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SEISMIC DESIGN OF BASE-ISOLATED STRUCTURES USINGCONSTANT STRENGTH SPECTRAARTURO TENA-COLUNGA aa Departamento de Materiales , Universidad Autónoma Metropolitana Azcapotzalco , Av. SanPablo #180, Col. Reynosa Tamavlipas, 02200 México, DF, Mexico E-mail:Published online: 03 Jun 2008.

To cite this article: ARTURO TENA-COLUNGA (2002) SEISMIC DESIGN OF BASE-ISOLATED STRUCTURES USING CONSTANTSTRENGTH SPECTRA, Journal of Earthquake Engineering, 6:4, 553-585, DOI: 10.1080/13632460209350429

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Journal of Earthquake Engineering, Vol. 6, No. 4 (2002) 553-585 @ Imperial College Press

SEISMIC DESIGN OF BASEISOLATED STRUCTURES USING CONSTANT STRENGTH SPECTRA

ARTURO TENA-COLUNGA

Departamento de Materiales, Clniuersidad Autdnoma Metropolitans Azcapotzdco, Av. San Pablo # 180, Col. Reynosa Tamdipas , 02200 M b c o , DF, Mezico

atcOcoww. azc. uam.mz

Received 11 July 2001 Revised 22 May 2002 Accepted 8 June 2002

This paper presents the concept of constant strength design spectra for the design of base-isolated structures; particularly those structures using isoIators with a bilinear h y s teretic behaviour when subjected to dynamic loading. The constant strength'design spectra relate peak accelerations, velocities, displacements and effective isolated natural periods for bilinear systems with a given yield strength and pwt yield stiffness. Con- stant strength design spectra could be useful for the daign of base isolators with bilinear hysteretic behaviour, as these devices can be designed for fixed yield strength and post yield stiffness. The concept of constant strength design spectra and its application for the design of base isolated structures is illustrated with case studies of specific structures.

Keywordg: Base isolation; inelastic spectra; constant strength spectra; seismic design; displacement design methods.

1. Introduction

Base isolation has emerged as a viable structural option in seismic zones during the last decade as a consequence of concerted effort of researchers and practitioners worldwide, particularly in New Zealand during the 1970s and 1980s and in the United States and Japan since the 1980s. There have been extensive experimental and analytical studies on different types of base isolators that have allowed the development of design practices for specific base isolators and code procedures, such as those established in the Uniform Building Code (UBC) since 1991, the American Association of State Highway and Transportation Officials (AASHTO) since 1990, and the new International Building Code (IBC) of the United States recently published in April, 2000 ["International Building Code", 2000). It is the perception of the author that the growing interest in the use of base isolation in seismic zones of the United States seems to be related to the publication of these seismic code provisions; however, other researchers have different opinion 1i.e. Kelly, 19991. At present, Japan is the country that h s the most base isolated structures in the world and the number of their applications has risen after the AIJ published recommendations for the seismic design of base isolation. Other earthquake-prone

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5% A. Tena-Colunga

countries with a long-time interest in base isolation, such as New Zealand and Italy, have constructed several base-isolated projects for buildings and bridges using design methodologies proposed in those countries or adapted from the ones used in other leading nations. Many other nations that face earthquake hazard have conducted research studies and/or built base-isolated structures.

It is clear that the implementation of seismic isolation t h o l o g y in new or retrofit projects for buildmgs and bridges in countries like the united States and Japan is directly related to the availability of relatively simple design guidelines and/or the publication of code provisions. In order to promote the use of seismic isolation in other countries, one of the first steps is to provide the structural en- gineering communities with suitable design procedures. Therefore, in Mexico the first steps in the development of design provisions for seismic isolation were based upon UBC guidelines, New Zealand practice, and the regional seismicity of the country [i.e. Tena et al., 1997, Viegas-Jimhez and Tena-Colunga, 20001; these developments are still under way. The Mexican effort is also considering alterna- tive design procedures based upon the use of inelastic spectra, for the reasons explained below.

As stated before [Tena-Colunga et ai., 19971 the seismic design of base isola- tors is generally controlled by their maximum allowable displacement for dynamic stability rather than strength. This fact has been recognised before in the liter- ature on base isolation. However, design practice of base isolation advocated by some building codes is currently based on a procedure where the design displace- ment is obtained indirectly from a given pseud~acceleration spectra specified for conventional structures and an equivalent viscous damping concept to model the non-linear response of base isolators. The UBC code provisions [1991, 1994, 1997 versions] and the IBC code [2000 version] share this design philosophy.

However, an "optimal" design of base-isolated structures would require hav- ing all relevant information at hand, including inelastic responses. In this regard, a pseudo-acceleration response spectrum gives aIl of the required information, as peak responses for velocities and displacements are algebraicaily related with those provided for accelerations if an equivalent viscous damping concept is considered to model the non-linear response of base isolators. Peak responses for displacements are important for the design of the isolation system, whereas peak accelerations are of particular interest for the design of the structure above. Acceleration versus displacement spectrum is increasingly used in the design of conventional structures and could also be useful for the design of base isolators. However, in this spectrum the corresponding periods are usually not included in the plot. Effective isolated natural periods are essential information for the design of base isolated structures. Thus, the use of an inelastic tripartite design spectrum [i.e. Newmark and Hall, 19821 would be potentially more useful, as the non-linear action of base-isolated structures is concentrated on the isolators, 'and this spectrum gives all the needed information directly in a single chart, as peak responses in acceleration, velocity and displacements for given periods are included. However, the inelastic design

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Seismic Design of Base-Isolated Structures 555

- spectrum as-presented -by Newmark -and Hall (19821 is based-upon the concept-of fixedsiisplacement ductility demands, a condition that is not the best concept for base isolators. For a given excitation, a displacement ductility demand can be as sociated to different yield strengths; that is, the ductility demand is not unique, as illustrated by others [for example, Miranda, 19931.

Base isolators, particularly those with a bilinear hysteretic behaviour, can be designed for a fixed yield strength and post yield stifhess. Therefore, constructing constant strength design spectra (CSDS) as presented here could be useful for the design of base-isolated structures. The CSDS relate peak accelerations, velocities, relative displacements and effective isolated natural periods for bilinear systems with a given yield strength and post yield stifhess.

Some authors have proposed the use of inelastic spectra, particularly for the preliminary design of sliding isolation systems. Among these efforts it is worth mentioning the inelastic spectra presented by Kartoum et at! [I9921 and by Tsopelas et al. [I9961 for the design of sliding isolation systems in terms of: (a) coefficient of hiction, (b) period of isolation, (c) damping ratio of the isolation system, (d) period of the free standing pier, (e) damping ratio of the free standing pier and, (f) weight ratio between the pier and the deck. The inelastic spectra presented in these references can be considered CSDS, but they dBer from those presented here in that: (a) they were developed for sliding systems with bictional behaviour, not for systems with bilinear hysteretic behaviour, and (b) peak displacement responses and normalised pier shears are presented on separate plots and not in a single tripartite plot.

2. Inelastic Response Spectra

In the elastic range of response, a tripartite plot can be used to relate, in a sin- gle chart, the maximum dynamic response of a single degree of heedom system (SDOF) subjected to an earthquake excitation, in terms of S,, S, and Sd, for a given natural period T. However, in the non-linear range, the maximum responses in acceleration, velocity and displ&ement are no longer proportional. Nevertheless, a tripartite plot can still be used for non-linear systems, although it is worth not- ing that in this case, accelerations, velocities and displacements have to be read with reference to their corresponding axes. Based upon the study of the dynamic response of elastic-perfectly-plastic SDOF systems subjected to earthquake ground motions to achieve fixed displacement ductility demands (p ) , Newmark and Hal1 [I9821 presented the concept of a ''modified response spectrum" (MRS). It can be observed in this spectrum that peak accelerations, displacements and velocities are not proportional, so different envelope curves have to be defined for each response quantity for a given value of a displacement ductility demand (p) . It can also be observed that there exist frequency (period) ranges where peak responses are con- trolled by the non-linear displacements, whereas in other zones, peak responses are controlled by other response quantities.

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3. Constant Strength Response Spectrum: Concept and Computation

The constant strength design spectrum (CSDS) is basically a modihation of the "modified response spect rumn (MRS) proposed by Newmark and Hall (1 9821, where the normalised yield strength (V , /W) of a SDOF system is fixed rather than the dtsplacement ductility demand (p ) . The CSDS is obtained from constant strength response spectrum (CSRS) computed individudy for specific ground motions and a given hysteretic model. A constant strength design spectrum (CSDS) can be defined for any suitable hysteretic model. In this paper, the CSDS is defined for bilinear systems with a given yield strength and post yield stihess (Fig. 1). Many commercial bme isolators have this type of hysteretic behaviour, among others, rubber bearings and steel hysteretic dampers.

To compute a CSRS for a given ground motion excitation, the following steps must be followed:

(1) Define the parameters of the hysteretic model. For a bilinear system, define V';IW, k1 and k2/k. .

(2) D e h e the equivalent viscous damping ratio for the structural system alone (t), the acceleration record, initial (T;) and final (TI) periods of interest, and the period increment (AT) For the computation of dynamic responses. The increments could be in arithmetic or logarithmic scales. The use of logarithmic increments is recommended.

(3) DO Tj = Tj-1 +ATi Ti 5 Tj 5 Tf. (4) For each period of interest Tj.

A 0.2A Y max

Deformation, A

Fig. 1. Design envelope curve for bilinem isolators that follow the restrictions of the UBC code.

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Seismic Design of Bme-Isolated Structurw 357

... -- (a)-Check that-the integration time step (At) for the acceleration record is suitable for the computation of non-linear problems. A rule of thumb is to check that At < Tj/lO. Otherwise, interpolate the ground motion record. A selective interpolation algorithm should be defined. There is no need to use very small integration time steps for long periods while they are needed for short periods (close to zero). For each time step At, solve the equation of motion of a non-linear SDOF system using a suitable numerical method (for example, Newmark-P method) given by:

mx(t) + c(t)x(t) + k(t)x(t) = F(t) (3-1)

where m is the mass of the system, c(t) , k( t ) and F(t) are respectively the damping coefficient of the system, the st ihess of the system associated to Ti, and the effective load at time t ; and x( t ) , x(t) and x(t) are respectively the acceleration, velocity and displacement at time t, as defmed in the literature. Save the maximum responses in acceleration, velocity, displacement and non-linear system force. Then, the effective isolated period TI of the system can be computed as follows:

+ where F,, jF2a and A& jA,, are respectively the maximum nega- tive and positive forces and displacements and k e ~ is the effective stiffness of the non-linear SDOF system with an initial elastic period of interest Ti.

(5) Go to Step 3 untiI T' = Tf.

As it can be observed, .the computation of a CSRS is relatively simple. A CSRS computed for a bilinear system with V,/W = 0.10, kz/kl = 0.10 and 5 = 0.05 when subjected to the ground acceleration record UNIO-NS (Fig. 2) registered during the 1985 Michoaccin earthquake is depicted in Fig. 3. It can be observed that: (a) peak non-linear responses in acceleration, velocity and displacement are not directly related and, (b) there are period ranges where the non-linear response is controlled

0.2

5=5x h w bl - 0.0 ::I 6 VJ

-0.2 0.0 0 40 80 0 1 2 3

n?dJ3 (8) PERIOD (a)

Fig. 2 . UNIO-NS acceleration record for the 19/09/85 Michoacan Earthquake.

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i ----------- Acceleration Velocity ----- Displacement

- -

10 -2 10 -' 10 O 10 ' PERIOD (s)

Fig. 3. CSRS for UNIO-NS acceleration record for bilinear isolators with design parameters V,/W = 0.10 and kz/kl = 0.10.

by the displacements, but in other regions the velocities or the accelerations rule. These are also illustrated with the MRS presented by Newmark and Hall. It can also be observed that, for a period close to zero (T = O.O), the peak non-linear response in acceleration approaches the peak ground acceleration (dotted line, Table 1) and that the reIative displacement tends to zero (dashed line), as it should also be expected for a non-linear system.

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Tab

le 1.

Som

e ch

arac

teri

stic

s of

the

sele

cted

acc

eler

atio

n re

cord

s ty

pica

l of

roc

k si

tes.

Scal

e F

acto

r (f

.,)

to M

atch

th

e Sp

ectr

al A

ccel

erat

ion

of

Dur

atio

n (s

) a,,,

(cm

/s2)

Z

one

D-I

of MOG93 fo

r T

= 2.24

s

Eve

nt.

St

atio

n Record

Stro

ng P

hase

E

W

N-S

E

W

N-S

09/19/85

AZ

IH

71.8

20

162.0

101.0

2.241

2.141

CALE

48.9

10

138.0

138.0

2.468

1.570

PAPN

59.1

5

114.0

157.0

12.909'

7.282

PARS

52.6

16

89.0

116.0

13.041'

6.722

SUCH

59.6

5 81.0

102.0

7.224

4.989

UNIO

62.7

25

147.0

163.0

3.695

2.124

VILE

63.6

7 120.0

125.0

4.369

3.668

20/09/85

AZL

H

54.0

15

153.0

134.0

3.154

4.543

04/25/89

CPDR

37.8

5

93.0

103.0.

7.642

8.492

'Acc

eler

ogra

m not

incl

uded

bec

ause

does

not

mee

t th

e se

lect

ion

crit

eria

.

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4. Constant Strength Design Spectrum

Constant strength design spectrum (CSDS) could be defined for the design of base- isolated structures. The folIowing items have to be dehed for a CSDS: (I) the hysteretic model of interest and its parameters, (2) a set .of representative ground motion records for a given seismic zone and soil type a d , (3) a criterion to define the design crurves. These three items have to be carefulIy assessed if the CSDS is intended for seismic guidelines, recommendations or design procedures for speci6c building codes. In this paper, CSDS is defined for representative strong ground motions recorded in the Mexican Pacific Coast during recent strong earthquakes using a crude statistical criterion for base isolators with bilinear behaviour. The CSDS presented in this study were computed to assess their eEectiveness for the design of base isolated structures, but they have not been developed yet to comply with the seismic code criteria of ruling Mexican seismic mdes for the Mexican Pacific Coast. The specific criteria used for items 1 to 3 mentioned above are briefly described below.

4.1. Selected hysteretic model

For the present study, a bilinear hysteretic model with a post to preyielding stifhess ratio k ~ / k l = 0.10 was selected (Fig. 1). This was done because this is a typical ratio for most laminated rubber bearings and laminated lead rubber bearings [i.e. Skinner et a l , 19931, which are of particular interest to the author. Two normalised yield strengths were selected, V,/W = 0.05 and V,/W = 0.10, in order to cover a wide range where most elastomeric base isolators could be used in regions of severe ground shaking.

4.2. Selected acceleration rec-mrds

Typical accelerograms for the Mexican Pacific Coast recorded during recent earth- quakes were selected for the present study. The following earthquakes were consid- ered: (a) the M, = 8.1 September 19,1985 Michoacb earthquake, (b) the M, = 7.6, September 21, 1985 aftershock for the Michoack earthquake, (c) the M, = 6.9, April 25, 1989 earthquake and, (d) the M, = 8.0, October 9, 1995 Manzanillo earthquake. A total of 42 accelerograms for the horizontal ground motions for 15 different stations were available.

A preliminary selection criterion was to include only records typical of rock sites not close to the epicentre; thus, a total of 12 stations and 34 accelerograms remained. All remaining records were then scaled in order to match the spectral acceleration for T = 2.24 s of the design spectrum for zone D-I of MOC-93 code [MOC-93, 1993, Tena-Calunga, 19991, as illustrated for some selected records in Fig. 4. The effective period of the isolated structure T = 2.24 s was arbitrar- ily selected as is an intermediate period in the period range 1.5 s 5 TI 5 3.0 s where it is recognised in the literature that base isolation is most appropriate, as

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Seismic Design oj Bape-Isolated Structums 561

PERIOD (s)

Fig. 4. Scaling procedure for some selected accelerograms to match the spectral acceleration for the design spectra of zone D-I of MOC-93 code for T = 2.24 s.

further explained in Sec, 4.4. When the scaling amplification factor (f,) required for some accelerograms was very large, the resulting peak ground accelerations for the scaled records were unrealistically high (for example, a,, = 5.11g for the scaled N-S record of VIGA station of the 04/25/89 Earthquake). Thus, a final se- lection criteria for the scaled records was: (a) that scaled peak ground accelerations would not surpass a,, = 1.2g and, (b) the scaling amplification factor will not surpass 10 (f, 5 10). Therefore, only 16 accelerograms of 9 stations fulfilled all these requirements and they are identified in Table 1. The average peak ground acceleration of the 16 selected scaled records is a,, = 0.5589. It is worth noting that the criteria specifically used in this study are somewhat arbitrary and could potentially be unsafe, depending on the seismic hazard for a given region.

4.3. Criterion to define design curves

The criterion to d e h e design curves for the CSDS was iduenced by the selection and scaling of the ground motions and by the main objective of the present study, that was to assess the potential effectiveness of CSDS for the design of,base-isolated structures, rather than &lining CSDS associated to specific building codes. The definition of CSDS for specific building codes would require complete seiskc hazard

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analyses, where further considerations should be made in the selection of ground motions, sizes of design earthquakes for different performance levels, exceedence rates, etc. In the present study, CSDS were dehed for the mean plus one standard deviation (a f Sdev) of the 16 selected acceleration records. This criterion was selected, among other considerations, because it is less conservative than defining an envelope curve for the 16 selected acceleration records, noting that higher multiples for the standard deviation have lower rates of exceedence. Alternatively, other more complex and complete probabilistic criteria may be used.

4.4. . Procedure to .define specific CSDS

For illustration purposes, this section presents the procedure used to define the CSDS for isolators with bilinear behaviour with V,/W = 0.10 and k / k l = 0.10 (Fig. 5), emphasising the constant strength design spectrum for displacements (CSDSD) and for accelerations (CSDSA). The procedure follows the general cri- teria described in previous sections and was used also for the other case study (Vv/W = 0.05, Fig. 6). The constant strength response spectra corresponding to B + Sdev for the 16 selected acceleration records are depicted in Fig. 5. Peak re- sponses below an effective isolated natural period of 1.5 s (TI < 1.5 s) are of little interest for the design of the base isolators, although they can be important for the

Fig. 5. CSRS for cr + Sdev and CSDS for bilinear isolators with design parameters V,/W = 0.10 and k p / k l = 0.10.

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Seismic Design of Base-Isolated Structum 563

Fig. 6. CSRS for v + Sdsv and CSDS for bilinear isolators with design parameters Vy/W = 0.05 and k3/kl = 0.10.

design of the superstructure. Therefore, spectra are presented for the period range ' I s < T r < 10s.

In order to define the design envelopes for displacements (CSDSD, thick solid line) and accelerations (CSDSA, thick broken line) shown in Fig. 5, the following considerations were made. It is recognised in the literature that base isolation is most appropriate when the effective period of the isolated structure is in the range 1.5 s 5 TI 5 3 s. Skinner et al [I9931 propose the lower limit and the upper l i t is defined by the UBC code for using static design procedures and some options for dynamic design proced&es ("Uniform Building Code", 19971. To the author's howledge, the highest effective period considered for a retrofit project with base isolators is the one considered for Los Angeles City Hall, close to 4 s [Youssef, 1996a and 1996bl. Therefore, the design envelopes were defined to reasonably cover the period interval 1.5 s 5 TI 5 4 s, being less conservative for periods longer than six seconds (TI 5 6 s) or lower than 1.5 s (TI < 1.5 s), as it can be observed in Fig. 5. An attempt was made to define the envelopes with a few straight lines while still reasonably protecting the period range 1.5 s 5 TI 5 3 s. The design envelopes should cover the response maxima in terms of acceleration (CSDSA) and displacement (CSDSD). The smoothed curves of Figs. 5-7 seem to contain anoma- lies for TI > 6 s (particularly the increments observed for displacements) that

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Fig. 7. CSDS far bilinear isolators with design parameters V,/W = 0.05, Vv/W = 0.10 and h / k l = 0.10.

probably reflect the ground motion sample and statistics, as well as the correction procedure used for the accelerogrgns. In fact, for long periods (TI around 15 s), dis- placements should tend to converge to the peak ground displacement [i.e. Chopra, 19951.

4.5. Proposed CSDS

Constant strength design spectra for displacements (CSDSD) and accelerations (CSDSA) for Vu/W = 0.05 and 1/,/W = 0.10 are depicted in Fig. 7. It can be observed from the CSDSD shown that, for the period range of interest for most base isolation applications (1.5 s 5 TI 5 3 s), it would be more convenient to design the isolators for lower normalised yield strength ratios (Vu/W = 0.05), as peak displacements are smaller for this envelope. However, one has to look also at: (a) the design curves for the acceleration transmitted to the superstructure (CSDSA), shown in the same figure or in a separate figure, as the design spectra for the maximum normalised base shear transmitted to the superstructure (V,,/W), depicted in Fig. 8, and (b) the displacement ductility demands associated with the definition of the curves corresponding to u + Sdev for the 16 selected acceleration records, as shown in Fig. 9.

It can be observed from Figs. 7 and 8 that the base shear transmitted to the superstructure decreases as the period increases, since the non-linear response of

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Se&mic Design of Bue-Isolated Structures 565

r - CSDSA lor V,/W=0.10

CSDSA for V,/W=0.05

10 ' PERIOD (s)

Fig. 8. CSDSA for design of the superstructure with design parameters Vv/W = 0.05, Vv/W = 0.10 and kp/k l = 0.10.

Fig. 9. Displ~ement ductility demands associated to the CSRS and CSDS for u + Sdav shown in Figs. 5 and 6.

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systems (i.e. ductility demands) with long periods is smaIler when subjected to ground motions for rock conditions, However, one can also observe that for 1.5 s 5 TI 5 2 s, higher shear forces are transmitted to the superstructure for systems with Vy/W = 0.05 than for systems with V,/W = 0.10. It can be observed from Fig. 9 that peak displacement ductility demands (p) w c i a t e d to the design curves for V,/W = 0.05 are very high for the period range of interest (1.5 s 5 TI 5 3 s), and that for the same period range p is more reasonable for the design curves for Vy/W = 0.10. Then, one can conclude that higher shear forces are transmitted to the superstructure for systems with Vy/W = 0.05 than for systems with Vy/W = 0.10 in the period range 1.5 s 5 TI 5 2 s because higher force increments are associated to the postyielding s t f i e s s kz as p increases. It can also be concluded that the selection of the yield strength ratio for the isolation system (V, / W ) that it is more adequate for a given structure depends on many factors, so it is not a good strategy to decide the selection of the characteristics of the isolation system based exclusively on the observation of the constant strength design spectra for displacements (CSDSD) .

The design spectra depicted in Figs. 8 and 9 are also important because they allow to define the period range where elastic responses are expected (the range where V,,/W for the superstructure is lower than the target V9/W for the isolators or p is around one). This can help engineers to avoid poor designs, as high damping rubber bearings (HFU3) and lead rubber bearings (LRB) shodd be designed to work in the inelastic range of response when subjected to moderate and strong earthquake loading.

5. Design of Base-Isolated Structures Using CSDS

The design procedure involves an iterative process, which is described in detail in Tena et al. [1997]. The key steps are surnmarised below:

Select a trial effective period for the isolated structure (TI), considering the following restrictions:

where T is the natural period for the fixed-base structure. Select the normalised yield strength (Vv/W = P) for the isolation system, by selecting the minimum P d u e that would transmit the smaller shear to the superstructure (Figs. 7 and 8) with an acceptable displacement ductility demand p (Fig. 9). Obtain the maximum design displacement for the isolation system, D, from the CSDS of Fig. 7.

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as:

Propose the number of isolators to be used, Ni,,. Compute the effective lateral stifkess for each isolator:

Compute the yield shear force of each isolator:

Compute the ultimate shear force of each isolator:

Check that each isolator satisfies the minimum mechanical requirements spec- ified. The author suggest to adopt a recommendation of the UBC code that establishes that the effective stifbess of the isolation system at the design dii- placement should be greater than one third of the effective stiffness at 20 per- cent of the design displacement (Fig. 1 ) . This recommendation is called here 'VBC stiffness restriction". This restriction is instrumental for the design of isolators and makes the design process iterative. Otherwise, if any unrestricted bilinear curve could be taken, there will be no need for an iterative procedure. According to Fig. 1, the UBC restriction is given by:

vy + kz(0.2 - A,) - V, + kz(0.2D - A,) v, 2 - 0.6 Q (5.9)

An iterative procedure based upon the bisection method is proposed here by introducing an a variable (Eq. (5.9)) that satisfies the UBC stifhess re- striction. It is proposed to limit cr values in the following range in order to assure having reasonably flexible isolation systems under lateral loading: 0.5 5 5 0.6. The most appropriate value is that of the upper limit, because when a = 0.6 one obtains the most flexible isolator under the UBC stiffness restriction. And if k z / k l = 0.10 is selected, then kl = 5keR, as it can be de- ducted from Fig. 1, Eqs. (5.7)-(5.10), as shown in detailed elsewhere (Tena, 1997). Therefore, one should initially propose a = 0.6.

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566 A. Tma-Colurrga

(10) Compute the elastic stifEness (kl) and the post yielding s t f i e s s (k2) of the isolators:

kl = 12.5ketr(l - a) (5.10)

kz = 0- lk l . (5.11)

(11) Compute the yield displacement for the bilinear isolators:

Care should be taken that the yield displacement obtained would assure that peak displacement ductility demands p for the isolators are within reasonable bounds for the assumed a. It can be shown from Eqs. (5.6) and (5.9)-(5.12) that:

Therefore, A, should be in the following range:

Compute the a, value associated to the preliminary design:

Analyse the obtained value of a,. Ifa, > 0.6, it is obvious that the method will not converge for the desired a values. Then, the process should be stopped and a smaller value of TI should be proposed and start again. If ac < 0.5, the method can or cannot converge in the proposed range of values for a, as the outlined procedure is based on a bisection method. Therefore, if after two consecutive iterations o, < 0.5, the iteration should be stopped and the solution might be to propose a higher TI and start again. Compare a, with a, using a rational convergence criterion, for example:

If this condition is met, the design is accepted and one can continue with Step 15. Otherwise, one should propose a = a, and repeat the procedure horn Step 10. Do a preliminary dimensioning of the isolators based upon a recognised method. here are many methods already available in the literature that can be used for this (for example, Skinner et d, 1993; Kelly, 1993; Tena, 1997; Naeim and Kelly, 19993, including design aids and tables from a given manu- facturer. In this work, the following expressions based on those presented by

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Seismic Design of Base-lsolatd Structures 569

- . Skinner et d. [(1993]-were used. For-laminated rubber bearings-of circular cross . .

section, its diameter 4 and its height h can be computed as:

where Gi,, is the shear modulus for the rubber. Similar simple expressions can be used for the design of laminated Iead-rubber bearings (LRB) as presented elsewhere [Tena, 19971.

If the dimensions obtained are those of a very slender isolator, probably one is proposing more isolators than those needed to achieve the required lateral flexibility. Therefore, one solution is to propose fewer isolators, until an adequate slenderness aspect ratio (h/4) is achieved, as it may be clear by analysing Eqs. (5.4) and (5.18). On the other hand, if the dimensions obtained are those of a very short isolator, it is likely that one is proposing fewer isolators than those needed to meet the required lateral flexibility. Therefore, one solution is to propose more isolators until an adequate slenderness aspect ratio (hi#) is achieved.

5.1. Orthogonal eflects

The CSDS shown in Fig. 7 are design envelopes of peak responses for unidirectional input only. However, for the design of 3D structures (with or without base isolation systems) it is important to include multidirectional actions of the ground motions. It has been common practice in the design of structural systems to account for the simultaneous action of the two main horizontal components of the ground motion; this is what has been called uorthogonal effects". The most popular and widespread rule used in seismic codes worldwide is the called "100% + 30% combination rule", that basically states that: Urequirements of orthogonal effects may be satisfied by designing such elements for 100% of the prescribed design seismic forces in one direction plus 30% of the prescribed design seismic ,forces in the perpendicular di- rection". This 100% + 30% combination rule was proposed many years ago based upon studies with a reduced acceleration data set (relative to today's standards) for lateral load combinations. Therefore, extrapolation of this rule to combine max- imum displacements for the design of isolators may not have a justification other that its use is widely accepted in the structural engineering design community. FEMA-273 document under Sec. 9.2.4.5.C basically endorses the 100% + 30% rule to compute the m h u m displacement of the isolation system FEMA-273, 19971. For the design of the isolation system using dynamic analyses, the 1997 UBC code requires an increase of 30% in the target design spectra to account for bilateral ground motions. As shown by Naeim and Kelly [1999], the resulting vector summa- tions of the requirement of the UBC-97 Code and the 100%+30% rule (FEMA-273) are very different.

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570 A. Tena-Colunga

In the opinion of the author, the questions to answer regarding orthogonal effects for the design of isolation systems are: (1) is the 100% + 30% combination rule still valid and reasonable to compute design displacements? and, (2) whether a rational rule for the combination of orthogonal effects can be independent of the structural period and the characteristics of the ground motion. In order to gain some insight on this topic, Tena-Colunga and Mmez-Sober6n [ZOO21 started a study where the ratio between peak dqiacements of the isolators when subjected to bi-directional seismic input (AzD) were compared with those obtained for unidirectional input (Am) for symmetric and asymmetric systems. From the relatively small ,simulations done in Tena-Colunga and Gmez-Sober6n[2002] it is not clear how a constant 100%+30% combination rule can be justified for the design of b s e isolators in the selected period range.

6. Design Examples of Base-Isolated Structures Using CSDS

The proposed CSDS were calibrated for the design of the base isolators for three low-rise school buildings and an eight-storey reinforced concrete (RC) building; these studies are present4 in detail in Tena et a1 (19971. The school buildings were selected as they are benchmark structures for the author, as his research team has previously used other strategies for the design of base isolators for them [Tena-Colunga, 1996; Tena, 1997, Tena et aL, 19971. For these school buildings, a normalised yield strength ratio Vu/W = 0.10 was selected, as it was done in previous studies. The eight-storey RC office building was selected as an irregular structure where base isolation could be used. A norrnalised yield strength ratio V,/W = 0.10 was also used for this building. For illustration purposes, the details of one of the school buildings and the eight-storey RC building, the design of the isolators, and the non-linear dynamic analyses conducted for these designs are presented in following sections.

6.1. EP2 school building

EP2 is a four-storey school building 12.4 m tall (storey height of 3.1 m) with typical bay width of 3.5 m in the longitudinal direction (EW) and 8.7 m in the transverse direction (N-S). Transverse iddl unreinforced hollow concrete block masonry walls are placed every two bays. Transverse outer walls are reinforced concrete walls. Longitudinal unreinforced clay masonry walls do not run the entire story height, and they shorten the columns (Fig. 10). The main structural system consists of moment frames with 25 x 50 cm rectangular RC columns oriented in the N-S direction, 25 x 50 c m rectangular RC beams, and 10 cm thick RC slabs as floor system. Longitudinal reinforcement is the same for all columns ( p = 0.046). Transverse reinforcement consists of closed hoops made of No. 3 bars placed a t 5 cm (2E#3 @ 5 cm) at the columns ends in a 50 cm length and 2E#3 @ 25 cm in the remaining length. The longitudinal reinforcement supplied at the top and bottom of the beams is symmetric and varies from p = 0.0057 for the top storey beams to p = 0.0095

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Seismic Design of Base-Isolated Structures 571

+iY (3 (3 ;;;) (5 (;) ('5) (2 (" I,@) (ii) @) $2) l~jj) 8 '7

. -

/ 8.7m stair I

I A

(a) Plan View

(b) Elevation axis A

( c ) Elevation axis B

Fig. 10. Plan view and elevations for EP2 school building.

for the first storey beams (p = ptop = pbottom). Transverse reinforcement consists of 2E#3 @ 10 cm a t tlie beams ends in a 50 cm length and 2E#3 @ 20 cm in the remaining distance. The specified compressive strength of the concrete (fb) was 200 kg/cm2 (20.39 : m a ) and the specified yield strength of the reinforcement steel (f,) was 4200 kg/cm2 (428.1 MPa). The assumed compressive strength of the masonry (f;) was 15 kg/cm2 (1.53 MPa) for the clay units and 20 kg/cm2 (2.04 MPa) fo:r th.e conc1:ete blocks, according to the masonry provisions of the 1995 Mexico's Federal District Code. Different 3D elastic models for the EP2 building were made with ETABS assuming that the building was fixed a t the base and using all represented modes that insure having at least 90% of the total modal mass acting ixa each main direction. The details of each model and their dynamic char act erist ics are described in Tena-Colunga [1 9961. The natural period for the structure is T = 0.63 s when the longitudinal "non-structural" walls are included in the modelling. Some of the dynamic characteristics of the first two mode shalpes are summarised in Table 2. The total weight for EP2 building is W = 1530 Ton (15 009.3 kN).

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Table 2. Main dynamic characteristia for EP2 school building.

Modal M a s I%) Mode Direction Period is) EW N-S Rotation

1 E-w 0.63 88.35 0.0 0.00 2 N-S 0.12 0.00 85.54 0.00 .

6.2. ECOl building

ECOl is an eight-storey, irregular office building composed of reinforced concrete (RC) waffle flat-slab frame system and peripheral RC shear walls. Typical plan views, elevations and gross dimensions of the structure are depicted in Fig. 11. The structure is irregular in plan and it has a major irregularity in frame 1 of Fig. 11, where there is no wde-slab for bay A-B up to the roof level. The typicaI cross section for columns is square. The columns are 70 x 70 cm in the first two

7.91 ' 8.24 -,' BU -1 N*

(a) Typical plan

(c) Elemtion axis D

7.83 8.21

(b) Heliport plan

(d) Elemtion axis 1

Fig. 11. Plan views and elevations for ECOl building (dimensios in m).

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Tab

le 3

. M

ain

dyna

mic

cha

ract

eris

tics

for

ECOl

buil

ding

.

Mod

al M

ass

(%)

r M

ode

Dir

ecti

on

Per

iod

(s)

EW

N-S

Ro

tati

on

1 E

W

1.01

67

.59

0.14

2.

07

2 N-S

0.68

0.

23

71.2

6 0.

16

3 R

ota

tio

n

0.40

1.

73

0.45

67

.36

Tab

le 4

. D

esig

n pr

oces

s of

the

isol

atio

n sy

stem

for

sch

ool b

uild

ing

EP

2, c

onsi

deri

ng u

nidi

rect

iona

l ac

tion

s fo

r th

e gr

ound

mot

ion

and

the

CSD

SD o

f F

ig.

7.

"Fix

ed"

par

amet

ers

Var

iabl

e It

erat

ion

1

Iter

atio

n 2

It

erat

ion

3

Iter

atio

n 4

Ta (

4

2.0

(I

0.6

0.52

2 0.

548

0.54

5 W

(T

on)

1530

K1 (T

on/c

m)

7.70

9.

20

8.70

8.

76

P =

VvI

W

0.10

Kz (T

on/c

m)

0.77

0.

92

0.87

0.

88

D (

cm)

(Fig

. 7)

21

.2

Av

(4

1.

99

1.66

1.

76

1.75

N

im

10

A

VID

0.

094

0.07

8 0.

083

0.08

2 K

est

(Ton

/cm

) 15

.39

UC

0.52

2 0.

548

0.54

5 0.

545

keff

(T

on/c

m)

1.54

Vv

(T

on)

15.3

0 K

, (T

on

) 32

.63

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storeys and 60 x 60 cm in the remaining stories. The floor system is a RC waffle flat-slab 5 cm thick with 16 cm wide main ribs measuring 30 cm in depth. The '%af£iesn are formed by hollow lightweight concrete blocks. The thickness of the concrete walls is 20 cm. Yield strength of reinforcement steel is f, = 4200 kg/cm2 (428.1 MPa) and compressive strengths for concrete are 300 kg/cm2 (30.58 MPa) for the two first stories and 250 kg/cm2 (25.48 MPa) for the upper stories. 3D eIastic models for the building were made with ETABS, assuming that the building was fixed at the base and using sufficient modes to insure having at least 90acting in each main direction. Young modulus for reinforced concrete was taken according to the concrete nonns from Mexican codes. The remaining modelling assumptions for structural and non-structural elements are described in Tena et al. [1997]. The dynamic characteristics for ECOl building are reported in detail .elsewhere and some of the main characteristics of the first three mode shapes are summarked in Table 3. The natural period for the structure is T = 1.0 1 s. Despite the irregularities, the mode shapes are just lightly coupled. The total weight for the building is W = 4793.5 Ton (47024.2 W).

Table 5 . Summary of design parameters for the isolation system and the superstructure, considering unidirectional actions for the ground motion and the CSDSD (Fig. 7) and CSDSA (Figs. 7 or 8).

EP2 ECOl Global design

T (s) 0.63 1.01 Ta (s) 2.0 2.5 W (Ton) 1530.0 4793.5 P = v, IW 0.10 0.10 D (cm) (Fig. 7) 21.2 28.0 Ni, 10 16 Kern (Ton/cm) 15.39 30.865 a 0.545 0.600

Parameters for the design of the superstructure K/W (Fig. 8) 0.154 0.135 VS (Ton) 235.6 647.1

Individual characteristics of the isolators (HRB) Vu (Ton) -V, (Ton) .

A, (-4 A M = D (cm)

(Ton/cm) kl (Tan/cm) h (Ton/cm) AvlD 4 (-1 H (4 Gi, (kg/cma)

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6.3. Design of base isolators

High damping rubber bearings (HRB) were designed for the EP2 and ECOl build- ings using the CSDSD depided in Fig. 7 and the procedure outlined in Sec. 5. V,/ W = 0.10 was selected for the-design of the isolation systems of both buildings.

The key step in the proposed method is the selection of the design displacement D from the CSDSD depicted in Fig. 7. In order to calibrate the validity of the CSDSD of Fig. 7, only unidirectional action of the ground motion records should be considered. Therefore, the design procedure for the isolation system of school building EP2 under unidirectional action of the ground motions is illustrated in Table 4. The h a 1 designs of the isolation systems for EP2 and ECOl buildings under unidirectional action of the ground motions are sumrnarised in Table 5.

It is also interesting to study how wel does the 100% + 30% rule for orthogonal effects work for these particular structures. Therefore, the design procedure for the isolation system of school building EP2 using this combination rule for orthogonal effects is illustrated in Table 6. The final designs of the isolation systems for EP2 and ECOl buildings under bi-directional action of the ground motions using the 100% + 30% combination ride are surnrnarised in Table 7.

Table 7. Summary of design parameters for the isolation system and the superstructure, considering bi-directional actions for the ground motion and the CSDSD (Fig. 7) and CSDSA (Figs. 7 or 8).

EP2 ECOl

Parameters for the design of the superstructure V,/W (Fig. 8) 0.135 0.135 V,2D/.W = V,/W + 0.3VS/w 0.176 0.176 v . 2 ~ (Ton) 268.5 843.7

Individual characteristics of the isolators (HRB) v, (Ton) 59.76 70.22 4 (Ton) 25.50 29.96 Av ( 4 2.52 2.52 AM = D ~ D (cm) 36.4 36.4 k0ff (Ton/cm) 1.64 1.93 kl (Ton/cm) 10.10 11.86 k2 (Ton/cm) 1.01 1.19 a v / D 2 ~ 0.069 0.069 4 ( 4 110 110 h ( 4 58 50 Gina (kg/cm2) 10.2 10.2

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Seismic Design of Bme-Isolated Structures 577

- . -. -. - Different-arrangements-and-numbers-of-HRB--were-considered--in--the -design-- -

process. The number of KRB presented in Tables 4 to 7 corresponds to the best design of such isolators taking into account their dimensions. It is worth noting that the dimensions for the HFU3 of Tables 4 to 7 correspond to a preliminary design, as the actual dimensions of the HEU3 for a final design have to be adjusted to commercial sizes working together with a manufacturer.

6.4. Design of the superstructure

The design of the structural system was not done as EP2 and ECOl buildings involve the retrofit of existing buildings. However, the base shear coefficient for the design of the superstructure can be defined with the curves depicted in Figs. 7 and 8. The corresponding designs are summarised in Tables 5 and 7 for unidirectional and bi- directional action of the ground motions respectively.

6.5. Non-linear dynamic analyses

The proposed designs for the isolation systems for EP2 and EGO1 buildings were tested with non-linear dynamic analyses of the base-isolated models when subjected to unidirectional and bi-directional acceleration input using the 3D-Basis program [Nagarajaiah et a l , 19911. Unidirectional input was used for the designs surnmarised in Table 5 whereas bi-directional input was used to evaluate the designs summarised in Table 7. Analyses for unidirectional input were conducted considering the E W components as the "x componentn and the N-S as the "y component", orthogonal to both the short and long direction, one at the time. For these case studies, the acceleration records were scaled with the corresponding amplification factor f,, for each component identified in Table I. For bi-directional input, an "x-y" quake is defined when the E W component is acting in the long direction, whereas a "y- x" quake is defined when the N-S component is acting in the long direction. In addition, for bi-directional input, the amplification factor f,, corresponding to the strongest component was used to scale both acceleration records. For example, for station UNIO, f,, = 2.124 associated to the N-S component (Table 1) was used to scale both the N-S and the E W component.

Results obtained from these anaiyses are summarised for EP2 school building in Tables 8 (unidirectional action) and 9 (bi-directional action) and for ECOl building in Tables 10 (unidirectional action) and 11 (bi-directional action). In these tables, Ai is the maximu& dynamic displacement for a given isolator at an angle 8 from the x axis, AM is the maximum allowable isolator displacement for dynamic stabil- ity as defined in Tables 5 and 7, A, ,, and A, ,, are the maximum relative roof displacements with respect to the isolation system in the x and y directions respec- tively, V,, and V,, are the peak base shear forces transmitted to the structure in the x and y directions respectively, VZi and V., are the peak shear forces developed for the isolators in the x and y directions respectively, and W is the weight for the structure.

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Tab

le 8

. P

eak

dyna

mic

res

pons

es f

or t

he

isol

atio

n pr

ojec

t un

der

unid

irec

tion

al a

ctio

n of

th

e gr

ound

mot

ion

for

1SP2

sc

hool

bui

ldin

g (T

I = 2

.0 8

).

--

.

AZ

IH

Y 19

.0

0.1

12.6

2 0.

60

0.83

0.

71

0.13

5 0.

003

CA

LE

y

14.8

0.

0 11

.42

0.54

0.

73

0.75

0.

114

0.00

1 U

NIO

Y

21.8

0.

1 11

.53

0.54

0.

92

0.90

0.

144

0.00

1 P

AP

N

y 21

.7

0.1

20.3

0 0.

96

0.81

0.

86

0.16

8 0.

001

VIL

E

31.4

0.

2 20

.49

0.97

0.

99

0.73

0.

176

0.00

0 S

UC

H

y

24.9

0.

1 16

.35

0.77

0.

89

0.70

0.

165

0.00

1

AM

= 2

1.2

cm,

W =

153

0 T

on =

150

09.3

kN.

Tab

le 9

. P

eak

dyna

mic

res

pons

es f

or t

he

isol

atio

n pr

ojec

t un

der

bi-d

irec

tion

al a

ctio

n of

th

e gr

ound

mot

ion

for

EP

2

scho

ol b

uild

ing

(TI =

2.5

s).

Sta

tio

n

Qua

ke

Azm

ax (

mm

) A

Ym

a, (

mm

) A

i (c

m)

A~

/AM

Vze

/Vzi

V

ve/V

ui

VA

/W

Vve

/W

AZ

IH

9-2

15.8

0.

6 14

.79

0.41

0.

86

0.72

0.

113

0.07

7 C

AL

E

y-z

12.9

0.

5 16

.79

0.46

0.

74

0.71

0.

101

0.06

5 U

NIO

y-

z 16

.7

0.6

14.3

4 0.

39

0.84

0.

71

0.11

2 0.

078

PA

PN

z-

y

12.4

0.

9 25

.13

0.69

0.

86

0.71

0.

090

0.12

5 V

ILE

y

-z

24.3

0.

6 28

.22

0.78

0.

99

0.71

0.

168

0.08

4 S

UC

H

y-s

20.0

0.

6 17

.37

0.48

0.

90

0.71

0.

134

0.07

9

AM

= 3

6.4

cm,

W =

153

0 T

on =

150

09.3

kN

.

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It can be observed from Tables 8 and 10 that the proposed designs for unidirec- tional action are adequate for all ground motions, as the quotient 4 i/AM is always less than one, except for station PAPN for ECOl building, where the maximum allowable -lacement is surpassed by 6%. However, the design procedure based on the CSDSD of Fig. 7 can be taken as satisfactory, considering the statistical criterion used to define such curves. CSDS shown in Fig. 7 were defined born a reduced set of ground motions using as statistical criterion the mean plus one stan- dard deviation (associated with an accumulated probability density function equal to 0.8413 for a normal distribution). Improved results would have been obtained adding higher mdtipliers for the standard deviation. On the other hand, it can be observed from Tables 9 and 11 that the proposed designs for bi-directional input us- ing the 100% + 30% combination rule are adequate for all ground motions for these particular structures, as the quotient Ai/AM is always less than one. Maximum responses for the isolators are related to the amplified motions for stations PAPN and V Z E for both unidirectional and bi-directional input. Relative roof displace- ments are very small for both buildings for both unidirectional and bi-directional input as weU.

The effectiveness of the isolation system in reducing the base shear transmitted to the superstructure (V,,/Vzi and VI,/VYi ratios) is between 70% and 99% for EP2 building (Tables 8 and 9) and from 76% to 100% (Tables 10 and 11) for ECOl building for most stations, but it can be even 7% higher as it happens for station SUCH and unidirectional input on the direction of interest (Table 10). Higher effectiveness in reducing the base shear transmitted to the superstructure has been observed for other buildings studied by the author [for example, Tena et d , 19971.

The maximum norrnalised dynamic base shear transmitted to the superstructure (V,,/W) for EP2 schooI building under unidirectional input (Table 8) obtained for stations VILE, PAPN and SUCH surpass the one obtained from ICDSA (Vs/W = 0.154, Table 5), but the ones obtained for stations AZIH, UNIO and C U E are less than the one reported in Table 5. For ECOl building, the normalised base shear obtained from CSDSA (Vs/W = 0.135, Table 5) is only surpassed for station VILE under unidirectional input (Table 10). Therefore, for most stations the estimate of the maximum base shear from CSDSA is reasonable, considering the statistical criterion used to define such curves. On the other hand, the VZe/W ratios for bi- directional input for buildings EP2 (Table 9) and ECOl (Table 11) do not surpass the normalised base shear obtained from ICDSA for EP2 and ECOl buildings using the 100% + 30% combination rule (Vs/W = 0.176, Table 7).

The non-linear dynamic analyses conducted for EP2 and ECOl buildings sug- gest that the CSDS presented in Figs. 7 and 8 were useful and can be reliable for the design of base isolators, despite the shortcomings of the present study, among them, the use of a statistical criterion based upon the mean plus one standard deviation with a limited strong ground motion data base for defining the CSDS.

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Seismic Design of Base-fsolated Stmctures 581

- -- - - - - - Therefore, the concept of CSDS<=tO be a~i0I ; ; i ; ; inEGZl-o GliablZ d&ign of

-

base isolators with bilinear hysteretic behaviour, although a more rigorous proce- dure should be use to define design curves if CSDS are intended to be associated with a specific building code.

7. Summary and Conclusions

This paper presents the concept of constant strength design spectra (CSDS) for the design of base-isolated structures, particularly those structures using iso- lators with a bilinear hysteretic behaviour when subjected to dynamic loading. The CSDS relate peak accelerations, velocitia, displacements, and effective iso- lated natural periods for bilinear systems with a given yield strength and post yield stifhess. CSDS could be usefd for the-design of base isolators with bilinear hys teretic behaviour as these devices can be designed for a fixed yield strength and post yield stf iess.

In this paper, CSDS were defined for representative strong ground motions recorded in the Mexican Pacific Coast during recent strong earthquakes using a crude statistical criterion for base isolators with bilinear behaviour. The CSDS presented in this study were computed to assess their effectiveness for the design of base-isolated structures, but they have not been developed yet to comply with code criteria of ruling Mexican seismic codes for the Mexican Pacific Coast. The development of CSDS associated to specific building codes would require complete seismic hazard analyses, where detailed considerations should be made in the selec- tion of ground motions, sizes of design earthquakes for different performance levels, exceedence rates, etc., steps that will be taken in future works.

The concept of CSDS and its application for the design of base isolated struc- tures is illustrated in two buildings. Non-linear dynamic analyses conducted for EP2 and ECO1- buildings (and other structures, not shown) suggest that the proposed CSDS are useful and could be reliable for the design of base-isolated structures, despite the shortcomings of the study described in previous sections. Among these shortcomings, one can highlight the following: (a) using a simple statistical proce dure with a limited strong ground motions data bae , and (b) using the 100%+30% combination rule to account for bi-directional effects, as there are no specific stud- ies yet devoted to propose more rational magnification factors due to this loading condition for base-isolated structures.

Nevertheless, the concept of CSDS seems to be a promising tool for reliable de- sign of base isolators with bilinear hysteretic behaviour. Further research is needed in order to define CSDS for specific building codes where, in addition to the items described above for seismic hazard analyses, a consideration must be made in order ta incorporate the impact of bi-directional ground motions and the vertical com- ponent for the acceleration in a rational basis, b e d on specific studies devoted to baseisolated structures.

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Acknowledgements

Financial support of Conacyt (National Science and TechnoIogy Council of Mexico) and Universidad Aut6noma Metropolitma is gratefully acknowledged. Constructive comments from anonymous reviewers for this paper were helpful to improve it and are gratefully acknowledged.

Appendix A. Notation

The following symbols are used in this paper: a,, = peak ground acceleration c( t ) = damping coefficient at time t for a single degree of freedom system D = design displacement for the isolation system under unidirectional input DzD = design displacement for the isolation system under bi-directional input f = frequency of vibration fi = compressive strength of concrete f,, = scale ampUcation factor for the ground motions f, = yield strength of reinforcement steel F ( t ) = effective load at kme t F,& = the maximum negative force of the non-linear SDOF system with an

initial elastic period of interest Tj. . F k j = the maximum positive force of the non-linear SDOF system with an

initial elastic period of interest Tj. Gk, = shear modulus for the elastomeric bearing k ( t ) = stifbess at time t of a single degree of freedom system kew = total effective stiffness of the isolation system at the design displacement ken = effective stifhess of an isolator unit at the design displacement kerrz = effective stifhess of an isolator unit at 20% of the design displacement kl = elastic (pre-yield) stiffness of a bilinear system kz = postyielding st ihess of a bilinear system m = mass of a single degree of heedom system M, = surface wave magnitude of an earthquake M, = moment magnitude of an earthquake Ni,, = number of isolators to be used S, = peak spectral acceleration Sd = peak spectral relative displacement Sdev = standard deviation S, = peak spectral'velocity T = period of vibration Tf = ending period of interest T, = initial period of interest TI, = effective period of the base-isolated structure

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Seismic Design of Bme-Isolated Structures 583

- maximum designhear-force transmitted-to-the-superstr-ucture-for-the - - -- isolation system for unidirectional input

Vs2D = maximum design shear force transmitted to the superstructure for the isolation system for bi-directional input

V- = ultimate shear force for an individual isolator V, = yielding shear force for an individual isolator or the complete

isolation system V,, = maximum base shear transmitted to the superstructure by the

isolation system V,, = maximum base shear force transmitted to the superstructure, in the

x direction V,, = maximum shear force developed for the isolation system, in the

x direction V,, = maximum base shear force transmitted to the superstructure, in the

y direction V,i = maximum shear force developed for the isolation system, in the

y direction W = weight of a structurd system x(t) = displacement at time t x(t) = velocity at time t x(t) = acceleration at time t a, ac working variables ,B = normalised shear yield strength for the isolation system A; = maximum dynamic displacement for a given isolator in an angle 8 from the

x axis A,, = maximum allowable displacement for base isolators for dynamic stability AM = maximum allowable diiplacement for base isolators for dynamic stability At = integration time-step A,,, = maximum relative roof diiplacement with respect to the isolation

system, in the x direction A, ,, = maximum relative roof displacement with respect to the isolation

system, in the y direction A, ,,, = yield disphcernent for an isolator unit

A;, = the maximum negative diiplacement of the non-linear SDOF system with an initial elastic period of interest Tj .

+ A,, = the maximum positive displacement of the non-linear SDOF system with an initial elastic period of interest Tj.

p = displacement ductility demand u = statistical mean 0 = measured angle (degrees) from the x axis

6 = equivalent viscous damping ratio.

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References

Chopra, A. K. (19951 *amics of Structures. Theory and Applications to Earthquake Engineering, Prentice Hd, New Jersey, pp. 211-217, 254-256.

FEMA-273 [I9971 WEHRP guidelines for the seismic rehabilitation of buildings," FEMA Publication 273, Federal Emergency Management Agency, Washington, D.C., October.

FEMA-274 [I997 UNEHRP Commentary on the guidelines for the seismic rehabilita- tion of buildings," FEMA Publication 274, Federal Emergency Management Agency, Washington, D.C., October.

Habibullah, A. (19911 ETABS, Building Analysis and Design, Computer & Structures Inc. International Building Code, [2000], International Building Council, Whittier, California,

2000 Edition. Kartoum, A., Constantinou, M. C. and Reinhorn, A. M. [I9921 "Sliding isolation system

for bridges: analytical study," Earthq. Spectm, 8(3), 345-372. Kelly, J. M. (19931 Earthquake-Resistant Design with Rubber, Springer-Verlag, New York. Kelly, J. M. [1999] "Recent development in seismic isolation in the United States," Revista

de hgenien'a S h i c a 61, 57-72. Miranda, E. [I9931 "Evaluation of sitedependent inelastic seismic design spectra," ASCE

J. Stmct. Engrg. 119(5), 1319-1338. MOG93 [1993] "Manual de diseiio de obras civiles. Diseiio por sismo," Institute de Inves-

tigaciones Elktricas, Comisibn Federal de Electricidad, M h c o (in Spanish). Naeim, F. and Kelly, J. M. (19991 Design of Seismic Isolated Structures, John Wiley &

Sons, New York. Nagarajaiah, S., Reinhorn, A. M. and Constantinou, M. C. [1991] IL3D-Basis: Non-linear

dynamic analysis of three-dimensional base isolated structures: Part 11," Technicnl Re- port NCEER-91-0005, National Center for Earthquake Engineering, State University of New York at Buffalo.

Newmark, N. M. and Hall, W. J. (19821 Earthquake Spectm and Design, Monograph Series, Earthquake Engineering Research Institute, Oakland.

Skinner, R. I., Robinson, W. H, and Mc Verry, G. H. (19931 An Introduction to Seismic Isoiation, John Wiley and Sons, London.

Tena-Colunga, A. [I9961 "Some retrofit options for the seismic upgrading of old low-rise school buildings in Mexico," Earthq. Spectm 12(4), 883-902.

Tena-Colunga, A., G6mez-Soberbn, C. and Muiioz-Loustaunau, A. [I9971 "Seismic isola- tion of buildings subjected to typical subduction earthquake motions for the Mexican Pacsc Coast," Earthq. Spectm 13(3), 505-532.

Tena, A. [I997 "Evaluaci6n de un metodo de disejio eststico para el aislamiento sismico de estmcturas de la costa mexicana del Pacifico," Revista de Ingenienb Sismica 57, 1-25 (in Spanish).

Tena, A., Gdmez, L. A. A. and Salazar, M. (19971 "Criterios de disefio y reglamentacidn de estructuras con aisladores de base para la costa del Pacifico," Report FJBS/CIS- 97/17, Centro de Investigaci6n Slsmica, AC, h d a c i 6 n Javier Barros Sierra, December (in Spanish).

Tena-Colunga, A. [I9991 "International seismic zone tabulation proposed by the 1997 UBC code: Obsemtions for Mexico," Earthq. Spectm 15(2), 331-360.

Tena-Coluaga, A. and Gbmez Soberbn, L. A, [2002] "Torsional response of base- isolated structures due to asymmetries in the superstructure," Engy. Struct. 24(12), 1587-1599.

TsopeIas. P., Constantinou, M. C., Okamoto, S., Fujii, S. and Ozaki, D. [I9961 "Experimental study of bridge seismic sliding isolation systems," Engq. Struct. 18(4), 301-310.

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Seismic Design of Base- Isolated Structures 585

- - -. - - - Uniform -Building-Code-(-l99l-]-International--Gonference-of-Building-OficiaIs, Whittier,-- - - -

California, 1991 Edition. Uniform Building Code [I9941 International Conference of Building Officials, Whittier,

California, 1994 Edition. Uniform Building Code [I9971 International Conference of Building Officials, Whittier,

California, 1997 Edit ion. Viilegas-JimBnez, 0 . and Tena-Colunga, A. (20001 "Dynamic design procedure for the

design of base isolated structures located on the Mexican Pacific Coast," Proc. of the 12th World Conference on Earthquake Engineering, Auckland, New Zealand, Paper No. 929, February.

Youssef, N. [1996a] "Application of hybrid damping system with base isolation for the seis mic retrofit of Los Angeles Hall," Pmc. of the 11th World Conference on Earthqunke Engineering, Acapulco, Mbxico, June, Paper No. 2090.

Youssef, N, (1996bj Personal communication iprovided in the orai presentation of the paper Youssef (1996a)l.

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