non-structural components in low-moderate seismic regions

8/11/2019 Non-structural Components in Low-moderate Seismic Regions

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Earthquake Engineering in the low and moderate seismic regions of Southeast Asia and Australia (2008)

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1 INTRODUCTION

Non-structural components in the context of this pa-

per refer to architectural features, mechani-cal/electrical equipment providing services to thebuilding and building contents (refer Table 1).Widespread damage to non-structural components inbuildings continues to be observed in recent earth-quakes. Whilst statistical cost data for non-structuraldamage are scarce, it is widely agreed and reportedthat the economic effects of all non-structural dam-age combined generally exceed those of structuraldamage in an earthquake (Brunsdon & Clark, 2001).For example, in a survey of 355 high-rise buildings

after the 1971 San Fernando earthquake, it wasshown that in dollar value terms, 79% of the damagewas non-structural (Arnold et al, 1987). Despite this,earthquake engineering research worldwide has beendirected mainly to performance issues associated di-rectly with the structural elements or the buildingstructure as a whole.

The argument for explicit considerations of non-structural damage is even stronger in low to moder-ate seismicity regions which are characterized by theinfrequent occurrences of earthquakes of low-medium magnitude (


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adequate support by effective brick ties. Anotherclass of potentially vulnerable items which has be-come a feature of the urban streetscape in cities likeHong Kong is advertisement signs that proliferateabove the road pavement. Gantries supporting thesigns from the building facade can become vulner-able in an earthquake because of their sensitivity toforce (acceleration) demand at ultimate conditions.Furthermore, the seismically induced inertia forcesapplied to the sign gantry can superpose on the gra-vitational forces (whilst wind forces would not nec-essarily superpose in the same way). When the forcecapacity of the attachment has been overcome, theamount of displacement required to dislodge thegantry can be merely the embedment depth of theanchor bolts.

The objective of this paper is to review our cur-

rent state of knowledge on the key issues that havebeen outlined. Section 2 contains a review of theconventional force-based approach in contemporarycodes of practices for designing the full restraints ofnon-structural components. Section 3 introduces thealternative displacement-based (DB) methodologywhich can be used for assessing the overturning vul-nerability of items that are unrestrained, or inade-quately restrained. Non-structural components thatare the subject matter of interests in this paper arefloor motion sensitive components. Another class ofNS components includes facades and vertical piping.The performance of this latter class of componentsin an earthquake depends on the amount of inter-storey drift which is directly translated into the de-formation of the component. The performance as-sessment of drift-sensitive components are outsidethe scope of this paper.

Table 1. Non-structural components.

2 FORCE-BASED ASSESSMENT OF FULLYRESTRAINED COMPONENTS

Current Standard provisions for protecting floormounted objects in buildings as outlined above aremainly about estimating the peak acceleration of thefloor in order that the required strength of the re-straints can be estimated (FEMA302, NZ4203 & AS

1170.4). Design calculations are always aimed at es-timating the transmission and amplification of thepeak horizontal acceleration from the ground to theindividual floor, and eventually to the centre of iner-tia of the component (Clark, 1993; Hall, 1995; Ar-nold et al, 1987 and Arnold, 1991; Lam et al, 1998;Beattie, 2000 & 2001). In designing the restraints ofan acceleration sensitive component, the seismic de-sign force (F) is basically the product of the self-weight of the component (Wc) and the peak groundacceleration (aground). Meanwhile, the importancefactor (Ic) is introduced as a scaling factor. Amplifi-cation by the component mounting is taken into ac-count by the factor ac , whilst amplification by thebuilding floor is taken into account by the factor af.The overall principle is illustrated in Figure 1.Major earthquake loading standards around the

world are based on similar principles, but differentnotations have been used and expressions used forthe calculation of the individual factors can vary agreat deal between the standards for similar condi-tions and component type. Whilst the notationsadopted in equation 1 and Table 2 are based on pro-visions in AS 1770.4 (2007) developed for Australia,this section is intended to provide a generic over-view on the framework adopted by major designcodes of practices around the globe.

c

cfcc

RaaIZW

F....

= (1)

The seismic hazard zone factor (Z) can be de-scribed as the notional peak ground acceleration onan average rock site for the area under considerations(and can be taken as the value of agroundin Figure 1).In regions of low and moderate seismicity such asAustralia, the value of Z typically varies in therange: 0.05g 0.15g and may increase up to 0.4g inregions of high sesimicity such as California.

The importance factor (Ic) typically varies be-tween 1.0 and 1.5 depending on the consequence of

failure of the component in regard to life-safety andto the continuous functioning of the affected facili-ties. In the New Zealand Standard, the importance ofthe building and the importance of the componentare represented by separate factors.

The height amplification factor of the floor (af) insimplified code models typically varies linearly fromthe ground level to the roof level. In Australia, thevalue of af at the roof level can be taken as 3 butmuch lower values are stipulated for low-rise build-ings (refer Figure 2a). NEHRP recommendations

adopt the more rational approach of defining af atroof level as the product of (i) the normalised elasticresponse spectral acceleration at the fundamentalnatural period of the building (which is dependent onthe site class) and (ii) a participation factor of 2.

Categories Examples

Architectural Features

Mechanical/ElectricalEquipmentBuilding Contents

Partitions, false ceilings, fa-

cades, parapets, chimneys, ca-nopies.Boilers, transformers, pumps,motors, piping.Furniture, shelving, heavy itemson racks and other free-standingitems.


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Provisions in the New Zealand Standard is more ela-borate as ductility and over-strength in the buildingare both taken into account in the calculation of thefloor responses. Alternatively, the floor accelerationmay be obtained by dividing the seismic design forceof the floor by the mass of the floor in which casethe calculated floor accelerations might not necessar-ily vary linearly between the ground and the roof ofthe building (refer Figure 2b). Whilst rigorous analy-sis of the building structure can be employed to pro-vide accurate estimates of the floor response, they donot offer a convenient way of estimating the behav-iour of existing buildings when their design calcula-tions are not readily available.

The component amplification factor (ac) typicallyvaries between 1 for components which are generallyregarded as rigid and 2.5 for flexibly mounted com-

ponents, or spring isolated components. In theNEHRP recommendations, values of ac are clearlystated for different component types. In the NewZealand Standard, the response behaviour of thecomponent and its mounting is modeled in a mannersimilar to that for the aseismic design of a building.Thus, the inelastic response spectra stipulated in theStandard for the calculation of the seismic forces ap-plied to the side of a building are also used for thecalculation of the seismic forces applied to a non-structural component. With this calculation ap-proach, the amplification response behaviour and theenergy dissipation characteristics of the componentmounting are covered by similar factors.

The Reduction Factor (Rc) varies a great deal be-tween the Standards, and very different values arespecified by the same standard for different compo-nents. The Australian Standard is relatively conser-vative given that Rc = 1.0 is specified for compo-nents made of ceramic materials (ie. no reduction)and a default value of 2.5 for other components.Provisions developed for high seismicity countriessuch as NEHRP allow Rc= 6 to be taken for certain

ductile components. For the majority of components,the recommended values of Rcdoes not exceed 3.

Inconsistencies between the Standards are evidentfrom the brief review presented above. A compre-hensive comparison of the force-based provisions inmajor codes of practices for the restraining of NScomponents in buildings was given by Phan & Tay-lor (1996) which revealed up to five-fold discrepan-cies in the recommended amplification factors.

The review publication by Rodriguez et al (2002)made recommendations for the peak floor accelera-

tions based on rigorous non-linear dynamic analysisof building structures ranging between three andtwelve stories. An independent study by Yao & Chiu(2001) developed floor spectra from floor accelero-grams recorded in 19 buildings during the 1999 Chi-

Chi earthquake (Taiwan). These studies revealedvery high amplification factors as well as consider-able uncertainties in the prediction of the peak flooraccelerations. It should be noted that none of thesestudies directly addresses motions and shocks ex-perienced by components which have not been ade-quately restrained to the floor.

To illustrate this knowledge gap, a floor mountedliquid container is used herein as an example. If thestrength of the restraining device is exceeded duringmoderate floor shaking, damage is initiated by yield-ing of the bolts and yielding/tearing of the brackets.Repair work would then be required. However, thecontinuous functioning of the container is not neces-sarily interrupted, provided the connector pipes re-main intact. It should be noted that high accelerationmay only cause rattling or limited rotation of the

container in the vertical plane without necessarilycausing overturning (which is dependent on the dis-placement at the centre of gravity of the container).The vulnerability to damage initiation of the restrain-ing device must be distinguished from the vulner-ability to loss of function or overturning of the con-tainer which can result in extensive collateraldamage.

A recent field survey undertaken by the authorand his collaborators in Melbourne, Australia re-vealed a total lack of restraints to a whole range ofbuilding components including boilers, cabinets andstorage racks (Al Abadi et al, 2003 & 2004). Imple-menting a blanket policy to restrain all existingcomponents is a major undertaking. The costs in-volved in this undertaking would be difficult to jus-tify particularly in regions of low and moderate seis-micity where risks of damage and destruction by anearthquake are widely perceived to be remote. Fur-thermore, building contents such as furniture itemsare beyond the scope of control of building designregulators and yet the performance of these items hasimportant life safety implications in the event of an

earthquake. For example, the overturning of free-standing tall furniture items (eg. shelving racks) withheavy storage items are potentially fatal and couldhinder the safe egress of occupants following anearthquake whilst fires are often triggered by earth-quake induced shaking of the building. With objectswhich are unrestrained, or inadequately restrained, itis important to know precisely how vulnerable arethese objects to overturning in the event of an earth-quake (noting that the failure of the restraining de-vice is not necessarily translated into overturning).

Resolving these unknowns would result in the cor-rect ranking of relative vulnerability of componentsin a building.


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Table 2. Factors controlling the seismic force applied to a non-structural component.

Factor DescriptionWc Weight of the component.Z Seismic hazard zone factor.Ic Importance factor.

afHeight amplification factor of the floor which takes into account the dy-namic response behaviour of the building up its height.

acAmplification factor of the component which takes into account the dy-namic amplification behaviour of the component mounting.

RcReduction factor which takes into account the effects of energy dissipationof the component mounting.

F = Wc . Ic . ac . a floor/ Rc

F = Wc . Ic . aground

Wc

F = Wc . Ic . ac . a ground/ Rc

a floor

a ground

Wc

Wc

note: afloor = af . aground

F = Wc . Ic . ac . a floor/ Rc

F = Wc . Ic . aground

Wc

F = Wc . Ic . ac . a ground/ Rc

a floor

a ground

Wc

Wc

note: afloor = af . aground

Figure 1. Schematic illustration of code model for seismic force on component.

(a) Simplified Model (b) Rigorous Model

Figure 2. Height amplification of floor acceleration.

afloor = aground x height amplification factor

Simplified approach :

a round

(1+)aground

= 2 typicallyreduced to 1/6 if h < 12m

Typical provisions :

afloor = aground x height amplification factor

Simplified approach :

a round

(1+)aground

= 2 typicallyreduced to 1/6 if h < 12m

Typical provisions :

afloor = Design inertia force of floor / floor mass, or Fi/ Mi

The alternative analytical approach :

Fi on a particular floor canbe obtained from either theequivalent static analysisor dynamic modal analysis

make sure this is aground

afloor = Design inertia force of floor / floor mass, or Fi/ Mi

The alternative analytical approach :

Fi on a particular floor canbe obtained from either theequivalent static analysisor dynamic modal analysis

make sure this is aground


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Clearly, the current approach of calculating peakacceleration and seismic inertia force is too restric-tive to distinguish between tolerable and intolerabledamage for the purpose of retrofit planning. Thislack of knowledge in the component vulnerability isconceded in code commentaries (e.g. FEMA303)and is reflected in the very conservative responsefactors specified for components mounted on com-mon anchoring devices (FEMA273, FEMA303 &NZ4203).

Velocity, as opposed to acceleration, has beenused as the alternative parameter to characterize therisk of damage to free-standing objects. For exam-ple, isolated studies by (Ishiyama,1984) have identi-fied the direct link between floor velocity and theoverturning vulnerability of uniform objects basedon idealized representation of the floor motion.

However, the developed model based on the consid-erations of velocity could not be generalized to therealistic excitations of a small-medium sized earth-quake which is characterized by displacement con-trolled behaviour (wherein the highest displacementdemand of the earthquake can be accommodated bythe component). Risk assessment for overturningbased on displacement controlled principles will bedescribed in detail in Section 3.

3 DISPLACEMENT-BASED ASSESSMENT OFVULNERABILITY TO OVERTURNING OFFREE-STANDING OBJECTS

Studies reported in this section were based purely onfree-standing conditions, and without any restraints.The authors believe that the condition of free-standing is a conservative assumption when ap-plied to components that are with some, but inade-quate, restraints in which case the component is onlyfree of restraints in the later part of the excitationsfollowing failure of the holding-down connections.

The accurate modelling of the behaviour of partiallyrestraint components is outside the scope of thisstudy.

The classical model for overturning, which wasinitiated by Housner (1963) and refined by Lips-combe (1990) and Makris & Roussos (1998), isbased on the dynamic equations of equilibrium of anobject (of homogenous distribution of mass) experi-encing rotational, or rocking, displacement. Thisrocking model which satisfies the principles of theconservation of momentum has incorporated the ab-

rupt change in the angular velocity of the object im-mediately following the impact of its base with theground. Parametric studies have since been under-taken to study the response of free-standing objectsto periodic motions, pulse-type motions and seismi-

cally induced motions (Yim et al, 1980; Spanos &Koh, 1984; Hogan, 1989; Tso & Wong, 1989a; Ma-kris & Roussons, 2000). Experimental investigationsinvolving the calibration of the modelling parame-ters have also been undertaken (Aslam et al, 1980;Priestley et al, 1978; Ishiyama, 1982; Tso & Wong,1989b).

The dynamic equations of motion for a rectangu-lar rigid object undergoing rocking motion can bederived from the principles of statical equilibrium.This involves summing moments about the edge ofthe object that is in contact with the ground (the pi-votal edge). The equations of moment equilibriumof a slender object experiencing positive and nega-tive rotation are represented by equations 2a & 2bare respectively.

[0] (2b)

where (t)and && (t)is the change in rotation androtational acceleration of the rocking object respec-tively, ( )gU t

&& is the time-history of the accelerationof the base support and R is the diagonal distancebetween the centre of mass of the object and the piv-otal edge.

The dynamic equilibrium conditions cannot berepresented by a single equation due to a discontinu-ity at zero displacement (when the object is vertical).Thus, a dual expression is required for the formula-tions of the non-linear F - relationship associ-ated with the rocking motion (as represented by thedotted lines in Figure 3a). Whilst individual terms inthe equations are linear, the signs associated with in-dividual terms of the expressions are not representa-

tive of linear behaviour.In the substitute-structure method of analysis, the

effective displacement (eff) of a single-degree-of-freedom (SDOF) system is the displacement of theobject at the effective height which is two-thirds upthe height of the object as shown in Figure 3b. Over-turning is defined at the instance when the centre-of-gravity is displaced to a point which is directlyabove the pivotal edge of rocking. Thus, the effec-tive displacement at the threshold of overturning(OT) is equal to two-thirds of the object thickness(ie. OT= 2/3 t).

( ) ( )3 3( ) ( )4 4gU tg

t tR R

= &&&&


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Resistance

Effective Displacement

(at centre of inertia)

time

Keff

Teff

l gl

Teff 2=

Teff

eff

(a) (b)

(c) (d)

OT

OT: Overturning Displacement

g

hT

eff3

22=h

Initial

period

shiftedperiod

Maximum Displacement Demand: Max eff


Naturalperiod

displacement

at rest:

limit of overturning

4 sec

h3

2

Mg

h

tMg

4

3

OT= 2/3 t

h

tMg4

3

limit of overturningat rest

Resistance


(at centre of inertia)

time

Keff

Teff

l gl

Teff 2=

Teff

eff

(a) (b)

(c) (d)

OT

OT: Overturning Displacement

g

hT

eff3

22=h

Initial

period

shiftedperiod

Maximum Displacement Demand: Max eff


Naturalperiod

displacement

at rest:

limit of overturning

4 sec

h3

2

Mg

h

tMg

4

3

OT= 2/3 t

h

tMg4

3

limit of overturningat rest

According to the basic principles of statics, the

force required to initiate overturning is equal to times Mgt/h (see Figure 3b). In summary, the F relationship of Figure 3a has two key features : (i) avertical line at zero displacement and (ii) a straight-line representing the linear decrease in resistance tooverturning with increasing displacement.

The slope of the linearised force-displacementline (solid line in Figure 3a) is defined by equation 3and is denoted herein as the effective stiffness (Keff)of the system. The linearization is based on the ex-cursion of the object to the limit of overturning.

h

Mg

t

h

Mgt

Keff

8

9

32

43

== (3)

The effective mass (or generalised mass) Meff is de-fined by equation 4 assuming rigid body behaviour.

MMeff 43= (4)

Figure 3. Linearised model for rocking

Equation 5 which provides an estimate for the effec-tive natural period (Teff) is obtained by combiningequations 3 and 4.

g

hT

eff 3

22= (5)

The correlation of the object height, h, with theeffective natural period Teffas defined by equation 5

is shown in Figure 4 for object heights varying be-tween 0.5 m and 4.0 m. By the pendulum analogy,a pendulum with length equals to two-thirds theheight of the rectangular object will have a naturalperiod equal to the effective natural period of rock-ing (see Figure 3c). By linearisation, the object ef-fective displacement demand (eff) can be estimated

from an elastic displacement response spectrum ofthe ground, or the displacement response spectrumof the floor (ie. the floor spectrum) for any given ef-fective natural period of rocking (refer Figure 3d). Ifthe maximum displacement of the object is restrictedto 50% of its displacement capacity, the (modified)effective stiffness is then defined by equation 6 andthe modified effective natural period (Tm-eff) byequation 7.


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The effective natural period which is calculated inaccordance with equations 6 & 7 based on the newlimit is approximately 0.6 times (i.e. 1/ 3 ) of thatdefined by equation 5. The value of Tm-eff calculatedfor a range of object heights is also shown in Figure4. The concept of linearisation as described in thissection was based purely on free rocking responses.It is shown that the value of Tm-efffor building con-tents would not be expected to exceed 2 seconds. Inother words, buildings with fundamental natural pe-riod exceeding 2 seconds (ie. buildings taller than 30storeys) are unlikely to develop resonance with theirbuilding contents based on equation 7 (which as-sumes that all objects are displaced by no more than50% of its capacity for overturning).

9

4m eff

MgK

h = (6)

23

m eff

hT

g = (7)

In the foregoing developments, the rocking response

behaviour has been simplified to linear elastic re-

sponse behaviour through the linearization of the ef-

fective stiffness. The amount of equivalent viscous

damping which represents energy dissipation during

rocking has yet to be quantified in order to provide acomplete definition of the linearised model. The ra-

tio of decrement in velocity (r) associated with en-

ergy loss on impact (of the base of the object with

the ground) during rocking may be estimated using

equation 8 (Al Abadi et al, 2006).

r= 1- 1.5/ (1+(h/t)2) (8)

where h/t is the aspect ratio of the object

The rate of velocity decrement that are resultedfrom viscous damping ratio is given by equation 9.

= -loger/ (9)

Combining equations 8 and 9 enables the equiva-lent damping ratio () to be determined for emulat-ing the loss of energy through rocking. This is illus-trated in Figures 5a & 5b which shows that theusually assumed (notional) damping ratio of 5% inelastic response spectra is consistent with a rate ofdecrement (r) of 0.85 which is predicted for objects

with an aspect ratio of 3. It is shown that the valueof r becomes insensitive to the aspect ratio (AR)when AR is greater than 3.

The actual dissipation of energy experienced by the

rocking object can be much higher than the modelled

values due to energy losses in both the flooring mate-

rial and the rocking object itself. This is in contrasts

with the damping relationships outlined above which

were based on a hard floor surface with zero coeffi-

cient of restitution on impact. Other sources of energy

dissipation in the system can add to the differences.Shaking table experimentations on unreinforced ma-

sonry (URM) parapet walls for out-of-plane rocking

behaviour reported an average damping ratio of 0.03

(3%) for a wall aspect ratio of 9 (Lam et al, 1995a &

b). Similar experimentations with URM walls with ef-

fective aspect ratios varying between 4 - 8 reported

damping ratios varying between 4% and 10%, and

with large scatters (Griffith et al, 2004). These results

suggest that the actual level of equivalent damping

could be 2-3% higher than what is predicted using

equations 8-9. On the other hand, the damping level

could well be lighter than is predicted because of the

asperity on the underside of the object (Lipscombe,

1990). Thus, the estimated amount of dissipated en-

ergy could err either way. A rigorous procedure which

incorporates a variable damping parameter (ie. vari-

able rand ) does not seem to be justified in view ofthe uncertainties with real behaviour. Recognising

this, it seems reasonable to adopt a constant value of for reasons of simplicity. The common (default)

Effective natural period of rocking

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5

Object Height (m)

Naturalperiod(secs)

Eff ective Period T-eff

Eff ective Period Tm-ef f

Figure 4. The effective natural period for rocking

damping value of = 5 % seems to be most consis-tent with the behaviour of objects with aspect ratio of

3 or higher.

In essence, the proposed linearised model for over-

turning is about predicting the effective displacement

demand on the object (eff) based on the displacementresponse spectrum of the base excitations and the

comparison of effwith the thickness (t) of the object.


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Decrement in amplitude of elastic vibration

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50

Equivalent Damping Ratio

rateofdecrement

5 % damping

Decrement in amplitude

of rocking

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10

aspect ratio (h/t)

rateofdec

rement

Figure 5. Rate of velocity decrement and equivalent dampingratio for rooting

A free-standing object is considered to be unlikely

to overturn if effis less than or equal to t/3 (risk levelis low). This limit is based on a 50% margin for

safety. In contrast, the object is expected to overturn if

eff is greater than 2/3 t (risk level is high). Thereare uncertainties in the behaviour of objects in be-

tween the two limits due to errors arising from non-

linear behaviour (risk level is moderate). Table 3

and Figure 6 provides a summary of the stated risk

criteria. In the estimation of eff there are uncertaintiesas to what natural period should be assumed when

taking readings from the response spectrum. The pe-

riod-shift behaviour of rocking means that the object

actually experiences a range of natural periods as the

rocking displacement is increased. It is proposed by

the author that the highest displacement demand (Max

eff) over the period range of 0 4.0 seconds be taken

as the estimated amount of rocking displacement for

the purpose of Table 3 and Figure 6.An extensive parametric study by Al Abadi et al

(2006) involving some 2800 non-linear time-history

analyses for rocking responses was undertaken to

validate this model. About 1800 of these cases were

classified as having low overturning risks according

to the classification criterion defined by Table 3. Non-

linear time-history analyses undertaken on these low

risk cases indicated that only 2 cases (out of a total of

1800 cases) actually experienced overturning. In con-trasts, cases that were classified as having high risks

had an overturning rate of about 80%.The simple displacement model described above

can be used for the quick-scan assessment of theoverturning vulnerability of free-standing objects ina building. The calculations involved are very sim-ple. For example, take an area where the level ofseismicity is characterized by the design peak groundvelocity of about 60 mm/sec on rock (which is gen-erally representative of the average level of seismic

hazard in Australia for 10% exceedance in a designlife of 50 years, or a return period of 500 years). Thehighest displacement demand on an elastic dis-placement response spectrum for 5% damping is ac-cordingly 20 30 mm on rock sites and be amplifiedto around 80 100 mm on soft soil sites.

First, consider free-standing objects which are lo-cated at the ground level of the building where theeffects of height amplification can be neglected. Theresponse spectrum of the site and that of the floor aretherefore identical. Thus, the maximum value of eff(ie. Max effas illustrated in Figure 3c) for the pur-pose of assessing overturning of objects is in the or-der of 80 - 100 mm. In such conditions, free-standing objects (components) with base dimensionexceeding 300 mm (ie. 3 x 100mm) may be consid-ered safe from overturning if homogeneous distribu-tion of mass is assumed (refer Figure 6a). Detailed(follow-up) assessment of the stability of compo-nents in the building would only be required if thebase dimension of the object is less than 300 mmand if their overturning could result in serious con-sequences. The risks model of Figure 6 enable vul-

nerable items to be identified for any given value ofMax eff. However, a realistic estimate of Max effrequires an accurate modelling of the potential siteresponse and building floor responses to earthquakeexcitations. Developing these response spectra re-quire the dynamic properties of the site (ie. site natu-ral period) and the building to be ascertained withgood accuracies. The current approach of broad-based site classification would not serve this pur-pose. The current building regulations do not requiredesigners to produce floor spectra which accuratelyincorporates the dynamic properties of the site.

It can be shown that similar recommendations canbe made of components contained within low-risebuildings of up to around 5-storeys irrespective ofthe positioning of the component within the build-ing.


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Table 3. Criteria for risk levels for overturning (after Al Abadiet al, 2006)(notation max eff is abbreviated herein as)

It is shown in Franke et al(2005) that conditions donot necessarily become more onerous as the building

becomes so tall that the natural period of the build-ing is considerably higher than that of the site. Thisis the case with buildings possessing a fundamentalnatural period of 2 seconds or higher. It has beendemonstrated by analyses that when this happens thebuilding effectively behaves as an isolation medium.The potential damaging effects of the ground shak-ing can be tempered, rather than accentuated, by thefiltering of the motion up the height of the build-ing. Research into the behaviour of the displacementfloor spectra in tall buildings is on-going.

Clearly, the overturning model developed in this sec-

tion was based on the behaviour of uniform rectangu-

lar objects. A similar model (details not presented

herein) that are generalised to all geometrical shapes

with a vertical axis of symmetry could also be devel-oped. The generic model is parameterised by (i) the

mass radius of gyration and (ii) diagonal distance R

which is measured from the centre of mass of the ob-

ject to its pivotal edge. For an object of any arbitrary

shape and non-uniform distribution of mass, an

equivalent rectangular object with identical values of

the rocking parameters could be identified. Conse-

quently, the presented overturning model could be ex-

tended for the stability assessment of a much wider

class of (non-uniform and non-rectangular) objects.The overturning model reviewed in this section

was first applied by the author and his collaboratorsto the vulnerability assessment of unreinforced ma-sonry parapet walls and gable walls subject to seis-mic loading in the out-of-plane direction (Doherty etal, 2002; Lam et al, 2003). The presented modelconsiders rocking responses only. Therefore, condi-tions under which the response is of rocking natureonly are examined. For example, vertical accelera-tions of the building floor is neglected and jumpingof the object is assumed not to occur.

Figure 6. Risk of overturning based on displacement

Inequality statements Risk Level

3

t Low

t3

2

3

t


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Also, sliding is assumed not to occur implying thatthe base horizontal acceleration has not surpassedthe coefficient of friction between the base of the ob-

ject and the flooring surface. The aspect ratio of atypical computer cabinet is in the order of 3 (recip-rocal of 0.33), while the coefficient of friction is inthe range 0.60-0.90 (Ferdinand et al, 2004) whenrubber attached to the base of the cabinet is in con-tact with a concrete floor. The assumption of no-sliding appears to be generally valid for this type ofinstallations.

4 DISCUSSION

A range of models have been reviewed in this paper.The force-based model presented in Section 2 is

about estimating the force demand on restraineditems (and the associated literature underpinning theprovisions) and provides little indication of howvulnerable items that are without adequate restraints.The model for overturning as presented in Section 3can potentially become very useful as technical ref-erence when it comes to identifying potentially haz-ardous items which risk overturning if unrestrained.Objects which have been classified having moderate,or high, overturning risks by the overturning modelcould be retrofitted with holding down devices inaccordance with conventional force-based principlesto ensure that large (rocking) displacement wouldnot take place.

An accurate prediction for Max eff which formspart of the evaluation framework requires the poten-tial motion behaviour of the building floors to bemodelled. Uncertainties in the demand predictionscan be translated into difficulties in modelling thebehaviour of our building infrastructure and its con-tents in the projected seismic conditions in order thattheir safe and satisfactory performances can be guar-anteed. These design challenges are compounded

with additional challenges with effectively imple-menting the intentions of the building designer intoactual practices. Clearly, the designer of the buildinghas little control over installations of componentsand the management of the utilization of the buildingwhilst in service.

Engineering for earthquake safety in a building isclearly much broader than merely regulating its ar-chitectural and structural design. What is essential isproper control of all major installations and regularinspection of the utilization of building during its en-

tire service life. Tight legislative controls and in-spection procedures are already well established inmost established community to ensure responsiblebehaviour of the building owners and operators forcountering the risks of fire. However, there are hard-

ly any parallel provisions for countering potentialearthquake hazards. The author proposes that inspec-tion procedures for countering the risks of fire bebroadened to address a diversity of potential hazardsincluding earthquake hazards given that they are allto do with the safe and proper ultilization of spaceand the storage of hazardous items.

Effective control of seismic risks in buildings isonly possible if the items of concern have been cor-rectly targeted. Building operators and authorities re-sponsible for the monitoring must be well informedof the behaviour of both restrained and unrestraineditems in the building in the projected earthquakescenarios. For example, realistic modelling for over-turning requires the dynamic behaviour of both thebuilding and the site sub-soil to be ascertained. Thesame can be said of deformation modelling of the

building facades and vertical piping. Both types ofmodelling requires much more information than isreadily available in a form that can be practicallyimplemented and monitored. In the opinion of theauthor, this is exactly where future research and de-velopment efforts should be directed at.

5 CONCLUSION

a) The full restraints of non-structural components,the overturning of slender objects, the vulnerabil-ity of sign gantries and the brittle failure of build-ing facades and vertical piping have been identi-fied as issues to be addressed.

b) Typical provisions in contemporary standards forcalculating the seismic design forces for the fullrestraints of non-structural components have beenreviewed (refer Table 2 and Figures 1 and 2). Theoverall modelling framework adopted in the dif-ferent standards are generally consistent but thestipulated factors can be at large discrepancies.

The shortcomings of the force-based approach inassessing the potential seismic performance ofnon-structural components has been illustrated us-ing the case-study of a floor mounted liquid con-tainer.

c) The mechanics of rocking and the linearised ver-sion of the rocking model has been briefly intro-duced (refer Figure 3). The risk of overturning of afree-standing object can be assessed by comparingthe thickness of the object against the maximum

effective displacement demand (Max eff) as readoff from the elastic displacement response floorspectrum (refer Table 3 and Figure 6). A free-standing object is considered unlikely to overturn


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if eff is less than or equal to t/3 (risk level islow).

d) The overturning behaviour of objects in tall build-ings depends on the dynamic properties of thebuilding and the natural period of the site. For ex-ample, if the natural period of the building is con-siderably higher than that of the site the buildingeffectively behaves as an isolation medium. Thepotential damaging effects of the ground shakingcan be tempered, rather than accentuated, by thefiltering of the motion up the height of the build-ing.

e) Design regulations alone would not necessarilyimprove the level of preparedness significantly(because regulations for controlling the design of a

new building would not cover for installations anddisposition of storage items during its service life).The engineering of non-structural components andbuilding contents for countering potential earth-quake hazards should not be restricted to merelydesigning restraints, and particularly so for re-gions of low and moderate seismicity. The authorproposes that inspection procedures for counteringthe risks of fire be broadened to address a diver-sity of potential hazards including earthquake haz-ards given that they are all to do with the safe andproper ultilization of space and the storage of haz-ardous items.

f) Modelling the potential seismic performance forthe whole range of NS components in a buildingrequires much more information than is readilyavailable in a form that can be practically imple-mented and monitored. In the opinion of the au-thor, this is exactly where future research and de-velopment efforts should be directed at.

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