SEISMIC PROTECTIVE SYSTEMS:
SEISMIC ISOLATION
Developed by:
Michael D. Symans, PhD
Major Objectives
•
Rensselaer Polytechnic Institute
•
•
•
Instructional Material Complementing FEMA 451, Design Examples
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- 1
Seismic Isolation 15 - 7- 2
Configuration of Building Structure
with Base Isolation System
Outline
Seismic 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 Seismic
Isolation Bearings
Basemat
Superstructure
–
Base
Isolation
System
• Elastomeric Bearings
• Sliding Bearings
–
Modeling of Seismic Isolation Bearings in Computer Software
–
Code Provisions for Base Isolation
Instructional Material Complementing FEMA 451, Design Examples
Isolation Bearing
Three-Dimensional View of Building
Structure with Base Isolation System
Passive Damper
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 3
Seismic Isolation 15 - 7- 4
Installed Seismic Isolation Bearings
Elastomeric
Bearing
Sliding
Bearing
Sliding Bearing
Elastomeric
Bearing
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 5
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 6
Behavior of Building Structure
with Base Isolation System
Objectives of Seismic Isolation Systems
•
Enhance performance of structures at
all hazard levels by:
ƒ Minimizing interruption of use of facility
(e.g., Immediate Occupancy Performance Level)
ƒ Reducing damaging deformations in structural and
nonstructural components
ƒ Reducing acceleration response to minimize contentsrelated damage
Base-Isolated Structure
Conventional Structure
Instructional Material Complementing FEMA 451, Design Examples
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 7
Characteristics of Well-Designed
Seismic Isolation Systems
Effect of Seismic Isolation (ADRS Perspective)
1.2
T=1.0
T=.50
•
•
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
5% Damping
Pseudoacceleration,
g g
Pseudo-Spectral
Acceleration,
•
Seismic Isolation 15 - 7- 8
1.0
T=1.5
10%
0.8
20%
30%
0.6
T=2.0
40%
Decreased Shear Force
Increased Displacement
0.4
T=3.0
0.2
T=4.0
0.0
0
5
10
15
20
Spectral Displacement, Inches
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 9
Effect of Seismic Isolation with Supplemental Dampers
(ADRS Perspective)
1.2
Effect of Seismic Isolation
Increase Period of Vibration of Structure
to Reduce Base Shear
5% Damping
1.0
Pseudoacceleration,
g g
Pseudo-Spectral
Acceleration,
Seismic Isolation 15 - 7- 10
(Acceleration Response Spectrum Perspective)
T=1.0
T=.50
Instructional Material Complementing FEMA 451, Design Examples
T=1.5
10%
0.8
Base Shear
20%
30%
0.6
T=2.0
40%
Decreased Shear Force
Slightly Increased Displ.
0.4
Increasing Damping
T=3.0
0.2
T=4.0
0.0
0
5
10
15
20
Spectral Displacement, Inches
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 11
T1
T2
Without
Isolation
With
Isolation
Instructional Material Complementing FEMA 451, Design Examples
Period
Seismic Isolation 15 - 7- 12
Increase of period increases displacement
demand (now concentrated at base)
Displacement
Increasing Damping
T1
Without
Isolation
T2
Period
With
Isolation
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 13
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- 15
Application of Seismic Isolation to Retrofit Projects
Motivating 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- 17
Effect of Soil Conditions on
Isolated Structure Response
Soft Soil
Base Shear
Effect of Seismic Isolation
(Displacement Response Spectrum Perspective)
Stiff Soil
Period
T1
T2
Without
Isolation
With
Isolation
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 14
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- 16
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- 18
Geometry of Elastomeric Bearings
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
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- 19
Low Damping Natural or Synthetic
Rubber Bearings
High-Damping Natural Rubber Bearings
• Maximum shear strain = 200 to 350%
• Damping increased by adding extrafine
Linear behavior in shear for shear
strains up to and exceeding 100%.
carbon black, oils or resins, and other
proprietary fillers
Damping ratio = 2 to 3%
• Damping ratio = 10 to 20% at shear
Advantages:
- Simple to manufacture
- Easy to model
- Response not strongly sensitive to
rate of loading, history of loading,
temperature, and aging.
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
Disadvantage:
Need supplemental damping system
Instructional Material Complementing FEMA 451, Design Examples
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 21
Lead-Rubber Bearings
Seismic Isolation 15 - 7- 20
Seismic Isolation 15 - 7- 22
Elastomeric Bearing Hysteresis Loops
• Invented in 1975 in New Zealand and
used extensively in New Zealand, Japan,
and the United States.
Shear
Force
Axial
Force
Displacement
• Low damping rubber combined with
central lead core
• Shear modulus = 85 to 100 psi at 100%
• Lead yield stress = 1500 psi
(results in high initial stiffness)
• 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)
• Yield stress reduces with repeated cycling
High Damping
Rubber Bearing
due to temperature rise
strongly displacement-dependent
Instructional Material Complementing FEMA 451, Design Examples
Shear Force
press-fitted into central
hole of elastomeric bearing
• Hysteretic response is
Lead-Rubber Bearing
shear strain
• Solid lead cylinder is
Low Damping
Rubber Bearing
Displacement
Seismic Isolation 15 - 7- 23
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 24
Shear Deformation of Elastomeric Bearing
Full-Scale Bearing Prior to Dynamic Testing
1.3 m (4.3 ft)
Deformed
Shape
Load
Cell
25.4 cm (10 in.)
- Bearing Manufactured by Scougal Rubber Corporation.
- Test Performed at SUNY Buffalo.
- Shear strain shown is approximately 100%.
Instructional Material Complementing FEMA 451, Design Examples
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 25
Seismic Isolation 15 - 7- 26
Harmonic Behavior of Elastomeric Bearing
Cyclic Testing of Elastomeric Bearing
u ( t ) = u 0 sin( ω t )
Phase
Angle
(Lag)
Imposed Motion
Loading Frequency
Assumed Form of Total Force
P ( t ) = P0 sin(ω t ) cos(δ ) + P0 cos(ω t ) sin(δ )
Bearing Manufactured by
Dynamic Isolation Systems Inc.
δ
ω
1500
FORCE, KIPS
1000
ELASTIC FORCE
DAMPING FORCE
TOTAL FORCE
500
0
-500
-1000
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
-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
Note: Damping force 90o out of phase with elastic force.
Instructional Material Complementing FEMA 451, Design Examples
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 27
P ( t ) = K S u ( t ) + C u& ( t )
P
P0
K
cos( δ ) K L = 0 sin( δ ) C = L
u0
u0
ω
Storage Stiffness
Loss Stiffness
Damping Coeff.
Shear Force, P
Po
PZ
P ( t ) = K S u ( t ) + C u& ( t )
⎛ PZ
⎝ P0
δ = sin −1 ⎜⎜
⎞
⎟⎟
⎠
Phase Angle
1
ξ = tan (δ )
2
KS
uo
KS =
G' A
tr
KL =
Storage Stiffness
Shear Stress
KS =
Seismic Isolation 15 - 7- 28
G' ' A
tr
Loss Stiffness
C=
δ = sin −1 ⎜⎜
ω
Damping Coeff.
η=
τo
τZ
⎛τZ ⎞
⎟⎟
⎝ τ0 ⎠
KL
Phase Angle
G ′′(ω )
= tan (δ )
G ′(ω )
Loss Factor
G′
γo
ξ=
PZ = K L u o
Shear Strain
τ ( t ) = G ′γ (t ) + G ′′γ& (t ) / ω
Displacement, u
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 29
Instructional Material Complementing FEMA 451, Design Examples
η
2
=
1
tan (δ )
2
Damping Ratio
Seismic Isolation 15 - 7- 30
Experimental Hysteresis Loops
of Low Damping Rubber Bearing
8
6
Bearing Force (kN)
4
2
0
-2
-4
-6
-8
-3
-2
-1
0
1
Bearing Deformation (cm)
2
3
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
Shear Storage Modulus (psi)
Shear Storage Modulus of High-Damping Natural Rubber
200
Increasing Pressure
Increasing Frequency
100
0
100
0
15
10
Increasing Pressure
K eff
300
P
Shear Strain (%)
Displacement
WD = 4Q(D − DY )
If Q >> DY, then:
WD ≈ 4QD
P(t ) = keff u (t ) + ceff u& (t )
keff
F
Q
= = αK +
D
D
W
ξ eff = D
4πWS
1
WS = K eff D 2
2
ξ eff =
Instructional Material Complementing FEMA 451, Design Examples
2Q(D − DY )
πD(Q + αKD )
Seismic Isolation 15 - 7- 35
Seismic Isolation 15 - 7- 34
Refined Nonlinear Mathematical Model for
Natural and Synthetic Rubber Bearings
Shear Force, P
K eff
D
= Effective damping coefficient
associated with design
displacement
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 33
Equivalent Linear Properties from Idealized
Bilinear Hysteresis Loop
F
keff =
F
Area =WD
Fy
D
α
K
Q
DY
ceff
Ceff
Instructional Material Complementing FEMA 451, Design Examples
−D
= Effective stiffness at design
displacement
u
0
K
keff
Displacement, u
5
200
Seismic Isolation 15 - 7- 32
Linear Mathematical Model for
Natural and Synthetic Rubber Bearings
Shear Force, P
Increasing Frequency
100
300
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 31
20
0
Force
200
Shear Strain (%)
Effective Damping Ratio of High-Damping Natural Rubber
Effective Damping Ratio (%)
300
Displacement, u
P(t ) = α
Py
uy
α
= Post-to-pre yielding stiffness ratio
Py
= Yield force
uy
= Yield displacement
Z
= Evolutionary variable
γ , β ,η ,θ
= Calibration constants
u (t ) + (1 − α )Py Z (t )
η −1
η
u y Z& + γ u& Z Z
+ βu& Z − θu& = 0
Shear Force in Bearing
Evolutionary Equation
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 36
Spherical Sliding Bearing:
Friction Pendulum System (FPS)
Stainless Steel
Concave Surface
Mathematical Model of Friction
Pendulum System Bearings
Housing Plate
With PTFE
Coating Above
Slider
W
Free-Body Diagram
of Top Plate and
Slider Under
Imposed Lateral
Force F
F
θ
N
Concave Plate and Slider
for FPS Bridge Bearing
Articulated
Slider With
PTFE
Coating
Concave
Plate
Ff
θ
- Seismic retrofit of Benicia-Martinez Bridge,
San Francisco, CA
- 7.5 to 13 ft diameters
- Displ. Capacity of 13 ft bearings = +/- 4.3 ft
Instructional Material Complementing FEMA 451, Design Examples
F = W tan θ +
Ff
cos θ
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 37
Seismic Isolation 15 - 7- 38
Mathematical Model of Friction
Pendulum System Bearings
Radius of Curvature of FPS Bearings
R
For u < 0.2R, θ is small
(2% error in u)
θ R cos θ
u
R sin θ
R
sin θ = θ −
+
cos θ = 1 −
θ3
+ ... ≈ θ
3!
θ2
Rθ
R
⎡
⎛
⎛ u ⎞ ⎞⎤
v = R ( 1 − cos θ ) = R ⎢1 − cos ⎜⎜ sin − 1 ⎜ ⎟ ⎟⎟ ⎥
⎝ R ⎠ ⎠⎦
⎝
⎣
Rθ 2
u2
≈
v≈
2
2R
θ R cos θ
u
v
R sin θ
sin θ = θ −
cos θ = 1 −
R
θ R
Rθ
θ3
3!
θ
2
2!
+ ... ≈ θ
N =
W
≈W
cos θ
F f = μ N sgn (u& )
W
u + μW sgn (u& )
R
Seismic Isolation 15 - 7- 40
Components of FPS Bearing Lateral Force
sgn (u& )
W
1
F = u + μW sgn (u& ) = Fr + F f
R
-1
Ff
Fr
u&
F
μW
T = 2.75 sec
u
+ ... ≈ 1
+
u
=
u
− μW
0.5
u
R
u
R
F=
cosθ
1
v ( in .)
θ ≈
Ff
θ ≈
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 39
Vertical Displacement of FPS Bearings
θ R
+ ... ≈ 1
2!
F = W tanθ +
Instructional Material Complementing FEMA 451, Design Examples
R
Slope =
0
0
Note: Vertical frequency is twice
that of lateral frequency
10
5
u ( in .)
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 41
W
R
+ u&
− u&
Note: Bearing will not recenter if Fr < F f ( u < μR )
For large T, and thus large R, this can be a concern.
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 42
Hysteretic Behavior of Friction
Pendulum System Bearings
Mechanical Model of Friction Pendulum
System Bearings
sgn (u& )
W
1
F = u + μW sgn (u& )
R
&
W
u + μW sgn (u& )
R
u
-1
W
R
F=
Free
Vibration
Period
R
g
T = 2π
Time
F
u
F
F
F f = μW
F
F
u
D
F
F
u
u
u
u
Rigid Model with
Strain Hardening
Instructional Material Complementing FEMA 451, Design Examples
Idealized FPS Bearing Hysteresis Loop
Axial
Force
Shear
Force
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 43
Seismic Isolation 15 - 7- 44
Actual FPS Bearing Hysteresis Loop
10
Displacement
8
Stick-Slip
6
Bearing Force (kN)
4
F
Area = W
D
Force, F
Ff
2
0
-2
-4
K eff
W
R
-6
Stick-Slip
-8
-10
-5
D
F =
-4
-3
-2
-1
0
1
2
3
4
5
Bearing Displacement (cm)
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)
W
u + μ W sgn (u& )
R
Displacement, u
Instructional Material Complementing FEMA 451, Design Examples
Velocity-Dependence of Coefficient of Friction
W
u + μW sgn (u& )
R
F=
μ
μ max
μs
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 45
Pressure-Dependence of Coefficient of Friction
μd
μ
μ max
p=
Coulomb Model
μ min
μ min
u&
Actual
Velocity-Dependence
Seismic Isolation 15 - 7- 46
W ⎛ u&&v Ps ⎞
⎜ 1 + + ⎟⎟
A ⎜⎝
g W⎠
Equal Increments of
Increasing Pressure, p
Typically
Neglected
u&
Approximate
Velocity-Dependence
μ = μ max − (μ max − μ min ) exp(− a u& )
u&
Pressure- and Velocity-Dependence
- Shear strength of PTFE depends on rate of loading.
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 47
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 48
Pressure-Dependence of Coefficient of Friction
Refined Model of FPS Bearing Behavior
μ = μ max − (μ max − μ min ) exp(− a u& )
μ max
Coefficient of Friction
0.15
Z
1
1
u&
o
-1
μ max = μ max o − Δμ max tanh( αp )
0.10
sgn (u& )
Δμ max
u&
-1
Viscoplasticity Model
η −1
Y Z& + α u& Z Z
+ β u& Z
η
− γ u& = 0
Evolutionary
Equation
0.05
μ min
Coefficient of Friction
μ = μ max − (μ max − μ min ) exp(− a u& )
0.00
0
50
25
Bearing Pressure (ksi)
Figure is based on studies of PTFE-based
self-lubricating composites used in FPS bearings.
Instructional Material Complementing FEMA 451, Design Examples
F (t ) =
W
u (t ) + μW sgn (u& )
R
F
Keff
K eff =
ξ eff =
Nonlinear Dynamic Response History Analysis
W
R
(
K eff
Linear Model
F
Ceff
u
ξ eff
u
0
F (t ) = K eff u (t ) + C eff u& (t )
2 μR
=
π (μR + u )
K eff =
W μW
+
R
u
Ceff = 2 mω neff ξ eff
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 53
Seismic Isolation 15 - 7- 52
Slope = K eff =
Slope =
2000
F
F
Effective Damping Ratio
at Displacement u
Example: Seismic Response Using
Nonlinear and Linear Models
4000
W
F (t ) = u (t ) + μW sgn (u& )
R
u
)
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 51
Force (lb)
Ff = μW
Effective (Secant) Stiffness
at Displacement u
Effective linear properties are displacement-dependent. Therefore,
design using effective linear properties is an iterative process.
u
F
F W μW
=
+
R
u
u
Ed
4 μWu
2 μR
=
=
4πE s 4π 0.5 K eff u 2
π (μR + u )
Seismic Analysis using Nonlinear
and Equivalent Linear Models
Nonlinear Model
W
u (t ) + μW sgn (u& )
R
u
Area = Ed
• Equivalent Linear Static Analysis Using
Instructional Material Complementing FEMA 451, Design Examples
F (t ) =
K
Nonlinear and Often Strongly Nonlinear
• Final Design Should be Performed Using
Seismic Isolation 15 - 7- 50
Equivalent Linear Properties of FPS Isolation Bearings
• Isolation Systems are Almost Always
Effective Bearing Properties is Commonly
Utilized for Preliminary Design
W
u (t ) + μ WZ (t )
R
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 49
Evaluation of Dynamic Behavior
of Base-Isolated Structures
F (t ) =
Fmax
W
R
2 μW
-2000
u max
W μW
+
R u max
Nonlinear
u max = 1.65 in .
Fmax = 2 ,069 lb
Linear
u max = 1.68 in .
Fmax
Fmax = 2 ,261 lb
u max
Displacement (in)
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 54
Flat Sliding Bearings
Examples of Computer Software for
Analysis of Base-Isolated Structures
For Spherical Bearings:
F (t ) =
• ETABS
W
u (t ) + μW sgn (u& )
R
Linear and nonlinear analysis of buildings
F
μW
• Flat Bearings:
R → ∞ ∴ F (t ) = μW sgn (u& )
• SAP2000
General purpose linear and nonlinear analysis
u
• Bearings do NOT increase natural period of structure;
Rather they limit the shear force transferred into the
superstructure
− μW
• Requires supplemental self-centering mechanism
to prevent permanent isolation system displacement
• DRAIN-2D
Two-dimensional nonlinear analysis
• 3D-BASIS
Analysis of base-isolated buildings
• Not commonly used in building structures
Instructional Material Complementing FEMA 451, Design Examples
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 55
Simplified Evaluation of Dynamic Behavior
of Base-Isolated Structures
Eigenproblem
Analysis
Results:
Seismic Isolation 15 - 7- 56
Modeling Isolation Bearings Using the
SAP2000 NLLINK Element
ISOLATOR1 Property – Biaxial Hysteretic Isolator
1
3
2
TI1 >> Tf
Base-Isolated
Mode 1
(T = TI1)
TI1 >> TI2
Force, F2
Mode 1
(T = Tf)
Force, F3
Fixed-Base
Instructional Material Complementing FEMA 451, Design Examples
F2 = β 2 k 2 D2 + ( 1 − β 2 ) Fy 2 Z 2
Shear Force Along Each
Orthogonal Direction
F3 = β 3 k 3 D3 + ( 1 − β 3 ) F y 3 Z 3
Range of
Z 22 + Z 32 ≤ 1 Evolutionary
Variables
if D& 3 Z 3 > 0
otherwise
2
Coupled
Evolutionary
Equations
if D& 2 Z 2 > 0
otherwise
1
Z 22 + Z 32 = 1
Instructional Material Complementing FEMA 451, Design Examples
Force, F2
⎧1
a2 = ⎨
⎩ 0
⎧1
a3 = ⎨
⎩ 0
ISOLATOR2 Property – Biaxial Friction Pendulum Isolator
3
⎧ k2 & ⎫
D2 ⎪
− a3 Z 2 Z 3 ⎤ ⎪⎪ Fy 2
⎪
⎬
⎥⎨
1 − a3 Z 32 ⎦ ⎪ k 3 D& ⎪
3
⎪⎩ Fy 3
⎪⎭
Seismic Isolation 15 - 7- 58
Modeling Isolation Bearings Using the
SAP2000 NLLINK Element
Force, F3
⎧ Z& 2 ⎫ ⎡ 1 − a2 Z 22
⎨& ⎬=⎢
⎩ Z 3 ⎭ ⎣ − a2 Z 2 Z 3
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 57
Coupled Plasticity Equations
Displacement, D2
Displacement, D3
Mode 2
(T = TI2)
Displacement, D3
Displacement, D2
Defines Yield Surface
Seismic Isolation 15 - 7- 59
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 60
Mechanical Model of FPS Bearing in SAP2000
Spherical Slider
Force, F
ISOLATOR2 Property
– Biaxial Friction Pendulum Isolator
Forces in Biaxial FPS Isolator
⎧k D
F1 = P = ⎨ 1 1
⎩ 0
if D1 < 0
otherwise
P
F2 =
D2 + Pμ 2 Z 2
R2
Displacement, D
P
F3 =
F(t)
P
P
D3 + P μ 3 Z 3
R3
P
Axial Force:
+ = Comp.
- = Tension
k1
D1
μ 2 = μ max 2 − (μ max 2 − μ min 2 )e − rv
μ 3 = μ max 3 − (μ max 3 − μ min 3 )e − rv
Friction Coefficients
D(t)
Hookean Spring
Sliding Friction Element
v=
D& 22 + D& 32
Resultant Velocity
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 61
Forces in Biaxial FPS Isolator
⎧ Z& 2 ⎫ ⎡ 1 − a2 Z 22
⎨& ⎬=⎢
⎩ Z 3 ⎭ ⎣ − a2 Z 2 Z 3
⎧1
a2 = ⎨
⎩ 0
⎧1
a3 = ⎨
⎩ 0
k 2 , k3
⎧ k2
− a3 Z 2 Z 3 ⎤ ⎪⎪ Pμ 2
⎥⎨
1 − a3 Z 32 ⎦ ⎪ k 3
⎩⎪ Pμ 3
if D& 2 Z 2 > 0
otherwise
if D& 3 Z 3 > 0
otherwise
Z 22
+
⎫
D& 2 ⎪
⎪
⎬
&
D3 ⎪
⎭⎪
Z 32
≤1
Z 22 + Z 32 = 1
Coupled
Evolutionary
Equations
Range of
Evolutionary
Variables
For FPS
Bearing,
R2 = R3
Shear Force Along Each
Orthogonal Direction
r=
r2 D& 22 + r3 D& 32
v2
Effective Inverse Velocity
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 62
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”
Defines Yield Surface
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- 63
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 for
New 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- 65
•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 for
New 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- 64
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- 66
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 increasing
displacement
• Have non-degrading properties under repeated
cyclic loading
• Have quantifiable engineering parameters
Instructional Material Complementing FEMA 451, Design Examples
• 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
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 67
2000 NEHRP and 2000 IBC Base Isolation Provisions
General Design Approach
Design Earthquake
10%/50 yr = 475-yr return period
- Loads reduced by up to a factor of 2 to allow for limited
Inelastic response; a similar fixed-base structure would
be designed for loads reduced by a factor of up to 8
EQ for Isolation System Design (and testing)
Maximum Considered Earthquake
2%/50 yr = 2,500-yr return period
- No force reduction permitted for design of isolation system
Analysis Procedures of 2000 NEHRP
and 2000 IBC Base Isolation Provisions
• Applicable for final design under limited circumstances
• Provides lower bound limits on isolation system
displacement and superstructure forces
• Useful for preliminary design
• 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)
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 69
2
⎞ S D 1T D
⎟
⎠ BD
Seismic Isolation 15 - 7- 70
Design Response Spectrum
Design Spectral Acceleration
at One-Second Period (g)
Effective Period of Isolated
Structure at Design Displacement
Damping Reduction Factor
for Isolation System at Design
Displacement
Design is evaluated at two levels:
Design Earthquake: 10% / 50 yr = 475-yr return period
Maximum Considered Earthquake: 2% / 50 yr = 2,500-yr return period
Spectral Acceleration, Sa
⎛ g
DD = ⎜
⎝ 4π
Presented
Herein
• Dynamic Lateral Response Procedure
Isolation System Displacement (Translation Only)
Design Displacement
Seismic Isolation 15 - 7- 68
• Equivalent Lateral Response Procedure
EQ for Superstructure Design
Instructional Material Complementing FEMA 451, Design Examples
Design Objectives of 2000 NEHRP and
2000 IBC Base Isolation Provisions
S DS
Sa =
S D1
T
S D1
0 . 4 S DS
TO
TS
1.0
Natural Period, T
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 71
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 72
Effective Isolation Period
Damping Reduction Factor
Reduction Factor, BD
2.5
(B D )max
2
Effective Period
= 2
T D = 2π
1.5
W
k D min g
Total Seismic Dead Load Weight
1
0.5
Minimum Effective Stiffness of Isolation
System at Design Displacement
0
0
5
10 15 20 25 30 35 40 45 50 55 60
Isolation System Damping Ratio, βD (%)
Instructional Material Complementing FEMA 451, Design Examples
Minimum stiffness used so as to produce largest period
and thus most conservative design displacement.
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 73
Isolation System Displacement
(Translation and Rotation)
Total Design Displacement
Eccentricity (actual + accidental)
Between CM of Superstructure
and CR of Isolation System
⎡
⎛ 12 e
D TD = D D ⎢ 1 + y ⎜ 2
⎝b + d
⎣
2
⎞⎤
⎟⎥
⎠⎦
Use only if isolation
system has uniform
spatial distribution of
lateral stiffness
Seismic Isolation 15 - 7- 74
Base Shear Force
Isolation System and Elements
Below Isolation System
Vb = k D
max
DD
No Force Reduction; Therefore Elastic
Response Below Isolation System
Maximum Effective Isolation System Stiffness
Distance Between CR of Isolation
System and Element of Interest
Shortest and Longest Plan
Dimensions of Building
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.
Shear Force Above Isolation System
Structural Elements Above
Isolation System
VS =
RI
kD
max
RI
DD
Response Modification Factor
for Isolated Superstructure
3
R
R =
=
≤ 2
8
2 . 67
Ensures essentially elastic
superstructure response
Minimum Values of VS:
• Base shear force for design of conventional structure
of 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
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 75
Seismic Isolation 15 - 7- 77
Seismic Isolation 15 - 7- 76
Design Shear Force for Conventional
and Isolated Structures
Shear Force, VS
Instructional Material Complementing FEMA 451, Design Examples
Elastic System
Isolated
Conventional
Difference Results in
Superior Superstructure
Response for Isolated
Structures
Natural Period, T
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 78
Example: Evaluation of Design Shear Force
Distribution of Shear Force
Base Shear Coefficient
VS w xhx
Fx =
V
k
D
S D1
BSCI = S = D max D =
Isolated Structure
W
WRI
BD R ITD
VS
S D1
BSCC =
= CS =
Conventional Structure Having
W
T ( R / I ) Period of One-Second or More
Standard Inverted Triangular
Distribution of Base Shear
n
∑
i=1
w i hi
Lateral Force at Level x of the Superstructure
BSCI T (R / I )
=
BSCC BD R ITD
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
BSCI
= 1.18
BSCC
Result:
Isolating structure results in 18% increase
in shear force for design of superstructure
Instructional Material Complementing FEMA 451, Design Examples
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 79
Displacement and Shear Force Design Spectrum
Displacement and Shear Force
Interstory Drift Limit
Displacement at Level x of Superstructure
Deflection Amplification Factor
δ
x
=
C dδ
I
xe
Displacement at Level x of
Superstructure Based on
Elastic Analysis
Occupancy Importance Factor
Note: For Isolated Structures, Cd is replaced by RI.
Interstory Drift of Story x
Vb
D TD
VS
DD
V
1.0
Δ x ≤ 0 . 015 h sx
Vb = k D
Natural Period, T
max
DD
VS =
Required Tests of Isolation System
• Check Wind Effects
• 20 fully reversed cycles at force corresponding to wind design force
For cyclic tests, bearings must carry specified vertical (dead and live) loads
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 83
max
V = C SW
DD
RI
Seismic Isolation 15 - 7- 82
Effective Linear Properties of
Isolation Bearing from Cyclic Testing
Prototype Tests on Two Full-Size Specimens
of Each Predominant Type of Isolation Bearing
• 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
kD
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 81
Area = Eloop
Force, F
• 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
4.0
3.0
2.0
Height of Story x
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 80
F+
keff =
keff
Δ−
Δ+
F−
β eff =
F+ + F−
Δ+ + Δ−
2
(
Effective Stiffness
of Isolation Bearing
Eloop
π k Δ+ + Δ−
eff
Displacement, Δ
)
2
Equivalent Viscous
Damping Ratio of
Isolation Bearing
Effective properties determined
for each cycle of loading
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 84
Effective Linear Properties of Isolation
System from Cyclic Testing
Absolute Maximum Force at Positive DD over 3 Cycles of Motion at 1.0DD
∑
k D max =
FD+
max
+ ∑ FD−
max
2 DD
k D min =
∑
FD+
min
+∑
2 DD
FD−
min
βD =
1
2π k D max DD2
• Buckling and stability of elastomeric bearings
• High-strain stiffening of elastomeric bearings
Maximum Effective Stiffness
of Isolation System
• Longevity (time-dependence) of bearing materials
Minimum Effective Stiffness
of Isolation System
• Displacement capacity of non-structural
components that cross isolation plane
Use smallest value from cyclic tests
∑ ED
Additional Issues to Consider
Seismic Isolation 15 - 7- 85
Example Design of Seismic Isolation
System Using 2000 NEHRP Provisions
Seismically Isolated Structures by Charles A. Kircher
Chapter 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
Instructional Material Complementing FEMA 451, Design Examples
• Displacement capacity of building moat
• Second-order (P-Δ) effects on framing above
and below isolation system
Equivalent Viscous Damping
Ratio of Isolation System
Instructional Material Complementing FEMA 451, Design Examples
(Property Modification Factors to appear in 2003 NEHRP Provisions)
Seismic Isolation 15 - 7- 87
Instructional Material Complementing FEMA 451, Design Examples
Seismic Isolation 15 - 7- 86