC “Recommended Lateral Force Requirements and Commentary”- Chapter 1, Sections 150 to 161 (chapters/sections parallel those of 1994 UBC)
• 1997 Uniform Building Code- Appendix entitled: “Earthquake Regulations for Seismic-Isolated Structures”- Essentially the same as 1991 and 1994 UBC
• 1997 NEHRP Recommended Provisions for Seismic Regulations forNew Buildings and Other Structures(FEMA 302 – Provisions; FEMA 303 - Commentary)
- Chapter 13: Seismically Isolated Structures Design Requirements- Based on 1997 UBC (almost identical)
• 1997 NEHRP Guidelines for the Seismic Rehabilitation of Buildings(FEMA 273 – Guidelines; FEMA 274 - Commentary)
- Chapter 9: Seismic Isolation and Energy Dissipation- Introduces Nonlinear Static (pushover) Analysis Procedure- Isolation system design is similar to that for new buildings but superstructure
design considers differences between new and existing structures
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 66
Historical Development of Code Provisions for Base Isolated Structures
• 1999 SEAOC “Recommended Lateral Force Requirements and Commentary”- Chapter 1, Sections 150 to 161 (chapters/sections parallel those of 1997 UBC)
• 2000 NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures(FEMA 368 – Provisions; FEMA 369 - Commentary)
- Chapter 13: Seismically Isolated Structures Design Requirements
• 2000 Prestandard and Commentary for the Seismic Rehabilitation of Buildings (FEMA 356)
- Chapter 9: Seismic Isolation and Energy Dissipation
• 2000 International Building Code (IBC)- Section 1623: Seismically Isolated Structures- Based on 1997 NEHRP Provisions- Similar to FEMA 356 since same key persons prepared documents
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 67
General Philosophy of Building Code Provisions
• No specific isolation systems are described
• All isolation systems must:• Remain stable at the required displacement• Provide increasing resistance with increasingdisplacement
• Have non-degrading properties under repeatedcyclic loading
• Have quantifiable engineering parameters
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 68
• Minor and Moderate Earthquakes• No damage to structural elements• No damage to nonstructural components• No damage to building contents
• Major Earthquakes• No failure of isolation system• No significant damage to structural elements• No extensive damage to nonstructural components• No major disruption to facility function• Life-Safety
Design Objectives of 2000 NEHRP and2000 IBC Base Isolation Provisions
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 69
2000 NEHRP and 2000 IBC Base Isolation Provisions
General Design ApproachEQ for Superstructure DesignDesign Earthquake10%/50 yr = 475-yr return period- Loads reduced by up to a factor of 2 to allow for limitedInelastic response; a similar fixed-base structure wouldbe designed for loads reduced by a factor of up to 8
EQ for Isolation System Design (and testing)Maximum Considered Earthquake2%/50 yr = 2,500-yr return period- No force reduction permitted for design of isolation system
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 70
• Equivalent Lateral Response Procedure• Applicable for final design under limited circumstances• Provides lower bound limits on isolation systemdisplacement and superstructure forces
• Useful for preliminary design
• Dynamic Lateral Response Procedure• May be used for design of any isolated structure• Must be used if structure is geometrically complex
or very flexible• Two procedures:
- Response Spectrum Analysis (linear)- Response-History Analysis (linear or nonlinear)
Analysis Procedures of 2000 NEHRPand 2000 IBC Base Isolation Provisions
PresentedHerein
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 71
Isolation System Displacement (Translation Only)
D
D1D2D B
TS4
gD ⎟⎠⎞
⎜⎝⎛=
π
Design Displacement Design Spectral Acceleration at One-Second Period (g)
Effective Period of IsolatedStructure at Design Displacement
Damping Reduction Factorfor Isolation System at DesignDisplacement
Design is evaluated at two levels:Design Earthquake: 10% / 50 yr = 475-yr return periodMaximum Considered Earthquake: 2% / 50 yr = 2,500-yr return period
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 72
Spec
tral
Acc
eler
atio
n, S
a
Natural Period, TOT ST 1.0
1DS
DSST
SS 1Da =
Design Response Spectrum
DSS4.0
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 73
0
0.5
1
1.5
2
2.5
0 5 10 15 20 25 30 35 40 45 50 55 60
Isolation System Damping Ratio, βD (%)
Red
uctio
n Fa
ctor
, BD
Damping Reduction Factor
( ) 2B maxD =
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 74
gkW2TminD
D π=
Effective Period
Total Seismic Dead Load Weight
Minimum Effective Stiffness of IsolationSystem at Design Displacement
Minimum stiffness used so as to produce largest periodand thus most conservative design displacement.
Effective Isolation Period
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 75
Isolation System Displacement (Translation and Rotation)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
++= 22DTD db
e12y1DD
Total Design Displacement
Eccentricity (actual + accidental)Between CM of Superstructure and CR of Isolation System
Shortest and Longest PlanDimensions of Building
Distance Between CR of Isolation System and Element of Interest
Note: A smaller total design displacement may be used (but not less than 1.1DD)provided that the isolation system can be shown to resist torsion accordingly.
Use only if isolationsystem has uniform spatial distribution oflateral stiffness
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 76
Isolation System and ElementsBelow Isolation System
Maximum Effective Isolation System Stiffness
Base Shear Force
DmaxDb DkV = No Force Reduction; Therefore ElasticResponse Below Isolation System
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 77
267.2RR
83R I ≤==
Response Modification Factor for Isolated Superstructure
Shear Force Above Isolation System
I
DmaxDS R
DkV =
Structural Elements AboveIsolation System
Ensures essentially elastic superstructure response
Minimum Values of VS:• Base shear force for design of conventional structureof fixed-base period TD
• Shear force for wind design.• 1.5 times shear force that activates isolation system.
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 78
Design Shear Force for Conventionaland Isolated Structures
Shea
r For
ce, V
S
Natural Period, T
Isolated
Elastic System
ConventionalDifference Results inSuperior SuperstructureResponse for IsolatedStructures
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 79
Example: Evaluation of Design Shear ForceBase Shear Coefficient
Conventional Structure HavingPeriod of One-Second or More
Example:• Fire Station (I = 1.5)• Conventional: Special steel moment frame (R = 8.5) and T = 1.0 sec• Isolated: TD = 2.0 sec, damping ratio = 10% (BD = 1.2), RI = 2
Isolated Structure
Result: Isolating structure results in 18% increasein shear force for design of superstructure18.1
BSCBSC
C
I =
( )DIDC
I
TRBI/RT
BSCBSC
=
DID
1D
I
DmaxDSI TRB
SWR
DkWVBSC ===
)I/R(TSC
WVBSC 1D
SS
C ===
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 80
Lateral Force at Level x of the Superstructure
Distribution of Shear Force
∑=
= n
1iii
xxSx
hw
hwVF Standard Inverted TriangularDistribution of Base Shear
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 81
Displacement at Level x of Superstructure
Interstory Drift Limit
IC xed
xδδ =
Deflection Amplification Factor Displacement at Level x ofSuperstructure Based on Elastic Analysis
Occupancy Importance Factor
Note: For Isolated Structures, Cd is replaced by RI.
sxx h015.0≤Δ
Interstory Drift of Story x
Height of Story x
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 82
DmaxDb DkV =
Displacement and Shear Force Design Spectrum
I
DmaxDS R
DkV =
Dis
plac
emen
t and
She
ar F
orce
Natural Period, T
1.0 2.0 3.0 4.0
DD
TDD
SV
bV
V
WCV S=
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 83
Required Tests of Isolation SystemPrototype Tests on Two Full-Size Specimens of Each Predominant Type of Isolation Bearing
• Check Wind Effects• 20 fully reversed cycles at force corresponding to wind design force
• Establish Displacement-Dependent Effective Stiffness and Damping• 3 fully reversed cycles at 0.25DD• 3 fully reversed cycles at 0.5DD• 3 fully reversed cycles at 1.0DD• 3 fully reversed cycles at 1.0DM• 3 fully reversed cycles at 1.0 DTM
• Check Stability• Maximum and minimum vertical load at 1.0 DTM
• Check Durability• 30SD1BD/SDS, but not less than 10, fully reversed cycles at 1.0 DTD
For cyclic tests, bearings must carry specified vertical (dead and live) loads
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 84
Effective Linear Properties of Isolation Bearing from Cyclic Testing
−+
−+
+
+=
ΔΔ
FFkeff
( )2eff
loopeff
k
E2−+ +
=ΔΔπ
β
Equivalent ViscousDamping Ratio ofIsolation Bearing
Effective Stiffnessof Isolation Bearing
−Δ
−F
Displacement, Δ
Forc
e, F
+Δ
+F
effk
Area = loopE
Effective properties determined for each cycle of loading
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 85
Effective Linear Properties of Isolation System from Cyclic Testing
D
maxDmaxDmaxD D2
FFk
∑∑ −+ +=
2DmaxD
DD Dk
E21 ∑=π
β Equivalent Viscous Damping Ratio of Isolation System
Maximum Effective Stiffnessof Isolation System
D
minDminDminD D2
FFk
∑∑ −+ +=
Minimum Effective Stiffnessof Isolation System
Use smallest value from cyclic tests
Absolute Maximum Force at Positive DD over 3 Cycles of Motion at 1.0DD
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 86
Additional Issues to Consider• Buckling and stability of elastomeric bearings
• High-strain stiffening of elastomeric bearings
• Longevity (time-dependence) of bearing materials(Property Modification Factors to appear in 2003 NEHRP Provisions)
• Displacement capacity of non-structuralcomponents that cross isolation plane
• Displacement capacity of building moat
• Second-order (P-Δ) effects on framing aboveand below isolation system
Instructional Material Complementing FEMA 451, Design Examples Seismic Isolation 15 - 7- 87
Example Design of Seismic IsolationSystem Using 2000 NEHRP Provisions
Seismically Isolated Structures by Charles A. KircherChapter 11 of Guide to the Application of the 2000 NEHRP Provisions; Note: The Guide is in final editing. Chapter 11 is in the handouts.
Structure and Isolation System- “Hypothetical” Emergency Operations Center, San Fran., CA- Three-Story Steel Braced-Frame with Penthouse- High-Damping Elastomeric Bearings
Design Topics Presented:- Determination of seismic design parameters- Preliminary design of superstructure and isolation system- Dynamic analysis of isolated structure- Specification of isolation system design and testing criteria