SEISMIC DESIGN OF SECONDARY STRUCTURES: STATE OF THE ART

By Roberto Villaverde, l Member, ASCE

ABSTRACT: The developments in the last three decades in the area of seismic design of mechanical andelectrical equipment, architectural components, as well as other secondary structures and nonstructural compo­nents. attached to the floors, roof, and walls of buildings are reviewed here. A description is made of whatconstitutes a secondary structure, the characteristics that make these systems particularly susceptible to the effectsof earthquakes, an~ the par~eters that af~ect t.heir response to earthquakes. The methods that have been pro­posed and are avatlable to Improve and slmphfy the analysis of this type of structure, the methods that arecurrently use~ as refl~cted by various ~uildin.g codes and seismic provisions, and the experimental studies andfield observ~ttons carned out to further IOvestigate some of their dynamic properties and response characteristicsare also reviewed here. The paper closes with a summary of what research is still needed to advance currenteff~rts to protect .these sys~ems against the effects of earthquakes and to develop methods and techniques toachieve thIS goal 10 a practIcal and economical way.

INTRODUCTION

Secondary structures are those systems and elements housedor attached to the floors, roof, and walls of a building or in­dustrial facility that are not part of the main or intended load­bearing structural system for the building or industrial facility,but may also be subjected to large seismic forces and mustdepend on their own structural characteristics to resist theseforces. In general, these secondary structures may be classifiedinto three broad categories: (1) Architectural components; (2)mechanical and electrical equipment; and (3) building con­tents. Examples in the first category are elevator penthouses,stairways, partitions, parapets, heliports, cladding systems,signboards, lighting systems, and suspended ceilings. Someexamples in the second category are storage tanks, pressurevessels, piping systems, ducts, escalators, smokestacks, anten­nas, cranes, radars and object-tracking devices, computer-anddata-acquisition systems, control panels, transformers, switch­gears, emergency power systems, fire protection systems, boil­ers, heat exchangers, chillers, cooling towers, and machinerysuch as pumps, turbines, generators, engines, and motors.So~e examples in the third category include bookshelves, filecabmets, storage racks, decorative items, and any other pieceof furniture commonly found in office buildings and ware­houses. Alternative names by which these systems are alsoknown are "nonstructural components," "nonstructural ele­ments," "building attachments," "architectural, mechanical,and electrical elements," "secondary systems," and "second­ary structural elements."

In spite of their name, secondary structures are far frombeing secondary in importance. It is now widely recognizedthat the survival of secondary structures is essential to provideemergency and recovery services in the aftermath of an earth­quake. Experience from earthquakes has shown that the failureof equipment, and the debris caused by falling objects andoverturned furniture, may critically affect the performance ofvital facilities such as fire and police stations, emergency com­mand centers, communication facilities, power stations, water~upply and treatment plants, and hospitals. For example, dur­109 the 1994 Northridge earthquake in the Los Angeles, Calif.,area, several major hospitals had to be evacuated. This wasnot because of structural damage, but because of the waterdamage caused by the failure of water lines and water supply

'Prof., Civ. Engrg. Dept., University of California, Irvine, CA 92697.Note. Associate Editor: Chia-Ming Uang. Discussion open until Jan­

uary I, 1998. T? extend the closing date one month, a written requestm~st be filed WIth the ASCE Manager of Journals. The manuscript forthIS paper wa~ sUbmitt~d for review and possible publication on February20, 1996. ThIS paper IS part of the ]ourlUll of Structural EngineeringVol. 123, No.8, August, 1997. ©ASCE, ISSN 0733-9445197/oo08~1011-1019/$4.00 + $.50 per page. Paper No. 12654.

tanks; the failure of emergency power systems and heating,ventilation, and air conditioning units; damage to suspendedceilings and light fixtures; and some broken windows (Hall1994, 1995).

It is also recognized that damage to secondary structuresrepre~ents a threat to life, may seriously impair a building'sfunction, and may result in major direct and indirect economiclo~s~s. Clearly, ~h.e collapse of suspended light fixtures, hungcelhngs, or partItIOn walls; the plunging onto the ground offailed cladding panels, parapets, signboards, ornaments, orglass panels; the overturning of heavy equipment, book­shelves, storage racks, or pieces of furniture; and the ruptureof pipes or containers with toxic materials are all capable ofcausing serious injury or death. A most unfortunate case inpoint is the death of a student, who, during the 1987 WhittierNarrows earthquake in California, was struck by a falling pre­cast panel while walking out of a parking structure (Taly1988). Likewise, it is easy to see that the normal activities ina building may be critically disrupted when some essentialequipment fails or when debris from failed architectural com­ponents obstruct living and working areas. Examples that il­lustrate the consequences of such an event are the unwantedsolidification of melted metal in an industrial facility, the in­acces~ibility of financial records in a banking institution, andthe fal~ure to fill pending orders in a manufacturing plant. Fi­nally, 10 regard to the economic impact caused by the failureof nonstructural components, evidence from earthquakes hasrepeatedly shown that the cost associated with the loss of thenonstructural components themselves, the loss of inventory,and the loss of business income may easily exceed the replace­ment cost of the building that houses those nonstructural com­ponents (NonstructuraI1984). And in today's high-technologyenvironment, it is likely that such cost may be exacerbated asa r~sult of the widespread use of electronic and computerequipment and the dependence of industry on this type ofequipment. It is thus clear that secondary structures should bethe subject of a rational and careful seismic design (in muchthe same way as their supporting structures) and should be thecontinuing object of a careful performance assessment follow­ing strong earthquakes.

GENERAL PHYSICAL CHARACTERISTICS

Some secondary structural elements have an insignificantlysmall mass, are exceptionally rigid, or are hinged-connectedto their supporting structure (Le., hung from above). These~ypes of secondary elements, therefore, are usually not signif­Icantly affected by earthquake ground motions. Many others,~0.wever, possess several of the following physical character­IStiCS that make them particularly susceptible to the effects ofearthquakes:

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1. They are usually attached to the elevated portions of abuilding, and thus they are subjected not to the groundmotion generated by an earthquake, but to the amplifiedmotion generated by the dynamic response of the build­ing.

2. Their weight is light in comparison with that of the struc­ture to which they are connected, and their stiffness isalso much smaller than that of the structure as a whole.As a result, some of their natural frequencies are oftenequal, or nearly equal, to the natural frequencies of thestructure. Hence, their dynamic response to the motionat their supports may be extraordinarily high.

3. Their damping ratios may be quite low, much lower thanthose for the structure, and thus they do not possess thedamping characteristics that are necessary for their pro­tection against sharp resonant motions.

4. They may be connected to the structure at more than onepoint and, hence, may be subjected to the distortions in­duced by the differential motion of their supports.

5. They are often designed to perform a function other thanto resist forces. As such, they are built with materialsthat are far from the ideal materials to resist seismicforces and may possess parts that are sensitive to eventhe smallest level of vibration.

GENERAL RESPONSE CHARACTERISTICS

The special physical characteristics described make second­ary structural elements not only susceptible to earthquakedamage, but also make their response to earthquake groundmotions unique and different from that of a building structure.That is, the response of a secondary structural element exhibitscharacteristics that are not common in the response of a struc­ture; following are some of these characteristics:

1. The response of a secondary element depends on theresponse of the structure to which it is connected, andthus it depends not only on the characteristics of theground motion that excite the base of the structure, butalso on the dynamic characteristics of the structure.

2. The response of a secondary element depends on its lo­cation within the structure. As a result, identical elementsrespond differently to the effects of an earthquake if theyare located on different floors of the structure.

3. The motion of a secondary element may modify the mo­tion of its supporting structure, which in turn may mod­ify the response of the secondary element itself. That is,there may be a significant interaction between a second­ary element and its supporting structure. In such cases,therefore, one cannot predict the response of the second­ary element without knowing in advance the dynamicproperties of both the secondary element and the struc­ture.

4. When the secondary element is connected to the structureat more than one point, the element's supports are ex­cited by motions that are different and out of phase.

5. Since the damping in the secondary element is usuallymuch lower than the damping in the structure, the damp­ing in the system formed by the structure and its sec­ondary elements, which is the system that characterizesthe response of the secondary elements, is not uniform.This means that the response of the secondary elementis governed by the response of a system whose naturalfrequencies and mode shapes are complex valued. Thatis, the response of a system without classical modes ofvibration.

6. Since, as mentioned earlier, some of the natural frequen­cies of a secondary element may be close in value tothose of its supporting structure, the combined structure-

10121 JOURNAL OF STRUCTURAL ENGINEERING 1AUGUST 1997

secondary element system may result in a system withclosely spaced natural frequencies. As such, the responseof a secondary element may be controlled by its responsein two or more of its modes of vibration, as opposed tojust a single mode, as is common for structures.

7. The response of a secondary structural element is af­fected by its own inelastic behavior as well as that of itssupporting structure.

METHODS OF ANALYSIS: HISTORICALPERSPECTIVE

A great deal of research effort has been devoted over thepast 30 years to the development of rational methods for theseismic analysis of secondary structures. For the most part,however, this effort has been driven by the need to guaranteethe survivability of critical equipment such as piping and con­trol systems in nuclear power plants. Therefore, these methodshave been successfully applied in the analysis of such facilitiesbut have not been used extensively for the analysis of ordinarysecondary elements in conventional buildings. Notwithstand­ing this fact, many methods of analysis have been proposedas a result of this research effort, some of them with a strongempirical base and others based on rigorous principles ofstructural dynamics.

In the development of methods for their analysis, it is gen­erally recognized that secondary structures are difficult to an­alyze accurately and efficiently. It is always possible to con­sider them in conjunction with the analysis of their supportingprimary structures, but a combined primary-secondary systemgenerally results in a system with an excessive number of de­grees of freedom and a large difference in the values of itsvarious masses, stiffnesses, and damping constants. Such char­acteristics usually render conventional methods of analysis ex­pensive, inaccurate, and inefficient. For example, a modalanalysis presents difficulties in the computation of natural fre­quencies and mode shapes; a step-by-step integration methodbecomes extraordinarily sensitive to the selected integrationtime step; and a random vibration approach turns out to beparticularly susceptible to the assumptions made about sta­tionarity and earthquake duration in the probabilistic modeladopted. Furthermore, such an approach is impractical since,during the preliminary design of the secondary structure, theprimary structure would have to be reanalyzed every time achange is introduced in one of the parameters of the secondaryelements. Considering that primary and secondary structuresnormally are designed by different teams at different times,this would result in serious problems of schedule and effi­ciency in the design process. Thus, most of the proposed meth­ods have been the result of an effort to avoid the analysis ofa combined primary-secondary system and to overcome theaforementioned difficulties.

One of the simplified methods first used in the analysis ofsecondary structures is the so-called systems-in-cascade, orfloor response spectrum, method. In this method, the acceler­ation time history of the point or floor of the structure to whichthe secondary structure is attached is determined by means ofa step-by-step integration with a recorded time history or asynthetic one consistent with a given ground response spec­trum. Then, this in-structure acceleration time history is usedto generate a response spectrum-that is, a floor responsespectrum or in-structure spectrum, which in turn is used asinput to carry out a response spectrum analysis of the second­ary system in much the same way a primary structure may beanalyzed using a ground response spectrum. Although simplein concept and somewhat rational, this method was quicklyrecognized to be impractical since it requires lengthy numer­ical integrations. For this reason, several methods were pro­posed to generate floor response spectra directly from a spec-

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Hied ground response spectrum, or design spectrum, withoututilizing a time-history analysis. These methods use as inputa specified ground response spectrum and the dynamic prop­erties of the structure. Examples are the methods proposed byBiggs and Roesset (1970), Amin et al. (1971), Kapur and Shao(1973), Peters et al. (1977), Vanmarcke (1977), Atalik (1978),and Singh (1980).

Floor response spectrum methods have been proven accu­rate for secondary elements whose masses are much smallerthan the masses of the supporting structure and whose naturalfrequencies are not too close to the natural frequency of thestructure. However, these methods may yield overly conser­vative results for secondary elements that do not have suchcharacteristics [Toro et al. (1989) report that errors may besignificant when secondary to primary mass ratios are greaterthan 1O-3J. The reason for this conservatism is that, by con­sidering a secondary element separately from its supportingstructure, floor response spectrum methods neglect the dy­namic interaction between the primary and secondary systems.That is, they do not account for the fact that the response ofthe secondary system may modify the response of the sup­porting structure and vice versa. An additional reason is thatfloor response spectrum methods cannot take into considera­tion the fact that the masses of the primary and secondarysystems vibrate out of phase, which results from the fact that,in general, a combined primary-secondary system does notpossess classical modes of vibration and cannot be assumedto do so without introducing a significant error. There is nowample analytical evidence that demonstrates that ignoringthese two effects may indeed lead to gross errors in the cal­culation of some secondary systems' responses [refer, for ex­ample, to Igusa and Der Kiureghian (1985a), and Chen andSoong (1988)].

Another problem with floor response spectrum methods isthat they cannot be rationally applied for the analysis of asecondary structure with multiple points of attachment (Wanget al. 1983). This is because these methods cannot realisticallytake into account the fact that each of the supports of such asecondary structure is subjected to a different, and out-of­phase, motion. Attempts have been made to overcome thisproblem, but for the most part these attempts have been in theform of empirical or ad-hoc procedures. For example, it hasbeen proposed to determine the maximum response of a mul­tiply supported secondary system on the basis of the floorspectra obtained for each of its supports as follows. First, thesystem is analyzed using each of these floor spectra as theearthquake input (one at a time) to obtain a series of esti­mates of the system's maximum response. Then these esti­mates are combined in an empirical way to calculate the sys­tem's true maximum response (Shaw 1975; Thailer 1976).Common among these empirical procedures is the selection ofthe largest of all the maximum response estimates, or the com­bination of them on the basis of the square root of the sum oftheir squares. Other techniques use a spectrum obtained byenveloping all the floor spectra corresponding to the secondarysystem's supports, or that of including a "pseudostatic" com­ponent of the response, determined in terms of the differencebetween the peak displacements at the various attachmentpoints. It is now recognized, nevertheless, that these tech­niques are often too crude and may lead in some cases tooverconservative results.

In view of the limitations of the floor response spectrummethods and the impracticality of a direct analysis of a com­bined primary-secondary system, several alternative methodshave been developed that not only take into account the afore­mentioned effects, but also overcome the practicality problemsassociated with a direct analysis of the combined system. Ingeneral, two approaches have been followed. In one of these

approaches, in recognition of the convenience and flexibilityof the floor response spectrum method and its wide use in thenuclear power industry, corrections are introduced to thismethod to account (in an approximate manner) for the inter­action between the primary and secondary subsystems and theout-of-phase support motions. Examples of these methods arethose proposed by Lee and Penzien (1983), Igusa and DerKiureghian (1985b), Singh and Sharma (1985), Asfura andDer Kiureghian (1986), Gupta and Jaw (1986), Burdisso andSingh (1987), and Suarez and Singh (1987a). In the other ap­proach, the response of the secondary structure is obtained onthe basis of an approximate modal or random vibration anal­ysis of the combined primary-secondary system, but using,through a modal synthesis, the dynamic properties of its sep­arate components. This approach eliminates the main sourceof error inherent in the floor response spectrum method since,by considering the two subsystems together as a single unit,the interaction between the two subsystems and the differentand out-phase support motions are implicitly taken into ac­count. This approach is also a practical one. By formulatingthe analysis in terms of the dynamic properties of independentprimary and secondary systems, one avoids the numerical dif­ficulties associated with the large difference in the values ofparameters of the primary and secondary systems when con­ventional methods of analysis are used. Furthermore, oneavoids the solution of large eigenvalue problems, the need togenerate intermediary floor response spectra (since the earth­quake input is defined at the ground level), and the need toreanalyze the structure every time the parameters of the sec­ondary system are changed.

Conceptually, the idea of determining the response of a sec­ondary element in terms of an analysis of the compound sys­tem it forms with its supporting structure, but utilizing onlythe properties of the individual components, is a simple one.Its implementation, however, is not free of complications anddifficulties. For example, if one wants to analyze such a com­pound system by means of the response spectrum method, oneneeds to determine first its natural frequencies, mode shapes,damping ratios, and maximum modal responses. Then, oneneeds to combine these modal responses using a modal com­bination rule. However, the system that results from combiningtwo structures with such a drastic difference in the values oftheir masses, stiffnesses, and damping constants is a systemwithout classical modes of vibration and with closely spacednatural frequencies. This means that the natural frequenciesand mode shapes of the system are complex-valued and thatthe combination of its modal responses requires, and highlydepends on, an accurate rule to combine the modal responsesof a system with nonclassical damping and closely spaced nat­ural frequencies. Notwithstanding such difficulties and com­plications, several methods that use this technique have beenproposed throughout the years-methods that basically differin the way the dynamic properties of the components are syn­thesized in order to obtain the dynamic properties of the com­bined system, and in the assumptions made to simplify theprocedure. In chronological order, some of these methods arethose suggested by Newmark (1972), Sackman and Kelly(1979), Newmark and Villaverde (1980), Der Kiureghian et al.(1983), Hernried and Sackman (1984), Gupta (1984), Igusaand Der Kiureghian (1985c), Villaverde (1986), Suarez andSingh (1987b), Muscolino (1990), and Villaverde (1991).

All the methods referred to have been derived specificallyfor linear secondary systems mounted on linear primary struc­tures without due consideration to the fact that most of thestructures to which secondary systems are attached are de­signed to yield under the effects of a strong earthquake, andthat the secondary systems themselves or their anchors are alsocapable of resisting large inelastic deformations. However, as

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pointed out by Lin and Mahin (1985), Aziz and Ghobarah(~988), Toro et at. (1989), Sewell et at. (1989), Igusa (1990),Smg~ et at. (1993), and Schroeder and Backman (1994), thenonhn~ar .behavior of the structure and the secondary systemmay slgmficantly affect the behavior of the latter, in somecases in the form of a significant reduction over its linear re­sponse, and in other cases in the form of an increase. Thosemethods, therefore, may lead to either nonconservative or un­economical designs. On recognizing the importance of suchnonlinear behavior, a few investigators have made an effort tode;ive simplified methods that incorporate the nonlinearity ofpnmary and secondary structures. However, given the diffi­culties in obtaining explicit solutions for such a complex prob­lem, most of the effort has been directed towards the devel­~pment of reduction and amplification factors by which ahnear floor spectrum may be modified to approximately takeinto account the nonlinearity of a supporting structure (Ka­wakatsu et al. 1979, Lin and Mahin 1985, Viti et at. 1981).Some exceptions are the works of Villaverde (1987) and Igusa(1990). Villaverde (1987) develops a method based on the useof inelastic ground response spectra for the analysis of linearmulti-degree-of-freedom secondary systems mounted on anelastoplastic multi-degree-of-freedom primary structure. Igusa(1990) derives an analytical solution for the response of atwo-degree-of-freedom primary-secondary system with smallnonlinearities using random vibration theory and equivalentlinearization techniques.

Current methods of analysis also include those that, albeitin a limited way, properly account for the influence of a sec­ondary system on the response of another secondary systemsupported by the same structure but at a different location, andfor t~e torsional response of the structure in the case of asym­metric structures. Observing that when a building has morethan one secondary system attached to it each secondary sys­tem may influence the response of the structure and thus, in­directly, the response of all the other secondary systems,Suarez and Singh (1989) proposed a procedure to calculate themodal properties of a primary structure that supports two sec­ondary systems. Similarly, recognizing that the torsional re­sponse of the structure may be an important factor that maysignificantly increase the response of a secondary system ifthis system is connected to a structure with significant tor­sional modes, Yang and Huang (1993) proposed a simplifiedmethod to compute the seismic response of a secondary systemin such a case. Their method, however, is limited to linearprimary-secondary systems with classical damping and to thecase of floor eccentricities in only one direction.

Finally, it is worth mentioning that, just recently, three code­and design-oriented simplified methods have been proposedby Soong et at. (1993), Singh et at. (1993), and Villaverde(1997). These design-oriented methods represent an importanteffort towards the development of methods of analysis that,on one hand, incorporate the current level of understandingwith regard to the seismic behavior of the secondary elementsunder consideration, but, on the other, are adequately simplefor design purposes and for their incorporation into buildingcodes.

For a detailed description of the difference between themethods of analysis cited, the reader is referred to the excellentstate-of-the-art reviews by Chen and Soong (1988), Singh(1990), and Soong (1994).

DESIGN PROVISIONS IN BUILDING CODES

Overview

Several building codes and seismic provisions give recom­mendations for the seismic design of equipment and other sec­ondary structural elements. In the United States, some of these

1014/ JOURNAL OF STRUCTURAL ENGINEERING / AUGUST 1997

include. the Uniform Building Code (UBC) (Uniform 1994);the ~~tlOnal Earthquake Hazard Reduction Program (NEHRP)provlslOns (1995); the Recommended Lateral Force Require­ments a~ Co~entary (1990); and the American Society ofMechamcal Engmeers (ASME) boiler and pressure vessel code(ASME, 1993). Only the provisions in the UBC and NEHRPcodes will be discussed here. The UBC is selected for thediscussion because it is well-known worldwide. Similarly the!'lEHRP provisions are selected because they have rec~ntlymcorporated a set of modern and comprehensive recommen­dations that are more rational than those in most other codes.

Uniform BUilding Code

The UBC requires that elements of structures (e.g., infillwalls, penthouses, diaphragms), permanent nonstructural com­ponents, and the attachments (e.g., connections and anchor­ages) for permanent equipment supported by a structure bedesigned to resist at least the lateral seismic force calculatedfrom the following

Fp =ZIpCpWp (1)

where Z = a zon~ factor, which essentially represents the peakground acceleratlOn expected at the site under consideration in~n average recurrence .interval of 475 years; lp = an equipmentImportance factor, which is set equal to 1.0 and 1.5 for ordi­nary and critical components, respectively; and W = totalweight of the component. Cp is a coefficient specifi:d by thecode, which varies from 0.75 to 2.0 depending on the type ofcomponent or equipment, and is intended to account for thedyn~ic amplification of the ground motion by the buildingfor Items located above grade. The equation is intended foruse in conjunction with working stress design principles.~h~ values of Cp that are explicitly given by the code apply

to ngld ele.ments and components and to rigid or rigidly sup­ported equipment. For that purpose, the code defines a rigidcomponent or element and a rigid or rigidly supported equip­ment as those having a fundamental period that is less than orequal to 0.6 s. In the absence of a dynamic analysis or em­piric,,:l data, the code recommends use of a value of Cp equalto tWice the values specified for rigid components and rigidlysupported equipment for the design of nonrigid componentsand flexibly supported equipment located above grade, exceptthat the value of Cp need not exceed 2.0. Another exceptionis in the design of ductile piping, ducting, and conduit systems,for which the Cp values given for rigid components may beused.

The code also requires that, for the design of equipment,structural elements, and nonstructural elements, the relativemotion between the points of the structure to which they areattached be considered. It does not specify, however, how totake this effect into account.

As seen, the approach used by the UBC for the seismicdesign of secondary structural elements is largely empiricaland judgmental, and is not based on formal principles of struc­tural dynamics. The specified values of Cp are set primarilyby (1) examining the performance of nonstructural compo­nents in past earthquakes; (2) using the results from the anal­ysis of some linear multistory buildings, which show that floorto ground acceleration factors usually vary between 1.6 and2.3; and (3) considering inherent inelastic behavior as anadditional capacity in reserve (Porush 1990). It does not ex­plicitly account for the dynamic interaction between the com­ponent and its supporting structure, the location of the com­ponents within the building, the way the component is con­nectedto the building, the tuning or detuning of thecomponent to the natural frequencies of the structure, the dif­ferential motion between the component supports, and theyielding of the structure.

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where

1994 NEHRP Provisions grade of component supports at levels x, y; aaA, aaB = allow­able story drifts for buildings A, B; and hsx = story height. Theequations in terms of the allowable interstory drifts are pro­vided in recognition of the fact that the building displacementsmay not be available at the time the component is designed.The provisions require that nonstructural components be de­signed to resist the relative displacements determined fromthese equations when they are combined with the effects ofother displacements, such as those generated by thermal andstatic loads.

The foregoing equations take into account the expectedground motion amplification at those points of the structurethat are above grade, the location of the component within thestructure, the amplification of floor motion associated with thedynamic characteristics of the component, the ductility andenergy-absorption capabilities of the component, and the per­formance expectations of the component. As such, these equa­tions explicitly incorporate many of the factors that mayinfluence the seismic behavior of nonstructural components onbuildings and are, thus, more discriminating than, and a sig­nificant improvement over, their counterparts in other buildingcodes (VBC included). Notwithstanding this improvement, theNEHRP provisions still have some limitations. For example,the given equations are expressed in terms of two separate andindependent amplification factors. One factor accounts for theground motion amplification by the structure at the locationwhere the component is attached to the structure, and the otherfor amplification by the component of the motion at this lo­cation. Consequently, the equations do not fully consider theinteraction between the structure and the component. Simi­larly, the provisions give two separate sets of equations, oneto compute the maximum forces and the other to compute themaximum relative displacements between the component's at­tachment points. The effect of these forces and that of theserelative displacements on the structure are intended to beadded directly. This procedure implies that these two maxi­mum effects occur simultaneously, which is an assumption thatin most cases leads to overly conservative results. Anotherlimitation pertains to the recommended amplification factors.A factor of 2.0 is proposed for the structural amplification anda maximum of 2.5 for the component amplification. These aread-hoc factors that are justified on the basis of limited ex­perimental results and observations from past earthquakes(Soong et al. 1993), but lack a theoretical basis. Furthermore,when combined, these factors give a maximum amplificationfactor of 5.0, which, when compared with those that are the­oretically possible (Villaverde 1997), may not be sufficientlylarge to cover all cases. To make matters worse, the provisionsexplicitly account for component yielding to reduce the mag­nitude of a component's design forces, and thus the inelasticbehavior of the component cannot be used as a reserve capac­ity to resist forces that exceed those of the design. Finally, therecommended equations do not account for the yielding of thestructure. Although it is recognized that in many cases thedesign of a structure is governed by drift limits or other loads,and that for the purpose of nonstructural component design itis difficult to define the magnitude of the forces that in actu­ality make a structure yield, it is also recognized that structuralyielding may significantly affect the magnitude of the seismicforces that act on a component, and that some localized yield­ing will always occur whenever the structure is subjected toan earthquake ground motion comparable in size to that con­sidered in its design. Structural yielding is, therefore, an im­portant parameter that should be considered explicitly in theseismic design of nonstructural components.

EXPERIMENTAL STUDIES AND FIELDOBSERVATIONS

In contrast to the vast analytical work, experimental testsand field observations of secondary structural elements appear

(3)

(5)

(2)

As = 1.2CJT'lJ3 =:;; 2.5Ca

The NEHRP provisions are based on ultimate strength de­sign principles and establish, as the VBC recommendationsdo, minimum design criteria for architectural, mechanical, andelectrical systems; nonstructural components and elements per­manently attached to buildings; and their supporting systemsand attachments. These design criteria are presented in termsof a required minimum equivalent static force and a minimumrelative displacement demand when the component is con­nected to the structure at multiple points.

To determine the required minimum static force, the pro­visions provide two alternative equations. The first one is con­servative but simple and easy to apply. The form of this equa­tion is as follows:

Ap = Ca + (A r - Ca)(xlh) (4)

in which A r = (2.0A s ) =:;; 4.0Ca ).

In the foregoing equations, Fp = seismic design force ap­plied at the component's center of gravity vertically, laterally,or longitudinally, in combination with the dead and live loadsacting on the component; ap = component amplification factorspecified in the provisions according to component type (var­ies between 1.0 and 2.5); Ap = acceleration (expressed as afraction of gravity) at the point of attachment to the structure;lp = component importance factor specified in the provisionsaccording to component type (equal to either 1.0 or 1.5); Wp

= component operating weight; Rp = component responsemodification factor specified according to component type(varies between 1.5 and 6.0); Ca = seismic coefficient (ex­pressed as a fraction of gravity) specified for the design of thestructure (Le., effective peak ground acceleration); Ar = accel­eration (expressed as a fraction of gravity) at the structure'sroof level; As = structural response acceleration coefficient(Le., ground response spectrum ordinate), expressed as a frac­tion of gravity, and given by

The other equation is more complex, as it takes more factorsinto account, but it generally leads to smaller forces and isgiven by

in which Cv = velocity-related effective ground acceleration(expressed as a fraction of gravity) specified for structural de­sign; and T = effective fundamental period of the structure.

To determine the required minimum relative displacementdemand between two of the connection points of a nonstruc­tural component with multiple connection points-such ascladding, stairwells, windows, ducts, and piping systems-theprovisions recommend use of the smaller of the values ob­tained from the following two equations:

Dp =8xA - 8yA; Dp =(X - Y)AaAlhsx (6,7)

For nonstructural components with connection points on sep­arate structures or buildings, the corresponding two equationsare

Dp = 18xA I + /8,\'B I; Dp = XAaAlhsx + YAaB/hsx (8, 9)

In these and the foregoing equations, Dp = relative seismicdisplacement between component supports; 8xA, 8yAo 8xB , 8YB =deflections of building under design forces, multiplied by anamplification factor to account for inelastic deformations, atbuilding levels x, y of buildings A, B; X, Y = heights above

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scarce. Many experimental tests have been conducted and re­ported to qualify equipment and other nonstructural elements,but only a few have been perfonned either to further investi­gate their seismic behavior when mounted on a structure or toverify the findings from analytical investigations. In general,the experimental work reported in the literature consists ofeither the testing of secondary elements mounted on a primarystructure to analyze their behavior or the testing of the sec­ondary elements by themselves to investigate their dynamicproperties and load capacity.

Within the first category are the tests carried out by Kellyand Tsai (1985), Japan's Building Research Institute (Wang1987), Nims and Kelly (1990), Juhn et al. (1990), and Japan'sNuclear Power Engineering Center (Ohtani et al. 1992). Abrief summary of these tests follows:

Test by Kelly and Tsai (1985)

In this test the researchers investigate, among several otherthings, the response of light equipment in structures isolatedusing rubber bearings and compare it against the equipment'sresponse in a fixed-base system. For that purpose, three oscil­lators representing pieces of light equipment were attached tothe fifth floor of a one-third-scale, five-story frame mountedon four rubber, or lead-rubber, isolators. The total mass of thestructure with the added masses was 36,320 kg. Three isolatorswere used. Their masses were 36, 18, and 9 kg and they weretuned to the fundamental natural frequency of the fixed frame,the second natural frequency of the base-isolated frame, andthe third natural frequency of the base-isolated frame, respec­tively.

Test by Japan's Building Research Institute(Wang 1987)

In this experiment, conducted under the auspices of theU.S.-Japan Cooperative Research Program, a full-scale, three­dimensional frame with a full-scale cladding system was testedto observe the behavior of cladding systems and their connec­tions. The frame had six stories, a total height of 22.38 m, anda 15 X 15 m plan, with two equal bays in each direction. Thecladding system consisted of precast concrete and fiber-rein­forced glass panels with a variety of sway-type connections.The tests were carried out under static loading, free vibrations,and forced vibrations. In the test under static load, the framewas defonned up to story drifts of 1/40.

Test by Nims and Kelly (1990)

In this test a piping system was mounted on two indepen­dent full-scale steel frames and tested, together with theframes, on a shaking table. One of the frames had a single bayand three stories, with a total height of 5.28 m and a planearea of 3.66 X 1.83 m. The other frame had three bays andfour stories, with a total height of 4.27 m and a plane area of5.49 X 1.83 m. The piping system, configured to represent atypical one in a nuclear power plant, was approximately 30.5m long. It was made of pipes 51 and 76 mm in diameter andmounted on seven rigid supports and five restraining devices.The test was perfonned to evaluate the perfonnance of threetypes of restraining devices (snubbers, seismic stops, and en­ergy dissipating restraints), but also served to study the inter­action between the piping system and the frames.

Test by Juhn et al. (1990)

This test consisted of a shaking table experiment with asecondary system in the fonn of an inverted pendulum at­tached to the second story of a quarter-scale, three-story, fixed­base steel frame. The secondary system had a mass equal to

10161 JOURNAL OF STRUCTURAL ENGINEERING 1AUGUST 1997

1/10 the mass of its supporting floor. Both tuned and detunedcases were considered. The excitations considered were timehistories representing a white-noise process and a scaled ver­sion of a recorded earthquake ground motion. The tests wereconducted to obtain experimental evidence on the behavior ofsecondary systems mounted on a seismically excited structure,and to verify the results of a proposed analytical method ofgenerating floor response spectra.

Tests by Japan's Nuclear Power Engineering Center(Ohtani et at 1992)

These tests involved a series of shaking table experimentswith full-scale, or close to full-scale, models of critical equip­ment in nuclear power plants. These tests were conducted atthe 1,0OO-t shaking table at Tadotsu Engineering Laboratoryin Shikoku Island. They were part of a program started in 1982to confinn the integrity of critical equipment in nuclear powerplants, and to validate the methods used for their seismic de­sign. The tests were reported in a series of papers presentedat the Tenth World Conference on Earthquake Engineering[see, e.g., Ohtani et al. (1992)].

The second category of tests includes those by Craig andGoodno (1981), Rihal (1988), Chiba et al. (1992), Rihal(1994), Pantelides and Behr (1994), and Behr et al. (1995).These tests may be summarized as follows.

Test by Craig and Goodno (1981)

These investigators measured in the laboratory the naturalfrequencies, mode shapes, and damping ratios of a window ina full-scale glass cladding panel. Their specimen consisted ofa single-story section of a cladding system and included themullions, munitions, spandrel framing, glazing materials, andfour double-pane vision lights (2.51 X 1.45 X 0.0254 m).

Test by Rlhal (1988)

Rihal conducted cyclic in-plane racking tests of a precastconcrete cladding panel with bearing connections at the bot­tom and threaded-rod lateral connections at the top. The ob­jective of the tests was to obtain quantitative data on the in­plane resistance and defonnation capability of precast claddingpanels. The tested specimen consisted of a solid precast con­crete cladding panel 2.44 m wide, 3.05 m high, and 114 mmthick, with two threaded-rod lateral connections at the top ofthe panel and two bearing connections at the bottom. The bear­ing connections consisted of a steel angle assembly with fourstuds, 16 mm in diameter, welded to the back of the angle andembedded in the cladding pane. The specimen was tested un­der cyclic displacements applied to the threaded rods of thelateral connections.

Test by Chiba et al. (1992)

These researchers tested on a shaking table a three-dimen­sional piping system mounted on a combination of rigid re­straints and elastoplastic dampers. The purpose of the test wasto investigate the dynamic behavior of a cracked pipe sup­ported on elastoplastic dampers and to clarify the effect of thepipe support stiffness on the crack growth. The piping systemtested was 27.4 m in length and 165.2 mm in diameter. Theelastoplastic dampers were made of three-layer steel plates.

Test by Rlhal (1994)

Rihal conducted experimental in-plane and out-of-plane cy­clic tests of loaded library shelving units, representative ofthose designed using current standards. The objective of thetests was to assess the adequacy of the provisions in current

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codes and the standards governing the design and installationof cantilever library shelving systems in seismic zones. Forthe in-plane test, the shelving specimen consisted of threeunits, each 0.91 m wide and 2.29 m high. In the out-of-planetest, the specimen consisted of only two such units.

Tests by Pantelides and Behr (1994) andBehr et al. (1995)

These researchers conducted tests to investigate the generalglass breakage and glass fallout behavior during earthquak~s

of some of the architectural glass utilized in dry-glazed curtainwalls. A 4.56 X 3.68 m section of a dry-glazed curtain wall,containing three 1.52 X 1.84 m glass panels and a wide mul­lion, was employed in the tests. The type of glass tested in­cluded annealed, heat-strengthened, and fully tempered glassin monolithic and laminated configurations, having differentthicknesses. The specimen was subjected to in-plane and out­of-plane dynamic motions in these tests.

If experimental investigations are scarce, field observationsfrom instrumented secondary structural elements are evenmore so. To the writer's knowledge, the only report of fieldinstrumentation of equipment to observe its seismic responseis that from Hiramatsu et al. (1988). In this report, Hiramatsuand his coworkers describe a field observation system estab­lished in Japan in 1982 to monitor the seismic response oftelecommunication equipment in a five-story telephone officebuilding. In this system, accelerometers were installed on theequipment in several floors of the building at 16 points, on aroof steel tower at two points, and on an antenna above thetower at one point. So far, the system has recorded severalearthquakes of moderate magnitude. In regard to field obser­vations it is worthwhile to mention the study conducted byRihal (1992) to investigate the influence of peak floor accel­eration, frequency content, and interstory drift on the nonstruc­tural damage observed during an earthquake. In his study, Ri­hal used the data recorded during the 1989 Loma Prietaearthquake in an instrumented building and the correspondingobserved nonstructural damage.

RESEARCH NEEDS

As seen from the foregoing review, much progress has beenmade towards the understanding of the seismic behavior ofsecondary structural elements, the development of simplifiedmethods of analysis, and the development of code provisionsfor life safety and damage mitigation. Notwithstanding thisprogress, it is also clear from the discussion in this review,and from the damage sustained by this type of elements duringrecent earthquakes, that the problem is a complex one, and assuch, has not been completely solved. Thus, there are severalproblems concerning secondary structural elements that de­mand further research.

One area of research that is urgently needed to advance theunderstanding of the seismic behavior of secondary structuralelements, and to derive improved simplified methods for theiranalysis, is that related to the effect on this behavior of theirnonlinearity and that of their supporting structures. As men­tioned earlier, current analytic evidence seems to indicate thatsuch nonlinearity may significantly affect the behavior of asecondary element, that in some cases it may considerablyreduce the response of the secondary element in comparisonwith the response attained when both subsystems are assumedto remain linear at all times, and that in other cases this re­sponse may actually increase. However, only a limited numberof studies have been conducted to clarify and quantify suchan effect, and only a few simplified methods of analysis thattake into account such nonlinearity have been proposed.

Research is also needed to study the influence of the tor-

sional motion of a supporting structure on the response of asecondary element attached to it. As discussed, this torsionalresponse may significantly increase the response of a second­ary system if the structure is highly asymmetric and the sec­ondary element is located near the periphery of the structure.Hence, ignoring this effect may lead to unconservative de­signs. This problem has received little attention in the past, sothere is not enough information to assess the importance ofthis factor. Work is thus needed to assess its importance andto develop simplified methods of analysis that take structuraltorsion into account.

Another area of research that deserves full consideration isthat related to the base isolation and structural control of sec­ondary structures. Given their relatively small size and thehigh accelerations to which they can be subjected, secondarystructures are ideal for application of these techniques. Un­doubtedly, important benefits may be realized from their use.Particular topics of interest in this regard include the influenceof structural yielding on the effectiveness of such techniqueswhen they are applied to secondary structures, and the devel­opment of simplified methods for the analysis of secondarystructures that incorporate any of these techniques in their de­signs.

Despite the high level of understanding that has been gainedabout the behavior of secondary structural elements mountedon a primary structure, and despite the numerous rational pro­cedures that have been proposed over the last few years forthe analysis of these secondary structural elements, the stan­dards and specifications in current building codes stilI do notreflect such level of understanding and have not yet incorpo­rated many of these rational procedures. Undoubtedly, this hasbeen the case because, for the most part, these rational meth­ods of analysis are too complicated or too cumbersome for thedesign of ordinary secondary elements in conventional build­ing structures. Thus, as pointed out by Chen and Soong(1988), a great challenge for researchers is the developmentof methods of analysis that, on one hand, are rational andaccurate, but on the other, are simple enough for their incor­poration into building codes. As noted in the section on meth­ods of analysis, some progress has been made in the last cou­ple of years, but further work is still needed. In particular,research is needed to develop simplified guidelines to accountin a rational way for the effect of yielding in a structure onthe response of the secondary elements attached to it.

Finally, an extensive program of experimental work andfield instrumentation is needed to complement the ongoing an­alytical studies. Laboratory tests, mainly in the form of shak­ing table tests, are needed to verify the findings from the an­alytical studies; to define the stiffness, damping, ductility, anddrift limits of specific secondary structural elements and theiranchorages; to define the acceleration limits at which particularpieces of equipment cease to be operational; to test the suita­bility of current and new bracing methods and anchoring sys­tems; and to test the effectiveness of base isolation and struc­tural control schemes. The field instrumentation of realsecondary systems in real structures is needed to collect dataabout their performance during real earthquakes (Le., underactual field conditions) and to compare this performanceagainst the results from analytical and experimental studies.

ACKNOWLEDGMENT

The writer wishes to express his gratitude to one of the anonymousreviewers, who thoroughly read the paper and made insightful sugges­tions. The suggestions significantly improved its content and presentation.

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