Approximate Earthquake Analysis for Regular Base Isolated Buildings Subjected to Near Fault Ground Motions

Approximate Earthquake Analysis for RegularBase Isolated Buildings Subjected to Near Fault

Ground Motions

Leblouba Moussa (IAENG Member) ∗Zerzour Ali †

Abstract—An approximate earthquake modal anal-ysis of base isolated regular buildings (AMA-BI) sub-jected to near fault ground motions is developed andpresented in this paper. The basis of this procedurebenefits from two important properties of base iso-lated structures; the concentrated nonlinearity at thebase isolation level and the fact that the base isola-tion and the superstructure behave as two bodies incontact with discontinuity at the isolation layer. TheAMA-BI treats the base as it is; a nonlinear system,and the superstructure as elastic. This latter can bedecomposed into subsystems so that when superposedand combined with the response of the base they givean overall behavior and response very close to that ob-tained when using the nonlinear time history analysis(NLTHA) of the base isolated structure. An exampleof application is treated to evaluate the accuracy ofthe procedure.

Keywords: Base Isolation, Superstructure, Nonlinear-

ity, Modal Analysis, Near Fault

1 Introduction

Now, evident is the performance of structures mountedon an isolation system during earthquakes. The isolationsystem deflects the seismic energy so that will not betransferred to the superstructure. The benefits gained byusing such technique are substantial and can be itemizedafter Stanton and Roeder (1991) [13] as:

• Reduced floor accelerations and interstory drifts;

• Reduced (or no) damage to structural elements;

• Better protection of buildings’ contents;

• Concentration of nonlinear, large deformation be-havior into one group of elements (the isolation bear-ings and dampers).

∗Manuscript received March 5, 2010. Accepted March 14, 2010.This work was supported in part by the Algerian Ministry ofHigher Education and Scientific Research. Leblouba Moussa iswith the High National School of Public Works, Algiers Algeria16051. (corresponding author mobile: +213 667 897 968; e-mail:[email protected]).

†Zerzour Ali is with the High National School of Public Works,Algiers Algeria 16051. (e-mail: [email protected]).

The last item highlights an important inherent propertyof a well selected and designed isolation system. The su-perstructure may remain elastic under these conditionsand most deformations occur at the isolation level, sothat the structure’s expensive contents and equipmentsremain intact from minim damages. However, the chal-lenge is how to select the appropriate isolation systemparameters. Several design and analysis methods wereproposed, but a common problem arise in the complex-ity of implementation that require an extensive effort tobe performed. Therefore, we are interested in developingsimple but efficient procedures that lead to an appropri-ate design with minimum effort.Based on the above itemized seismic isolation features,an approximate earthquake modal analysis procedure(AMA-BI) is developed and illustrated through exam-ples.

2 Approximate Earthquake Modal Anal-ysis (AMA-BI)

2.1 Uncoupled Equations of Motion

The matrix form of differential equations governing theresponse of a MDOF base isolated structure (see figure1) to earthquake induced ground motion are as follows:

MU + CU + KU = −MR(ug(t) + xb) (1)

RT M[U + R(ug(t) + xb)

]+mb(ug(t)+ xb)+ f = 0 (2)

Eq. 1 corresponds to the superstructure while Eq. 2 cor-responds to the base isolation level, where M and K arethe mass and lateral stiffness matrices of the superstruc-ture, R is the vector of earthquake influence coefficients.The damping matrix C would not be needed in the ap-proximate modal analysis of earthquake response (AMA-BI); instead modal damping ratios suffice.The idealization of a base isolated structure as a blockmass mounted on isolation system is reasonable since thethe peak and overall response will not be altered [10].Also, the structural period and damping ratios have nonoticeable effect on the peak response [9]. For this and asa reasonable approximation we neglect the term RT MU

Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.

ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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Figure 1: MDOF base isolated structure

from Eq.2, this gives:

xb +f

Mtot

= −ug(t) (3)

where Mtot = Ms + mb; Ms is the total mass of thesuperstructure and mb is the base mass.The procedure consists to solve Eq.3 for xb that will beadded to the ground motion acceleration to constitutea new excitation for the superstructure to determinefinally the total response quantities of interest.Figure 2 illustrates the AMA-BI procedure for MDOFbase isolated systems. The MDOF system is equivalentto combination of the response of the total mass Mtot

mounted on the isolation system subjected to theearthquake acceleration ug(t) and series of SDF systemspinned at their bases having unit mass and naturalperiods Ti subjected to the excitation (ug(t) + xb).Shown in the same illustration are the equations tobe solved for each subsystem and the correspondingvibration properties. The modal matrix for the MDOFbase isolated structure is denoted by Φ while that forthe superstructure is denoted Φsup, their shapes aredepicted in figure 3. The use of the modal matrix Φsup

(Φsup = Φ(1 : N, 1 : N)) instead of the modal matrixcomputed using M and K is due to the fact that wehave to keep the nodal motion shapes. In addition, thenatural frequencies (or natural periods Ti) used for thesuperstructure (Ω2

sup = Ω2(2 : N + 1, 2 : N + 1) arethose calculated using the mass matrix of the wholestructure and its corresponding stiffness matrix afterelimination of the first entry (first period) which is theisolation period, the rest is taken as the periods of theSDF systems constituting the superstructure. The floordisplacements relative to the base ui are computed as asuperposition of the modal contributions as follows:

Figure 2: AMA-BI procedure for MDOF base isolatedstructures

Figure 3: Determination of Φsup and Ω2

sup the modal andspectral matrices of the superstructure



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U = ΦsupQ where Q =

⎛⎜⎜⎜⎜⎜⎜⎝

q1

q2

.

.

.qN

⎞⎟⎟⎟⎟⎟⎟⎠

=

⎛⎜⎜⎜⎜⎜⎜⎝

Γ1D1

Γ2D2

.

.

.ΓNDN

⎞⎟⎟⎟⎟⎟⎟⎠

and U =

⎛⎜⎜⎜⎜⎜⎜⎝

u1

u2

.

.

.uN

⎞⎟⎟⎟⎟⎟⎟⎠

Γi is the modal participation factor, which is a measureof the degree of to which the ith mode participates inthe response of the superstructure, and it is described asfollows:

Γi =φT

sup iMR

φTsup iMφsup i

Furthermore, the modal floor displacements relative tothe base are combined to compute the total response us-ing the base displacement and the transformation matrix,Ψ:

X =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

x1

x2

.

.

.xN

xb

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎭

= Ψ

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

u1

u2

.

.

.uN

xb

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎭

where Ψ =

(Φsup [1][0] 1

)

The same procedure as done for displacements determina-tion is to be followed for floor accelerations computation:

U = ΦsupQ where Q =

⎛⎜⎜⎜⎜⎜⎜⎝

q1

q2

.

.

.qN

⎞⎟⎟⎟⎟⎟⎟⎠

=

⎛⎜⎜⎜⎜⎜⎜⎝

Γ1D1

Γ2D2

.

.

.

ΓN DN

⎞⎟⎟⎟⎟⎟⎟⎠

and U =

⎛⎜⎜⎜⎜⎜⎜⎝

u1

u2

.

.

.uN

⎞⎟⎟⎟⎟⎟⎟⎠

Therefore the floor accelerations relative to the groundare then computed as a superposition of the abovecalculated quantities:

X =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

x1

x2

.

.

.xN

xb

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎭

= Ψ

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

u1

u2

.

.

.uN

xb

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎭

Forces in each floor are computed from the total flooraccelerations as follows:

F = MT Xtot; Xtot = Rug(t) + x and R = (1 1 ... 1)T

where MT is the mass matrix of the structure includingthe base.It should be noted that in the solution of Eq.3 the totalmass of the structure is to be adjusted so that the isola-tion period resulted is equal to the first period determinedfrom the solution of the eigenproblem characterizing thewhole structure. For 2DOF base isolated structures (onestory + base level) the transformation matrix is differentfrom that given for MDOF systems and is described asfollows:

Ψ =

(1

Mtot

1

0 1

)

2.2 Six-Story Structure with Lead-RubberBearing Isolation System

The analysis of a six-story reinforced concrete base iso-lated structure with LRB isolation system is considered.The 3D, plan and elevation views are shown in figure 4.The reinforced concrete superstructure is designed to re-sist lateral loads using column elements. The vertical axisof centers of mass is offset from the geometric center ofthe structure from inducing a mass eccentricity of 17 cmin the Y direction. The uncoupled translational periodof the superstructure Ts = 0.64 sec. in both X and Ydirections for a complete three-dimensional representa-tion and Ts = 0.39 sec. in both X and Y directions fora three-dimensional shear representation assuming rigidfloors. Damping of 5% of critical is used for the super-structure in all the modes.The LRB isolation system designed based on practicalparameters. The average isolation yield strength Qy isset 5%W , where W is the total weight of the structureW = 13560.47 kN . The yield displacement uy is set to1 cm. The postyield stiffness is determined based on anisolation period Tb of 2 sec.

Eight records are selected from the CDMG (Califor-nia Division of Mines and Geology, Sacramento, USA)suite of ground motions representing near fault effects,low and large ground velocities which are specifically sug-gested by the CDMG for design of seismically isolatedstructures [6]. The records and their characteristics aresummarized in table 1. The superstructure is modeled asa three-dimensional shear structure. Lead-Rubber Bear-ings are modeled using biaxial model for elastomeric bear-ings to capture the interaction and keeping its effect onthe seismic response. The dynamic response is computedfor the selected accelerograms, the structure is subjectedto each component in the X direction only, but keepingthe biaxial interaction so that the response will be af-fected. In the application of AMA-BI procedure the su-perstructure was simulated as lumped mass model (stickmodel) with condensed stiffness at each story calculated



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Table 1: Selected components of CDMG suite of earthquakes

Earthquake PGA (g) PGV (cm/sec.) PGD (cm)El Centro 1979 (Array#6 station) 230o 0.436 108.709 55.165Loma Prieta 1989 (Hollister station) 90o 0.178 30.891 20.418

Loma Prieta 1989 (Lexington Dam station)90o 0.409 94.982 25.814Landers 1992 (Lucerne valley station) Long. 0.703 25.718 8.824

Northridge 1994 (Newhall station) 90o 0.583 74.841 17.595Petrolia 1992 (Petrolia station) 90o 0.662 89.454 30.577

Northridge 1994 (Sylmar station) 90o 0.604 76.936 15.217Landers 1992 (Yermo station) 360o 0.151 29.032 22.779

CMb

0.17 m

2 m

X

Y

c) Plan view

Base

Floor 1

Floor 2

Floor 3

Floor 4

Floor 5

Roof

Lead−Rubber Bearingsb) Elevation (XX)

a) 3D View

Figure 4: Six-story reinforced concrete structure on lead-rubber bearing isolation system

by summation of column stiffnesses in the X direction.The AMA-BI implies introduction of mass matrix, modaland spectral matrices in addition to the rest of inherentinputs (see section 2.1), they are given in table 2 (units:kN, m, s).To test the AMA-BI procedure, the response of the six-story reinforced base isolated structure (figure 4) to theeight components (table 1), was determined using twomethods: (1) rigorous nonlinear time history analysis bysolving the governing coupled equations of motion; and(2) the AMA-BI procedure. Such a comparison for roofdisplacement, roof and base accelerations, roof and baseforces and base shear force is presented in figures 5 to 12.The peak response values due to the induced ground mo-tions in the X direction are shown in tables 3 and 4 withthe corresponding errors in the AMA-BI.

2.3 Discussion

The AMA procedure which is based on uncoupling theequations of motion gave results very close to that ob-tained when using NLTHA with negligible errors thateven could happen to any comparison between twocomputer programs that use the rigorous NLTHA (e.g.ETABS and 3D-BAIS). Also, the AMA predicted accu-rately the shape of peak floor forces distribution through-out the hight of the structure.The large errors in floor forces occurred when the struc-ture is subjected to the Loma Prieta, Hollister 90o com-ponent, but still under 5% which can also be neglected,but lets interpret it: the isolation system works betterunder sever ground motions with large peak velocities;the yield strength achieves its higher value under highervelocity ([7],[8],[10]), if an earthquake has lower peak ve-locity (which is the case of Loma Prieta, Hollister 90o)the isolation system do not perform properly as shouldbe, the indirect result in this case is that the AMA-BI pre-dicts peak responses with larger errors since the approx-imate procedure was developed mainly benefiting fromthe isolation property.The accuracy of AMA-BI was proven using the abovestructure, however, its efficiency is demonstrated by thefact that the time spent for complete analysis of the struc-ture subjected to an earthquake component with 4000points using AMA-BI procedure is about 3 seconds, while



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Time, sec.Time, sec.

(a) Approximate Modal Analysis (AMA) (b) ”Exact” Analysis (NLTHA)

ub,

cma6,

ga

b,

gf 6

,kN

f b,

kN

Vb,

kN

31.824 31.972

0.42856 0.43107

0.42819 0.42606

642.3116 644.4522

694.9226 693.7037

5017.7912 5016.7293

00

00

00

00

00

00

55

55

55

55

55

55

1010

1010

1010

1010

1010

1010

1515

1515

1515

1515

1515

1515

2020

2020

2020

2020

2020

2020

−50−50

0

0

0

0

0

0

0

0

0

0

0

0

5050

−0.5

−0.5

−0.5

−0.5

0.5

0.5

0.5

0.5

−1000−1000

1000

1000

1000

1000

1000

1000

−8000−8000

80008000

Figure 5: Comparison of response histories obtained byNLTHA and AMA-BI for the six-story structure withLRB subjected to El Centro 1979, Array#6



ub,

cma6,

ga

b,

gf 6

,kN

f b,

kN

Vb,

kN

6.9744 7.0103

0.2358 0.24015

0.23573 0.23542

209.8931 206.317

226.7166 227.797

1629.2759 1636.5983

00

0

0

0

0

0

0

0

0

0

0

55

5

5

5

5

5

5

5

5

5

5

1010

10

10

10

10

10

10

10

10

10

10

1515

15

15

15

15

15

15

15

15

15

15

2020

20

20

20

20

20

20

20

20

20

20

2525

25

25

25

25

25

25

25

25

25

25

3030

30

30

30

30

30

30

30

30

30

30

−10−10

0

0

0

0

0

0

0

0

0

0

0

0

1010

−0.5

−0.5

−0.5

−0.5

0.5

0.5

0.5

0.5

−500−500

500

500

500

500

500

500

−3000−3000

30003000

Figure 6: Comparison of response histories obtained byNLTHA and AMA-BI for the six-story structure withLRB subjected to Loma Prieta, Hollister 90o



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ub,

cma6,

ga

b,

gf 6

,kN

f b,

kN

Vb,

kN

31.6098 31.7341

0.5773 0.58878

0.57713 0.58396

640.5721 641.4882

693.8108 697.43

4989.6198 5005.9206

00

0

0

0

0

0

0

0

0

0

0

55

5

5

5

5

5

5

5

5

5

5

1010

10

10

10

10

10

10

10

10

10

10

1515

15

15

15

15

15

15

15

15

15

15

−50−50

0

0

0

0

0

0

0

0

0

0

0

0

5050

−1

−1

−1

−1

1

1

1

1

−1000−1000

1000

1000

1000

1000

1000

1000

−8000−8000

80008000

Figure 7: Comparison of response histories obtained byNLTHA and AMA-BI for the six-story structure withLRB subjected to Loma Prieta, Lexington 90o



ub,

cma6,

ga

b,

gf 6

,kN

f b,

kN

Vb,

kN

4.2161 4.2714

0.74473 0.737

0.74437 0.73719

160.6914 162.9617

173.8496 173.6404

1252.7774 1257.8842

00

0

0

0

0

0

0

0

0

0

0

55

5

5

5

5

5

5

5

5

5

5

1010

10

10

10

10

10

10

10

10

10

10

1515

15

15

15

15

15

15

15

15

15

15

2020

20

20

20

20

20

20

20

20

20

20

2525

25

25

25

25

25

25

25

25

25

25

3030

30

30

30

30

30

30

30

30

30

30

−5−5

0

0

0

0

0

0

0

0

0

0

0

0

55

−1

−1

−1

−1

1

1

1

1

−200−200

200

200

200

200

200

200

−2000−2000

20002000

Figure 8: Comparison of response histories obtained byNLTHA and AMA-BI for the six-story structure withLRB subjected to Landers, Lucerne Long.



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ub,

cma6,

ga

b,

gf 6

,kN

f b,

kN

Vb,

kN

17.1378 17.2293

0.75434 0.75568

0.75425 0.75326

386.0223 385.6431

417.6491 417.4217

3013.8248 3016.7357

00

00

00

00

00

00

55

55

55

55

55

55

1010

1010

1010

1010

1010

1010

1515

1515

1515

1515

1515

1515

2020

2020

2020

2020

2020

2020

−20−20

0

0

0

0

0

0

0

0

0

0

0

0

2020

−1

−1

−1

−1

1

1

1

1

−500−500

500

500

500

500

500

500

−5000−5000

50005000

Figure 9: Comparison of response histories obtained byNLTHA and AMA-BI for the six-story structure withLRB subjected to Northridge, Newhall 90o



ub,

cma6,

ga

b,

gf 6

,kN

f b,

kN

Vb,

kN

31.0158 31.168

1.0248 1.0306

1.0247 1.0224

629.3074 639.8905

680.7138 676.5087

4908.596 4913.6081

00

00

00

00

00

00

55

55

55

55

55

55

1010

1010

1010

1010

1010

1010

1515

1515

1515

1515

1515

1515

2020

2020

2020

2020

2020

2020

−50−50

0

0

0

0

0

0

0

0

0

0

0

0

5050

−2

−2

−2

−2

2

2

2

2

−1000−1000

1000

1000

1000

1000

1000

1000

−8000−8000

80008000

Figure 10: Comparison of response histories obtained byNLTHA and AMA-BI for the six-story structure withLRB subjected to Petrolia, Petrolia 90o



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ub,

cma6,

ga

b,

gf 6

,kN

f b,

kN

Vb,

kN

30.8739 30.9849

0.6915 0.70863

0.69164 0.69087

625.7377 624.9018

676.9112 675.4673

4888.9973 4882.3812

00

00

00

00

00

00

55

55

55

55

55

55

1010

1010

1010

1010

1010

1010

1515

1515

1515

1515

1515

1515

2020

2020

2020

2020

2020

2020

−50−50

0

0

0

0

0

0

0

0

0

0

0

0

5050

−1

−1

−1

−1

1

1

1

1

−1000−1000

1000

1000

1000

1000

1000

1000

−8000−8000

80008000

Figure 11: Comparison of response histories obtained byNLTHA and AMA-BI for the six-story structure withLRB subjected to Northridge, Sylmar 90o



ub,

cma6,

ga

b,

gf 6

,kN

f b,

kN

Vb,

kN

7.9441 8.0102

0.20427 0.20891

0.20371 0.20011

225.4669 227.8539

243.9131 243.3898

1760.6819 1761.958

00

00

00

00

00

00

55

55

55

55

55

55

1010

1010

1010

1010

1010

1010

1515

1515

1515

1515

1515

1515

2020

2020

2020

2020

2020

2020

2525

2525

2525

2525

2525

2525

3030

3030

3030

3030

3030

3030

3535

3535

3535

3535

3535

3535

4040

4040

4040

4040

4040

4040−10−10

0

0

0

0

0

0

0

0

0

0

0

0

1010

−0.5

−0.5

−0.5

−0.5

0.5

0.5

0.5

0.5

−500−500

500

500

500

500

500

500

−3000−3000

30003000

Figure 12: Comparison of response histories obtained byNLTHA and AMA-BI for the six-story structure withLRB subjected to Landers, Yermo 360o



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the application of the NLTHA takes more than 180 sec-onds.Also, the reader may be referred to the paper [12] wherehas been presented a response spectrum analysis pro-cedure (RSA-BI) which constitutes the particular casewhen the AMA-BI is specialized for peak responses. Thisprocedure is based on a response spectrum developedfor base isolated buildings (were called in the paper”SIRS” or Seismic Isolation Response Spectrum). Theidea of construction of the SIRS was initiated by Zayaset al [14] for friction pendulum system, after; Ryan andChopra [10] have developed the theory to include othersystems and structures. The RSA-BI was found to giveconsistent peak response values when compared againstresults of the NLTHA, hence, it can replace the existenttheory of linearization that uses the effective stiffness andeffective damping.

References

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[3] A.M. Reinhorn, S. Nagarajaiah, M.C. Constranti-nou, P. Tsopelas and R. Li, 3D-BASIS: Version 2.0

Computer Program for Nonlinear Dynamics Analy-

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[4] Datafit, version 8.2.79. Oakdale Engineering,RC133, 1995/2006; Oakdale, PA 15071, USA.

[5] Dr Finely and A. Charney, NONLIN v6.0 ComputerProgram, FEMA, Advanced Structural Concepts,Golden, Colorado.

[6] Farzad Naeim and James M.Kelly, Design of Seismic

Isolated Structures: From Theory to Practice. NewYork, John Wiley and Sons, Inc., 1999.

[7] Gianmario Benzoni and Chiara Casarotti, Perfor-

mance of Lead-Rubber and Sliding Bearings under

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[8] James M. Kelly and Shakhzod M. Takhirov, An-

alytical and Numerical Study on Buckling of Elas-

tomeric Bearings with Various Shape Factors. Re-port No. EERC.04/03, Earthquake Engineering Re-

search Center, College of Engineering, University ofCalifornia at berkeley, 2004.

[9] Jangid, Parametric Study of Base Isolated Struc-tures. In Advances in structural engineering, Mul-tiscience Publishing Co Ltd., 2002; 5(2):113–122.

[10] Keri L. Ryan and Anil K. Chopra, Estimating the

response of base isolated buildings including torsion,

rocking and axial load effects. Earthquake Engineer-ing Research Center, Berkeley, California, 2005; Re-port No. UCB/EERC 2005-01, 8–20, 86–91.

[11] Leblouba Moussa, Base isolated buildings: Para-

metric dynamic analysis and computer simula-

tions. Technical University of Civil Engineering,Bucharest, 2008; Report No. 2/2008, Chapters 3–6.

[12] Leblouba Moussa, Marioua Aissa, Estimating

the Seismic Response of Base Isolated Buildings

Through a Response Spectrum Analysis Procedure.Computational Methods in Structural Dynamicsand Earthquake Engineering, COMPDYN 2009,Rhodes, Greece, 22–24 June 2009;

[13] Marvin W.Halling, Investigation of base-isolated

structures during recent earthquakes and computer

simulations utilizing near-source long-period ground

motions. Earthquake Engineering Research Labora-tory, California Institute of Technology, Pasadena,California, 2005; Report No. EERL 95-09, 6–7.

[14] Victor Zayas, Stanley Low, Luis bozo, StephenMahin, Feasibility and performance studies on im-

proving the earthquake resistance of new and existing

buildings using the friction pendulum system. Earth-quake Engineering Research Center, Berkeley, Cal-ifornia, 1989; Report No. UCB/EERC-89/09, 189–255.



WCE 2010

Table 2: Eigenvalues and Eigenvectors of the structureMode(ω2) Story(mass kN.s2/m) φ

6 (176.59) 0.026965 (197.61) 0.026964 (201.39) 0.02695

1(9.874)3 (201.39) 0.026942 (201.39) 0.026921 (209.62) 0.02690

B (191.083) 0.026886 0.040345 0.029764 0.01656

2(13579.259)3 -0.000022 -0.016591 -0.02978B -0.035526 0.042225 0.002154 -0.02678

3(49129.860)3 -0.035912 -0.018491 0.01260B 0.030546 0.032805 -0.029454 -0.02924

4(98243.604)3 0.014202 0.036651 0.00491B -0.028046 0.018665 -0.038404 0.01236

5(158261.570)3 0.033682 -0.025221 -0.02406B 0.026926 0.009365 -0.029624 0.03801

6(215497.986)3 -0.017632 -0.016101 0.03764B -0.023836 0.003855 -0.014994 0.02820

7(253309.931)3 -0.036112 0.037221 -0.03133B 0.01542



WCE 2010

Table

3:

Pea

kresp

onse

results

ofA

MA

-BI

com

pared

with

NLT

HA

Quake

Sto

ryD

ispla

cemen

t(cm

)A

cceleratio

n(g

)Force

(kN

)Shea

r(k

N)

AM

A-B

IN

LT

HA

Erro

r(%)

AM

A-B

IN

LT

HA

Erro

r(%)

AM

A-B

IN

LT

HA

Erro

r(%)

AM

A-B

IN

LT

HA

Erro

r(%)

631.8

231.9

7-0

.46

0.4

30.4

3-0

.58

642.3

1644.4

5-0

.33

642.3

1644.4

5-0

.33

531.8

231.9

5-0

.42

0.4

30.4

3-0

.46

718.6

4720.2

8-0

.23

1361.0

01364.7

0-0

.27

431.8

231.9

0-0

.26

0.4

30.4

3-0

.27

732.4

3733.2

1-0

.11

2093.4

02097.9

0-0

.21

Array

#6

331.8

231.8

10.0

40.4

30.4

3-0

.08

732.4

2732.1

10.0

42825.8

02830.1

0-0

.15

231.8

231.7

30.2

70.4

30.4

3-0

.07

732.4

0731.5

40.1

23558.2

03561.6

0-0

.10

131.8

231.7

30.2

80.4

30.4

30.0

1762.3

5761.4

30.1

24320.6

04323.0

0-0

.06

B31.8

231.7

60.1

70.4

30.4

30.5

0694.9

2693.7

00.1

85017.8

05016.7

00.0

26

6.9

77.0

1-0

.51

0.2

40.2

4-1

.81

209.8

9206.3

21.7

3209.8

9206.3

21.7

35

6.9

77.0

0-0

.41

0.2

40.2

4-1

.34

234.3

7229.1

72.2

7444.2

6435.4

92.0

14

6.9

76.9

9-0

.22

0.2

40.2

4-0

.72

239.0

2235.0

41.6

9683.2

9670.5

31.9

0H

ollister

36.9

76.9

70.0

60.2

40.2

40.2

8239.0

2241.8

9-1

.19

922.3

1909.3

61.4

22

6.9

76.9

60.2

50.2

40.2

31.1

7238.9

5251.8

8-5

.13

1161.3

01153.7

00.6

61

6.9

76.9

50.2

60.2

40.2

31.0

5248.7

9262.4

1-5

.19

1410.0

01408.8

00.0

9B

6.9

76.9

50.2

70.2

40.2

40.1

3226.7

2227.8

0-0

.47

1629.3

01636.6

0-0

.45

631.6

131.7

3-0

.39

0.5

80.5

9-1

.95

640.5

7641.4

9-0

.14

640.5

7641.4

9-0

.14

531.6

031.7

2-0

.35

0.5

80.5

9-1

.55

717.7

1720.2

6-0

.35

1357.5

01360.1

0-0

.19

431.6

131.6

7-0

.20

0.5

80.5

8-0

.54

731.0

4734.9

9-0

.54

2088.6

02093.4

0-0

.23

Lex

ingto

n3

31.6

131.5

70.1

00.5

80.5

80.1

6731.1

2733.6

4-0

.34

2819.7

02822.0

0-0

.08

231.6

131.5

00.3

30.5

80.5

8-0

.02

731.4

4732.7

1-0

.17

3551.1

03554.7

0-0

.10

131.6

131.5

00.3

40.5

80.5

70.5

0761.0

9765.1

6-0

.53

4312.2

04319.8

0-0

.18

B31.6

131.5

30.2

40.5

80.5

8-1

.17

693.8

1697.4

3-0

.52

4989.6

05005.9

0-0

.33

64.2

24.2

7-1

.29

0.7

40.7

41.0

5160.6

9162.9

6-1

.39

160.6

9162.9

6-1

.39

54.2

14.2

7-1

.20

0.7

40.7

40.5

2179.7

9183.5

1-2

.03

340.4

8345.6

5-1

.50

44.2

24.2

5-0

.93

0.7

40.7

40.1

8183.2

4187.5

1-2

.28

523.7

2531.2

8-1

.42

Lucern

e3

4.2

24.2

3-0

.43

0.7

40.7

5-0

.41

183.2

4185.4

4-1

.19

706.9

6711.6

2-0

.65

24.2

14.2

2-0

.05

0.7

40.7

5-0

.72

183.2

3187.3

5-2

.20

890.1

9889.6

30.0

61

4.2

24.2

2-0

.03

0.7

40.7

5-0

.72

190.7

1194.7

6-2

.08

1080.9

01084.4

0-0

.32

B4.2

14.2

2-0

.17

0.7

40.7

40.9

7173.8

5173.6

40.1

21252.8

01257.9

0-0

.41



WCE 2010

Table

4:

Pea

kresp

onse

results

ofA

MA

-BI

com

pared

with

NLT

HA

(contin

ued

)Q

uake

Sto

ryD

ispla

cemen

t(cm

)A

cceleratio

n(g

)Force

(kN

)Shea

r(k

N)

AM

A-B

IN

LT

HA

Erro

r(%)

AM

A-B

IN

LT

HA

Erro

r(%)

AM

A-B

IN

LT

HA

Erro

r(%)

AM

A-B

IN

LT

HA

Erro

r(%)

617.1

417.2

3-0

.53

0.7

50.7

6-0

.18

386.0

2385.6

40.1

0386.0

2385.6

40.1

05

17.1

317.2

2-0

.48

0.7

50.7

50.1

4431.9

1429.3

50.6

0817.9

3814.9

90.3

64

17.1

417.1

9-0

.31

0.7

50.7

50.2

5440.1

9437.1

60.6

91258.1

01252.1

00.4

8N

ewhall

317.1

417.1

4-0

.04

0.7

50.7

50.0

6440.1

8440.7

5-0

.13

1698.3

01691.5

00.4

02

17.1

417.1

10.1

70.7

50.7

6-0

.22

440.1

7445.8

2-1

.27

2138.5

02135.4

00.1

51

17.1

417.1

00.1

80.7

50.7

6-0

.28

458.1

7464.0

9-1

.28

2596.6

02599.3

0-0

.10

B17.1

417.1

10.1

20.7

50.7

50.1

3417.6

5417.4

20.0

63013.8

03016.7

0-0

.10

631.0

231.1

7-0

.49

1.0

21.0

3-0

.57

629.3

1639.8

9-1

.65

629.3

1639.8

9-1

.65

531.0

131.1

5-0

.46

1.0

21.0

3-0

.56

703.9

2715.5

4-1

.62

1333.2

01355.4

0-1

.64

431.0

131.1

0-0

.28

1.0

21.0

3-0

.36

717.4

8724.8

1-1

.01

2050.7

02080.2

0-1

.42

Petro

lia3

31.0

130.9

90.0

61.0

21.0

20.1

3717.4

6714.7

00.3

92768.2

02794.9

0-0

.96

231.0

130.9

10.3

21.0

21.0

20.5

0717.4

2706.7

31.5

13485.6

03501.7

0-0

.46

131.0

130.9

10.3

31.0

21.0

20.5

1746.7

9735.4

41.5

44232.4

04237.1

0-0

.11

B31.0

130.9

50.1

91.0

21.0

20.2

2680.7

1676.5

10.6

24908.6

04913.6

0-0

.10

630.8

730.9

9-0

.36

0.6

90.7

1-2

.42

625.7

4624.9

00.1

3625.7

4624.9

00.1

35

30.8

730.9

7-0

.32

0.6

90.7

0-1

.40

700.0

4701.5

9-0

.22

1325.6

01325.7

0-0

.01

430.8

730.9

2-0

.16

0.6

90.6

9-0

.47

713.4

2715.9

4-0

.35

2039.1

02041.5

0-0

.12

Sylm

ar

330.8

730.8

30.1

40.6

90.6

90.6

7713.4

2714.1

8-0

.11

2752.5

02755.6

0-0

.11

230.8

730.7

50.3

70.6

90.6

81.4

9713.4

3711.6

50.2

53465.9

03467.2

0-0

.04

130.8

730.7

50.3

90.6

90.6

81.1

9742.5

7739.7

50.3

84208.4

04206.9

00.0

4B

30.8

730.7

80.2

80.6

90.6

90.1

1676.9

1675.4

70.2

14889.0

04882.4

00.1

46

7.9

48.0

1-0

.83

0.2

00.2

1-2

.22

225.4

7227.8

5-1

.04

225.4

7227.8

5-1

.04

57.9

48.0

0-0

.78

0.2

00.2

1-1

.80

252.2

3254.4

3-0

.86

477.7

0482.2

3-0

.94

47.9

47.9

9-0

.54

0.2

00.2

1-0

.90

257.0

8258.3

0-0

.47

734.7

8740.5

0-0

.77

Yerm

o3

7.9

47.9

5-0

.04

0.2

00.2

00.2

8257.0

8256.6

30.1

8991.8

6997.1

3-0

.53

27.9

47.9

10.3

50.2

00.2

00.6

9257.0

7255.4

70.6

31248.9

01252.6

0-0

.30

17.9

47.9

10.3

70.2

00.2

01.1

7267.5

9265.9

90.6

01516.5

01518.6

0-0

.14

B7.9

47.9

30.1

40.2

00.2

01.8

0243.9

1243.3

90.2

11760.7

01762.0

0-0

.07



WCE 2010

Documents

Approximate Earthquake Analysis for Regular Base Isolated Buildings Subjected to Near Fault Ground Motions