Engineering Structures 53 (2013) 25–37

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Engineering Structures

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Parametric study on acceleration-based design of low-rise base isolatedsystems

0141-0296/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engstruct.2013.03.012

⇑ Corresponding author. Address: Departamento de Materiales, UniversidadAutónoma Metropolitana, Av. San Pablo 180, Col. Reynosa Tamaulipas, Azcapotz-alco, 02200 México, DF, Mexico. Tel.: +52 53 18 94 59; fax: +52 53 18 90 85.

E-mail addresses: oscarzc@prodigy.net.mx (O. Zuniga-Cuevas), atg@correo.azc.uam.mx (A. Teran-Gilmore).

Oscar Zuniga-Cuevas ⇑, Amador Teran-GilmoreDepartamento de Materiales, Universidad Autónoma Metropolitana, Av. San Pablo 180, Col. Reynosa Tamaulipas, 02200 México, DF, Mexico

a r t i c l e i n f o

Article history:Received 7 October 2011Revised 6 March 2013Accepted 8 March 2013Available online 29 April 2013

Keywords:Seismic isolationFloor response spectraFloor acceleration demandsNon-structural componentsNon-classical damping

a b s t r a c t

The dynamic response of a series of base isolated systems subjected to ground motions that wererecorded in firm soils of the Mexican Pacific Coast was estimated in order to evaluate the influence ofthe structural properties of these systems in their floor acceleration demands. While the super-structureswere assumed to remain elastic and to exhibit 2% of critical damping, the isolation systems were assumedto exhibit linear behavior with viscous damping ranging from 10% to 30% of critical damping. The differ-ent damping levels assigned to the super-structures and isolation systems were taken into accountthrough a non-classical damping approach. After identifying in general terms the structural propertiesof the systems that are able to better control their floor acceleration demands, it is concluded that flexibleisolation systems with low levels of damping coupled with stiff super-structures result in substantialreductions of the participation of upper modes to the global dynamic response of isolated structures.Within this context, an equivalent single-degree-of-freedom system that can be used within an acceler-ation-based format to conceive base isolation systems is formulated, and implications for its practical usediscussed.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The excessive losses derived from the unsatisfactory seismicperformance of buildings designed according to worldwideaccepted standard practice has created discomfort in the commu-nity of structural engineering. This has gained particular impor-tance since the unacceptably high material and socio-economiclosses that have resulted from the excessive damage suffered bynonstructural systems and acceleration-sensitive contents duringrecent worldwide seismic events (Northridge 1994, Kobe 1995,Taiwan 1999, Sichuan 2008, Chile 2010). The level of loss hashighlighted the need to: (A) establish design criteria distinct fromthat specified in current building codes; and (B) develop innovativedesign approaches that can explicitly control the level of damageand losses suffered by buildings that are built in high seismicityzones. In remarkable contrast with the past, the performance ofmodern buildings should transcend the prevention of catastrophicstructural failure during severe seismic events, in such a mannerthat they satisfy the multiple and complex socio-economic needsof modern human societies. This implies that structural as wellas nonstructural damage should be explicitly controlled.

The main objective of performance-based formats is to promotethe design of earthquake-resistant structures that are able tocontrol their dynamic response within thresholds associated towell-defined damage levels. Currently, the most used designresponse parameter to achieve adequate seismic performance isthe maximum lateral displacement/drift demand [31,8,37,32].Nevertheless, under some circumstances, there are other demandsthat should be controlled to achieve adequate overall seismic per-formance [48,45,9]. For instance, acceleration-sensitive contents infacilities that allocate museums, healthcare facilities and manufac-turing facilities represent a large percentage of the cost of thebuilding [36,46,30]. The nature of the dynamic response of somenonstructural components implies controlling their velocity andacceleration demands to reach an adequate seismic performance.

Villaverde [48] provides a detailed classification of equipmentand nonstructural components, and offers an interesting discus-sion on the social and financial need to control their seismicdamage. Within this context, equipment and nonstructural compo-nents can be defined as those housed or attached to the floors, roofand walls of a building that are not part of the main or intendedload-bearing structural system, but may also be subjected to largeseismic forces and must depend on their own structural characteristicsto resist these forces.

Recent studies suggest that the estimation of accelerationdemands for nonstructural components on fixed-based buildingsdepends on several variables, in such a manner that the formula-tion of rational design methods rapidly becomes too complicated

Fig. 1. Shear model of four-story structure with linear base isolation system.

26 O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37

for practical application. Among other things, accelerationdemands depend on the: (A) type of structural system and thevariation of its mass and structural properties along the height;(B) height of the building and location of the nonstructural compo-nent along the height; and (C) interaction that occurs between thedynamic and mechanic characteristics of the structural system andthe frequency and energy content of the ground motion[27,19,48,9,30,41,11]. Within this context, current designapproaches exhibit some shortcomings: (A) oversimplificationand underestimation during the quantification of accelerationdemands; and (B) the use of a design approach in which thenonstructural components are revised and their supports designedafter the seismic design of the main lateral load carrying system iscarried out. The supports and anchors of nonstructural compo-nents are designed so that they are able to withstand withoutcollapse, toppling and shifting the acceleration demands imposedon them by the design ground motion [9]. Within this black-boxapproach, no effort is carried out to control the dynamic responseof sensitive and valuable contents housed within some nonstruc-tural components.

In highly refined facilities, such as hospitals and high-techmanufacturing facilities, a black-box design approach may easily re-sult in loss of operation and unacceptable damage on sensitiveequipment and contents, in such a manner that methodologiesshould be developed for the conception and preliminary design ofstructural systems that are capable of controlling the accelerationdemands on the building. On one hand, a growing effort is being de-voted to the analytical, field and experimental study of acceleration-sensitive nonstructural components [28,12,24,38,21]. This has led tothe formulation of vulnerability functions and design recommenda-tions aimed at establishing acceleration thresholds associated tovarious limit states of different type of nonstructural components.

Within performance-based seismic engineering, a naturalcomplement for the formulation of design acceleration thresholdsis the definition of a design methodology that allows the determina-tion of structural properties for a building that are able to control itsacceleration demands. An option to reduce acceleration demands onnonstructural components is to allow plastic behavior on the mainstructural system or to provide it with added viscous damping[44,2,30,49,35,26]. An efficient alternative in terms of accelerationreduction is to provide energy dissipation capability directly to thenonstructural component [1,23,49]. Nevertheless, in terms of effec-tive and efficient overall acceleration control, there is ample analyt-ical, experimental and field evidence that base isolation is the bestoption [22,10,28,14,47,29]. In spite of their potential for accelerationcontrol, the design of the properties of base isolation systems and oftheir super-structures is usually based on strength or displacement-based formats [34,37]. Accelerations demands, if at all, are estimatedas a byproduct of the design procedure, and this may lead to severaldesign iterations when acceleration demands on nonstructural com-ponents need to be explicitly controlled.

Previous research has been aimed at characterizing themaximum absolute floor accelerations on base isolated super-structures [25,6,7]. Although these studies have concluded thatfloor accelerations can be significantly reduced through increasingthe lateral stiffness of the super-structure relative to that of thebase isolation system, there is still a need to directly quantify theacceleration demands at the content level, and to establish simpledesign methodologies that, according to the type of content and itssocio-economic and cultural importance, can explicitly formulate acapacity–demand acceleration approach to damage control. Withinone such methodology, the structural engineer needs to establishfirst, the design lateral absolute acceleration threshold at the floorlevel as a function of that allowed in the acceleration-sensitivecontents; and second, design values for the global structural prop-erties of the base-isolation system and its super-structure in such a

way that the building is able to control its global an local dynamicresponse within such threshold. The methodology should also besimple and conceptually robust, in such a manner that the engineercan easily explore several design options and the use of differentbase isolation systems in the preliminary phases of a designproject.

This paper evaluates the influence of the structural properties ofelastic base isolated systems in the absolute floor accelerationdemands and their respective floor spectra, and through theintegration of the results that it presents, discusses the basis foran acceleration-based format for the conception and preliminarydesign of base isolation systems that are capable of controllingthe acceleration demands at the content level. The paper focuseson elastic and viscously damped base isolation systems subjectedto intense ground motions recorded at firm soil sites located inthe Mexican Pacific Coast.

2. Dynamics of base-isolated systems

The base isolated systems under consideration contemplate anelastic super-structure consisting of a series of masses (one perstory), connected through elastic shear springs that condense thelateral stiffness at the inter-story level. The values of lateral stiff-ness, reactive mass and damping were considered constant alongthe entire height of the super-structure. In this sense, the stickmodels represent low-rise structures with a lateral behaviordominated by global shear deformations in such a manner thatthey are not sensitive to overturning effects and the verticalcomponent of the ground motion. While several authors have usedsimilar considerations to model low-rise base isolated super-struc-tures [25,6]; Alhan and Sürmeli [7] have shown the pertinence ofusing this type of model for elastic super-structures with linearbase isolation systems.

For the isolation systems, an elastic model with viscousdamping was considered. It should be mentioned that this typeof modeling is appropriate for normal and high damping rubberbearing isolators, or rubber bearing isolators complemented withviscous damping devices [25,42,13]; and that current analysis toolsprovide reasonable modeling of the global and local dynamicbehavior of actual base isolated structures [22,34,47].

The equation of motion for an isolated system, such as thatshown schematically in Fig. 1, can be formulated as [34]:

M�€v� þ C� _v� þ K�v� ¼ �M�r�€ug ð1Þ

where M�, C� and K� are the mass, damping and lateral stiffnessmatrices of the isolated system, respectively; v� is an array of

Table 1Structural properties of isolated systems.

Stories Super-structure Isolation system

TS (s) nS (%) TB (s) nB (%)

2 0.05, 0.17, 0.28, 0.40 2 1.5 104 0.15, 0.30, 0.50, 0.70 2.0 15

2.5 208 0.30, 0.50, 0.70, 1.00 3.0 25

O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37 27

relative displacements with respect to the ground that are associ-ated to the lateral (horizontal) degrees-of-freedom of that system;r� is an array that relates the lateral displacements of v� to that ofthe ground; and €ug is the ground acceleration.

Consider a planar (two-dimensional) super-structure having nstories and one lateral degree-of-freedom per story (see Fig. 1).Eq. (1) can be expressed as:

mþmB rT M

Mr M

� �€uB

€U

� �þ

cB 00 C

� �_uB

_U

� �þ

kB 00 K

� �uB

U

� �

¼ � mþmB rT M

Mr M

� �10

� �€ug

ð2Þ

where m is the sum of all masses assigned to the degrees-of-free-dom of the super-structure; mB, cB and kB are the mass, dampingand lateral stiffness of the isolation system, respectively; M, C andK are the mass, damping and stiffness matrices corresponding tothe super-structure on a fixed base condition; r is an array of ones;uB is the lateral displacement corresponding to the isolation system;and U is an array of the lateral displacements corresponding to thesuper-structure measured relative to that of the isolation system.The total number of degrees-of-freedom of the isolated system isequal to n + 1.

In terms of non-classical damping, the damping matrix is notorthogonal to the modal shapes of the isolated system. As a result,the modes of the system cannot be uncoupled in terms of damping,and the modal shapes, frequencies and damping levels, depend onthe damping matrix of the system. According to Hurty [18], thedynamic response of a system with non-classical damping can beestimated through transforming the equation of motion accordingto the following change of variable:

z ¼_v�

v�

� �ð3Þ

where z contemplates the lateral displacements and velocities ofthe isolated system. Eq. (1) can be reformulated in terms of Eq.(3) as:

½A� _zþ ½B�z ¼ �f0g

M�f1g

� �€ug ð4Þ

where [A] and [B] are defined as:

½A� ¼½0� M�

M� C�

� �ð5Þ

½B� ¼�M� ½0�½0� K�

� �ð6Þ

The homogeneous solution of Eq. (4), which can be expressed as:

z ¼ yept ð7aÞ

_z ¼ pyept ð7bÞ

leads to the following equation:

ð½B��1½A�p� ½I�Þy ¼ 0 ð8Þ

where p and y are eigen-values and eigen-vectors that allow for theestimation of the modal frequencies, shapes and damping levels ofthe isolated system. While the size of the arrays in Eq. (8) is2(n + 1); p and y can be expressed as:

p ¼ 1k

ð9Þ

y ¼p/

/

� �ð10Þ

The solution to the eigen-value problem results in complexfrequencies:

kj ¼ xnjfj þ ixdj ð11aÞ

where

jkjj ¼ xnj ð11bÞ

xdj ¼ xnj

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffij1� f2

j jq

ð11cÞ

and xnj, xdj and fj are the natural and damped frequencies and thepercentage of critical damping, respectively, associated to the jthmode.

Once the dynamic properties of the non-classical dampedsystem have been established, it is possible to establish its modalparticipation factors [18]:

Cj ¼ 2ImðpjÞj/jM

�f1gyT

j ½A�yjj ð12Þ

where Cj is the modal participation factor of the jth mode; andIm(pj) is the imaginary part of pj. Although the term modal partici-pation factor implies a measure of the degree to which the jth modeparticipates in the dynamic response of an isolated system, it hassome drawbacks in the sense that it does not provide a quantitativecharacterization of the contribution of the mode to a given responsequantity. Because of this, in this paper the modal participationfactor is normalized to provide it with a quantitative meaning.Particularly, a normalized modal participation factor for the jthmode ðC�j Þ equal to one implies that all the reactive mass of thestructure is mobilized by that mode, and thus, that the dynamicresponse of the structure is fully dominated by that mode.

Table 1 summarizes the properties of the super-structures andisolation systems under consideration. While nB and nS denotethe percentage of critical damping in the isolation system andthe super-structure, respectively; TB is the period of vibration theisolation system would have if all the mass in the system wasassigned to its degree-of-freedom (also known as rigid-body modeperiod); and TS the fundamental period of vibration the super-structure would have if supported on a fixed base. As shown inTable 1, 16 base-isolation systems combine four values of TB andnB. For each base-isolation system, 12 super-structures that con-template three different numbers of stories (two, four and eight)are considered. The values of TS for each super-structure are indi-cated in the table.

Two parameters that are relevant to the dynamic response ofisolated structures are: (A) the ratio between the periods TB andTS; and (B) the relation between the mass of the super-structureand that assigned to the isolation system. Within this context,the results that will be presented next will be discussed in termsof the period ratio TB/TS, and the mass ratio c, defined by Naeimand Kelly [34] as:

c ¼Pn

i¼1mi

mB þPn

i¼1mið13Þ

28 O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37

where mi is the mass assigned to the ith degree-of-freedom of thesuper-structure; and mB is the mass assigned to the isolation system.

Fig. 2 shows, for isolated two-story super-structures, thenormalized modal participation factor corresponding to their firstmode of vibration ðC�1Þ. According to the definition given before, avalue of one for C�1 corresponds to a global lateral response fullydominated by the fundamental mode of vibration. While the damp-ing of the isolation system does not have a significant influence onthe normalized participation factor, the influence of c in this factortends to be moderate. Particularly, as c increases (the mass in thesuper-structure increases relative to that of the isolation system);the normalized participation factor tends to increase. Note that asthe value of TB/TS increases from 0 to 10, C�1 increases rapidly. OnceTB/TS reaches the value of 10, C�1 tends to increase at a smaller rate;and even at a much smaller rate once it exceeds the value of sixteen.This implies, in congruency with the linear theory discussed by Nae-im and Kelly [34] that an increase in the value of TB/TS results, forsmall and moderate values of this ratio, in a significant decrease ofthe participation of upper modes to the lateral deformation and dy-namic response of the super-structure.

Figs. 3 and 4 respectively show the normalized participationfactor for four and eight-story isolated systems. Contrary to whatis shown in Fig. 2, nB exhibits a moderate influence on C�1, particu-larly in the cases in which TB/TS is less than eight. While c keepsexhibiting a moderate influence in the value of C�1, it is possibleto observe that an increase in c results in larger participationfactors, except for very small values of TB/TS.

3. Floor response of base-isolated systems

In terms of acceleration control, it is convenient to study thedynamic response of isolated systems subjected to the action ofintense ground motions. With this purpose, a set involving 22ground motions recorded at the Mexican Pacific Coast was formed.The motions, included in Table 2, were compiled from a databaseestablished by the Sociedad Mexicana de Ingenieria Sismica [43].

ΓΓ

ξξξξ

ξξξξ

Γ

(a)

(c)Fig. 2. Normalized participation factor of fundamental mode of vibration of two

The motions were linearly scaled in such a manner as to exhibitpeak ground acceleration (PGA) of 0.6 g, which corresponds to areturn period of five hundred years for the coast of the state ofGuerrero. In general terms, the set of motions represents thedesign earthquake for structures built in firm soil sites locatedalong the coast of Guerrero. Fig. 5 shows mean pseudo-acceleration(Sa) and pseudo-displacement (Sd) spectra for the set of motions,elastic behavior, and different percentages of critical damping (n).Note the moderate displacement demands for periods larger than2 s, in such a manner that unlike high intensity epicentral motionswith directivity effects recorded in California and Japan, displace-ment demands at the base of an isolated structure located in theMexican Pacific would not represent a limitation in terms of itsacceleration-based conception.

The lateral motion exhibited by the floors of an isolated systemcan be used to identify the participation of its different modes ofvibration. This can be achieved in two manners: (A) in thefrequency domain through Fourier Amplitude Spectra, and (B) inthe time domain through Absolute Acceleration Floor Spectra. Theintegration of the information provided by both types of spectraprovides useful insights into the disaggregated dynamic responseof isolated structures.

3.1. Frequency domain

A Fourier Amplitude Spectrum provides direct information aboutthe frequency content of the floor response, and in this sense,allows for an understanding on how the motion is filtered by the iso-lated structure from the ground level to its floor levels. Figs. 6 and 7show Fourier Amplitude Spectra for the time-history of the absoluteroof acceleration of four-story isolated systems. While the lateralstiffness and level of damping of the isolation systems are varied, cof 0.80 is considered for all them. Note that while the super-struc-tures analyzed in Fig. 6 can be considered flexible (TS = 0.7 s for afour-story super-structure on fixed base), the ones in Fig. 7 can beconsidered stiff (TS = 0.15 s).

ξξξξ

γγγ

Γ

Γ

(b)

(d)-story isolated systems: (a) c = 0.80; (b) c = 0.67; (c) c = 0.50; (d) nB = 0.25.

ΓΓ

ξξξξ

ξξξξ

ξξξξ

γγγ

Γ

Γ Γ

(a) (b)

(c) (d)Fig. 3. Normalized participation factor of fundamental mode of vibration of four-story isolated systems: (a) c = 0.89; (b) c = 0.80; (c) c = 0.67; (d) nB = 0.25.

ΓΓ

ξξξξ

ξξξξ

ξξξξ

γγγ

Γ

Γ Γ

(a) (b)

(c) (d)Fig. 4. Normalized participation factor of fundamental mode of vibration of eight-story isolated systems: (a) c = 0.94; (b) c = 0.89; (c) c = 0.80; (d) nB = 0.25.

O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37 29

The spectra included in Figs. 6 and 7 exhibit a large peak in afrequency band located around the fundamental frequency ofvibration of the isolated system. In the particular case of Fig. 6,the spectra exhibit noticeable but smaller response peaks in highfrequencies, which are associated to the upper modes of vibration.While the location of the smaller peaks is fairly independent of nB,their amplitude increases moderately in relative terms with anincrease in nB. The results shown in Fig. 6 are consistent with the

results reported previously by Alhan and Gavin [3] and theparticipation factors shown in Fig. 3 for the fundamental mode ofvibration of four-story isolated systems. Particularly, a larger levelof damping in the isolation system is reflected in a smaller partic-ipation factor for the fundamental mode of vibration, which in turnis reflected in a larger contribution of upper modes.

The comparison of the results shown in Figs. 6 and 7 also allowsfor an understanding of the influence of TB/TS in the dynamic

Table 2Ground motions recorded at the Mexican Pacific Coast.

Station Date MW Component PGA (cm/s/s) Coordinates

Atoyac 9/19/1985 8.1 EW 59.96 17.211�N 100.431�W9/21/1985 7.5 NS 79.66

Aeropuerto Zihuatanejo 9/19/1985 8.1 EW 153.93 17.603�N 101.455�WCaleta 9/19/1985 8.1 EW 140.68 18.073�N 102.755�W

NS 139.73Cayaco 9/19/1985 8.1 EW 48.43 17.045�N 100.266�W

NS 40.889/21/1985 7.5 EW 42.23

NS 58.38Coyuca 9/21/1985 7.5 EW 24.85 16.968�N 100.084�WCerro de piedra 9/21/1985 7.5 EW 11.83 16.769�N 99.633�WOcotito 9/19/1985 8.1 EW 53.22 17.250�N 99.511�WEl Súchil 9/19/1985 8.1 EW 81.45 17.226�N 100.642�W

NS 103.129/21/1985 7.5 EW 72

NS 85.98Unión 9/19/1985 8.1 EW 148.58 17.982�N 101.805�W

NS 165.299/21/1985 7.5 EW 76.98

NS 49.54La Venta 9/21/1985 7.5 EW 19.14 16.923�N 99.8160�W

NS 13.4

ξξξξξξξ

(a) (b)Fig. 5. Mean elastic spectra for ground motions recorded at firm soil sites located at the Mexican Pacific Coast: (a) pseudo-acceleration and (b) pseudo-displacement.

30 O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37

response of isolated systems. The end result of the larger values ofTB/TS under consideration in Fig. 7 is the disappearance of the min-or but well defined peaks located in the higher frequency region.

3.2. Time domain

Although it is not possible to use Absolute Acceleration FloorSpectra to assess the acceleration demands on any type of content,this representation can be useful to develop an understanding ofwhat needs to be done from a structural point of view to controlthe acceleration demands in isolated systems. It should bementioned that Absolute Acceleration Floor Spectra cannot be ap-plied to assess the performance of those contents that are capable,due to their mass and dynamic properties, of dynamically interact-ing with the super-structure to such degree as to modify the globalresponse of the entire isolated system. Within this context, AbsoluteAcceleration Floor Spectra have been observed to provide reasonableestimates of acceleration demands for nonstructural componentswith masses that are much smaller than those of the supportingstructure, and whose frequencies are not close to one of the naturalfrequencies of the structural system [48,49]. Because the use ofthese spectra neglect the dynamic interaction between nonstruc-tural component and structural system, and do not take intoconsideration the out-of-phase components of motion that takeplace in elements with different damping, their use yields overlyconservative acceleration demands for ‘‘resonant’’ components.

According to the observations made by Sankaranarayanan [40]and Sankaranarayanan and Medina [41], three regions of periodcan be considered for Absolute Acceleration Floor Spectra: (A) short;(B) fundamental period (intermediate); and (C) long. As illustratedin Fig. 8a, the first region contemplates nonstructural componentswhose periods are such that the ratio between their period (TC) andTB does not exceed 0.5. The period ratios for the second regionrange from 0.5 to 1.5, and those corresponding to the third regionexceed the value of 1.5. In terms of acceleration-sensitive contents,Hamaguchi et al. [17] observe that a range of TC going from 0 to0.5 s contemplates the most common contents used in buildings.

Figs. 8 and 9 show absolute acceleration and velocity floor spec-tra for the roof motion of four-story isolated systems. The spectra,which were obtained for contents exhibiting 2% of critical damping(nC), represent the mean spectra of those corresponding to allground motions under consideration. Note that the figurescontemplate different values of nB and TB/TS.

Because of the significant participation of upper modes in thedynamic response of flexible super-structures, the accelerationspectra included in Fig. 8 exhibit considerable amplification ofaccelerations in the short period range. Particularly, there aretwo noticeable spectral peaks within this range, which are closelyrelated to the second and third modes of vibration of the isolatedsystem. Although noticeable in the velocity spectra of Fig. 8, theinfluence of upper modes does not seem to define the performanceof the contents in the short period range. In this sense, velocity

(a) (b)

(c) (d)Fig. 6. Fourier Amplitude Spectra of the time-history of absolute roof acceleration in flexible four-story isolated systems: (a) TB/TS = 2.14, TB = 1.50 s, TS = 0.70 s, nB = 0.10; (b)TB/TS = 2.14, TB = 1.50 s, TS = 0.70 s, nB = 0.25; (c) TB/TS = 4.29, TB = 3.00 s, TS = 0.70 s, nB = 0.10; (d) TB/TS = 4.29, TB = 3.00 s, TS = 0.70 s, nB = 0.25.

(a) (b)

(c) (d)Fig. 7. Fourier Amplitude Spectra of the time-history of absolute roof acceleration in stiff four-story isolated systems: (a) TB/TS = 10.00, TB = 1.50 s, TS = 0.15 s, nB = 0.10; (b) TB/TS = 10.00, TB = 1.50 s, TS = 0.15 s, nB = 0.25; (c) TB/TS = 20.00, TB = 3.00 s, TS = 0.15 s, nB = 0.10; (d) TB/TS = 20.00, TB = 3.00 s, TS = 0.15 s, nB = 0.25.

O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37 31

control does not seem to be as critical as acceleration control interms of defining the overall seismic performance of contents.

The results shown in Fig. 9 help understand the consequences ofincreasing the lateral stiffness of the super-structure relative to

ξξξξξ

(A) (B)

(C) (D)Fig. 8. Mean absolute acceleration and mean velocity floor spectra at roof of flexible four-story isolated systems (nC = 2%): (A) TB/TS = 2.14, TB = 1.50 s, TS = 0.70 s; (B) TB/TS = 2.14, TB = 1.50 s, TS = 0.70 s; (C) TB/TS = 4.29, TB = 3.00 s, TS = 0.70 s; (D) TB/TS = 4.29, TB = 3.00 s, TS = 0.70 s.

ξξξξξ

(A) (B)

(C) (D)Fig. 9. Mean absolute acceleration and mean velocity floor spectra at roof of stiff four-story isolated systems (nC = 2%): (A) TB/TS = 10.00, TB = 1.50 s, TS = 0.15 s; (B) TB/TS = 10.00, TB = 1.50 s, TS = 0.15 s; (C) TB/TS = 20.00, TB = 3.00 s, TS = 0.15 s; (D) TB/TS = 20.00, TB = 3.00 s, TS = 0.15 s.

32 O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37

that of the isolation system. In general terms, and in congruencywith the linear theory discussed by Naeim and Kelly [34], it canbe said that the contribution of upper modes to the accelerationdemands on the contents diminishes considerably. While anincrease of nB results in a noticeable reduction of the accelerationdemands in the intermediate range of periods, it may be reflectedin small increments of acceleration in the short range of periods

(which includes the majority of common contents). The resultssummarized in Figs. 8 and 9 emphasize once more that in termsof upper mode control, the ideal situation for an isolated systemcan be formulated in terms of a flexible isolation system integratedwith a very stiff super-structure.

Note that an increase in the level of damping of the isolation sys-tem reduces the response of contents that fall in the intermediate

O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37 33

region of the floor acceleration spectra, and that this increase is notreflected in smaller acceleration demands in the short periodregion. In this sense, an increase in the level of damping of theisolation will be usually detrimental for the seismic performanceof typical contents. This observation is consistent with what hasbeen observed for the acceleration demands on fixed-basedsystems in terms of the ineffectiveness of energy dissipation inreducing acceleration demands in contents located in the shortperiod region [39,15,11]. It is also worthy to note that an increasein the lateral stiffness of the super-structure relative to that of itsisolation system results for a complex multi-degree-of-freedomsystem with multi-peaked floor response spectra (like thosedescribed in Medina et al. [30], Sankaranarayanan and Medina[41], Clayton and Medina [11], and Dowell et al. [15]), to exhibit asingle-degree-of-freedom behavior with single-peak floor spectra(as those described by Lin and Mahin [27] and Igusa [19]).

4. Acceleration ratios

An acceleration ratio can be used to characterize the amplifica-tion of acceleration in a base isolated structure:

Rn ¼maxð€unÞmaxð€uBÞ

ð14Þ

where n is the number of stories of the super-structure; €un repre-sents the time-history of absolute acceleration at the roof level;and €un represents the time-history of absolute acceleration at theisolation (base) level.

Fig. 10a shows acceleration ratios for four-story isolated sys-tems having nB of 10% and c of 0.80. There is a noticeable tendencyfor the median value and dispersion of R4 to decrease with respectto an increase in TB/TS. It can be said that not only does the level ofamplification of motion decreases in the super-structure as its lat-eral stiffness increases, but that a reduction of the effects of upper

(A)

(C)Fig. 10. Acceleration ratio for four-story isolated systems: (A) dispersion for nB = 0.10 ancentral tendencies for c = 0.89.

modes is reflected in a larger certainty in terms of predicting thelevels of acceleration. Fig. 10b–d shows tendencies for the medianvalue of R4. As the value of c increases, the value of R4 tends todecrease for a given value of TB/TS, particularly for small values ofthis period ratio. An increase in nB results in larger values of R4.

The tendencies discussed herein for the acceleration ratio areconsistent with the findings of other researchers. Particularly,while Kulkarni and Jangid [25] comment that an increase in thelateral stiffness of the super-structure is reflected in a noticeabledecrease in peak floor accelerations; Alhan and Sahin [6] observe,in congruency with what is shown in Fig. 10, that the influenceof the super-structure lateral flexibility on peak floor accelerationsbecomes more pronounced as this flexibility increases. Also and incongruency with the tendencies shown in Fig. 10, Alhan and Sahin[6] observe that a significant increase in the lateral stiffness of thesuper-structure results in a fairly uniform pattern for the accelera-tion demand along height that tends to maximize at the roof level.In terms of the uncertainty, the decreasing uncertainty observed inthe estimation of the acceleration ratio with increasing lateral stiff-ness of the super-structure is consistent with the results presentedin Seguin et al. [42].

5. Equivalent system for base-isolated structures

Response spectra are a valuable source of information for theconception of complex earthquake-resistant structures [8,32]. Aslong as the parameter that defines the seismic performance ofthe structure can be estimated reasonably well from its fundamen-tal mode of vibration, a spectrum can be used during the prelimin-ary stages of design to conceive a set of global structural propertiesthat can adequately control the global dynamic response of thestructure. Within this context, it is of interest to compare theresponse of isolated systems with their corresponding spectralordinates to study the possibility of establishing simple accelera-tion-based methodologies for the conception of isolated structures.

(B)

(D)d c = 0.80; (B) central tendencies for c = 0.67; (C) central tendencies for c = 0.80; (D)

(A) (B)Fig. 11. Comparison of mean absolute acceleration demands in four-story isolated structures (c = 0.8) and corresponding mean spectral ordinates: (A) roof and (B) base.

34 O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37

In terms of this paper, the response parameter of interest is themaximum absolute acceleration. Fig. 11 superimposes the maxi-mum absolute roof and base acceleration demands of severalfour-story isolated systems with c of 0.8 and nB of 0.10, to elasticpseudo-acceleration spectra obtained for a percentage of criticaldamping that is equal to the level of damping corresponding tothe isolation system. While the abscissa assigned in the plots tothe absolute roof and base acceleration demands correspond tothe period of vibration of the isolation systems (TB), the spectralordinates as well as the absolute acceleration demands correspondto the mean value of the ordinates and demands, respectively,corresponding to all ground motions under consideration.

It is usually considered that a reasonable estimate for the max-imum absolute acceleration demand in an earthquake-resistantstructure requires from the explicit consideration of at least thefirst three modes of vibration. It is not surprising then that theacceleration demands in Fig. 11 exceed their corresponding spec-tral ordinates. Nevertheless, note that by adequately designingthe stiffness of the super-structure relative to that of the isolationsystem, it is possible to maximize the contribution of the funda-mental mode of vibration to the dynamic response of the isolatedsystems. Under these circumstances, the absolute roof and baseacceleration demands fit well within their corresponding spectra.In these terms, the ideal situation implies a flexible isolation sys-tem with a fairly low level of damping, and a stiff super-structure.To illustrate this, note in Fig. 11 that the acceleration demands thatcorrespond to isolated systems with TB/TS equal or larger than 10(red1 circles), practically fall over their corresponding pseudo-accel-eration spectra. Note that absolute acceleration demands on systemsexhibiting flexible super-structures may move away in a consider-able manner from their corresponding spectra, in such a manner thatan equivalent single-degree-of-freedom system in terms of accelera-tion cannot be formulated for them. Although not illustrated inFig. 11, it was observed that an increase on the level of damping ofthe base isolated system resulted, as a consequence of a larger influ-ence of higher modes, in the absolute acceleration demands to moveaway from their corresponding spectra.

A reasonable estimate of absolute floor acceleration demandsfor contents located in isolated systems whose dynamic responseis dominated by their fundamental mode of vibration can beobtained from a slightly modified version of the direct method dis-cussed by Yasui et al. [50]:

ACðTC ; nCÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½ðTB

TCÞ2SaðTB; nBÞ�2 þ SaðTC ; nCÞ2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ðTB

TCÞ2 þ 4ðnB þ nCÞ2ðTB

TCÞ2

q ð15Þ

1 For interpretation of color in Fig. 11, the reader is referred to the web version ofthis article.

where AC denotes the absolute acceleration demand for a low-damped elastic content; Sa a pseudo-acceleration spectral ordinate;TC and TB the period of the content and the rigid-body mode periodof the base-isolation system, respectively; and nC and nB the damp-ing ratios corresponding to the component and the isolation system,respectively.

Fig. 12 compares the absolute acceleration demands derivedfrom time-history analyses with those estimated with Eq. (15).Different values of TB/TS and nB are considered. As expected, a goodapproximation of acceleration demands is obtained for systemshaving large value of TB/TS. In the case of base isolation systemswith flexible super-structures, TB does not represent a good esti-mate of the fundamental mode of vibration of the entire system,and Eq. (15) underestimates, as shown in Fig. 12c and d, the actualacceleration demands for contents whose period falls in the shortperiod range. The results summarized in Fig. 12a and b confirmsthe fact that a base isolated structural system behaves as asingle-degree-of-freedom system provided the lateral stiffness ofthe super-structure is large enough with respect to that of theisolation system.

6. Discussion

Analytical, experimental and field studies have consistentlyshown the reliability and capability of isolation systems to reducethe dynamic response of earthquake-resistant structures. Damagecontrol in contents is one of the most referred qualities of base iso-lated systems. Nevertheless, it is interesting to note that currently,there is a lack of performance-based formats for the preliminaryquantification of a set of global structural properties for isolatedsystems that can explicitly control their acceleration demandswithin well-defined thresholds. Perhaps one of the main reasonsfor the lack of such formats is that within the capacity-supplyapproach usually used during earthquake-resistant design, thereis not enough information to establish acceleration thresholdsassociated to different performance-levels of different types ofcontents.

In terms of acceleration supply, several studies are currently underway worldwide to understand the capacity of different types of con-tents in terms of accommodating lateral acceleration. The evolutionand maturity of these studies should allow the definition of acceler-ation thresholds in terms of the type of contents and their dynamiccharacteristics. In the meantime, it is important for the communityof structural engineers to work on the acceleration demand part ofthe equation. In these terms and on one hand, research efforts havebeen devoted to estimate the probability of failure of acceleration-sensitive contents housed in base-isolated structures [4]. On theother hand and in the same terms, the results summarized in this pa-per complement those obtained in previous studies [25,6] in such a

(A) (B)

(C) (D)Fig. 12. Comparison of absolute roof acceleration demands for contents with 2% of critical damping: (A) TB/TS = 10.00, TB = 1.50 s, TS = 0.15 s, nB = 0.20; (B) TB/TS = 13.33,TB = 2.00 s, TS = 0.15 s, nB = 0.10; (C) TB/TS = 5.00, TB = 1.50 s, TS = 0.30 s, nB = 0.25; (D) TB/TS = 4.29, TB = 3.00 s, TS = 0.70 s, nB = 0.25.

O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37 35

manner that it is possible to say that, if no other consideration re-stricts the design procedure, the structural properties of the isola-tion system and its super-structure can be established in such away as to control their global and local lateral acceleration demands.Particularly, if the lateral stiffness of the super-structure is properlydesigned with respect to that of the isolation system, the globalstructural properties of an isolation system and its superstructure(TB, nB and TS) can be determined within an acceleration-based for-mat with the aid of: (A) acceleration ratios such as those summa-rized in Fig. 10; (B) pseudo-acceleration spectra corresponding tothe design ground motion; and (C) Eq. (15). A practical accelera-tion-based methodology that conforms to what has been discussedherein is discussed and illustrated by Zuñiga et al. [52].

Although an increase in the level of damping in the isolation sys-tem tends to increment the contribution of upper modes, the use ofstiff structural systems (characterized by values of TB/TS rangingfrom 8 to 10) results in adequate control of upper mode contribu-tion. Note that the limit value of eight is much larger than the limitvalue of three discussed by Naeim and Kelly [34] to promote ade-quate structural and non-structural performance on the super-structure of isolated systems. The use of percentages of criticaldamping in the isolation system that are equal or smaller than 10%reduce the lateral stiffness requirements for the super-structure,in such a manner that values of TB/TS of at least six seem to be suffi-cient in terms of upper mode control. Within this context, it is inter-esting to note that the TB/TS value of five recommended by Kulkarniand Jangid [25] to promote a rigid-body motion of super-structuresisolated with linear isolation systems may not be enough to controlthe acceleration demands in contents located in the short periodrange. Finally and although the mass of a structure cannot be consid-ered a structural design parameter, the results reported herein sug-gest that a reduction of the mass at the isolation level with respect tothat of the super-structure usually leads to a reduction in the contri-bution of upper modes. In very simple terms, it can be said thatflexible isolation systems with low levels of damping coupled with

stiff super-structures result in substantial reductions of the partici-pation of upper modes to the global response of isolated structures.Within this context, it is possible to formulate a simple model forbase-isolated systems that would allow for the acceleration-basedconception of its global structural properties. Once these propertieshave been determined, they can be used, as discussed and illustratedby Zuñiga et al. [52], for the local sizing and design of the isolatorsand the structural elements of the super-structure.

In many cases, the displacement demand at the base of anisolation system does not define its seismic design. Take the caseof the Mexican Pacific Coast; studies carried out so far suggest thatthe largest displacement demands at the base of isolated structuresshould not exceed 25–30 cm (even for low levels of damping, asillustrated in Fig. 5b). Nevertheless, under certain circumstances,the lateral displacement in the isolators may be the defining aspectduring their seismic design and in this case, a compromise shouldbe taken between displacement control at the base and accelera-tion control in the super-structure. Current studies are underwayto establish the possibility for ground motions generated at theMexican Pacific to exhibit directivity effects.

It should be emphasized that providing low-rise structures withthe TB/TS values required for upper mode control should not be apractical problem. For instance, consider an isolation system withTB equal to 3.0 s. In terms of the threshold of eight discussed beforefor TB/TS, this would imply a TS equal to 0.375 s, which should notrepresent a problem for a low-rise structure. In case of taller orslender structures, careful considerations should be made toprovide stiff planes to reduce the period of the super-structure.Nevertheless and according to the linear theory discussed byNaeim and Kelly [34], the increased stiffness of the super-structureshould result in a considerably reduction in terms of its strengthand displacement demands. Thus, unlike what would be expectedin a fixed-based structure, careful addition of stiff elements to thesuper-structure of an isolated system may not result in excessiveconcentration of overturning moment in individual isolators.

36 O. Zuniga-Cuevas, A. Teran-Gilmore / Engineering Structures 53 (2013) 25–37

Another issue to emphasize is the fact that a reduction in uppermode effects results in predictable behavior of the super-structurein terms of its acceleration demands. Thus, not only are the accel-eration demands smaller, but the large uncertainty and complexityobserved in these demands on fixed-based systems are practicallyreduced to provide, through the use of an pseudo-accelerationspectrum, a reasonable estimate of the acceleration demand atthe base of the isolated structure.

Although not illustrated herein, there is ample evidence thatpassive nonlinear base isolation systems exhibit larger accelerationdemands than linear ones, and this is particularly true for tradi-tional sliding devices [25,6]. Also, some authors have discussedthe possibility of controlling the acceleration demands in flexiblebase isolated super-structures through providing them directlywith small amounts of added damping [6]. Finally, it should bementioned that innovative isolation systems have been developedto efficiently reduce acceleration demands in structures[20,51,5,33,16]. These active and intelligent isolation systems havebeen shown to reduce acceleration demands well beyond the capa-bilities of passive isolation systems (as the one under considerationin this paper). In this respect, it should be mentioned that the stud-ies summarized herein are part of an effort to implement low-costisolation systems in public medical facilities located in the MexicanPacific. Within this context, the use of simple rubber-based isola-tion systems has been considered a priority. Nevertheless, underthe consideration that a stiff enough super-structure reduces theeffects of upper modes, the conceptual framework discussed in thispaper can be easily adapted to any type of isolation system.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in theonline version, at http://dx.doi.org/10.1016/j.engstruct.2013.03.012.

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