Topic 15-7 - Seismic Isolation - University of Memphis · Seismic Base Isolation ... –...

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


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


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


Configuration of Building Structure with Base Isolation System

Passive DamperIsolation Bearing

BaseIsolationSystem

Supe

rstru

ctur

e Basemat


Three-Dimensional View of BuildingStructure with Base Isolation System

SlidingBearing

ElastomericBearing


Installed Seismic Isolation Bearings

ElastomericBearing

Sliding Bearing


Behavior of Building Structurewith Base Isolation System

Base-Isolated StructureConventional Structure


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


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


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

Pseu

do-S

pect

ral A

ccel

erat

ion,

g


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.

Pseu

do-S

pect

ral A

ccel

erat

ion,

g


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)


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)


Bas

e Sh

ear

Period

Soft Soil

Stiff Soil

Effect of Soil Conditions onIsolated Structure Response

WithoutIsolation

T1 T2

WithIsolation


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)


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)


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)


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


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


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


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


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


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


Elastomeric Bearing Hysteresis Loops

ShearForce Displacement

AxialForce

Shea

r For

ce

Displacement

Lead-Rubber Bearing

Low DampingRubber BearingHigh Damping

Rubber Bearing


Shear Deformation of Elastomeric Bearing

- Bearing Manufactured by Scougal Rubber Corporation.- Test Performed at SUNY Buffalo.- Shear strain shown is approximately 100%.

DeformedShape

LoadCell


25.4 cm (10 in.)

1.3 m (4.3 ft)

Full-Scale Bearing Prior to Dynamic Testing


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.


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


)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


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

=′′′

=


-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


Shear Storage Modulus of High-Damping Natural Rubber

Shea

r Sto

rage

Mod

ulus

(psi

)

Shear Strain (%)0 100 200 300

300

200

0

100 Increasing Frequency

Increasing Pressure


Effective Damping Ratio of High-Damping Natural Rubber

Effe

ctiv

e D

ampi

ng R

atio

(%)

Shear Strain (%)0 100 200 300

20

15

0

10

Increasing Frequency

Increasing Pressure

5


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


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


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


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


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


Radius of Curvature of FPS Bearings

+R


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


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


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


FuR

W

WFf μ=Rigid Model withStrain Hardening

( )usgnWuRWF &μ+=

Mechanical Model of Friction Pendulum System Bearings

F

u

u&

( )usgn &

-1

1


D

F F

u

F

u

F

u

Time

F

u

Hysteretic Behavior of FrictionPendulum System Bearings

( )usgnWuRWF &μ+=

gR2T π=

FreeVibrationPeriod


Forc

e, F

Displacement, u

fF

D

F

RW effK

Area =DW

Idealized FPS Bearing Hysteresis Loop

ShearForce Displacement

AxialForce

( )usgnWuR

WF &μ+=


-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


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+=


Pressure-Dependence of Coefficient of Friction

Pressure- and Velocity-Dependence

dμ

u&

Equal Increments of Increasing Pressure, p

⎟⎟⎠

⎞⎜⎜⎝

⎛++=

WP

gu1

AWp sv&&

TypicallyNeglected


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


( ) ( ) ( )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


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


F

uKeff

K

Equivalent Linear Properties of FPS Isolation Bearings


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.


Seismic Analysis using Nonlinearand Equivalent Linear Models


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=


-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


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


∞→R ( ) ( )usgnWtF &μ=∴

For Spherical Bearings:

F

u

Wμ

Wμ−


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


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


Modeling Isolation Bearings Using the SAP2000 NLLINK Element

Displacement, D2

Forc

e, F

2

ISOLATOR1 Property – Biaxial Hysteretic Isolator

Displacement, D3

Forc

e, F

3

1

23


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


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


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


⎩⎨⎧ <

==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


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.


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



• 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



• 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


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


• 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


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


• 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


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


Spec

tral

Acc

eler

atio

n, S

a

Natural Period, TOT ST 1.0

1DS

DSST

SS 1Da =

Design Response Spectrum

DSS4.0


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 =


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


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


Isolation System and ElementsBelow Isolation System

Maximum Effective Isolation System Stiffness

Base Shear Force

DmaxDb DkV = No Force Reduction; Therefore ElasticResponse Below Isolation System


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 structure

of fixed-base period TD• Shear force for wind design.• 1.5 times shear force that activates isolation system.


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


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 ===


Lateral Force at Level x of the Superstructure

Distribution of Shear Force

∑=

= n

1iii

xxSx

hw

hwVF Standard Inverted TriangularDistribution of Base Shear


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


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=


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


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


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


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


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

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