Análisis y diseño de elementos no estructurales

19

Seismic Analysisand Design of

Nonstructural Elements

19.1 Introduction

19.2 Importance of Nonstructural Elements

19.3 General Physical Characteristics

19.4 General Response Characteristics

19.5 Modeling of Nonstructural Elements

19.6 Methods of Analysis

Background • Floor Response Spectrum Method • Alternative Methods • Design-Oriented Simplified Method

19.7 Design Provisions in Building Codes

Overview • Uniform Building Code • NEHRP Provisions

19.8 General Design Considerations

Architectural Elements • Mechanical and Electrical Equipment

19.9 Role of Nonstructural Elements in Performance-Based Design

19.10 Future Challenges

19.11 Summary

19.1 Introduction

Nonstructural elements are those systems and components attached to the floors and walls of a buildingor industrial facility that are not part of the main or intended load-bearing structural system for thebuilding or industrial facility. Although not part of the main structural system, they may neverthelessalso be subjected to large seismic forces and depend on their own structural characteristics to resist theseseismic forces. In general, nonstructural elements may be classified into three broad categories: (1)architectural components, (2) mechanical and electrical equipment and (3) building contents. Examplesof the first category are elevator penthouses, stairways, partitions, parapets, heliports, cladding systems,signboards, lighting systems and suspended ceilings. Some of the second are storage tanks, pressurevessels, piping systems, ducts, escalators, smokestacks, antennas, cranes, radars and object trackingdevices, computer and data acquisition systems, control panels, transformers, switchgears, emergencypower systems, fire protection systems, boilers, heat exchangers, chillers, cooling towers and machinerysuch as pumps, turbines, generators, engines and motors. Among some of those in the third categoryare bookshelves, file cabinets, storage racks, decorative items and any other piece of furniture commonly

Roberto Villaverde

© 2004 by CRC Press LLC

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Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering

found in office buildings and warehouses. Alternative names by which these elements are also knownare “appendages,” “nonstructural components,” “building attachments,” “architectural, mechanical, andelectrical elements,” “secondary systems,” “secondary structural elements” and “secondary structures.”The name that best describes their nature is secondary structures, since it reflects the fact that they arenot part of the main structure but must possess, nevertheless, structural properties to maintain theirown integrity.

This chapter will describe why the survival of nonstructural elements is an important necessity in theevent of a strong earthquake and why they are particularly vulnerable to the effect of earthquakes. It willreview, in addition, the methods that are available for their seismic analysis and introduce in detail twosuch methods. In like manner, it will introduce the provisions contained in the Uniform Building Code(UBC) and the NEHRP provisions for the seismic design of nonstructural elements and illustrate theuse of these provisions by means of a numerical example. The chapter will also present some generaldesign recommendations and preventive measures that have been proven effective in improving theseismic resistance of some architectural elements and mechanical and electrical equipment. Finally, itwill examine the role nonstructural elements play in the performance-based design of buildings, andidentify the research needed to advance current efforts to protect nonstructural elements against theeffects of earthquakes and to develop methods and techniques to achieve this goal in a practical and eco-nomical way.

19.2 Importance of Nonstructural Elements

Despite the fact that they are not part of the main structure, nonstructural elements are far from beingsecondary in importance. It is nowadays widely recognized that their survival is essential to provideemergency services in the aftermath of an earthquake. Experiences from past earthquakes have shownthat the failure of equipment and the debris caused by falling objects and overturned furniture maycritically affect the performance of fire and police stations, emergency command centers, communicationfacilities, power stations, water supply and treatment plants, food treatment and cold storage plants,hospitals and collective transportation systems. For example, during the 1994 Northridge earthquake inLos Angeles, CA, area, several major hospitals had to be evacuated, not because of structural damage,but because of (1) water damage caused by broken water lines and water supply tanks; (2) the failure ofemergency power systems and heating, ventilation and air conditioning units; and (3) damage to sus-pended ceilings and light fixtures and some broken windows (Hall, 1994, 1995). Along the same lines,it is now recognized that damage to nonstructural elements represents a threat to life safety, may seriouslyimpair a building`s function and may result in major direct and indirect economic losses. Understandably,the collapse of suspended light fixtures, hung ceilings or partition walls; the fall of cladding components,parapets, signboards, ornaments or pieces of broken glass; the overturning of heavy equipment, book-shelves, storage racks and pieces of furniture; and the rupture of pipes and containers with toxic materialsare all capable of causing serious injury or death. Figure 19.1 through Figure 19.8 show a few examplesof the failure of nonstructural elements during past earthquakes and vividly illustrate how these failurescan cause serious injury and death. A most unfortunate demonstration that the failure of a nonstructuralelement indeed represents a threat to life safety was the death of a student who was struck by a fallingprecast panel while walking out of a parking structure during the 1987 Whittier Narrows earthquake inCalifornia (Taly, 1988). In like fashion, it is easy to visualize how the normal activities that take place ina building may be critically disrupted when some essential equipment fails, or when debris from failedarchitectural components gets in the way. Typical examples that illustrate the consequences of such anevent are the unwanted solidification of a melted metal in an industrial facility, the inaccessibility offinancial records in a timely manner in a banking institution and the failure to fill pending orders in amanufacturing plant. In regard to the economic impact caused by the failure of nonstructural elements,there is nowadays plenty of evidence that shows that because of the loss of the nonstructural componentsthemselves, loss of inventory and loss of business income, the cost of such failures may easily exceed thereplacement cost of the building (EERI, 1984). And in today’s highly technological environment, this


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Seismic Analysis and Design of Nonstructural Elements

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FIGURE 19.1

Collapse of signboard on street of Kobe, Japan, during the 1995 Great Hanshin earthquake. (Photocourtesy of Chris Arnold/Building Systems Development, Inc.)

FIGURE 19.2

Collapse of pipe originally suspended from below floor system of parking structure during the 1987Whittier Narrows earthquake. (Photo courtesy of S.S. Rihal/Cal Poly, San Luis Obispo.)


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http://www.crcnetbase.com/action/showImage?doi=10.1201/9780203486245.ch19&iName=master.img-000.jpg&w=383&h=257


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cost may be even accentuated as a result of the widespread use of electronic and computer equipmentand dependence of industry on this type of equipment.

It is thus clear that nonstructural elements should be the subject of a rational and careful seismicdesign in much the same way as their supporting structures are.

19.3 General Physical Characteristics

Several physical characteristics make nonstructural elements in buildings particularly vulnerable to theeffects of earthquakes. Some of these physical characteristics are:

1. Most nonstructural elements are attached to the elevated portions of a building, and thus theyare subjected not to the ground motion generated by an earthquake, but to the amplified motionsgenerated by the dynamic response of the building.

2. Their weight is light in comparison with the weight of the structure to which they are connected,and their stiffness is also much smaller that that of the structure as a whole. As a result, it is likelythat their natural frequencies are close to the natural frequencies of the structure, and hence theirdynamic response to the motion at their supports may be extraordinarily high.

FIGURE 19.3

Failure of hospital penthouse during the 1985 Mexico earthquake.


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3. Their damping ratios may be quite low, much lower than those for the structure, and thus theydo not possess the damping characteristics that are necessary for protection against sharp resonantmotions.

4. They may be connected to the structure at more than one point and therefore they may be subjectedto the distortions induced by the differential motion of their supports.

FIGURE 19.4

Failure of window frame in school building during the 1973 Orizaba, Mexico, earthquake.

FIGURE 19.5

Fallen precast element from parking garage, responsible for death of a student during the 1987Whittier Narrows earthquake in Los Angeles, CA, area. (Photo courtesy of Narendra Taly/California State University,Los Angeles; reproduced with permission of Earthquake Engineering Research Institute.)


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5. They are designed to perform a function other than to resist forces. As such, they are built withmaterials that are far from the ideal materials to resist seismic forces and they may possess partsthat are sensitive to even the smallest level of vibration.

19.4

General Response Characteristics

The special physical characteristics described above make nonstructural elements not only susceptible toearthquake damage, but also respond to earthquake ground motions differently from the way buildingstructures do. That is, the response of a nonstructural element exhibits characteristics that are notcommon in the response of a conventional structure. The following are a few of such characteristics:

1. The response of a nonstructural element depends on the response of the structure to which it isconnected, and thus it depends not only on the characteristics of the ground motion that excitesthe base of the structure, but also on the dynamic characteristics of the structure.

2. The response of a nonstructural element depends on its location within the structure. As a result,identical elements may respond differently to the effects of an earthquake if they are located atdifferent levels of the supporting structure.

3. There may be a significant interaction between a nonstructural element and its supporting struc-ture. That is, the motion of the nonstructural element may modify the motion of its supportingstructure, and vice versa. In such cases, therefore, one cannot predict the response of the non-structural element without knowing in advance the dynamic properties of both the nonstructuralelement and the supporting structure.

FIGURE 19.6

Collapse of building’s exterior wall during the 1994 Northridge, CA, earthquake. (Photo courtesy ofYousef Bozorgnia.)


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FIGURE 19.7

Dislocation of library bookshelves during the 1987 Whittier Narrows, CA, earthquake. (Photo cour-tesy of Narendra Taly/California State University, Los Angeles; reproduced with permission of Earthquake EngineeringResearch Institute.)

FIGURE 19.8

Collapse of 17-ton scoreboard at Anaheim Stadium (black object below stadium’s A logo and sur-rounded by billboards) during the 1994 Northridge, CA, earthquake.


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4. When a nonstructural element is connected to the structure at more than one point, the element’ssupports are excited by motions that are different and out of phase.

5. Since the damping in a nonstructural element is much lower than the damping in the supportingstructure, the damping in the system formed by the structure and its nonstructural elements,which is the system that characterizes the response of a nonstructural element, is not uniform.This means that the response of nonstructural elements is governed by the response of a systemwithout classical modes of vibration; that is, the response of a system whose natural frequenciesand mode shapes are complex valued.

6. Since, as mentioned earlier, it is likely that some of the natural frequencies of a nonstructuralelement may be close in value to some of those of the supporting structure, the combinedstructure–nonstructural system may result in a system with closely spaced natural frequencies. Assuch, the response of a nonstructural element may be dominated by its response in two or moreof its modes of vibration, as opposed to a single mode, which is the case for many low-rise andregular building structures.

7. The response of a nonstructural element is affected by its own yielding as well as the yielding ofits supporting structure.

19.5 Modeling of Nonstructural Elements

As may be inferred from the examples given in Section 19.1, and in contrast to building structures, thereexists a vast variety of nonstructural elements. Therefore, there are no general rules or accepted standardsfor the modeling of nonstructural elements. What is more, in many situations, the modeling is left tothe manufacturer of the particular element in question, who, in the majority of the cases, is the only onein a position to be able to identify the dynamic properties and significant characteristics that need to beconsidered in a mathematical model of the element. In general, however, it can be said that as far as theirmodeling is concerned, nonstructural elements can be considered as belonging to three broad categories:rigid, flexible, and hanging from above. If a nonstructural element is rigid, then its dynamic propertieswill depend primarily on the flexibility and ductility of its anchors. In this case, the nonstructural elementmay be modeled as a single-degree-of-freedom system with a mass equal to the total mass of the elementand stiffness and ductility equal to the stiffness and ductility of the anchors. Examples of these types ofnonstructural elements are engines and motors attached to the floors of a structure by means of steelbrackets and bolts. If, on the other hand, a nonstructural element is flexible, then it is necessary to modelthe element as a multi-degree-of-freedom system with distributed mass, stiffness and ductility, in muchthe same way as a building structure is normally modeled. In this regard, it should be noted that, unlikea building structure, a nonstructural element may be attached to multiple points of its supportingstructure and that it is important to consider these multiple attachments in the modeling of the non-structural element. Typical examples of flexible nonstructural elements are signboards and pipelines, thelatter also being an example of a nonstructural element with multiple points of attachment. Finally, ifthe nonstructural element hangs from above, then the element behaves and may be modeled as a single-mass pendulum. Ordinarily, however, hanging nonstructural elements are not analyzed since theseelements are seldom damaged by earthquakes. The exception is when the nonstructural element mayimpact its supporting structure or any other nearby object as a result of the large oscillations it may besubjected to during an earthquake. In these cases, an analysis should be performed to investigate theamplitude of such oscillations. Examples of hanging secondary structures are lighting systems, cable traysand some decorative items such as chandeliers.

19.6

Methods of Analysis

19.6.1 Background

A great research effort has been devoted over the last three decades to develop rational methods for theseismic analysis of nonstructural elements. For the most part, this effort has been fueled by the need to


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guarantee the survivability of critical equipment such as piping and control systems in nuclear powerplants. Therefore, many methods of analysis have been proposed as a result of this research effort, someof them with a strong empirical base, and others based on rigorous principles of structural dynamics.Up to now, however, none of these methods has become the industry standard or the one that is preferredby most analysts.

In the development of methods of analysis for nonstructural elements, it is generally recognized thatthey are difficult to analyze accurately and efficiently. It is always possible to consider them in conjunctionwith the analysis of their supporting structures, but a combined structure–nonstructural system generallyresults in a system with an excessive number of degrees of freedom and large differences in the values ofits various masses, stiffnesses and damping constants. As a consequence, the conventional methods ofanalysis become expensive, inaccurate and inefficient. For example, a modal analysis exhibits difficulties inthe computation of natural frequencies and mode shapes, and a step-by-step integration method becomesextraordinarily sensitive to the selected integration time step. Likewise, the analysis of a combined systemmay be too impractical since during the preliminary design of the nonstructural element, the supportingstructure would have to be reanalyzed every time a change is introduced in some of the parameters of thenonstructural element. Considering that normally structures and nonstructural elements are designed bydifferent teams at different times, this approach would also bring serious problems of schedule and efficiency.Thus, most of the methods proposed for the analysis of nonstructural elements have been the result of aneffort to avoid the analysis of a combined system and overcome the aforementioned difficulties.

The majority of the methods available for the analysis of nonstructural elements are based on conceptsnot covered in introductory courses on structural dynamics and, hence, beyond the scope of this discus-sion. Therefore, only two methods of analysis will be described in this chapter. One is the floor responsespectrum method, and the other is a design-oriented approximate method. Although with some limita-tions, these methods are easy to understand and thus useful to introduce the reader to a difficult problemand illustrate some of the fundamental concepts involved. A brief description of the concepts on whichsome other methods are based will also be presented.

19.6.2 Floor Response Spectrum Method

One of the first simplified methods used in the analysis of nonstructural elements is the so-called systems-in-cascade, in-structure response spectrum, or floor response spectrum method. In this method, firstthe excitation at the base of a nonstructural element is defined in terms of a response spectrum in muchthe same way as in the case of a building structure. Then, the nonstructural element is analyzed, also asin the case of a conventional structure, using such a response spectrum. Since, in general, the responsespectrum for the excitation at the base of a nonstructural element is different from the response spectrumof the ground motion that excites its supporting structure, the former is called “floor response spectrum”or “in-structure response spectrum” to distinguish it from the latter. Note also that a floor responsespectrum is needed for each of the points or floors of the structure where there is a nonstructural elementattached to it. The obvious reason is that the motion may be markedly different at different points orfloors of a structure.

Ordinarily, a floor response spectrum is obtained by means of a time-history analysis. That is, givena ground acceleration time history, a step-by-step integration analysis is carried out to determine theacceleration time history of the point or floor to which the nonstructural element under considerationwill be attached. Then, this time history is used to generate a response spectrum using any of theconventional methods currently in use. Since the use of a single time history is not acceptable for designpurposes, it is necessary to generate floor response spectra for several different ground acceleration timehistories and use an average or envelope to all these spectra. As this is a time-consuming process thatrequires lengthy numerical integrations, an alternative commonly employed in practice is the use of anartificial ground acceleration time history that is fitted to envelop a given ground design spectrum, suchas the design spectrum specified by a building code. However, caution should be exercised with thisalternative since such an artificial time history is not uniquely defined. That is, different time histories


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may envelop the target design spectrum but give significantly different results. Another alternative is touse one of the several methods that are now available to generate floor response spectra directly from aspecified ground response spectrum or a design spectrum without utilizing a time-history analysis. Thesemethods use as input a specified ground response spectrum and the dynamic properties of the structure.Examples are the methods proposed by Biggs and Roesset (1970), Amin et al. (1971), Kapur and Shao(1973), Peters et al

.

(1977), Vanmarcke (1977), Atalik (1978) and Singh (1980).

Example 19.1 Analysis of nonstructural element

by floor response spectrum method

A piece of equipment is mounted on the roof of the 10-story shear building shown in Figure 19.9a. Thispiece of equipment can be modeled as a single-degree-of-freedom system with a natural frequency of2.0 Hz. Determine, using the floor response spectrum method, the maximum acceleration of the pieceof equipment when the base of the building is subjected to the East-West component of the groundacceleration recorded at the Foster City station during the 1989 Loma Prieta, CA, earthquake (see Figure19.9b). Assume that the building’s damping matrix is proportional to its stiffness matrix and that thedamping ratio in its fundamental mode is 2%. Similarly, assume a damping ratio of 0.5% for the pieceof equipment.

Solution

: The first step in using the floor response spectrum method for the solution of this problem isthe generation of the floor spectrum corresponding to the roof of the building and the given earthquakeground motion. For this purpose, first a time-history analysis of the building is carried out. Then, usingthe time history corresponding to the acceleration response of the building at its roof level, the desiredfloor response spectrum is generated.

(a) (b)

(c) (d)

FIGURE 19.9

(a)Ten-story building considered in Example 19.1. (Note: Gg = 68, 525 slugs; 1 MN/m = 737.5 kips/ft); (b) E–W component of ground acceleration recorded at the Foster City station during the 1989 Loma Prieta,CA, earthquake. (Note 1 m/s

2

= 3.28 ft/s

2

); (c) Acceleration response for roof level of building considered in Example19.1 under E–W Foster City accelerogram. (Note 1/ms

2

= 3.28 ft/s

2

); (d) floor response spectrum for roof level ofbuilding considered in Example 19.1 under E–W Foster City accelerogram. (Note: 1 m/s

2

= 3.28 ft/s

2

).

1

2

6

5

4

3

7

8

9

10

Story12345678910

Mass(Gg)0.1790.1700.1610.1520.1430.1340.1250.1160.1070.098

Stiffness(MN/m)

62.4759.2656.1453.0249.9146.7943.6740.5537.4334.31

-3

-2

-1

0

1

2

3

0 10 20 30 40 50

Time (sec)

(Acc

eler

atio

n (m

/s2 )

60

-6

-4

-2

0

2

4

6

10 20 30 40 50Time (sec)

Acc

eler

atio

n (m

/s2 )

6000

10

20

30

40

50

60

70

0.01 0.1 10 100

Frequency (Hz)

Spe

ctra

l Acc

eler

atio

n (m

/s2 )

1


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The acceleration time history of the building’s roof and the corresponding floor response spectrumobtained are shown in Figure 19.9c and Figure 19.9d, respectively. From this floor response spectrum,it can be seen that the ordinate corresponding to a frequency of 2 Hz is equal to 14.4 m/sec

2

(47.2 ft/sec

2

).Therefore, the acceleration of the piece of equipment when the building is subjected to the given excitationis approximately equal to 1.47

g

.Floor response spectrum methods have been proven accurate for nonstructural elements whose masses

are much smaller than the masses of their supporting structure and natural frequencies that are not tooclose to the natural frequencies of the structure. However, these methods may yield overly conservativeresults for nonstructural elements that do not have these characteristics. (Toro et al

.,

1989, report thaterrors may be significant when nonstructural to structural mass ratios are greater than 10

-

3.

) The reasonfor this overconservatism is that in floor response spectrum methods nonstructural elements are con-sidered separately from their supporting structure, without due consideration to the fact that the responseof a nonstructural element may significantly affect the response of its supporting structure and vice versa.That is, floor response spectrum methods neglect the dynamic interaction between a structure and anonstructural element. An additional reason is that floor response spectrum methods cannot accountfor the fact that the masses of the structure and the nonstructural element vibrate out of phase, an effectthat arises because, in general, the combined system does not possess classical modes of vibration. Thereis now ample analytical evidence that demonstrates that ignoring these two effects may lead to grosserrors in the response calculation of some nonstructural elements (see, for example, Igusa and DerKiureghian, 1985a, and Chen and Soong, 1988).

FIGURE 19.10

Floor response spectra for fourth floor of six-story building in Figure 19.11 corresponding todifferent nonstructural to structural mass ratios. (Adapted from Singh, M.P. and Suárez, L.E.,

Earthquake Eng. Struct.Dyn

., 15, 871–888, 1987. With permission.)

FIGURE 19.11

Properties and natural frequencies of six-story shear building considered in study of interaction andnonclassical damping effects. (Note: 1 Gg = 68,525 slugs; 1 MN/m = 737.5 kips/ft.)

4.0

3.0

2.0

1.0AC

CE

LER

ATIO

N/G

13010 20 30 40 50 60 70 80 90 100 110 120

mass ratio, re = 0

re = 1/50

re = 1/10

re = 1

Frequency (RAD/SEC)

Mode

123456

NaturalFrequency (rad/s)

23.8761.5397.35

133.15153.59171.00

Story

123456

Mass(Gg)

707050504040

Stiffness(MN/m)

500500400400350350

1

2

6

5

4

3


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Another problem with floor response spectrum methods is that they cannot be rationally appliedfor the analysis of nonstructural elements with multiple points of attachment (Wang et al. 1983). Thisis so because these methods cannot consider that the motions at different attachment points arenormally different from one another and out of phase. Attempts have been made to overcome thisproblem, but for the most part these attempts have been in the form of empirical or ad-hoc procedures.For example, it has been proposed to determine the maximum response of a multiply supportednonstructural element by calculating first the maximum responses that result from using (one at atime) the floor spectra obtained for each of its supports. Then, these maximum responses are combinedin an empirical way to estimate the system’s true maximum response (Lin and Loceff, 1980; Shaw,1975; Thailer, 1976). Common among these empirical procedures is the selection of the largest of allthe response maxima, or a combination of them on the basis of the square root of the sum of theirsquares. Other techniques use a spectrum obtained by enveloping the floor spectra for all the non-structural element’s supports, or that of including a “pseudo-static” component of the response,determined in terms of the difference between the peak displacements at the various attachment points.It is now recognized, nevertheless, that these techniques are often too crude and in many cases maylead to overly conservative results.

The floor response spectra shown in Figure 19.10 illustrate the accuracy involved in the use of thefloor response spectrum method. These floor response spectra have been obtained for the fourth floorof the six-story shear building depicted in Figure 19.11, using as input an ensemble of 75 syntheticallygenerated ground motions and considering a damping ratio of 6% for the fundamental mode of thebuilding. The curve corresponding to a 0 mass ratio is obtained using the traditional procedure that isused to generate floor response spectra; i.e., ignoring the dynamic interaction between the structure andthe nonstructural element. The other curves are obtained for different mass ratios but fully consideringthis interaction. The mass ratio identified in each of these curves is determined by dividing the total massof the considered nonstructural element by the total mass of the structure.

It may be noted from the curves in Figure 19.10 that neglecting the interaction is always conservative,although in some cases it may be grossly conservative. It may also be noted that the interaction effectbecomes important when the mass ratio is not too small and the natural frequency of the nonstructuralelement is close to one of the dominant natural frequencies of its supporting structure.

In like fashion, Table 19.1 and Table 19.2 illustrate the importance of considering nonclassical dampingeffects in the analysis of nonstructural elements. In these two tables, the absolute acceleration responses

TABLE 19.1

Absolute Acceleration Response (Expressed as a Fraction of

g

) of Single-Degree-of-Freedom Nonstructural Element Mounted on Fourth Floor of Structure Depicted in Figure 19.11

When the Nonclassical Damping Nature of the Combined System is and is Not Taken Into Account

a

NonstructuralElement Natural

Frequency (rad/sec)

Mass Ratio

0.00156

0.000156

Classical Damping

Nonclassical Damping

Error (%)

Classical Damping

Nonclassical Damping

Error (%)

24 2.556 3.149 18.8 4.317 3.063 41.042 0.446 0.451 1.0 0.449 0.453 1.062 0.612 0.312 95.8 0.879 0.313 180.697 0.335 0.315 6.4 0.291 0.407 28.6

134 0.281 0.309 8.9 0.386 0.320 20.4154 0.258 0.257 0.5 0.295 0.258 14.4162 0.254 0.254 0.0 0.256 0.255 0.3171 0.252 0.252 0.1 0.252 0.254 0.7

a

Damping ratio in fundamental mode of structure = 6%; damping ratio of nonstructural element = 1%.

Source

: Singh, M.P. and Suárez, L.E.

Earthquake Eng. Struct. Dyn.

, 15, 871–888, 1987. With permission.


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of a single-degree-of-freedom nonstructural element are compared when this element is analyzed con-sidering the nonclassical damping character of the combined system and when it is analyzed assumingthat this combined system is classically damped. Table 19.1 summarizes the results for the case when thedamping ratios in the fundamental mode of the structure and the nonstructural element are 6 and 1%,respectively, while Table 19.2 summarizes those when these damping ratios are 8 and 0.5%.

It may be noted from these tables that some large errors may be possible if the nonclassical dampingeffects in question are not accounted for. It is also noted that, in general, such an effect becomes importantwhen the nonstructural to structural mass ratio is small, the natural frequency of the nonstructuralelement is close to one of the dominant frequencies of the structure and the difference between thedamping ratios of the structure and the nonstructural element is large. Furthermore, it is noted that the

FIGURE 19.12

Floor response spectrum ratios (inelastic structure/elastic structure) corresponding to floor accel-erations of five-story shear building with first-floor interstory ductilities of 2 and 4: (a) ratios for first floor whenbuilding is subjected to 1952 Taft acceleration record; (b) ratios for fifth floor when building is subjected to 1982Mitchell Lake acceleration record. Vertical lines identify the natural frequencies of the structure. (Adapted fromSewell, R.T., Damage Effectiveness of Earthquake Ground Motion: Characterizations Based on the Performance ofStructures and Equipment, PhD thesis, Stanford University, 1988. With permission.)

TABLE 19.2

Absolute Acceleration Response (Expressed As a Fraction of

g

) of Single-Degree-of-Freedom Nonstructural Element Mounted on Fourth Floor of Structure Depicted in Figure 19.11 When the Nonclassical Damping Nature of the Combined System Is and Is Not Taken into

Account

a

NonstructuralElement Natural

Frequency (rad/sec)

Mass Ratio

0.00156

0.000156

ClassicalDamping

Non-classicalDamping

Error (%)

ClassicalDamping

Non-classicalDamping

Error(%)

24 2.070 2.460 15.9 4.267 2.766 54.342 0.451 0.459 1.7 0.455 0.463 1.762 0.667 0.299 122.3 1.135 0.301 276.897 0.283 0.320 11.7 0.190 0.388 51.2

134 0.252 0.271 6.9 0.359 0.288 24.7154 0.231 0.231 0.0 0.283 0.234 21.4162 0.228 0.228 0.1 0.232 0.230 0.9171 0.225 0.226 0.4 0.225 0.227 0.8

a

Damping ratio in fundamental mode of structure = 8%; damping ratio of nonstructural element = 0.5%.

Source

: Singh, M.P. and Suárez, L.E.

Earthquake Eng. Struct. Dyn.

, 15, 871–888, 1987. With permission.

Floor response spectrum ratio,

Taftm = 4m = 2

Mitchell Lakem = 4m = 2

PS

A in

elas

tic/P

SA

ela

stic

4

3

2

1

00.1 1 10 100

PS

A in

elas

tic/P

SA

ela

stic

2

1

00.1 1 10 100

Floor #5Floor response spectrum ratio, Floor #1

Frequency (Hz)

(b)

Frequency (Hz)

(a)


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discrepancy between the results for the cases with classical and nonclassical damping becomes consistentlylarger as the nonstructural to structural mass ratio becomes smaller.

Finally, it should also be noted that traditionally floor response spectra are obtained under theassumption that a structure and its nonstructural elements behave as linear systems. As is well known,however, conventional structures are designed to resist strong earthquakes by incurring into their non-linear range of behavior. Similarly, many nonstructural components have the capability to resist inelasticdeformations. Hence, it is likely that a structure and its nonstructural elements will undergo inelasticdeformations during a severe earthquake, and that this nonlinear behavior will influence the responseof the nonstructural elements significantly.

At present, there is no clear understanding as to how structural nonlinearity may affect a floor responsespectrum. In general, response reductions are expected for nonstructural components with naturalfrequencies equal to or greater than the fundamental natural frequency of the structure. These reductionsresult from two main factors: (1) an increase in the damping ratio of the structure as a result of itsnonlinear behavior (hysteretic damping) and (2) a shift of the fundamental natural frequency of thestructure away from the natural frequency of the nonstructural element. A further reduction is attainedif the nonstructural element itself is allowed to go nonlinear in much the same way as is observed in atypical nonlinear response spectrum. Some numerical studies have shown, however, that floor responsespectrum ordinates for a nonlinear structure may actually increase in comparison to those obtained whenthe structure is assumed to remain linear at all excitation levels. Moreover, these studies have also shownthat this increase is particularly noticeable at high frequencies; that is, at frequencies higher than thestructure’s fundamental natural frequency.

Figure 19.12 illustrates the contrasting effect of structural nonlinearity in a floor response spectrum.This figure shows floor response spectrum ratios for a nonlinear five-story shear structure, where theseratios are obtained by dividing the floor response spectrum for the nonlinear structure by the corre-sponding floor response spectrum when the structure is assumed to have a linear behavior. Two valuesof the ductility factor

m

are considered for the structure’s first story:

m

= 2 and

m

= 4. All other storiesare assumed to remain in their linear range of behavior. Figure 19.12a shows the aforementioned ratiosfor the first floor of the structure when the structure is excited by the S69E component of the groundmotion recorded at Taft Lincoln School during the 1952 Kern County, CA, earthquake. Figure 19.12bshows those for the fifth floor of the structure when the structure is excited by the N28E component ofthe ground motion recorded at Mitchell Lake Road during the 1982 New Brunswick, Canada, earthquake.Note that in these figures a ratio of less than 1 represents a reduction in floor response spectrum ordinatedue to the structural nonlinearity. Conversely, a ratio of more than 1 represents an increase.

It can be seen from these figures that in one case (Figure 19.12a) there is a considerable amplificationin the high frequency range of the spectrum due to the nonlinearity of the structure. In the other case(Figure 19.12b) a reduction is observed over the entire frequency range of the spectrum. Worthwhile tonote too is the fact that in both cases the structural nonlinearity produces, as expected, a reduction forfrequencies that are near the fundamental natural frequency of the structure.

19.6.3 Alternative Methods

In view of the limitations of the floor response spectrum methods and the impracticality of a directanalysis of the combined structural–nonstructural system, several alternative methods have been devel-oped that take into account not only the aforementioned interaction and nonclassical damping effects,but also overcome the practicality problems associated with such a direct analysis. In general twoapproaches have been followed. In one of these approaches, in recognition of the convenience andflexibility of the floor response spectrum method and its wide use in the nuclear power industry,corrections are introduced to this method to account for, in an approximate manner, interaction andnonclassical damping effects. Examples of these methods are those proposed by Lee and Penzien (1983),Gupta (1984), Igusa and Der Kiureghian (1985b), Singh and Sharma (1985), Asfura and Der Kiureghian(1986), Gupta and Jaw (1986b), Burdisso and Singh (1987) and Suárez and Singh (1987a, 1989). In theother approach, the response of the nonstructural element is obtained on the basis of an approximate


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modal or random vibration analysis of the combined structural–nonstructural system, but using, througha modal synthesis, the dynamic properties of its separate components. This approach eliminates the mainsource of error inherent in the floor response spectrum method since by considering the two subsystemstogether as a single unit, the interaction between the two subsystems and the different and out-phasesupport motions are automatically taken into account. This approach is also a practical one. By formu-lating the analysis in terms of the dynamic properties of independent subsystems, one avoids the numer-ical difficulties associated with the large differences in the values of the parameters of the structure andthe nonstructural element when conventional methods of analysis are used. Furthermore, one avoidssolving a large eigenvalue problem, the need to generate intermediary floor response spectra (since theearthquake input is defined at the ground level) and the need to reanalyze the structure every timechanges are made to the parameters of the nonstructural element.

Conceptually, the idea of determining the response of a nonstructural element in terms of an analysisof the combined system it forms with its supporting structure, but utilizing only the properties of theindividual components, is a simple one. Its implementation, however, is not free of complications anddifficulties. For example, if one wants to analyze such a combined system by means of the responsespectrum method, one needs to first determine its natural frequencies, mode shapes, damping ratios,and maximum modal responses. Then, one needs to combine these modal responses using a modalcombination rule. However, the system that results from combining two subsystems with such a drasticdifference in the values of their masses, stiffnesses and damping constants is a system without classicalmodes of vibration and with closely spaced natural frequencies. This means that the natural frequenciesand mode shapes of the system are complex valued and that the combination of its modal responsesrequires, and highly depends on, an accurate rule to combine the modal responses of a system withnonclassical damping and closely spaced natural frequencies. Notwithstanding such difficulties andcomplications, several methods that use this technique have been proposed throughout the years —methods that basically differ in the way the dynamic properties of the components are synthesized toobtain the dynamic properties of the combined system, and in the assumptions made to simplify theprocedure. In chronological order, some of these methods are those suggested by Newmark (1972),Sackman and Kelly (1979), Newmark and Villaverde (1980), Der Kiureghian et al. (1983), Hernried andSackman (1984), Gupta (1984), Igusa and Der Kiureghian (1985c), Gupta and Jaw (1986a), Villaverde(1986a, 1986b), Singh and Suarez (1987), Suárez and Singh (1987b), Muscolino (1990), Villaverde (1991),Saudy et al. (1994) and Gupta (1997).

All the methods referred to above have been derived specifically for linear nonstructural elementsmounted on linear structures. However, as shown above and as pointed out by Lin and Mahin (1985),Aziz and Ghobarah (1988), Toro et al

.

(1989), Sewell et al. (1989), Igusa (1990), Singh et al

.

(1993),Schroeder and Backman (1994) and Adam and Fotiu (2000), the nonlinear behavior of a nonstructuralelement and that of its supporting structure may significantly affect the behavior of the nonstructuralelement, either in the form of an increase or a reduction over its linear response. These methods, therefore,may lead to either nonconservative or uneconomical designs.

Recognizing the importance of such nonlinear behavior, a few investigators have made an effort toderive simplified methods that incorporate structural and nonstructural nonlinearity. Given, however,the difficulties in obtaining explicit solutions for such a complex problem, most of the effort has beendirected toward the development of reduction and amplification factors by which a linear floor spectrumshould be modified to approximately take into account such nonlinearity (Kawakatsu et al., 1979; Linand Mahin, 1985; Viti et al., 1981). Exceptions are the works of Villaverde (1987) and Igusa (1990).Villaverde (1987) developed a method based on the use of nonlinear ground response spectra for theanalysis of linear multi-degree-of-freedom nonstructural elements mounted on an elastoplastic multi-degree-of-freedom building structure. Igusa (1990) derived an analytical solution for the response of atwo-degree-of-freedom structural–nonstructural system with small nonlinearities, using random vibra-tion theory and equivalent linearization techniques.

For a description of the difference between the methods of analysis cited above, the reader is referred tothe state-of-the-art reviews made by Singh (1990) and Soong (1994), as well as the book by Gupta (1990).


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19.6.4 Design-Oriented Simplified Method

A procedure to determine in a conservative but simple way equivalent static lateral forces for the seismicdesign of nonstructural elements attached to buildings is presented next. This procedure is derived onthe basis of a modal synthesis and the introduction of simplifying assumptions comparable to thoseemployed in the development of the static method for the seismic design of buildings. It is intended tobe valid for the design of nonstructural elements connected to a structure at one or two points, and thosethat together with their supporting structure form a system with nonclassical damping. It takes intoaccount the dynamic interaction between the two subsystems, the level above the base of the structureof the point or points of the structure to which the nonstructural element is attached, the number ofsuch attachment points and the nonlinear behavior of the structure and nonstructural elements. It uses,in addition, the design spectra specified by building codes for the design of the structure to also definethe earthquake input to the nonstructural element. The derivation of the procedure is lengthy and tedious,so it will not be shown here. Interested readers may find this derivation in some of the author’s publi-cations (Villaverde 1991, 1997, 2000).

The following are some of the major assumptions made in the derivation of the procedure:

1. The total response of the combined structural–nonstructural system is approximately given by theresponse in the two modes of the system that correspond to the fundamental natural periods ofthe two independent subsystems.

2. The fundamental natural period of the nonstructural element coincides with the fundamentalnatural period of the structure; that is, the fundamental mode of the nonstructural element is inresonance with the fundamental mode of the structure.

3. The fundamental mode shape of the structure varies linearly from 0 at its base to a maximumvalue at its top.

4. The fundamental mode of the nonstructural element varies linearly along its height. In the caseof a single point of attachment, it varies from 0 at its point where it is connected to the structureto a maximum value at its other end. In the case of two points of attachment, it varies from 0 atthe two attachment points to a maximum value at the point where it attains its maximumdisplacement when each of its masses is subjected to a static force equal to its own weight (seeFigure 19.13).

5. The generalized masses in the fundamental modes of the structure and the nonstructural elementare equal to their respective total masses.

6. The damping ratios in the fundamental modes of the structure and the nonstructural element areequal to 5 and 0%, respectively.

FIGURE 19.13

Assumed mode shapes for nonstructural elements with one and two points of attachment.

wpj

lk

wpk

wpj

(b)

lj

vpj

vpk

lj

vp

(a)


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19

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7. Both the structure and nonstructural element exhibit elastoplastic behavior and this behavior ischaracterized by an initial stiffness and a yield strength.

8. The input response spectrum for the combined structural–nonstructural system is the elasticresponse spectrum specified for the design of the structure.

The procedure involves the calculation of equivalent static lateral forces whose values are intended tobe greater than or equal to the maximum values of the lateral forces that may be generated on the massesof a nonstructural element by a specified design earthquake. These forces are determined according to

(19.1)

where

F

p

j

= force acting at the center of the

j

th mass of the nonstructural element.w

p

j

= weight of the

j

th mass of the nonstructural element.

l

j

= distance from attachment point to

j

th mass of nonstructural element in the case of a nonstructuralelement with a single attachment point (see Figure 19.13a), or distance from the lower or upperattachment point to the

j

th mass of the nonstructural element in the case of a nonstructuralelement with two attachment points. The lower attachment point is selected when such

j

th massis located below the point at which the element attains its maximum deflection when each massis subjected to a lateral force equal to its own weight; otherwise, the upper attachment point isselected (see Figure 19.13b).

n

= total number of masses in the nonstructural element.

V

p

= base shear or sum of the shears at the supports of the nonstructural element (see Figure 19.13),calculated according to

(19.2)

in which, if

f

is the fundamental natural frequency of the structure,

(19.3)

and

m

eq

is an equivalent ductility factor calculated according to

(19.4)

where

m

is the ductility factor specified for the structure,

m

p

is the ductility factor specified for thenonstructural element,

N

is the number of floors in the building and

n

¢

is the number of resisting elementsin the nonstructural system.

In addition,

I

= importance factor specified for the structure

pjpj j

j=1

n

pj j

pF = w l

w l

V

Â

p p p pV =IC

I C wl

lm

m

m

=£

- < <

+ - - -( ) £ £

Ï

Ì

ÔÔ

Ó

ÔÔ

eq if 2 Hz

if 2 8 Hz

if 8 33 Hz

f

f

ff

eq

eq

2 1

133

252 1 1

mm meq

pN n

N n=+ ¢

+ ¢ -[ ( )]1 1


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C

= spectral ordinate, expressed as a fraction of the acceleration of gravity, corresponding to thefundamental natural period of the structure in the response or design spectrum specified for thedesign of the structure

I

p

= importance factor for nonstructural element (specified by local code or arbitrarily selected bydesigner)

w

p

= total weight of nonstructural element

C

p

= amplification factor given by

(19.5)

where

W

= total building weight and

(19.6)

in which

h

i

= elevation above grade of building

’s i

th floor

h

av

= average of elevations above grade of points of the building to which the nonstructural element isattached

W

i

= weight of building

’

s

i

th floor

As noted earlier, this procedure is valid only for the case when a nonstructural element is attached tothe structure at no more than two points. However, a nonstructural element with more than twoattachment points can still be analyzed with this procedure by breaking it up into a series of subsystemswith one or two attachment points each, and by considering each of these subsystems separately. Forexample, a nonstructural element rigidly attached to the 4th, 7th and 10th floors of a supporting building(see Figure 19.14) may be considered as composed of two independent subelements with two attachmentpoints each, one attached to the 4th and 7th floors and the other attached to the 7th and 10th.

As noted earlier, too, the procedure is based on the assumption that the fundamental natural periodof the nonstructural element is in resonance with the fundamental natural period of the supportingstructure; i.e., that the values of these two periods are equal or are very close to one another. Althoughthis assumption offers the advantage of not having to know the natural periods of the nonstructuralelement to carry out its seismic design, it may be nonetheless overly conservative for those cases in whichtwo such natural periods are significantly different from one another. As a means to reduce the conser-vatism involved in the procedure for such cases, the amplification factor

C

p

may be replaced by a modifiedamplification factor

C

m

that varies linearly with the period ratio

T

p

/

T,

between the maximum value

C

p

,when this ratio is close to 1, and the minimum

F

0

, when such a ratio is substantially different from 1.0.In this period ratio,

T

p

represents the fundamental natural period of the nonstructural element and

T

the fundamental natural period of the structure.The variation of the modified amplification factor

C

m

is shown in Figure 19.15, together with thelimits of the period ratio beyond which the amplification factor for the nonstructural element should beconsidered equal to

F

0

, and the limits that define the range for which the structure and the nonstructuralelement should be considered in resonance with one another. In this figure,

b

is defined as

(19.7)

p

p

C =

|wW

- |

1

20 0025

12 5

02

0

..

F

F£

0F = Wh

W h

av

i=1

N

i iÂ

b = w / Wp12 0F


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Seismic Analysis and Design of Nonstructural Elements 19-19

Note, thus, that if the fundamental natural period of the nonstructural element is known, the graphin Figure 19.15 may be used to reduce, in terms of the aforementioned natural period ratio, the magnitudeof the amplification factor Cp in Equation 19.2 and, as a result, the magnitude of the seismic forcesdetermined with Equation 19.1.

FIGURE 19.14 Example of nonstructural element connected to multiple points of supporting structure.

FIGURE 19.15 Variation of modified amplification factor with natural period ratio.

FIGURE 19.16 Building and nonstructural element considered in Example 19.2. (Note 1 m = 3.28 ft.)

10

9

8

7

6

5

4

3

2

1

Cm

Cp

Φ0

Tp /T1.00.618 1.618

bb

6

5

4

3

2

1

6 @

3.3

m

3 @ 7 m


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19-20 Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering

Example 19.2. Lateral forces for design of nonstructural element using simplified procedure Using the simplified procedure presented above, determine the lateral forces on the masses of thenonstructural element shown in Figure 19.16, when, as indicated in this same figure, the nonstruc-tural element is rigidly connected to the fourth and sixth stories of a six-story office building. Thebuilding is located over a deposit of stiff soil in the city of Irvine, CA, and is structured with steelmoment-resisting frames. A ductility factor of 6 is specified for the design of these moment-resistingframes. The building’s weight per floor is 2200 kN (494.6 kips) and its total weight is thus equal to13,200 kN (2967.6 kips). The fundamental natural period of the building is 0.6 sec. The nonstructuralelement, an ordinary architectural fixture for which its importance factor may be considered equalto 1.0, is modeled as a three-degree-of-freedom shear beam with four equal segments, each with alength of 1.65 m (5.41 ft). Each of its three masses weighs 4.4 kN (0.99 kips), and hence its totalweight is 13.2 kN (2.97 kips); i.e., 0.1% of the total weight of the building. Its fundamental periodis estimated to be 0.5 sec when its two ends are considered fixed. A ductility factor of 2 may beconsidered in its design. Use the 1997 version of the UBC to define the earthquake input to thebuilding.

Solution: For the case under consideration, the average of the elevations aboveground of the nonstruc-tural element’s two attachment points is equal to16.5 m (54.1 ft). Hence, substitution of this value andthe floor weights given above into Equation 19.6 leads to

Similarly, by substitution of this value of F0 and the given total weights of the structure and thenonstructural element into Equation 19.5, one obtains

which exceeds the limit of 12.5F0 = 12.5(1.43) = 17.87. Therefore, the amplification factor Cp will beconsidered equal to

CP = 17.87

However, since in this case the fundamental natural frequencies of both the structure and the non-structural elements are known, it is possible to use a reduced value of this amplification factor using thegraph in Figure 19.15. To this end, note that the corresponding period ratio is given by

Note, too, that according to Equation 19.7, in the case under consideration the value of the parameterb in such a graph is equal to

013200 16 5

2200 3 3 6 6 9 9 13 2 16 5 19 81 43F =

W h

W h

av

i=1

N

i iÂ=

+ + + + +=( . )

( . . . . . . ).

p

p

2

C =

2 |w

W - |

1 1

213 2

13200

0 0025

1 43

33 5

02

0.0025

F

=-

=. .

.

.

T

Tp = =0 5

0 60 833

.

..

b = w / Wp12 0

12 1 43 13 2 13 200 0 023F = =( . ) . / , .


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Consequently, from Figure 19.15 the reduced amplification factor becomes

Now, by substitution of the specified ductility factors of 6 for the structure and 2 for the nonstructuralelement into Equation 19.4, and by considering that for the building and nonstructural element underanalysis N = 6 and n¢ = 4, the equivalent ductility factor for the structural–nonstructural system results as

In like fashion, for a structural frequency of 1/0.6 = 1.667 Hz, Equation 19.3 yields

l = m eq = 3.33

Also, according to the 1997 version of the UBC, for the building under consideration one has that

and hence, the spectral acceleration for the design of the building may be considered equal to

Finally, note that for an office building the UBC specifies an importance factor I equal to 1.0.Thus, after substitution of the values found above for l, C and Cm and the values specified for I and

Ip, Equation 19.2 leads to

Now, to distribute this force of 48.8 kN (11.0 kips) among the three masses of the nonstructuralelement, one needs to first determine its point of maximum deflection under lateral forces equal to theweight of its masses and define the distances lj that appear in Equation 19.1. It may be noted, however,that in this case the nonstructural element is symmetric in mass and geometry and that consequentlysuch a point of maximum deflection is located at its geometric center. By inspection, therefore, it can bedetermined that l1 = l3 = 1.65 m (5.4 ft) and l2 = 3.3 m (10.8 ft), where l1, l2 and l3 correspond, respectively,to the lower, middle and upper masses. As a result, Equation 19.1 gives

Cm = + --

- =1 430 833 0 618

0 977 0 61817 87 1 43 11 3.

. .

. .( . . ) .

mm meq

pN n

N n=+ ¢

+ ¢ =+

+ =- -[ ( )] [ ( )] .1 1

6 4

6

6

4

23 331 1

C Na a= = =0 44 0 44 1 0 0 44. . ( . ) .

C Nv v= = =0 64 0 64 1 2 0 77. . ( . ) .

TC

Csv

a

= = =2 5

0 77

2 5 0 440 7

.

.

. ( . ). sec.

C C a= = =2 5 2 5 0 44 1 10. . ( . ) .

p p m p p pV =IC

I C w w wl

= = = =( . )( . )

.( . )( . ) . . ( . ) .

1 0 1 10

3 331 0 11 3 3 7 3 7 13 2 48 8 kN (11.0 kips)

pp

j=1

pj j

pF = w l

w l

V11 1

3

4 4 1 65

4 4 1 65 3 30 1 6548 8 0 25 48 8 12 2

Â=

+ += =. ( . )

. ( . . . )( . ) . ( . ) . kN (2.75 kips)


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19.7 Design Provisions in Building Codes

19.7.1 Overview

Several building codes and seismic provisions give recommendations for the seismic design of equipmentand other nonstructural elements. In the United States, some of these include the UBC (1997), issuedby the International Conference of Building Officials; the National Earthquake Hazard Reduction Pro-gram (NEHRP) Recommended Provisions for Seismic Regulations for New Buildings (2000), issued by theBuilding Seismic Safety Council; the Recommended Lateral Force Requirements and Commentary (1990),issued by the Structural Engineers Association of California; the International Building Code (IBC, 2000);the Tri-Services Manual (Departments of the Navy, Army, and Air Force, 1992); and the American Societyof Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (ASME, 1993). Only the provisionsin the UBC and the NEHRP provisions will be discussed here, as these are the most frequently used forthe design of nonstructural elements in ordinary buildings. Although also worth discussing, the provisionsin the 2000 IBC will not be described since these provisions are based on and, except for some minormodifications and the values of a few coefficients, are identical to the 2000 NEHRP provisions.

In general, the intention of the provisions contained in the UBC and the NEHRP provisions fornonstructural elements is to ensure that nonstructural elements designed according to these provisionsare able to withstand the accelerations and deformations generated by the design earthquake withoutfracturing, shifting or toppling. In general, too, these provisions are based on concepts and techniquesthat are similar to those used for the design of building structures. Specifically, they specify an equivalentlateral force, where this force is expressed as a fraction of an element’s weight, and is a function of theground acceleration, location of the component relative to the height of the building, the component’sdynamic amplification and the component’s ability to absorb inelastic deformations. They also includeguidelines for the design of elements that are sensitive to story drifts.

The formulas specified to compute the equivalent lateral forces were developed empirically on thebasis of floor acceleration data recorded in buildings during strong earthquakes in California (Kehoe andFreeman, 1998), assuming that the floor accelerations within the structure vary from the ground to theroof according to a trapezoidal distribution. The acceleration at the ground level is intended to be theacceleration used as input for the structure itself. From the examination of the recorded data, assuminga maximum value for the roof acceleration equal to three to four times the ground acceleration wasfound reasonable. A response modification factor (Rp) is included in the formulas to account for theoverstrength and the inelastic deformation capability of the nonstructural element and/or its anchors.The inelastic behavior of the support structure was not included in the erroneous belief that (1) theextent of inelastic behavior is usually minor for structures designed by modern building codes, as theirdesign is in many cases governed by drift limits or other loads; (2) nonstructural components are oftendesigned without knowledge of the structure’s composition; and (3) it is a conservative consideration.Altogether, the formulas are intended to account for some of the most important factors that influencethe response of nonstructural components but without unduly burdening designers with complicatedformulations.

pp

j=1

pj j

pF = w l

w l

V22 2

3

4 4 3 30

4 4 1 65 3 30 1 6548 8 0 50 48 8 24 4

Â=

+ += =. ( . )

. ( . . . )( . ) . ( . ) . kN (5.50 kips)

pp

j=1

pj j

pF = w l

w l

V33 3

3

4 4 1 65

4 4 1 65 3 30 1 6548 8 0 25 48 8 12 2

Â=

+ += =. ( . )

. ( . . . )( . ) . ( . ) . kN (2.75 kips)


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19.7.2 Uniform Building Code

The provisions for nonstructural elements in the 1997 version of the UBC are based on ultimate strengthdesign principles. They specify the use of a lateral force for the seismic design of elements of structuresand their attachments, permanent nonstructural components and their attachments and the attachmentsof permanent equipment supported by a structure. Attachments include anchorages and required braces.Exemptions to these requirements are attachments for floor or roof-mounted equipment weighing lessthan 400 lb (181 kg) and furniture.

Two alternate formulas are provided to compute the required lateral force. The first one is conservative,but it is simple and easy to apply. This formula has the form

(19.8)

The other formula is more complicated, but it takes more factors into account. It is given by

(19.9)

except that Fp need not be greater than

(19.10)

and should not be less than

(19.11)

In the equations above,Fp = lateral force applied at the component or element’s center of mass and distributed in proportion

to the component or element’s mass distributionap = component amplification factor (i.e., factor that accounts for dynamic response of nonstructural

element to building motion) selected from Table 19.3 according to component or element type,varying between 1.0 and 2.5

Ca = seismic coefficient specified for the design of the structureIp = component or element importance factor, equal to 1.5 for essential and hazardous facilities and

1.0 for special and standard occupancy structuresRp = component response modification factor selected from Table 19.3 according to component or

element type, varying between 1.5 and 4.0 (considered equal to 1.5 for anchorages with shallowexpansion anchor bolts, chemical anchors or cast-in-place anchors and equal to 1.0 for anchorageconstructed with nonductile materials or adhesives)

hx = element or component elevation above grade, always considered to be greater than 0hr = elevation above grade of structure’s roofWp = element or component weight

For the purpose of determining the component amplification factor ap, the code defines flexiblecomponents or elements as those that together with their attachments have a fundamental natural periodgreater than 0.06 sec.

The code also specifies that components or elements attached to a structure at several points, such ascladding, stairwells, windows, ducts and piping systems, be designed to resist the effects of the relative

F C I Wp a p p= 4 0.

Fa C I

R

h

hWp

p a p

p

x

rp= +( )1 3

( ) .maxF C I Wp a p p= 4 0

( ) .minF C I Wp a p p= 0 7


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TABLE 19.3 Horizontal Force Factors ap and Rp

Elements of Structures and Nonstructural Components and Equipmenta ap Rp Footnote

1. Elements of structuresA. Walls including the following:

(1) Unbraced (cantilevered) parapets2.5 3.0

(2) Exterior walls at or above the ground floor and parapets braced above their centers of gravity

1.0 3.0 b

(3) All interior-bearing and nonbearing walls 1.0 3.0 bB. Penthouse (except when framed by an extension of the structural frame) 2.5 4.0C. Connections for prefabricated structural elements other than walls. See also UBC Section

1632.21.0 3.0 c

2. Nonstructural componentsA. Exterior and interior ornamentations and appendages 2.5 3.0B. Chimneys, stacks and trussed towers supported on or projecting above the roof:

(1) Laterally braced or anchored to the structural frame at a point below their centers of mass 2.5 3.0(2) Laterally braced or anchored to the structural frame at or above their centers of mass 1.0 3.0

C. Signs and billboards 2.5 3.0D. Storage racks (include contents) over 6 ft (1829 mm) tall 2.5 4.0 dE. Permanent floor-supported cabinets and book stacks more than 6 ft (1829 mm) in height

(include contents)1.0 3.0 e

F. Anchorage and lateral bracing for suspended ceilings and light fixtures 1.0 3.0 c, f, g, hG. Access floor systems 1.0 3.0 d, e, iH. Masonry or concrete fences over 6 ft (1829 mm) high 1.0 3.0I. Partitions 1.0 3.0

3. EquipmentA. Tanks and vessels (include contents), including support systems 1.0 3.0B. Electrical, mechanical and plumbing equipment and associated conduit and ductwork and

piping1.0 3.0 e, j, k, l, m,

n, o, pC. Any equipment laterally braced or anchored to the structural frame at a point below its

center of mass2.5 3.0 e, j, n, o, p

D. Anchorage of emergency power supply systems and essential communications equipment. Anchorage and support systems for battery racks and fuel tanks necessary for operation of emergency equipment. See also UBC Section 1632.2

1.0 3.0 q, r

E. Temporary containers with flammable or hazardous materials 1.0 3.0 s4. Other components

A. Rigid components with ductile material and attachments 1.0 3.0 aB. Rigid components with nonductile material or attachments 1.0 1.5 aC. Flexible components with ductile material and attachments 2.5 3.0 aD. Flexible components with nonductile material or attachments 2.5 1.5 a

a See UBC Section 1627 for definitions of flexible components and rigid components.b See UBC Section 1633.2.4 and Section 1633.2.8 for concrete and masonry walls and UBC Section 1632.2 for connectionsfor panel connectors for panels.c Applies to Seismic Zones 2, 3 and 4 only.d Ground supported steel storage racks may be designed using the provisions of UBC Section 1634. Chapter 22, DivisionVl, may be used for design, provided seismic design forces are equal to or greater than those specified in UBC Section 1632.2or Section 1634.2, as appropriate.e 0nly anchorage or restraints need to be designed.f Ceiling weight shall include all light fixtures and other equipment or partitions that are laterally supported by the ceiling.For purposes of determining the seismic force, a ceiling weight of not less than 4 psf (0.19 kN/m2) shall be used.g Ceilings constructed of lath and plaster or gypsum board screw or nail attached to suspended members that support a ceilingat one level extending from wall to wall need not be analyzed, provided the walls are not over 50 ft (15,240 mm) apart.h Light fixtures and mechanical services installed in metal suspension systems for acoustical tile and lay-in panel ceilingsshall be independently supported from the structure above as specified in UBC Standard 25-2, Part III.i Wp for access floor systems shall be the dead load of the access floor system plus 25% of the floor live load plus a 10-psf(0.48 kN/m2) partition load allowance.j Equipment includes, but is not limited to, boilers, chillers, heat exchangers, pumps, air-handling units, cooling towers,control panels, motors, switchgear, transformers and life-safety equipment. It shall include major conduit, ducting andpiping, which services such machinery and equipment and fire sprinkler systems. See UBC Section 1632.2 for additionalrequirements for determining ap for nonrigid or flexibly mounted equipment.


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motion between such attachment points. For this purpose, it is required that the calculation of thisrelative motion be based on the maximum inelastic displacements of the structure. Lastly, it specifiesthat the lateral forces determined with the above formulas be used to design the members and connectionsthat transfer these forces to the structure. In the design of these members and connections, it is necessaryto make use of the load combinations and factors specified for the design of structures, except that thereliability/redundancy factor used in such load combinations may be taken equal to 1.0.

19.7.3 NEHRP Provisions

As the UBC, the NEHRP provisions are also based on ultimate strength design principles and establishminimum design criteria for architectural, mechanical, electrical and nonstructural systems; components;

TABLE 19.3 Horizontal Force Factors ap and Rp (continued)

k Seismic restraints may be omitted from piping and duct supports if all the following conditions are satisfied: Lateralmotion of the piping or duct will not cause damaging impact with other systems; the piping or duct is made of ductilematerial with ductile connections; lateral motion of the piping or duct does not cause impact of fragile appurtenances (e.g.,sprinkler heads) with any other equipment, piping or structural member; lateral motion of the piping or duct does notcause loss of system vertical support; rod-hung supports of less than 12 in. (305 mm) in length have top connections thatcannot develop moments; and support members cantilevered up from the floor are checked for stability.l Seismic restraints may be omitted from electrical raceways, such as cable trays, conduit and bus ducts, if all the followingconditions are satisfied: Lateral motion of the raceway will not cause damaging impact with other systems; lateral motionof the raceway does not cause loss of system vertical support; rod-hung supports of less than 12 in. (305 mm) in lengthhave top connections that cannot develop moments; and support members cantilevered up from the floor are checked forstability.m Piping, ducts and electrical raceways, which must be functional following an earthquake, spanning between differentbuildings or structural systems shall be sufficiently flexible to withstand relative motion of support points assumingout-of-phase motions.n Vibration isolators supporting equipment shall be designed for lateral loads or restrained from displacing laterally byother means. Restraint shall also be provided, which limits vertical displacement, such that lateral restraints do not becomedisengaged. ap and Rp for equipment supported on vibration isolators shall be taken as 2.5 and 1.5, respectively, except thatif the isolation mounting frame is supported by shallow or expansion anchors, the design forces for the anchors calculatedby Equation 8 or 9 shall be additionally multiplied by a factor of 2.0.o Equipment anchorage shall not be designed such that lateral loads are resisted by gravity friction (e.g., friction clips).p Expansion anchors, which are required to resist seismic loads in tension, shall not be used where operational vibratingloads are present.q Movement of components within electrical cabinets, rack- and skid-mounted equipment and portions of skid-mountedelectromechanical equipment that may cause damage to other components by displacing, shall be restricted by attachmentto anchored equipment or support frames.r Batteries on racks shall be restrained against movement in all directions due to earthquake forces.s Seismic restraints may include straps, chains, bolts, barriers or other mechanisms that prevent sliding, falling and breachof containment of flammable and toxic materials. Friction forces may not be used to resist lateral loads in these restraintsunless positive uplift restraint is provided, which ensures that the friction forces act continuously.

Source: Uniform Building CodeTM, International Conference of Building Officials, Whittier, CA, 1987. With permission.Copyright 1997, International Conference of Building Officials (ICBO). ICBO assumes no responsibility for the accuracyor the completeness of this table.

TABLE 19.4 Component Importance Factors Ip

Component Importance Ip

Component required to function after an earthquake 1.5Component containing hazardous contents 1.5Storage racks in occupancies open to the general public

(e.g., warehouse retail stores)1.5

All components needed for continued operation of the facility, or whose failure could impair the continued operation of the facility (for structures in Seismic Group III)

1.5

All other components 1.0


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and elements permanently attached to structures, including supporting structures and components(henceforth collectively referred to as “components”). These design criteria recognize ground motionand structural amplifications, component toughness and weight, and performance expectations. Theyare presented in terms of a required minimum equivalent static force and a minimum relative displace-ment demand when the component is connected to the structure at multiple points.

The required minimum static force is given by

(19.12)

except that Fp need not be greater than

(19.13)

and must not be less than

(19.14)

In the foregoing equations:

Fp = seismic design force applied at the component’s center of mass and distributed according to thecomponent’s mass distribution

SDS = short-period design spectral acceleration, given by SDS = (2/3)SMS, where SMS, in turn, is equal toSMS = FaSs, in which Ss is the maximum spectral acceleration determined for the site underconsideration from the seismic maps in the provisions, and Fa is a coefficient that adjusts Ss forsite effects

ap = component amplification factor selected from Table 19.4 or Table 19.5 according to the type andflexibility of the component, varying between 1.00 and 2.50

Ip = component importance factor equal to either 1.00 or 1.50, selected according to componentimportance from Table 19.4

Rp = component response modification factor selected from Table 19.5 or Table 19.6 according to thetype and deformability of the component, varying between 1.0 and 5.0

z = height above grade of highest point of component attachment (for items at or below structurebase, consider z equal to 0)

h = average height of structure’s roof relative to grade elevationWp = component weight

The seismic force Fp is applied independently longitudinally and transversely in combination withservice loads acting on the component. Horizontal and vertical earthquake effects need to be combinedaccording to

(19.15)

when the vertical and horizontal effects are additive, and

(19.16)

when the vertical effects counteract the horizontal effects. In these two equations:

F Ia S W

R

z

hp p

p DS p

p

= +0 4

1 2.

( )

( ) .maxF S I Wp DS p p= 1 6

( ) .minF S I Wp DS p p= 0 3

E F S Dp DS= +r 0 2.

E F S Dp DS= -r 0 2.


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E = effect of horizontal and vertical earthquake-induced forcesD = dead loadr = reliability factor, allowed to be taken as 1.0 for the design of nonstructural elements

When positive and negative wind loads exceed the value of Fp for nonstructural exterior walls, thesewind loads will govern the design. Similarly, the code-specified horizontal loads will govern the designfor interior partitions when these loads exceed Fp.

TABLE 19.5 Coefficients ap and Rp for Architectural Components

Architectural Component or Element ap a Rp b

1. Interior nonstructural walls and partitions (see also NEHRP Section 6.8)a. Plain (unreinforced) masonry walls 1.0 1.5b. All other walls and partitions 1.0 2.5

2. Cantilever elements (unbraced or braced to structural frame below its center of mass)a. Parapets and cantilever interior nonstructural walls 2.5 2.5b. Chimneys and stacks where laterally supported by structures 2.5 2.5

3. Cantilever elements (braced to structural frame above its center of mass)a. Parapets 1.0 2.5b. Chimneys and stacks 1.0 2.5c. Exterior nonstructural walls 1.0 2.5

4. Exterior nonstructural wall elements and connections (see also NEHRP Section 6.2.4)a. Wall element 1.0 2.5b. Body of wall panel connections 1.0 2.5c. Fasteners of the connecting system 1.25 1.0

5. Veneera. High deformability elements and attachments 1.0 2.5b. Low deformability and attachments 1.0 1.5

6. Penthouses (except when framed by an extension of the building frame) 2.5 3.57. Ceilings (see also NEHRP Section 6.2.6)

a. All 1.0 2.58. Cabinets

a. Storage cabinets and laboratory equipment 1.0 2.59. Access floors (see also NEHRP Section 6.2.7)

a. Special access floors (designed in accordance with NEHRP Section 6.2.7.2) 1.0 2.5b. All other 1.0 1.5

10. Appendages and ornamentations 2.5 2.511. Signs and billboards 2.5 2.512. Other rigid components

a. High deformability elements and attachments 1.0 3.5b. Limited deformability elements and attachments 1.0 2.5c. Low deformability elements and attachments 1.0 1.5

13. Other flexible componentsa. High deformability elements and attachments 2.5 3.5b. Limited deformability elements and attachments 2.5 2.5c. Low deformability elements and attachments 2.5 1.5

a A lower value for ap may be justified by detailed dynamic analysis. The value for ap shall not be less than1.00. The value of ap = 1 is for equipment generally regarded as rigid and rigidly attached. The value of ap

= 2.5 is for flexible components or flexibly attached components. See NEHRP Chapter 2 for definitions ofrigid and flexible components including attachments.b Where flexible diaphragms provide lateral support for walls and partitions, the design forces for anchorageto the diaphragm shall be as specified in NEHRP Section 5.2.5.

Source: NEHRP Recommended Provisions for the Seismic Regulations for New Buildings, Building SeismicSafety Council, Washington, D.C., 2000.


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The required minimum relative displacement demand between two of the connection points of anonstructural component with multiple connection points is determined according to the followingequations:

For two connection points on the same structure or same structural system (Structure A), one pointat level x and the other at level y, the relative displacement is determined according to

(19.17)

except that Dp need not be greater than

(19.18)

For two connection points on separate structures or structural systems, Structure A and Structure B,one at level x and the other at level y, Dp is determined according to

TABLE 19.6 Coefficients ap and Rp for Mechanical and Electrical Components

Mechanical and Electrical Component or Elementa apb Rp

1. General mechanicala. Boilers and furnaces 1.0 2.5b. Pressure vessels on skirts and free-standing 2.5 2.5c. Stacks 2.5 2.5d. Cantilevered chimneys 2.5 2.5e. Other 1.0 2.5

2. Manufacturing and process machinerya. General 1.0 2.5b. Conveyors (nonpersonnel) 2.5 2.5

3. Piping systemsa. High deformability elements and attachments 1.0 3.5b. Limited deformability elements and attachments 1.0 2.5c. Low deformability elements and attachments 1.0 1.5

4. HVAC system equipmenta. Vibration isolated 2.5 2.5b. Nonvibration isolated 1.0 2.5c. Mounted in-line with ductwork 1.0 2.5d. Other 1.0 2.5

5. Elevator components 1.0 2.56. Escalator components 1.0 2.57. Trussed towers (free-standing or guyed) 2.5 2.58. General electrical

a. Distributed systems (bus ducts, conduit, cable tray) 2.5 5.0b. Equipment 1.0 2.5

9. Lighting fixtures 1.0 1.5

a Components mounted on vibration isolation systems shall have a bumper restraintor snubber in each horizontal direction. The design force shall be taken as 2Fp if themaximum clearance (air gap) between the equipment support frame and restraint isgreater than 1/4 in. If the maximum clearance is specified on the construction docu-ments to be not greater than 1/4 in., the design force may be taken as Fp.b A lower value for ap is permitted provided a detailed dynamic analysis is performed,which justifies a lower limit. The value for ap shall not be less than 1.00. The value ofap = 1 is for equipment generally regarded as rigid or rigidly attached. The value of ap

= 2.5 is for flexible components or flexibly attached components. See NEHRP Chapter2 for definitions of rigid and flexible components including attachments.

Source: NEHRP Recommended Provisions for the Seismic Regulations for New Build-ings, Building Seismic Safety Council, Washington, D.C., 2000.

Dp xA yA= -d d

D X Yhp

aA

sx

= -( )D


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(19.19)

except that Dp need not be greater than

(19.20)

In the foregoing equations:

Dp = relative seismic displacement a component must be able to resistdxA, dyA, dyB = deflection at level x of Structure A, deflection at level y of Structure A and deflection at

level y of Structure B, respectively, all determined from an elastic analysis and multipliedby the deflection amplification factor Cd

X = height of upper support attachment at level x as measured from the base of the structureY = height of lower support attachment at level y as measured from the base of the structureDaA, DaB = allowable story drift for Structure A, Structure Bhsx = story height used in the definition of allowable drift Da

In regard to the relative seismic displacements calculated according to the above equations, the NEHRPprovisions require that the effect of these displacements be considered in combination with the displace-ments induced by other loads, such as those generated by thermal and static loads.

The foregoing equations are introduced in recognition that components with multiple points ofconnection such as cladding, stairwells, windows and piping systems need to be designed to resist therelative displacement between their attachment points. The first equation involves the computed dis-placements of the structure. The second, an intended upper bound, is formulated in terms of structuralstory drift limits in consideration of the fact that the structural displacements are not always available atthe time a component is being designed.

For the purpose of the requirements introduced above, components are considered to have the sameseismic design category as that of the structure they occupy or to which they are attached. Similarly,flexible components are those that together with their attachments have a fundamental natural periodof 0.06 sec or greater. Exempted from such requirements are:

1. All components in Seismic Design Category A.2. Architectural components in Seismic Design Category B other than parapets supported by bearing

walls or shear walls when Ip is equal to 1.0.3. Mechanical and electrical components in Seismic Design Category B.4. Mechanical and electrical components in Seismic Design Category C when Ip is equal to 1.0.5. Mechanical and electrical components in Seismic Design Categories D, E and F that are mounted

at 4 ft (1.22 m) or less above a floor level, weigh 400 lb (1780 N) or less, have Ip equal to 1.0 andare provided with flexible connections between the components and associated ductwork, pipingand conduit.

6. Mechanical and electrical components in Seismic Design Categories C, D, E and F that weigh 20lb (95 N) or less (5 lb/ft [7 N/m] or less for distributed systems), have Ip equal to 1.0 and areprovided with flexible connections between the components and associated ductwork, piping andconduit.

Example 19.3. Design lateral force for equipment unit The reciprocating chiller shown in Figure 19.17 is mounted on the roof of a 10-story hospital building.The building is located on the coastal region of Irvine, CA, over a deposit of stiff soil and has a heightof 180 ft (54.9 m). The chiller weighs 15.0 kips (66.7 kN) and is mounted on four flexible isolators todamp the vibrations generated during the operation of the unit. Determine the shear and tension demands

Dp xA yB= +| | | |d d

DX

h

Y

hpaA

sx

aB

sx

= +D D


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on the vibration isolators under earthquake load using (1) the 1997 edition of the UBC; and (2) the 2000edition of the NEHRP provisions.

Solution: (1) For the building under consideration, one has that

hx = hr = 180 ft (54.9 m)

and for Irvine, CA (Zone 4), Soil Profile SD (stiff soil profile), and a near-source factor Na of 1.5 (asknown seismic sources around Irvine are at a distance of less than 2 km [1.2 mi]),

Additionally, according to Footnote of Table 19.3, the horizontal force factors ap and Rp for equipmentsupported on vibration isolators need to be considered equal to

Moreover, the code specifies that for an essential facility (hospital) Ip = 1.5. Therefore, according toEquation 19.9,

which is greater than

but exceeds

FIGURE 19.17 Equipment considered in Example 19.3. (Note: 1 ft = 0.305 m; 1 kip = 4.45 kN; adapted from Sabol,T.A. (1989). Design of nonstructural systems and components, in Seismic Design Handbook, Naeim, F., Ed., VanNostrand Reinhold, New York, chap. 12. With permission.)

5.0 ft

3.0 ftVibrationisolators

Fp

15 k

C Na a= = =0 44 0 44 1 5 0 66. . ( . ) .

a p = 2 5.

Rp = 1 5.

Fa C I

R

h

hWp

p a p

p

x

rp= +( )1 3

= + =2 5 0 66 1 5

1 51 3

180

1806 6

. ( . )( . )

.( ) .W Wp p

= =6 6 15 99 0. ( ) . kips (440.4 kN)

( ) . . ( . )( . ) . ( ) .minF C I W Wp a p p p= = = =0 7 0 7 0 66 1 5 0 69 15 10 4 kips (46.3 kN)


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Accordingly, the lateral force for the design of the chiller’s support system will be taken equal to

Fp = 59.4 kips (264.2 kN)

Correspondingly, the shear force in each vibration isolator becomes

To compute the uplift force on each isolator, the overturning moment is determined first. For thispurpose, note that the moment generated by the lateral force Fp is resisted by the moment generated bythe gravity load. Combining, then, the earthquake and gravity loads according to the load combination0.9D ± E, the resultant overturning moment is

M0 = 59.4(3) – 0/9(15)(2.5) = 144.5 kip-ft (195.9 kN-m)

Hence, the uplift force on each isolator is equal to

(2) From the seismic maps in the 2000 NEHRP provisions for the coastal region of Irvine, CA, themaximum considered earthquake spectral response acceleration for short periods corresponding to SiteClass B is equal to

and the value of the coefficient Fa to adjust for Site Class D, the site class corresponding to stiff soils, isequal to

Fa = 1.0

As a result, for the location under consideration, the maximum considered earthquake spectral acceler-ation for short periods, adjusted for class site, is

and the corresponding design spectral response acceleration for short periods is

In like fashion, from Table 19.6 one has that for vibration-isolated HVAC equipment, ap and Rp are equal to

( ) . . ( . )( . ) . ( ) .maxF C I W Wp a p p p= = = =4 0 4 0 0 66 1 5 3 96 15 59 4 kips (264.2 kN)

V Fp= = =/ . / .4 59 4 4 14 8 kips (66.1 kN)

Ft = =1

2

144 5

5 014 5

.

.. kips (64.5 kN)

Ss = 2 0.

S F SMS a s= = =( . )( . ) .1 0 2 0 2 0

S SDS MS= = =2

3

2

32 0 1 33( . ) .

a p = 2 5.

Rp = 2 5.


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and from Table 19.4, for equipment that is required to function after an earthquake,

Accordingly, since for the building and equipment location under consideration,

z = h = 180 feet

Equation 19.12 yields

which is greater than

but less than

It should be noted, however, that the provisions require that the force Fp be doubled for componentsmounted on vibration isolators. Therefore, the chiller’s support system should be designed for a lateralforce equal to

and, correspondingly, each isolator should be designed for a shear force equal to

In like fashion, if the vertical and horizontal earthquake effects are combined according to Equation19.15, the overturning moment due to earthquake effects results as

which, when combined with the gravity load according to the load combination 0.9D ± E, leads to

Consequently, the uplift force on each isolator is equal to

I p = 1 5.

F Ia S W

R

z

hp p

p DS p

p

= +0 4

1 2.

( )

= + =( . ). ( . )( . )

.( ) .1 5

0 4 2 5 1 33

2 51 2

180

1802 39W Wp p

= =2 39 15 35 9. ( ) . kips (159.7 kN)

( ) . . ( . )( . ) . . ( ) .minF S I W W Wp DS p p p p= = = = =0 3 0 3 1 33 1 5 0 60 0 60 15 9 0 kips (40.0 kN)

( ) . . ( . )( . ) . . ( ) .maxF S I W W Wp DS p p p p= = = = =1 6 1 6 1 33 1 5 3 19 3 19 15 47 9 kips (213.1 kN)

Fp = =2 35 9 71 8( . ) . kips (319.4 kN)

V Fp= = =/ . / .4 71 8 4 18 0 kips (79.9 kN)

M 0 71 8 3 0 2 1 33 15 2 5 225 4= + =. ( ) . ( . )( )( . ) . kip - ft (305.6 kN -m)

( ) .M D E0 225 4+ = = -0.9(15)(2.5) 191.6 kip - ft (259.8 kN -m)

Ft = =1

2

191 6

5 019 2

.

.. kips (85.4 kN)


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19.8 General Design Considerations

19.8.1 Architectural Elements

Past earthquakes have provided numerous examples of damage to architectural elements. The mostfrequently damaged architectural elements have been ceilings, partitions, stairways, facades and parapets.This damage has mainly been due to either inadequate strength or inadequate anchoring. In general,therefore, architectural elements can be made resistant to earthquake motions following one of twostrategies: (1) an isolation strategy and (2) a load-bearing strategy. In the isolation strategy the elementsare sufficiently separated from the structure so that the deformation of the structure will not producesignificant stresses in the architectural elements. In the load-bearing strategy the elements are designedto undergo the required stresses and deformations. An example of the application of these alternativestrategies is shown in Figure 19.18. This figure illustrates how an infill panel in a framed building maybe either isolated or integrated with the structure. It should be noted, however, that in many instancesit is difficult to justify the load-bearing strategy from an economic point of view. The exception wouldbe when the integration of the nonstructural elements with the structure favorably increases the strengthand stiffness of the structure. In any case, the designer must recognize that if the architectural elementsare not sufficiently separated from the structure, their stiffness and strength may have an unintended effecton the response of the structure itself. A classical example of such an unintended effect is the so-called short-column failures observed during past earthquakes (see Figure 19.19). These failures are induced by theshortening of a column’s height by a nonstructural wall and the consequent increase in the magnitudeof the shearing forces acting on the column (recall that the shear force in a column is equal to (MA +MB)/H, where MA and MB are the bending moments at the ends of the column and H its height). Whenthe isolation strategy is adopted, the separation required to prevent or limit the damage sustained by

FIGURE 19.18 Separated and integrated infill panels in a framed structure.

FIGURE 19.19 Schematic illustration of column failure caused by unintended restrain by infill wall. (Adapted fromSabol, T.A. (1989). Design of nonstructural systems and components, in Seismic Design Handbook, Naeim, F., Ed.,Van Nostrand Reinhold, New York, chap. 12. With permission.)

Integratedpanel

Separatedpanel

Column

Beam

Beam

Inte

nded

col

umn

heig

ht

Actual column height

Shear failure ofcolumn causedby restrain frommasonry wall

Masonry wall


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architectural elements should be established on the basis of the anticipated structural drifts. In addition,the nonstructural elements themselves must be restrained against the forces acting on them.

A variety of measures to prevent damage to architectural elements have been proven successful duringpast earthquakes. These measures, adapted here from those reported by Sabol (1989), are summarizedin Table 19.7 through Table 19.10. Useful additional guidelines and information may be found in FEMA74 (Federal Emergency Management Agency, 1994), FEMA 273 (NEHRP Guidelines for the SeismicRehabilitation of Buildings, 1997) and FEMA 274 (NEHRP Commentary on the Guidelines for the SeismicRehabilitation of Buildings, 1997).

19.8.2 Mechanical and Electrical Equipment

Earthquakes have also caused considerable damage to mechanical and electrical equipment, especially toboilers, chillers, generators, tanks, fans, pumps, air handlers, electrical distribution systems, emergencypower and lighting systems, elevators, light fixtures, HVAC ducts and piping systems. As opposed toarchitectural elements, however, most mechanical and electrical equipment units are purchased as man-ufactured items rather than being fabricated specifically for a project. Therefore, the susceptibility ofequipment to seismic damage is controlled mainly by the equipment manufacturer. It is possible, none-theless, to take preventive measures in the installation of equipment to minimize its susceptibility todamage.

In general, there are two classes of equipment installations that are of interest with respect to seismicdesign: (1) equipment anchored to the ground or to the building structure or (2) equipment mountedon vibration isolators. Vibrating equipment, such as chillers or emergency generators, has traditionally

TABLE 19.7 Design Recommendations for Facades and Glazing

1. Use heavy rigid facades only on rigid structural systems and not on relatively flexible building frames2. Securely attach curtain walls to the building frame. Design and installed flexible gaskets in curtain walls so that they do

not come loose when the wall is subjected to repeated racking3. Set all glass panels in resilient mounts with sufficient space for in-plane motions and supported by mullions designed to

withstand earthquake forces. Use tempered glass in exits or where large glazed areas are near public walks4. Avoid brick veneer facades on steel-frame buildings unless the brick veneer is securely tied to a separate wall that is

independent of the steel frame5. Do not use wire or straight-rod ties to anchor face brick to a wall, especially when a layer of insulation or an air gap

separates the two elements6. Consider large masonry facades as part of the structural system and not as nonstructural ornaments unless they are

properly attached to a structural wall

Source: Sabol, T.A. (1989). Design of nonstructural systems and components, in Seismic Design Handbook, Naeim, F., Ed.,Van Nostrand Reinhold, New York, chap. 12. With permission.

TABLE 19.8 Design Recommendations for Partitions and Infill Panels

1. Do not install concrete-masonry-unit filler walls in a manner that would restrain the lateral deflection of the building frame. Leave, instead, a gap with adequately sized resilient filler to separate the structural frame from the nonstructural filler walls (see Figure 19.20 through Figure 19.22 for illustrations of how this separation may be provided while at the same time bracing the wall against out-of-plane motion; Figure 19.20 illustrates one method for heavy partitions, while Figure 19.21 and Figure 19.22 illustrate methods for full and partial light-weight partitions)

2. Anchor partitions in buildings with flexible structural frames to only one structural element, such as a floor slab, and separate them by a physical gap from all other elements

3. Do not use unreinforced masonry for partitions or filler walls4. Consider reinforced masonry partitions tied to more than one structural element as part of the structural system5. Tie conduits and piping in partitions to the structural element to which the partition is anchored6. Properly reinforce openings in partitions for pipes, conduits and ducts and make them large enough to preclude direct

contact with fixtures



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been mounted on resilient mounting systems, particularly when the equipment is on the upper floorsof a structure. The resilient mounting devices used may be springs, pneumatic restraining devices orelastic restraining devices. Failure of equipment directly mounted on the ground or building normallyreflect insufficient anchor strength or the inability of connecting service piping to reconcile differentialsettlements. Failure of equipment mounted on vibration isolators occurs because of the isolators’ inability

FIGURE 19.20 Details to separate nonbearing masonry wall from structure: (a) under steel beam; (b) perpendicularto steel deck; (c) parallel to steel deck. (Adapted from Sabol, T.A. (1989). Design of nonstructural systems and components,in Seismic Design Handbook, Naeim, F., Ed., Van Nostrand Reinhold, New York, chap. 12. With permission.)

FIGURE 19.21 Seismic bracing of full lightweight partitions. (From Federal Emergency Management Agency,Reducing the Risks of Nonstructural Earthquake Damage, A Practical Guide, FEMA, Washington, D.C., 1994.)

3/16 2 – 10

L6 ´6 ´5/16 ´1' – 0"with 2 – 5/8" dia. exp.bolts @ 8" o.c. 5"

1/2"

Provide 5/8" dia.oversized holesin angle

(a)

L6 ´3– 1/2 ´5/16 ´1' – 0"with 2 – 5/8" dia. exp.bolts @8" o.c.

Provide 5/8" dia.oversized holesin angle

3"

1–1/2"

(c)

L4 ´4 ´1/4 ´1' – 0"each side with 2 – 5/8" dia. exp.bolts @ 9" o.c.

1/2" 3"

(b)

• HEAVIER GAGE METAL STUDS ANDATTACHMENTS MAY BE REQUIRED IFHEAVY SHELVES ARE TO BE LATERALLYSUPPORTED BY PARTITION.

• ADDITION OF MID-HEIGHT BLOCKING ORSURFACE-MOUNTED “SEISMICMOLDING” PROVIDES FLEXIBILITY FOR EQUIPMENT ANCHORAGE LOCATIONS.

• FOR GLAZED PARTITIONS, SEE“WINDOWS”.

STRUCTURE ABOVE

FLOOR

PARTITION FIXED AT BASE.

PARTITION FREE TO SLIDEAT TOP BUT RESTRAINEDLATERALLY. PACKING OR SEALANT REQUIRED FOR ACOUSTIC ISOLATION.FIRE RATING MUST BE CHECKED FOR FIRESEPARATION WALLS(“1-HOUR” WALLS, ETC.)

METAL ORWOOD STUDS


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to undergo the large lateral displacements they are subjected to during an earthquake, displacements thatare often significantly greater than those contemplated by the manufacturer. These large lateral displace-ments are caused by the long period of the resilient mounting devices, which in many cases are in therange of the building period.

FIGURE 19.22 Seismic bracing of partial lightweight partitions. (From Federal Emergency Management Agency,Reducing the Risks of Nonstructural Earthquake Damage, A Practical Guide, FEMA, Washington, D.C., 1994.)

TABLE 19.9 Design Recommendations for Ceilings

1. Do not install fluorescent lighting fixtures in or on exposed T-grid or concealed-spline suspended ceilings unless the ceiling suspension system is designed to carry the added weight of the fixtures during an earthquake or the fixtures are independently supported and laterally braced

2. Laterally brace exposed T-grid or concealed-spline suspended ceilings and provide them with a physical separation at the walls, particularly in large rooms with high ceilings and deep attic spaces (see Figure 19.23 and Figure 19.24 for general guidelines to brace suspended ceilings)

3. Do not fasten ceiling system to surrounding walls or partitions. Use soffits to return the ceiling to the supporting slab. Provide an angle wall trim, wide enough to allow for differential movements, where the ceiling must join a wall or partition. Provide hangers for the main and cross runners at the perimeter so that wall trims do not support the ceiling

4. Brace rigid ceiling systems at regular intervals against lateral and vertical movements5. Reinforce gypsum-board ceilings at nail points by the use of steel nailing strips. Use nails with large heads to install

gypsum-board ceilings6. In gypsum board and lath and plaster ceiling systems, make furring channel joints in irregular-shaped ceilings using

rivets, bolts and welds. Brace corners so that they do not pivot7. In gypsum board and lath and plaster ceiling systems, hold together large ceiling areas separated by rows of linear diffusers

or light fixtures with rigid ties and secure the diffusers and light fixtures to the ceiling system


TABLE 19.10 Design Recommendations for Storage Racks and Cabinets

1. Design storage racks to withstand earthquake forces and anchor them to the floor or brace them laterally from the top to the structural elements

2. Design racks with lateral bracing and anchor bolts so that they can withstand anticipated lateral and uplift loads3. Install rigid ties at the top of rows of racks to brace and stabilize the entire installation4. Anchor racks placed along walls to the walls to avoid battering between wall and rack5. Anchor filing cabinets and map or plan drawers to the floor or walls, and fit all drawers with positive-locking safety latches6. Anchor vital furniture and equipment to the floor or wall7. Held in place loose materials stored on high shelves by face bars8. Keep medical supplies in cabinets that are anchored to the floor or walls and fitted with latched doors


• Heavier braces or closer spacingmay be required if partition used to support or seismically restrain heavy shelves or other nonstructural items

60 ° Maximum

Partial-heightpartition

Anchor bolt or lag boltattached to structure above

Angle braces at approximately 6'on centers

5/6" diameterbolt/TYP

One bolt or three (3)#13 sheet metal orwood screws, TYP


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A variety of measures may be taken to minimize damage to mechanical and electrical equipment.These measures, also based on those reported by Sabol (1989), are summarized in Tables 19.11throughTable 19.18. FEMA 74 (Federal Emergency Management Agency, 1994), FEMA 273 (NEHRP Guidelinesfor the Seismic Rehabilitation of Buildings, 1997) and FEMA 274 (NEHRP Commentary on the Guidelinesfor the Seismic Rehabilitation of Buildings, 1997) offer useful additional guidelines.

19.9 Role of Nonstructural Elements in Performance-Based Design

It is estimated that approximately 70 to 85% of the cost of a building comes from its nonstructuralelements. Given the susceptibility of nonstructural elements to earthquake damage, this means that amajor portion of the damage induced in a building during an earthquake will most likely be that inflicted

FIGURE 19.23 Seismic bracing system for suspended T-bar ceiling systems. (From Federal Emergency ManagementAgency, Reducing the Risks of Nonstructural Earthquake Damage, A Practical Guide, FEMA, Washington, D.C., 1994.)

FIGURE 19.24 Bracing detail for suspended ceilings. (Adapted from Sabol, T.A. (1989). Design of nonstructural systemsand components, in Seismic Design Handbook, Naeim, F., Ed., Van Nostrand Reinhold, New York, chap. 12. With permission.)

Anchor wiresto structureabove

Approx. 45°

Provide 4-waydiagonal bracingand compressionstrutapproximatelyevery 12 ft. eachway.

45°

45°45°

Mainrunner

Min. 3tightturns in1–1/2"each endof wire

Cross runner

Adjustablelengthcompressionstrut topreventverticalmovement

Diagonal bracing wires(no. 12 gauge)

12 ga. wire to main runnerin 4 directions spaced @90°in addition to vertical supportrequirements

Vertical 12 ga. wireto support main runneror cross runner

8"max.

2" max.

Gap on 2 sidesto accommodatemovement

11

Suspended ceiling

Support angle

12' o.c. ea. direction (max.)

Self-bracing wall

Main runner


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to its nonstructural elements. This also means that a large portion of the potential losses to owners, occupants,insurance companies and other financial institutions will be those associated with nonstructural elements.Evidently, the overall seismic performance of a building greatly depends on the seismic performance ofits nonstructural elements.

The need for a satisfactory performance of nonstructural elements and the role of these elements inthe overall seismic performance of buildings have been widely recognized in the development of meth-odologies for the implementation of performance-based designs. As the major goal of a performance-based design is to produce buildings that will endure levels of damage that will not exceed preselectedacceptable levels under different ground motion intensities, performance levels have been established forboth structural and nonstructural elements. Similar to the performance levels developed for structuralsystems, the performance-based design concept applied to nonstructural elements also implies the def-

TABLE 19.11 Design Recommendations for Mechanical Equipment With Vibration Isolation

1. Do not mount heavy mechanical equipment on the upper floors of tall buildings unless all vibration-isolation mounts are carefully designed for earthquake resistance

2. Bolt floor-mounted vibration-isolation devices to the equipment base and to the structural slab3. Avoid the use of heavy bases under equipment mounted on vibration isolators to reduce inertial forces4. Provide lateral and vertical restraining devices around the base of vibration-isolated, floor-mounted equipment to restrict

its displacements5. Provide resilient material on the contact surface of the restraining devices to minimize impact loads. Tightly install the

vibration-isolation hangers for suspended equipment against the supporting structural member. Provide a structural restraining frame around suspended heavy equipment

6. Provide cross bracing between hanger rods on all fours sides of suspended lightweight equipment


TABLE 19.12 Design Recommendations for Mechanical Equipment without Vibration Isolation

1. Design the support for tanks and heavy equipment to withstand earthquake forces and anchor it to the floor or secure it otherwise

2. Strap suspended tanks and heavy equipment to their hanger system and provide them with lateral bracing3. Strap all horizontal tanks to their saddles, weld lugs to the tanks at support points to prevent horizontal movement, and

bolt saddles to the structural slab4. Provide frames supporting elevated tanks or equipment with adequate bracing and anchor them to the structural slabs

and walls5. Bolt all floor-mounted equipment to the structural slab


TABLE 19.13 Design Recommendations for Piping Systems

1. Tie pipelines to only one structural system2. Where structural systems change and relative deflections are anticipated, install movable joints in the piping system to

allow for such movement (see Figure 19.25 for an illustration of such an arrangement)3. Provide suspended piping systems with consistent freedom throughout. For example, do not anchor branch lines to

structural elements if the main line is allowed to sway4. If the piping system is allowed to sway, install movable joints at equipment connections5. Guide pipelines leading to thermal expansion loops or flexible pipe connections to confine the degree of pipe movement6. Do not make pipes cross seismic joints. If they must do so, make the crossing at the lowest floor possible, and carefully

evaluate all pipe deflections and stresses7. Provide pipes with flexible joints where pipes pass through seismic or expansion joints, or where rigidly supported pipes

connect to equipment with vibration isolation (see Figure 19.26 for a suggested detail for piping that crosses a seismic joint)8. Provide sway bracing in both longitudinal and transverse directions on all pipes with a diameter of 21/2 in. or larger to

limit the stresses in the pipes (Figure 19.27 illustrates a method to provide this sway bracing)



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FIGURE 19.25 Possible arrangement to allow for relative deflections in pipes. (Adapted from Sabol, T.A. (1989).Design of nonstructural systems and components, in Seismic Design Handbook, Naeim, F., Ed., Van Nostrand Reinhold, NewYork, chap. 12. With permission.)

FIGURE 19.26 Detail (plan view) to provide for pipe crossing seismic gap. (Adapted from Sabol, T.A. (1989). Designof nonstructural systems and components, in Seismic Design Handbook, Naeim, F., Ed., Van Nostrand Reinhold, NewYork, chap. 12. With permission.)

FIGURE 19.27 Pipe clamp and sway bracing. (Adapted from Sabol, T.A., Design of nonstructural systems andcomponents, in Seismic Design Handbook, Naeim, F., Ed., Van Nostrand Reinhold, New York, 1989. With permission.)

TABLE 19.14 Design Recommendations for Air Distribution Systems

1. Provide long hangers and supports for ductwork with lateral bracing2. Install flexible duct connections in a semifolded condition with enough material to allow for the expected differential

movement between fans and ductwork3. Make pipe sleeves or duct openings through walls or floors large enough to allow for the anticipated movement of the

pipes or ducts4. Support horizontal ducts as close as possible to the supporting structural member5. Secure ceiling diffusers and registers to the ductwork with sheet-metal screws6. Tie diffusers connected to flexible ducts with positive ties to the ductwork and/or wall opening


Ball joint

Possible lateraland longitudinaldisplacement

Possible longitudinal andlateral wall displacement

Seismic gap

Wall

Wall opening

Pipe

Anchor bolt

Steel strap

Pipe Pipe clamp


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inition of multiple target performance levels that are expected to be achieved when the structure issubjected to earthquake ground motions of specified intensities. Some of the proposed performancelevels for nonstructural elements are shown in Table 19.19 (Applied Technology Council, 1996). Similarperformance levels have also been introduced in the NEHRP Guidelines for the Seismic Rehabilitation ofBuildings (1997), although those in these guidelines are described separately for different architectural

TABLE 19.15 Design Recommendations for Elevators

1. Bolt vibration isolators under the motor generators to the floor and to the legs of the motor generators. Provide the isolators with sufficient strength to withstand the earthquake forces

2. Bolt selector and controller panels to the floor and, if possible, provide them with sway braces at the top3. Secure all electrical components within the panels to the panel frame, and fit all doors and hinged panels with positive-

locking latches4. Use counterweight guide rails that are 15 lb/ft or heavier for serving buildings of five or more stories, and design their

supports to withstand earthquake forces5. Use a safety shoe in the design of the counterweight guide-rail bracket. The type of bracket used should depend on the

building height and location in the hoistway6. Provide properly designed safety shoes for the roller guides to protect the roller assemblies from being damaged by the

counterweights7. Strengthen counterweight guide rails by using a section heavier than the typical 8-lb/ft rolled section. Strengthen brackets

using gusset plates or ties placed at frequent intervals8. Strengthen the car guide rails on long spans by installing spacers between the back-to-back rails at midpoints between

the separator beams. This increases the rigidity of both rails9. Connect ventilation, communications and lighting systems to emergency power systems and design them to operate

when the normal power fails10. Provide seismic switches to shut down the elevator during an earthquake and then lower the cars to the nearest floor11. Adequately reinforce and brace the elevator hoistway and the surrounding structural system to prevent distortion at the

doors and prevent debris from falling into the shaft12. Secure hydraulic elevator equipment to floors and walls, and use splash-proof oil tanks


TABLE 19.16 Design Recommendations for Light Fixtures

1. Provide pendant-hung fluorescent fixtures, especially when mounted end to end in long rows, with flexible lateral bracing at both the ceiling supports and the bottom connections to the fixtures

2. Locate lighting fixtures supported by flexible hangers so that they will not collide with other building elements3. Do not use support systems designed for pendant mounting from a horizontal surface on a sloping surface because some

of the freedom of movement is used up in the vertical alignment4. Do not locate pendant light fixtures below high ceilings. They should be surface mounted and secured to a supporting

grid system that meets the supporting and bracing requirements for suspended ceilings5. Preferably, directly attach surface-mounted fixtures to the building structure. However, suspended installations that use

positive-locking devices are an acceptable alternative


TABLE 19.17 Design Recommendations for Electrical Equipment

1. Anchor all electrical equipment such as transformers, switchgears and control panels to the building, etc.2. Use flexible braided connections in place of rigid copper bus, whenever relative movement may occur between switchboard

components3. Provide additional pull boxes with slack conductors in long conduit runs to avoid tension of conductors4. Avoid crossing seismic joints with conduits and bus ducts where possible. When seismic joints are crossed, use

arrangements that permit the required deflections. Make the crossing at the lowest possible floor5. Provide separate ground conductors in all conduit runs that cross seismic joints and elsewhere in the electrical system

where grounding systems could be broken



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elements and mechanical, electrical and plumbing equipment. Acceptability criteria, i.e., the conditionsthat must be satisfied to ensure that the performance objectives are met, have also been established fornonstructural elements. For the most part, these acceptability criteria have been formulated in terms ofkey limiting values of measurable structural response parameters such as floor accelerations and storydrift ratios. As an example of how these acceptability criteria may be set up, Bertero and Bertero (2002)suggest the format shown in Table 19.20, where the probabilities indicated are those of exceeding thestated performance objectives.

As in the case of structural systems, the selection of the performance levels for nonstructural elementsis based on a balance between potential losses and the cost of damage mitigation measures, consideringin the potential losses not only the direct cost of earthquake damage, but also indirect losses such asbusiness interruptions. Thus, for example, financial or physical constraints may compel a designer toselect the Reduced Hazards objective for the 970-year return period when rehabilitating an existingbuilding. On the other hand, the designer may select the Operational objective for essential facilities such

TABLE 19.18 Design Recommendations for Emergency Power and Lighting Systems

1. Mount emergency power generators installed in buildings on adequately designed vibration isolators2. Provide vibration isolators and connecting service piping with horizontal restraints3. Adequately secure starter battery racks to the structure. Attach each battery to the rack with a positive mounting to

restrain movement4. Securely tie battery-powered emergency lighting units to the building.


TABLE 19.19 Performance Levels for Nonstructural Elements

Performance Objective Damage State

Operational Nonstructural elements remain in place and functional with negligible damage; undamaged back-up systems provide protection against failure of external utilities, communications and transportation systems

Immediate occupancy Nonstructural elements remain in place but may not be functional. No back-up systems for failure of external utilities are provided

Life safety Nonstructural elements are damaged considerably, but there are no collapses of heavy items, nor secondary hazards such as breaks in high-pressure toxic or fire suppression piping

Reduced hazards Nonstructural elements are damaged extensively, but there are no collapses of large and heavy items that can cause significant injury to groups of people

Not considered Performance of nonstructural elements other than those having an effect in structural response is not evaluated

Source: Applied Technology Council, Seismic Evaluation and Retrofit of Concrete Buildings, Redwood City, CA, 1996. Withpermission.

TABLE 19.20 Example of Acceptability Limits for Nonstructural Elements

PerformanceObjective

Return Period (Years)

Probability of Exceedance

(%)

Nonstructural Damage Contents Damage

Story Drift Ratio Floor Acceleration

Fully operational 43 40 0.003 0.6 gOperational 75 30 0.006 0.9 gLife safety 475 25 0.015 1.2 gNear collapse 970 20 0.020 1.5 g

Source: Bertero, R.D. and Bertero, V.V., Earthquake Eng. Struct. Dyn., 31(3), 627–652, 2002.With permission.


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as hospitals, police and fire stations and emergency command centers since essential facilities are expectedto be fully functional during or shortly after an earthquake.

As a final note, it should be mentioned that a performance-based design of nonstructural componentsis based on the premise that their performance can be predicted and evaluated with sufficient confidenceso as to make an intelligent and informed decision on the cost and benefits of earthquake protection.However, as it may be inferred from the material presented in this chapter, such a capability is not quitethere yet. It should be realized, therefore, that much research is needed to develop reliable techniquesfor the assessment of seismic demands and capacities and establish effective damage mitigation measuresbefore the performance-based design of nonstructural elements may be brought into fruition (see alsoChapter 9).

19.10 Future Challenges

As seen from the discussion in the preceding sections, much progress has been made toward the under-standing of the seismic behavior of nonstructural elements, the development of simplified methods ofanalysis and the improvement of the code provisions for the seismic design of these elements. Notwith-standing this progress, it is also clear from the same discussion and the damage sustained by nonstructuralelements during recent earthquakes that the problem is a complex one and has not been completelysolved. Therefore, research is needed to further advance the understanding of the seismic behavior ofnonstructural elements, to derive methods of analysis that are rational but also simple enough for theirincorporation into building codes and to further improve the code provisions for the design of theseelements. One particular area of research that is urgently needed to advance the understanding of theseismic behavior of nonstructural elements and develop effective methods of analysis is that related tothe effect on this behavior of the nonlinearity of their supporting structures and the nonstructuralelements themselves. As discussed in Section 19.6.2, there is some analytical evidence that indicates thatthe nonlinearity of a supporting structure may significantly affect the seismic response of a nonstructuralelement. In some cases it may considerably reduce the response of the nonstructural element, but insome others it may increase it. However, only a limited number of studies have been conducted to clarifyand quantify such an effect, and only a few simplified methods of analysis that account for it have beenproposed. Another area of research that deserves full consideration is the application of modern isolationand protective systems to nonstructural elements. Given their relatively small size and the high acceler-ations to which they may be subjected, important benefits may be realized from the use of such systems.An extensive program of experimental tests and field studies is also needed. The experimental tests areneeded to verify the findings from analytical studies; to quantify the stiffness, damping, ductility anddrift limits of nonstructural elements and their anchorages; to test the adequacy of current and newbracing methods and anchoring systems; and to test the effectiveness of isolation and protective systems.The field studies are needed to study the performance of actual elements on actual buildings under realearthquakes, and to contrast this performance against the results from analytical and experimental studies.Finally, research is needed to develop rational and reliable methodologies for the implementation ofperformance-based designs (see also Chapter 9).

19.11 Summary

This chapter provided a basic depiction of the behavior of nonstructural elements under the effect ofearthquakes, the methods that are presently available to analyze them under such effects and the pertinentdesign recommendations given in current building codes. It began with a description of what preciselyare nonstructural elements, what has been their performance during past earthquakes and why it is soimportant to make them the subject of a rational seismic design. A description was also given of thecharacteristics that make nonstructural elements particularly vulnerable to the effects of earthquakes,and what is currently known about their behavior under earthquake excitations. In addition, two methods


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to perform the seismic response analysis of nonstructural elements were presented in some detail, anda brief description of some other methods that have been proposed to simplify such an analysis wasgiven. The methods discussed were (1) the floor response spectrum method and (2) a design-orientedsimplified method. The floor response spectrum method involves a time-history analysis to obtain theacceleration response of the point of the building to which the nonstructural element is attached andthe generation of the response spectrum that corresponds to this acceleration response. The design-oriented simplified method entails the application of a few simple formulas to calculate the magnitudeof the lateral seismic forces for which nonstructural elements should be designed. This method incor-porates an approximate scheme to take into account the nonlinear behavior of the nonstructural elementand the building that supports it. It is pointed out that, in general, nonstructural elements are difficultto analyze accurately and efficiently. The floor response spectrum method, for example, is cumbersomesince it requires time-history analyses and the generation of a response spectrum for each building pointwhere there is a nonstructural element attached to it. It ignores, in addition, the dynamic interactionbetween an element and its supporting structure. As a result, it may sometimes give overly conservativeresults. Similarly, the design-oriented simplified method, although simple to use, may give results thatdeviate significantly — usually on the conservative side — from those that one would obtain using arigorous approach. The chapter proceeded with a review of the recommendations given in the 1997version of the UBC and the 2000 NEHRP provisions for the seismic design of nonstructural elements.Some general design recommendations and preventive measures that have been proven effective toimprove the seismic resistance of some architectural elements and mechanical and electrical equipmentwere also included. Finally, a brief discussion was given of the important role that nonstructural elementsplay in the performance-based design of buildings and the research that is needed to further advance theunderstanding of the seismic behavior of nonstructural elements and improve the methods of analysisand code provisions for the design of these elements.

Glossary

Closely spaced natural frequencies — Natural frequencies with similar numerical values.Combined system — System that comprises nonstructural element and supporting structure.Dynamic interaction — Effect that a nonstructural element may have in the dynamic response of its

supporting structure and vice versa.Flexible element — Element having a fundamental natural period greater than 0.06 sec.Floor acceleration — Acceleration induced by an earthquake ground motion at the level of a building’s

floor.Floor response spectrum — Response spectrum of floor motion generated by an earthquake.In-structure spectrum — A floor response spectrum.Isolated element — Element separated from the structure in which it is installed to avoid stresses and

deformations in it when the structure is deformed.Load-bearing element — Element designed to resist stresses and deformations.Modal synthesis technique — Technique by means of which the dynamic properties of a combined

system are obtained from the dynamic properties of its separate components.Multiply connected element — Element connected to its supporting structure at more than one point.Nonclassical damping effects — Effects that arise when a structure does not possess classical modes of

vibration.Nonstructural element — Element attached to floor or wall of a building but not part of the building’s

main structural system.Rigid element — Element having a fundamental natural period equal to or less than 0.06 sec.


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List of Symbols

ap component amplification factorb variable defined by Equation 19.7C spectral ordinateCm modified amplification factorCp amplification factorD dead loadDp component relative displacementE effect of horizontal and vertical earthquake forcesf fundamental natural frequency of structureFa site coefficient for short periodsFp design force on nonstructural elementFpj force at center of jth mass of nonstructural elementh average height of structure’s roofhav average of elevations above grade of attachment pointshi elevation above grade of ith building floorhsx story height used in the definition of allowable drift Da

I importance factor for structurelj distance from attachment point to jth mass of nonstructural elementIp importance factor for nonstructural elementn number of masses in nonstructural elementn¢¢¢¢ number of resisting elements in nonstructural elementN number of floors in buildingRp component response modification factorSDS design short-period spectral accelerationSMS spectral acceleration adjusted for site effectsSs maximum spectral acceleration determined from seismic hazard mapsT fundamental natural period of structureTp fundamental natural period of nonstructural elementVp base shear or sum of the shears at the supports of nonstructural elementwp total weight of nonstructural elementwpj weight of jth mass of nonstructural elementW total building weightWi weight of building’s ith floorWp component weightX height of upper support attachmentY height of lower support attachmentz height of highest point of component attachmentdxA deflection at level x of Structure AdyA deflection at level y of Structure AdyB deflection at level y of Structure BDaA allowable story drift for Structure ADaB allowable story drift for Structure BF0 variable defined by Equation 19.6l variable defined by Equation 19.3m ductility factor of structuremeq equivalent ductility factormp ductility factor of nonstructural elementr reliability factor


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Análisis y diseño de elementos no estructurales

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