isolation bearings

U.S. Italy Workshop on Seismic Protective Systems for Bridges, 1998 Fenves, et al.

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MODELING AND CHARACTERIZATION OF SEISMIC ISOLATION BEARINGS

Gregory L. Fenves, Wei–Hsi Huang, Andrew S. Whittaker, Peter W. Clark, Stephen A. Ma

Pacific Earthquake Engineering Research CenterUniversity of California, Berkeley

Richmond, California 94804

ABSTRACT

A coordinated experimental and analytical research program sponsored by the California Dment of Transportation is underway to improve knowledge about seismic isolation and suppmental damping for highway bridges. The first phase of the study is to characterize the bi–directional response of elastomeric and sliding isolation bearings for static and dynamic extion in a thorough static and dynamic testing program. Analytical models based on classicaticity and smoothed plasticity (Bouc–Wen) are used for representing bearing behavior. Statdirectional load histories and earthquake response studies show the effect of bi–directionapling in these models compared with independent uni–directional models.

INTRODUCTION

Isolation bearings and supplemental damping devices can be effective techniques for contrthe forces and deformations transferred from a bridge superstructure to the substructure anings. Hysteretic energy dissipation in the isolation bearings and dampers, with careful desiglimit bearing deformations and overall displacements to acceptable levels. The use of protesystems in new bridge construction, however, has been hampered by questions about systbehavior, long–term durability, and clear definition of performance. Concerning system behthere is a lack of information about the following issues:

• Can isolation bearing and supplemental dampers be used close to faults which can genground motions with large velocity pulses?

• How can isolation devices be used effectively for bridges with flexible piers?

• Can limited yielding of piers be tolerated?

• What are the trade–offs between hysteretic energy dissipation in isolation bearings verscous or hysteretic energy dissipation in supplemental dampers?

• What is the bi–directional behavior of bearings and how does it affect bridge response?

To address these issues, the California Department of Transportation (Caltrans) is sponsorresearch project at the University of California, Berkeley, on seismic protective systems forbridges. The project consists of coordinated experimental and analytical studies that addrefundamental issues of how isolation bearings and supplemental damping devices can be uachieve specified bridge performance. The current project follows previous experimental anlytical studies of protective systems for bridges by Kelly et al. (1986), Constantinou et al. (11994), and Tsopelas et al. (1996). Extending these important studies, the current project exbi–directional behavior of isolated bridges, a range of isolation and damping devices, the resto near–fault ground motion, and the effect of pier yielding.

1


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The first phase of the project is to characterize the bi–directional behavior of elastomeric aning bearings. Limited experimental studies have been performed in Japan, such as reporteNagarajaiah et al. (1989) for high damping rubber bearings. To address this lack of informathe testing of isolation bearings under bi–directional static and dynamic excitation is now uway. This paper focuses on the models for bi–directional behavior, the experimental test proand selected pre–test analyses.

BI–DIRECTIONAL MODELS OF ISOLATION BEARINGS

Elastomeric bearings have highly nonlinear behavior that is a function of the shear strain, vstress, number and order of deformation cycles, and temperature. An accurate and detailestanding of all these effects under multi–directional loading is an ultimate goal. At this pointpler models with properties selected to account for the vertical stress and shear strain leveaddressed in this study. The approach focuses on macro–models of bearing behavior, as coto constitutive models at the micro– or meso–scale or phenomenological models. Experimeverified macro–models are readily incorporated into standard dynamic analysis procedurescan be effectively utilized in design. Although much progress has been made in understandconstitutive behavior of elastomers, such models are difficult to use for design applicationsnomenological models, such as by Kikuchi and Aiken (1997), are accurate for uni–directionbehavior, but they have many parameters and are difficult to generalize for bi–directional bior.

Two approaches for modeling the bi–directional behavior of bearings are investigated in thipaper. The first approach utilizes classical, rate–independent plasticity. The second approalizes a smoothed idealization of plasticity, commonly referred to as the Bouc–Wen model. Tconcept of “yield” in an elastomeric or sliding bearing is, of course, a simplifying idealizatioBoth approaches are based on assumption of isotropic behavior and neglect torsion of the bThe restoring force in a bearing is assumed to depend only on the translational (shear) def

tion of the bearing. The restoring force, , for the bearing is a function of defor

tion , in which , are the restoring force and deformation in orthogonal

horizontal direction, i=1,2. Two methods for determining the bi–directional relationship betweF and U are summarized below.

Rate–independent Plasticity

The first approach for representing behavior of bearings is to utilize rate–independent plas(Lubliner, 1990). The restoring force has an elastic–hardening component and a hystereticponent as follows:

(1)

In equation 1 is the hysteretic force, the initial stiffness of the bearing is , and the po

yield hardening stiffness is . A circular yield function is postulated,

F F1 F2

T=

U U1 U2

T= Fi Ui

F αK0U Fp+=

Fp K0

αK0

2


unc-

s the orm.

e. rned by resents i–

r. The i– using tween

as-

es the that iah et

rep- hys-xhibits

(2)

where is the uni–directional yield force. The plastic potential is selected to be the yield f

tion, which is an associated flow rule for the plastic displacement rate:

(3)

in which γ is the plastic multiplier. During plastic flow, , the plastic displacement rate igiven by equation 3, and the consistency condition must hold. Using standard procedures, plastic displacement, plastic force , and tangent matrices are computed in incremental f

Bouc–Wen Model

The Bouc–Wen model an endochronic model (Valanis, 1971), which utilizes an internal timThis class of models are used in stochastic analysis because evolution of the model is govea differential equation and it is not necessary to keep track of the yield state. The model repa smooth transition between elastic and yield states. Wen (1980) applied to the model to undirectional hysteretic behavior and Park et al. (1986) generalized it to bi–directional behaviobi–directional model is widely used, such as in 3D–BASIS (Nagarajaiah et al. 1991). The bdirectional form of the model considered here was generalized by Casciati (1989). Plasticitya yield function (such as equation 2) is replaced by smoothed functions for the transition beno–yield and yield states. With this approach, the plastic force in equation 1 is defined as

, where is a dimensionless variable that governs the pl

tic behavior and . The evolution equation is then written as (Casciati, 1989):

(4)

The parameters, γ, β, and η govern the evolution of the plastic variable, Z. For and

, it can be shown that,

(5)

For A=1 and , the model represents a circular yield surface. The parameter η governs the transition to yield. In the limit as , the transition between elastic and plastic states is instantaneous, as for the rate–independent, plasticity model. Integration of equation 4 providplastic state, and the tangent matrix in incremental form can be derived. It should be notedequation 4 is similar to the bi–directional equations given in Park et al. (1986) and Nagaraja

al. (1991). However, equation 4 includes complete information in the term whichresents the direction of loading. Although Bouc–Wen model is widely used for representingteretic behavior, some studies have show that the model violates plasticity conditions and e

F Fp( ) Fp 1 α–( )Fy–=

Fy

Up γ ∂F∂Fp---------⋅=

F 0=

Fp

Fp 1 α–( )K0 ZUy( )= Z Z1 Z2

T=

Uy Fy K0⁄=

ZUy AU γ β ZTU( )sgn+( ) Z η 2– ZZ T( )U–=

A 0>β γ 0>+

max ZA

β γ+------------

1η---

=

β γ+ 1=η ∞→

ZTU( )sgn

3


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two rgent aluate

keley’s rings.

ries in ted by sup- Four igure 2 the ntrol ved

ctors. ffects

shown are

its will f

arings: m). ctional in. in d–rub-

nal l. The uires ure more 3),

drift under unsymmetrical displacement or load cycles (Thyagarajan and Iwan, 1990). An ational discussion on this point is found in Appendix B of Spacone et al. (1992).

BI–DIRECTIONAL DISPLACEMENT CONTROLLED TESTING

Most testing of isolation bearings is uni–directional because of the complexity of loading indirections. Earthquake response of an isolated bridget is two–dimensional, so there is an uneed to perform bi–directional testing of bearings in order to understand the behavior and evthe efficacy of the models described in the previous section. The recent upgrade of UC Berearthquake simulator allows bi–directional testing of small– to moderate–scale isolation beaTesting of the bearings is planned for April and May 1998.

The testing program involves an isolation system subjected to specified displacement histotwo horizontal directions. Figure 1 shows the plan and elevation of the a rigid frame supporfour bearings with five–component load cells on the earthquake simulator. The rigid frame ports concrete and lead weights totalling 65 kip provide the vertical stress on the bearings.struts brace the frame against reaction buttresses located around the simulator platform. Fshows the testing frame supported on four bearings before placing the added weights. Withstruts fixing the frame against the buttresses, the platform is moved under displacement coaccording to specified bi–directional horizontal displacement histories. With the struts remothe isolated frame can be tested with earthquake ground motion histories.

The choice of the displacement histories for bi–directional testing is based on a variety of faThe displacement histories should be simple enough to illustrate bi–directional interaction ewithout the random nature of an actual earthquake. The displacement–controlled orbits arein figure 3. Varying levels of maximum strain in the two directions ranging from 25% to 250%used to evaluate the path–dependent behavior of the bearings. The box and hourglass orbbe run at a very slow rate. The uni–directional and figure–8 orbits will be run over a range ovelocities to assess rate effects.

SELECTION OF BEARINGS

The program involves testing and analysis of bridge systems with three generic types of behigh damping rubber, lead–rubber, and spherical sliding bearings (Friction Pendulum SysteThe high damping rubber bearings have been investigated in an extensive study of uni–direbehavior (Aiken et al., 1992). The KL301 Bridgestone bearings are 6.93 in. in diameter, 2.48height, with a total rubber thickness of 1.73 in. rubber thickness (shape factor=20). The leaber bearings and FPS bearings will be used with the target specifications in table 1.

The pre–test prediction of the bi–directional behavior has been examined for the bi–directiodisplacement controlled tests. Previous uni–directional tests (Aiken et al., 1992) of the highdamping rubber bearings were used to estimate the parameters for the mathematical modedownhill simplex method (Nelder and Mead, 1965) is an estimation procedure that only reqfunction evaluations and no gradient information. Given a displacement history, the procedminimizes the square of the difference in force between the model and the test over one orcycles. For the 100% shear strain level, the estimated properties are =1.52 kip ( =0.09Fy Cy

4


ased

. For the

figure–he hys-dels.

=0.115 in., α=0.065, which gives a second slope of 0.86 kip/in. The period of the frame b

on the second slope is 1.39 sec, and the secant period is 1.17 sec at a displacement of 4 inBouc–Wen model the parameters are: A=1, γ=β=0.5, and η=2.

Figure 1 – Bi–directional bearing test apparatus on earthquake simulator

Figure 2 – Testing apparatus without added weight

The model response for the box orbit at 100% shear strain is shown in figure 4 and for the 8 at 100% strain in figure 5. Each figures shows the total force and plastic force trace and tteretic loops in the two directions (X and Y) computed with the plasticity and Bouc–Wen mo

Uy

5


on, ing by the bi–

ctional than force

direc-tion. ts,

by l earth-ons, length ucture.

The solid line gives the computed response for the bi–directional formulation. For comparisthe dotted lines shows the response from independent uni-directional models in X and Y. Infigure 4 the independent uni–directional models overpredict the maximum force in the bear25% because of the square yield surface. In comparison, loading in one direction while on directional circular yield surface requires unloading in the other direction. The plasticity andBouc–Wen models give nearly identical results for the bi–directional models.

Figure 5 shows the model response for the figure–8 orbit at 100% shear strain. The bi–direinteraction effects are important in the Y direction because it is changing more less rapidly the X direction. Similar results are shown in Nagarajaiah et al. (1991). As can be seen in theplots, the uni–directional model overestimates the maximum force in the bearing. The uni–tional model also overestimates the hysteretic energy dissipation, particularly in the Y direcThe plasticity and Bouc–Wen models are very similar when considering bi–directional effecand both are superior for this load pattern compared with the uncoupled models.

Figure 3 – Displacement controlled orbits for bi–directional testing

EARTHQUAKE TESTING

The isolation bearing testing frame in figure 1 can be used for dynamic earthquake testing removing the struts. The objective of the earthquake testing is to examine the bi–directionaquake response of the isolated frame, evaluate the effects of different types of ground motiincluding near–fault ground motions, and calibrate the bearing models. With an appropriate scale factor, the testing frame represents a bridge with rigid superstructure and rigid substr

Table 1 – Target specifications for isolation bearings

High Damping Rubber

Bearings

Lead–Rubber Bearing FPS Bearing

Design Vertical Load (kip) 16.25 16.25 16.25

Isolated Secant Period (sec) 0.9 0.9 1.5

Equivalent Damping Ratio 0.13 0.15 0.15

Equivalent Yield Coefficient — 0.05 0.06

Uni–directional Displacement Capacity (in.)

5+ 5+ 6

Uni–directional Box Hourglass Figure–8

U1

U2

U1

U2

U1

U2

U1

U2

6


otions limit neces-the pro-

The challenge in selecting earthquake time histories lies in balancing the need to include mrepresenting different source types, soil types, intensities, and durations with the desire to the number of tests. The displacement and velocity limitations of the earthquake simulator sitate the adjustment and scaling of the structural models and ground motions to represent totype bridges and ground motion accurately.

Figure 4 – Box displacement controlled history (γ=100%); solid line is bi–directional model,dotted line is uncoupled uni–directional model

Figure 5 – Figure–8 displacement controlled history (γ=100%); solid line is bi–directional model, dotted line is uncoupled uni–directional model

−3 −2 −1 0 1 2 3−3

−2

−1

0

1

2

3

Force X (kips)

For

ce Y

(ki

ps)

−1 0 1

−1

0

1

Plastic Force X (kips)

Pla

stic

For

ce Y

(ki

ps)

−2 0 2

−2

0

2

Displacement X (in)

For

ce X

(ki

ps)

−2 0 2

−2

0

2

Displacement Y (in)

For

ce Y

(ki

ps)

−3 −2 −1 0 1 2 3−3

−2

−1

0

1

2

3

Force X (kips)

For

ce Y

(ki

ps)

−1 0 1

−1

0

1


Pla

stic

For

ce Y

(ki

ps)

−2 0 2

−2

0

2

Displacement X (in)

For

ce X

(ki

ps)

−2 0 2

−2

0

2

Displacement Y (in)

For

ce Y

(ki

ps)

Plasticity Model Bouc–Wen Model

−3 −2 −1 0 1 2 3−3

−2

−1

0

1

2

3

Force X (kips)

For

ce Y

(ki

ps)

−1 0 1

−1

0

1


Pla

stic

For

ce Y

(ki

ps)

−2 0 2

−2

0

2

Displacement X (in)

For

ce X

(ki

ps)

−2 0 2

−2

0

2

Displacement Y (in)

For

ce Y

(ki

ps)

−3 −2 −1 0 1 2 3−3

−2

−1

0

1

2

3

Force X (kips)

For

ce Y

(ki

ps)

−1 0 1

−1

0

1


Pla

stic

For

ce Y

(ki

ps)

−2 0 2

−2

0

2

Displacement X (in)

For

ce X

(ki

ps)

−2 0 2

−2

0

2

Displacement Y (in)

For

ce Y

(ki

ps)

Plasticity Model Bouc–Wen Model

7


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amped ociated site f ampli-presen-ecords d from ctions ar

d to

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cementlated at that the and 15

Earthquake Ground Motions

In support of Phase 2 of the FEMA/SAC project to develop guidelines for the seismic desigsteel structures, a comprehensive set of earthquake ground motion time histories has beenoped by Woodward–Clyde Federal Services of Pasadena, California (SAC, 1997). The recocompatible with the national seismic hazard maps released in 1997 by the United States Gcal Survey (USGS). The mean spectra of all of the records in each subset are matched to tUSGS target spectra at periods of 0.3, 1, 2, and 4 seconds. Only the ground motions develothe Los Angeles region have been evaluated for use in the current testing program. There asets of records:

• Los Angeles — 10% probability of exceedence in 50 years(LA01 to LA20, 10 pairs of time histories)



• Recorded near–fault records (NF01 to NF20, 10 pairs of time histories)

• Simulated near–fault records (NF21 to NF40, 10 pairs of time histories)

• Soft soil records (LS01A to LS20I, 90 pairs of time histories)

Records LA01 to LA60 have been amplitude and frequency scaled such that the mean 5% delastic spectrum for each set matches the USGS target spectrum corresponding to the assprobability of exceedence. They are intended to be representative of stiff soil sites (NEHRPtype D). The near–fault records have not been matched to any specific spectrum in terms otude or in the frequency domain. The resulting scatter in the suite of records is therefore retative of the scatter anticipated in ground motions near the source of major earthquakes. RNF01 to NF20 are from actual recorded time histories. Records NF21 to NF40 are computeseismological source modeling. The near–fault records are oriented along the principal direof the fault rupture. The soft soil records have been derived from the stiff soil, 10% in 50–yerecords by propagating them through various soil profiles. Soft soil sites 1 and 2 corresponNEHRP site types E and F, respectively.

Selection and Processing of Ground Motions

The limitations of the earthquake simulator and the considerations for scaling the model ar

• The peak displacement of the simulator platform is 5 in. in each direction.

• The peak attainable velocity of the simulator platform is 23 in/sec in each direction.

• The longest–period isolation system considered is 3.2 seconds.

• The maximum length scale factor considered is 6.

For each record in each suite of time histories, the peak acceleration, velocity, and displawere calculated for scale factors ranging from 1 to 6. Spectral responses were also calcuperiods of 1, 2, 3, 4, and 5 seconds. These calculations were then repeated assumingrecords were filtered with bandpass filters (0 to 5) that have a high corner and cut of 12 Hz

8


if thepectral

f sourcelected as

F17/F01/nents

1994 ias in

e circu-ce in el he

The 7. ing the lar to

Hz, respectively, and low cut frequencies between 0 and 0.25 Hz. A record is acceptablescaled velocity and displacement are within the limits of the earthquake simulator and the svalues of the filtered record are not reduced substantially below the unfiltered version.

Based on the above criteria, and assuring that an ensemble of records reflecting a variety oparameters, soil conditions, intensities, and durations, the records in table 2 have been sethe ground motions for the experimental and analytical studies.

Figure 6 shows the 5% damped response spectra for the Kobe record near–fault record (NNF18), Olive View record (NF15/NF16), and the record from the 1978 Tabas earthquake (NNF02). The spectra in figure 6 are plotted in fault normal (FN) and fault parallel (FP) compowith a length scale of 5 and a corresponding time scale of .

Response Predicted by Analytical Model

The response of the rigid frame using the properties of the HDR bearing for the Olive View (Northridge) record is shown in figures 7 and 8. The displacement histories have a strong bthe fault normal direction with a maximum displacement of 4 in. (γ=230%), which corresponds toa prototype bearing displacement of 20 in. The force space for the coupled model shows thlar yield surface, whereas the uncoupled model shows a square surface. The maximum forthe bearing is 4.8 kip, which corresponds to a seismic coefficient of 0.30. The coupled modshows considerable interaction effects in hysteresis loops, particularly in the FP direction. Tuncoupled FP hysteresis loop is a poor representation of the bi–directional loading history.response of the Bouc–Wen model in figure 8 is very similar to the plasticity model in figure Figures 9 and 10 show the response for the Kobe and Tabas earthquakes, respectively, usplasticity model. The response for the same cases using the Bouc–Wen model is very simi

Table 2 – Earthquake records selected for testing

SAC ID Record M R (km)Amplitude

ScaleLength Scale Filter No.

LA01/LA02 Imperial Valley,1940 El Centro

6.9 10 2.01 2–6 0

LA09/LA10 Yermo, 1992 Landers 7.3 25 2.17 2–6 3

LA13/LA14 Newhall, 1994 Northridge 6.7 6.7 1.03 3–6 0

NF09/NF10 1992 Erzincan 6.7 2 1 4–6 4

NF15/NF16 Olive View, 1994 Northridge

6.7 6.4 1 4–6 5

NF17/NF18 1995 Kobe 6.9 3.4 1 5 3

NF01/NF02 1978 Tabas 7.4 1.2 1 5 3

LA21/LA22 1995 Kobe 6.9 3.4 1.15 6–6 0

LS01C/LS02C 1940 El Centro – soft soil 1 6.9 10 2.01 4–6 0

LS01E/LS02E 1940 El Centro – soft soil 2 6.9 10 2.01 3–6 0

LS17C/LS18C 1940 El Centro – soft soil 1 6.7 6.4 0.99 6 0

LS17E/LS18E 1940 El Centro – soft soil 2 6.7 6.4 0.99 6 4

5

9


e is

n the e effect ent

length .

the plasticity model and is not shown here. The Kobe record produces strong FN bias in thresponse with two large displacement excursions in the FN direction. The FP force history strongly affected by the yielding in the FN direction.

The response for the Tabas record in figure 10 has more equal FN and FP components thaother near–fault records. The displacement orbits for the uncoupled model is different in thdetails of the large FN excursion and FP excursion compared to the uncoupled model. Theof bi–directional interaction is clearly seen in the FP hysteresis loop which shows a “turningaround” in the FP direction near a displacement of 2 in. as the large negative FN displacemtakes place. This bi–directional interaction is not represented with the uncoupled model.

Figure 6 – Earthquake response spectra (5% damping) for three near–fault records withscale factor of 5, resolved into fault normal (FN) and fault parallel (FP) components

0 1 2 3 40

1

2

3

4

Period (sec)

Spe

ctra

l Acc

el. (

g)

Kobe, Scaled, 5% damping

FN

FP

0 1 2 3 40

5

10

15

20

Period (sec)

Spe

ctra

l Dis

pl. (

in)

Kobe, Scaled, 5% damping

FN

FP

0 1 2 3 40

1

2

3

4

Period (sec)

Spe

ctra

l Acc

el. (

g)Olive View, Scaled, 5% damping

FN

FP

0 1 2 3 40

5

10

15

20

Period (sec)

Spe

ctra

l Dis

pl. (

in)

Olive View, Scaled, 5% damping

FN

FP

0 1 2 3 40

1

2

3

4

Period (sec)

Spe

ctra

l Acc

el. (

g)

Tabas, Scaled, 5% damping

FN

FP

0 1 2 3 40

5

10

15

20

Period (sec)

Spe

ctra

l Dis

pl. (

in)

Tabas, Scaled, 5% damping

FN

FP

10


Figure 7 – HDR bearing response for Olive View record (1994 Northridge),length scale 5, plasticity model

Figure 8 – HDR bearing response for Olive View record (1994 Northridge),length scale 5, Bouc–Wen model

Coupled Uncoupled

−4 −2 0 2 4−4

−2

0

2

Displacement FN (in)

Dis

plac

emen

t FP

(in

)

−4 −2 0 2 4

−2

0

2

4

Force FN (kips)

For

ce F

P (

kips

)

−4 −2 0 2 4

−4

−2

0

2

4


For

ce F

N (

kips

)

−2 0 2

−2

0

2

Displacement FP (in)

For

ce F

P (

kips

)

−4 −2 0 2 4

−4

−2

0

2


Dis

plac

emen

t FP

(in

)

−4 −2 0 2 4

−4

−2

0

2

Force FN (kips)

For

ce F

P (

kips

)

−4 −2 0 2 4

−4

−2

0

2

4


For

ce F

N (

kips

)

−2 0 2

−2

0

2


For

ce F

P (

kips

)

Coupled Uncoupled

−4 −2 0 2 4−4

−2

0

2


Dis

plac

emen

t FP

(in

)

−4 −2 0 2 4

−2

0

2

4

Force FN (kips)

For

ce F

P (

kips

)

−4 −2 0 2 4

−4

−2

0

2

4


For

ce F

N (

kips

)

−2 0 2

−2

0

2


For

ce F

P (

kips

)

−4 −2 0 2 4

−4

−2

0

2


Dis

plac

emen

t FP

(in

)

−4 −2 0 2 4

−4

−2

0

2

Force FN (kips)

For

ce F

P (

kips

)

−4 −2 0 2 4

−4

−2

0

2

4


For

ce F

N (

kips

)

−2 0 2

−2

0

2


For

ce F

P (

kips

)

11


per-se of a

Figure 9 – HDR bearing response for 1995 Kobe near–fault record,length scale 5, plasticity model

Figure 10 – HDR bearing response for 1978 Tabas near–fault record,length scale 5, plasticity model

SYSTEM RESPONSE

Another phase of the experimental program involves bi–directional testing of an isolated sustructure on flexible piers. To aid in the design of the system testing, the earthquake respon

−4 −2 0 2 4

−4

−2

0

2

4


Dis

plac

emen

t FP

(in

)

−4 −2 0 2 4 6

−4

−2

0

2

4

Force FN (kips)

For

ce F

P (

kips

)

−4 −2 0 2 4 6−6

−4

−2

0

2

4

6


For

ce F

N (

kips

)

−2 0 2

−2

0

2


For

ce F

P (

kips

)

−4 −2 0 2 4−4

−2

0

2

4


Dis

plac

emen

t FP

(in

)

−4 −2 0 2 4 6

−4

−2

0

2

4

Force FN (kips)

For

ce F

P (

kips

)

−4 −2 0 2 4 6−6

−4

−2

0

2

4

6


For

ce F

N (

kips

)

−2 0 2

−2

0

2


For

ce F

P (

kips

)

Coupled Uncoupled

−4 −2 0 2 4

−2

0

2


Dis

plac

emen

t FP

(in

)

−4 −2 0 2 4−4

−2

0

2

4

Force FN (kips)

For

ce F

P (

kips

)

−4 −2 0 2 4

−4

−2

0

2

4


For

ce F

N (

kips

)

−2 0 2−4

−2

0

2

4


For

ce F

P (

kips

)

−4 −2 0 2 4−4

−2

0

2


Dis

plac

emen

t FP

(in

)

−4 −2 0 2 4

−4

−2

0

2

4

Force FN (kips)

For

ce F

P (

kips

)

−4 −2 0 2 4

−4

−2

0

2

4


For

ce F

N (

kips

)

−2 0 2−4

−2

0

2

4


For

ce F

P (

kips

)

Coupled Uncoupled

12


tion. g and

ub-

is:

iers, gs

direc-tiff-range

ives a , the ement d of

is stiff-d sub-

reases n in the

istics of

r of d in

the Bouc–irec- and liding

rigid superstructure with four bearings, each on a linear elastic pier, is examined in this secThe effective stiffness, , of a single pier is defined from the sum of the linearized bearin

pier flexibilities:

(6)

where is the second slope stiffness of the bearing and is the stiffness of the s

structure. For a given and bearing–to–pier stiffness ratio , the bearing stiffness

(7)

The previously considered cases with the test frame and no substructure had =∞,

= =0.86 kip/in. with a period of 1.39 sec.

Figure 11 shows the maximum response of the frame with four HDR bearings on flexible psubjected to the Olive View (1994 Northridge) record for length scale factor of 5. The bearinhave the non–dimensional parameters considered previously ( =0.093, α=0.065). The figure

shows the superstructure displacement in each direction, the bearing deformation in each tion, and the displacement and deformation (in any direction) for a wide range of effective sness (equation 6) and for bearing–to–pier stiffness ratios from zero to unity. For in the

of 0.5 kip/in (period=1.8 sec), the constant displacement portion of the spectrum (figure 6) gmaximum displacement fairly independent of the bearing–to-pier stiffness ratio. As a resultbearing deformation decreases as the pier becomes more flexible. The peak in the displacand bearing deformation spectra occurs for =1.2 kip/in, which corresponds to the perio

1.2 sec at which the FN spectral displacement is largest. The maximum displacement in thness range is not only a function of (or period) but depends on the relative bearing an

structure stiffness. As the substructure becomes more flexible, the bearing deformation decand the maximum displacement increases because of reduced hysteretic energy dissipatiobearing. This example demonstrate that the designer must consider the spectral characterthe ground motion and the trade–off between deformation in the bearing and substructure.

SUMMARY AND FUTURE WORK

The static and dynamic tests will provide valuable information about bi–directional behavioseismic isolation bearings. Considering the models, bi–directional effects should be includeany analysis. Designs based on uncoupled inelastic springs may not accurately represent forces transferred to the substructure and hysteretic energy dissipation. The plasticity and Wen models produce very similar results, particularly with the complete terms for loading dtion in the latter model. Extensions of the models to account for softening under cyclic loadstiffnening of the elastomeric bearings are under investigation. Development of models for sisolation bearings is being pursued.

Keff

1Keff---------- 1

Ki----- 1

Ks------+=

Ki αK0= Ks

Keff Ki Ks⁄

Ki Keff 1Ki

Ks------+

=

Ks

Ki Keff

Cy

Keff

Keff

Keff

13


994

under , and esign

Figure 11 – Maximum responses of isolated frame on flexible piers, Olive View record (1Northridge), length scale 5, plasticity model

ACKNOWLEDGEMENTS

The protective systems project is supported by the California Department of TransportationContract 59A169. Caltrans staff Tim Leahy, Dorrie Mellon, Mohsen Sultan, Roberto LeCalleLi–Hong Sheng have worked closely with the project team. Dr. Amir Gilani assisted in the dand fabrication of the testing frame.

0 1 2 3 43

4

5

6

7

8

9

Keff

(kips/in)

Dis

plac

emen

t FN

(in)

0 1 2 3 40.5

1

1.5

2

2.5

3

3.5

Keff

(kips/in)

Dis

plac

emen

t FP

(in)

0 1 2 3 40

1

2

3

4

5

6

Keff

(kips/in)

Def

orm

. in

HD

RB

FN

(in)

0 1 2 3 40

0.5

1

1.5

2

2.5

3

Keff

(kips/in)

Def

orm

. in

HD

RB

FP

(in)

ki/k

s=0

ki/k

s=0.25

ki/k

s=0.5

ki/k

s=0.75

ki/k

s=1

0 1 2 3 43

4

5

6

7

8

9

Keff

(kips/in)

Max

Dis

p to

Gro

und(

in)

0 1 2 3 40

1

2

3

4

5

6

Keff

(kips/in)

Max

Def

orm

. in

HD

RB

(in)

14


tal,” 281-

and

rk at

ass of-

lateder,

ola-

of 3–

of 3–

iza-

under

tures,”

analy-sity

hyster-n

ory,”

REFERENCES

Aiken, I.D., Kelly, J.M, Clark, P.W., Tamura, K., Kikuchi, M., and Itoh, T. (1992). “Experimenstudies of the mechanical characteristics of three types of seismic isolation bearingsPro-ceedings, Tenth World Conference on Earthquake Engineering, Vol. 4, Madrid, pp. 22286.

Casciati, F. (1989). “Stochastic dynamics of hysteretic media,” Structural Safety, Vol. 6, pp. 259-269.

Constantinou, M.C., Kartoum, A., Reinhorn, A.M., and Bradford, P. (1991). “Experimentaltheoretical study of a sliding isolation system for bridges,” Report No. NCEER-91-0027,National Center for Earthquake Engineering Research, State University of New YoBuffalo.

Constantinou, M.C., Tsopelas, P., and Okamoto, S. (1994). “Experimental study of a clbridge seismic isolation systems,” Proceedings, Fifth U.S. National Conference on Earthquake Engineering, EERI, Vol. I, Chicago, pp. 901-910.

Kelly, J.M., Buckle, I.G., and Tsai, H.-C. (1986). “Earthquake simulator testing of a base-isobridge deck,” Report No. UCB/EERC-85/09, Earthquake Engineering Research CentUniversity of California, Berkeley.

Kikuchi, M. and Aiken, I.D. (1997). “An analytical hysteresis model for elastomeric seismic istion bearings,” Earthquake Engineering and Structural Dynamics, Vol. 26, pp. 215-231.

Lubliner, J. (1990). Plasticity, Macmillan, New York.Nagarajaiah, S., Reinhorn, A.M., Constantinou, M.C. (1989). “Nonlinear dynamic analysis

D base isolated structures (3D-BASIS),” Report No. NCEER-89-0019, National Center forEarthquake Engineering Research, State University of New York at Buffalo.

Nagarajaiah, S., Reinhorn, A.M., Constantinou, M.C. (1991). “Nonlinear dynamic analysis D base isolated structures,” Journal of Structural Engineering, ASCE, Vol. 117, pp. 2035–2054.

Nelder, J.A., and Mead, R. (1965). “Downhill simplex method on multi-dimensional minimtion,” Computer Journal, Vol. 7, p. 308.

Park, Y.J., Wen, Y.K., and Ang, A.H.–S. (1986). “Random vibration of hysteretic systems bi-directional ground motions,” Earthquake Engineering and Structural Dynamics, Vol.14, pp. 543-557.

SAC (1997). “Suites of earthquake ground motion for analysis of steel moment frame strucReport No. SAC/BD-97/03, Woodward–Clyde Federal Services, SAC Steel Project.

Spacone, E., Ciampi, V., and Filippou, F.C. (1992). “A beam element for seismic damage sis,” Report No. UCB/EERC-92/07, Earthquake Engineering Research Center, Univerof California, Berkeley.

Thyagarajan, R.S., and Iwan, W.D. (1990). “Performance characteristics of a widely used etic model in structural dynamics,” Proceedings, Fourth U.S. National Conference oEarthquake Engineering, EERI, Vol. 2, Palm Springs, pp. 177-186.

Tsopelas, P. et al. (1996). “Experimental study of FPS system in bridge seismic isolation,” Earth-quake Engineering and Structural Dynamics, Vol. 25, pp. 65-78.

Valanis, K.C. (1971). “A theory of viscoplasticity without a yield surface, Part I: General theArchives of Mechanics, Vol. 23, pp. 517-533.

Wen, Y.-K. (1976). “Method for random vibration of hysteretic systems,” Journal of the Engineer-ing Mechanics Division, ASCE, Vol. 102, pp. 249-263.

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isolation bearings

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