A simplified method for seismic analysis of rooftoptelecommunication towers

Rola Assi and Ghyslaine McClure

Abstract: A simplified method is presented in this paper for the estimation of forces at the base of telecommunicationtowers mounted on building rooftops due to seismic excitation. Although some codes and standards propose simplifiedmethods for the evaluation of base shear forces for towers founded on ground, no method yet exists for the evaluationof overturning moments. The proposed simplified method is based on numerical simulations using truncated modalsuperposition, which is widely used for seismic analysis of linear structures. The method requires the prediction of inputseismic acceleration at the buildingtower interface, the definition of an acceleration profile along the building-mountedtower, and the determination or evaluation of the mass distribution of the tower along its height. The method was developedon the basis of detailed dynamic analyses of three existing towers assumed to be mounted separately on three buildings.It was found that the method yields conservative results, especially for the overturning moments.

Key words: self-supporting towers, earthquake, horizontal excitation, dynamic analysis, acceleration, modal superposition.

Rsum : Cet article prsente une mthode simplifie destimation des forces agissant la base de pylnes de tlcommunicationinstalls sur les toits dimmeubles et causes par une excitation sismique. Alors que certains codes et normes proposentdes mthodes destimation simplifies des forces de cisaillement la base pour les pylnes autoportants installs sur lesol, aucune mthode nexiste encore pour lvaluation des moments de renversement. La mthode simplifie propose estbase sur des simulations numriques utilisant une superposition modale tronque qui est couramment utilise pour lanalysesismique de structures linaires. La mthode requiert la prdiction de lacclration sismique linterface immeuble-pylne,la dfinition dun profil dacclration le long et la dtermination de la distribution de la masse du pylne le long de sahauteur. La mthode a t dveloppe en se basant sur lanalyse dynamique dtaille de trois pylnes existants prsumstre installs sur trois immeubles existants. La mthode a produit des rsultats conservateurs, particulirement pour lesmoments de renversement.

Mots-cls : pylnes autoportants, sisme, excitation horizontale, analyse dynamique, acclration, superposition modale.

[Traduit par la Rdaction] Assi and McClure 1363

Introduction

To perform an adequate seismic design of telecommunica-tion equipment, it is necessary to evaluate seismic forcesrealistically. Because the design of towers on ground is usu-ally controlled by ice and wind loads, most of the researchand information resources on the analysis of steel latticetelecommunication towers are devoted to analysis under windand ice loads; therefore, research on the seismic response ofthese towers has not been abundant. In a survey of earth-quake performance of telecommunication towers (A.J. Schiff,

unpublished report, 1999), it was concluded that tall broadcasttowers and large building-supported microwave towers arethe most vulnerable to earthquakes, although none of thesetowers has been a direct threat to life safety during an earth-quake. In areas prone to earthquakes, the main issue forstrategic telecommunication towers is their functionality duringor immediately after an earthquake. Modern codes and stan-dards have recently addressed the seismic analysis of tele-communication towers on building rooftops by either proposinga simplified method for the estimation of seismic base shearforces (ICC 2000; NRCC 2005; ANSI/EIA/TIA 2005) or atleast acknowledging the importance of the problem (SAA1994; CSA 2001). The current seismic provisions availablein codes and standards address only the input base shearforce to telecommunication towers, whereas the base over-turning moment is not covered. In the opinion of the authorsbased on detailed dynamic analyses (Assi 2006), the simpli-fied approaches in codes and standards are often inappropriate,especially since most telecommunication towers are consid-ered as acceleration-sensitive components with distributedmass and stiffness (CSA 2001).

One of the first publications discussing earthquake effectson antenna-supporting lattice towers was authored by Konnoand Kimura (1973), who studied an instrumented tower owned

Can. J. Civ. Eng. 34: 13521363 (2007) doi:10.1139/L07-061 2007 NRC Canada

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Received 20 March 2006. Revision accepted 26 April 2007.Published on the NRC Research Press Web site at cjce.nrc.caon 2 November 2007.

R. Assi1 and G. McClure.2 Department of Civil Engineeringand Applied Mechanics, McGill University, 817 SherbrookeStreet West, Montral, QC H3A 2K6, Canada.Written discussion of this article is welcomed and will bereceived by the Editor until 29 February 2008.1Present address: SNC-Lavalin Group Inc., 620 Ren-Lvesque,Montral, QC H3B 1N7, Canada.

2Corresponding author (e-mail: ghyslaine.mcclure@mcgill.ca).

by the Nippon Telegraph and Telephone Corporation (NTT)and mounted on a building rooftop during the 1968 Off-Tokachi earthquake in Japan. Sato et al. (1984) analyzed thedata from strong-motion accelerographs in selected build-ings owned by the NTT in Japan. They studied the inputseismic force to be used for the design of appendages, par-ticularly telecommunication towers, and found that a maxi-mum acceleration amplification of 4 at the rooftop wasappropriate. A drawback of their study was that they aver-aged the amplifications calculated for the two main horizon-tal directions, considering that the structural system may bedifferent in both principal directions of the buildings andconsequently affect their response. Hiramatsu et al. (1989)reported the continuation of this investigation of the seismicresponse of NTT telecommunication equipment mounted onbuilding rooftops. In general, their results agreed with theearlier observations of Sato et al.

There have been unofficial reports of tower damage incurredduring the 1994 Northridge earthquake in California, involvingmostly localized damage in the vicinity of antenna mounts(Madugula 2002). Similar localized damage was reported byPierre (1995) following a visit to Japan after the HanshinAwaji (Kobe) earthquake that occurred on 17 January 1995.

Kanazawa and Hirata (2000) developed a seismic responsespectrum method for the analysis of secondary systems whileconsidering the dynamic interactions between the primaryand secondary structures and the transient response effects.To evaluate their proposed method, the researchers performedtimehistory analyses on a buildingtower model consistingof a tower mounted on a single-degree-of-freedom primarysystem. A similar approach had been developed at McGillUniversity by Khedr (1998) and Khedr and McClure (2000) forsteel lattice towers on firm ground and subjected to bothhorizontal and vertical earthquake accelerations, but theirmethod is not applicable to towers mounted on rooftops orother flexible supporting structures. In a preliminary study,McClure et al. (2004) used numerical simulations to explorethe correlation between the building accelerations and themaximum seismic base shear as well as the base overturningmoment of towers mounted on building rooftops. This studywas the precursor of the research reported in Assi (2006).

This paper presents a simplified, accurate, and yet easy toimplement static method for the analysis of telecommunica-tion towers mounted on building rooftops and subjected toearthquake excitation. The purpose of this method is to pro-vide tower designers a tool to quickly determine the seismicforces on telecommunication towers mounted on buildingrooftops, namely the tower base shear force and overturningmoment. In design, these seismic effects can then be com-pared to those of other environmental loads like wind andice. If this preliminary assessment indicates that seismic loads

govern the tower design, then a detailed dynamic analysis ofthe buildingtower combination would become necessaryfor a more accurate assessment of internal forces and basereactions.

Method of analysis

The proposed method is based on numerical simulationsusing truncated modal superposition analysis to determinethe maximum forces in the tower legs at the buildingtowerinterface. Three-dimensional (3D) finite element models forthree towers assumed to be mounted on three buildings weregenerated using the SAP2000 software (Computers andStructures, Inc.) (Wilson and Habibullah 2003). Elastic timehistory modal superposition analysis was performed for eachbuildingtower combination. The 20 lowest frequency modeswere considered, and a uniform viscous damping ratio of 3%critical was used for all modes, which is a common practicefor bolted steel lattice structures (Madugula 2002). Two ofthe modeled buildings are located in Taiwan, and the third islocated in downtown Montral, Quebec, Canada. The modelsof the Taiwanese buildings were calibrated using floor accel-erations recorded during the 1999 Chi Chi earthquake, andthe fundamental periods were extracted by system identifica-tion techniques using the same accelerograms (Assi 2006).The model of each buildingtower combination was sub-jected to two sets of earthquake records applied to both prin-cipal horizontal directions (U1 and U2) of the buildings.

Description of the buildingtower combinationsSome geometric details of the buildings and towers along

with a brief overview of the main finite element modelingassumptions are presented in the following sections. Theearthquake records applied to the base of the buildings arealso described.

BuildingsGeometric properties of the three buildings studied are

given in Table 1, and their isometric and facade elevationviews are shown in Figs. 13. The lateral load resistingsystem (LLRS) is either a reinforced concrete frame system(frame) or a moment-wall system (dual). Detailed 3D elasticmodels of the three buildings were generated in SAP2000.Rigid floor slabs were assumed, and the columns, beams,and walls were modeled in detail. The mass of nonstructuralcomponents and finishing was distributed to columns andwalls according to their tributary area. Table 2 summarizesthe lowest periods of vibration obtained for the buildingmodels, corresponding to the fundamental sway modes andthe torsional mode.

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Location BuildingYear ofconstruction Use LLRS

No. ofstoreys aboveground

Height(m)

Tainan, Taiwan CHYBA9 1980 Telecom Dual 4 20.0Jia-Yi, Taiwan CHYBA4 1983 Hospital Frame 6 24.2Montral, Quebec, Canada 2020 University 1973 Office Frame 27 115.2

Table 1. Properties of the buildings studied.

TowersThree typical medium-height self-supporting steel towers

were studied. Table 3 lists the geometric properties of thetowers, including their height, base width, top width, andmass. It should be noted that the mass of the towers does notinclude the mass of antennas, transmission lines and otherattachments, platforms, and ladders. The towers labeled TC1,TC2, and TC3 are three-legged steel lattice towers with anequilateral triangular base. The towers were modeled inSAP2000 as 3D frametruss linear elastic structures. Frameelements were used for the main legs, and truss elements fordiagonal and horizontal members. The tower models wereassumed rigidly connected to the roof of the building models.An example of such a connection is illustrated in Fig. 4 forthe telecom building in Tainan City, Taiwan. Figure 5 showsthe finite element meshes of the tower models, and Table 4gives the four largest sway and torsion natural periods calcu-lated for bare towers.

Earthquake recordsThe generated models in this study are subjected to two

sets of horizontal input accelerograms. The first set com-prises 44 historical records resulting from 23 events listed inTable 5. The records are classified in three categories accordingto the ratio (a/v) of the peak ground horizontal acceleration

(PGA) to the peak ground horizontal velocity (PGV), includ-ing 14 records with high a/v ratio labeled H, 15 records withmedium a/v ratio labeled M, and 15 records with low a/vratio labeled L. More details about these earthquake recordscan be found in Tso et al. (1992). The second set comprisesthree series, each including 10 synthetic timehistories com-patible with the target uniform hazard spectra for Montral

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Fig. 1. Isometric and facade elevation views of building CHYBA9,Tainan, Taiwan. FL, floor. Numbers indicated on elevation viewdenote labels of the various sensors.

Fig. 2. Isometric and facade elevation views of building CHYBA4,Jia-Yi, Taiwan. Numbers indicated on elevation view denote labelsof the various sensors.

Fig. 3. Isometric view of building at 2020 University Street,Montral, Quebec, Canada.

(Adams and Halchuk 2003), corresponding to probabilitiesof exceedance of 2%, 10%, and 50% in 50 years. The threeseries are labeled 2%, 10%, and 50% in the figures. Thesetimehistories were generated based on the stochastic approachpresented by Atkinson and Beresnev (1998). A total of 15magnitudedistance (MR) scenarios were applied to coverthe frequency range of interest. Due to the randomness ofthe generated records, two acceleration timehistories wereused for each MR scenario, as indicated in detail in Table 6.The time step for each accelerogram is equal to 0.01 s.

Different sets of records were used to investigate the effectsof frequency content of ground motion on the elastic responseof the towers and their supporting buildings. It is recognizedthat the intensity of an earthquake mostly affects the responseof nonlinear structures, and both the intensity and frequencycontent of an earthquake affect the response of linear elasticstructures. Sewell and Cornell (1989) have discussed theeffects of ground motion characteristics on floor responsespectra in both linear and nonlinear structures, and Mirandaand Taghavi (2003) have studied the effect of frequency con-tent on the acceleration demands in buildings.

Currently, the Canadian Standards Association standardCSA S37-01 (CSA 2001) defines the seismicity level basedon a simple classification of the peak horizontal groundacceleration, with three categories of high (>30% g), moder-ate (15%30% g), and low (

The prediction of the tower acceleration profile a(x) is thekey factor in this method. It was found that the accelerationamplification profile along a telecommunication towermounted on a building rooftop matches reasonably well itsfundamental mode shape when mounted on a rigid base.Equations [1] and [2] provide the basis for evaluating the

base shear force, Vbase, and the base overturning moment,Mbase, using the proposed method:

[1] V V x m x a x xxll

base d d

( ) ( )00

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Earthquake and location Date MagnitudeLong Beach, California, USA 10031933 ML = 6.3Lower California, USA 10121934 ML = 6.5Helena, Montana, USA 31101935 ML = 6.0Imperial Valley, California, USA 18051940 ML = 6.6Kern County, California, USA 21071952 ML = 7.6San Francisco, California, USA 22031957 ML = 5.3Honshu, Japan 5041966 MJMA = 5.4Parkfield, California, USA 27061966 ML = 5.6Borrego Mountain, California, USA 8041968 ML = 6.5Near east coast of Honshu, Japan 16051968 MJMA = 7.9Lytle Creek, California, USA 12091970 ML = 5.4San Fernando, California, USA 9021971 ML = 6.6Central Honshu, Japan 26021971 MJMA = 5.5Near south coast of Honshu, Japan 2081971 MJMA = 7.0Near east coast of Honshu, Japan 11051972 MJMA = 5.8Near east coast of Honshu, Japan 17061973 MJMA = 7.4Near east coast of Honshu, Japan 16111974 MJMA = 6.1Oroville, California, USA 1081975 ML = 5.7Monte Negro, Yugoslavia 9041979 ML = 5.4Monte Negro, Yugoslavia 15041979 ML = 7.0Banja Luka, Yugoslavia 13081981 ML = 6.1Michoacan, Mexico 19091985 MS = 8.1Nahanni, N.W.T, Canada 23121985 MS = 6.9

Note: Dates are given as daymonthyear. MJMA, Japan Meteorological Agency scale; ML, local mag-nitude; MS, surface wave magnitude.

Table 5. Earthquake historical records used in the study.

Record 1 Record 2Magnitude,M

Epicentraldistance (km)

PGA(g)

PGV(m/s)

PGA(g)

PGV(m/s)

Duration(s)

Return period(years)

6.0 30 0.430 0.170 0.520 0.150 8.89 25006.0 50 0.240 0.072 0.190 0.084 8.89 25007.0 50 0.510 0.190 0.630 0.290 12.39 25007.0 70 0.300 0.140 0.290 0.160 12.39 25007.0 100 0.240 0.150 0.260 0.210 20.56 25005.5 30 0.180 0.047 0.190 0.045 20.56 4756.0 50 0.240 0.072 0.190 0.084 20.56 4757.0 150 0.130 0.079 0.130 0.086 20.56 4757.0 200 0.084 0.072 0.087 0.067 24.08 4757.0 300 0.042 0.042 0.040 0.040 24.08 4755.5 50 0.069 0.022 0.083 0.028 23.08 756.0 70 0.045 0.015 0.045 0.018 23.08 757.0 100 0.039 0.015 0.035 0.015 5.83 757.0 200 0.084 0.072 0.087 0.067 5.83 757.0 300 0.042 0.042 0.040 0.040 12.39 75

Note: PGA, peak ground horizontal acceleration; PGV, peak ground horizontal velocity.

Table 6. Characteristics of magnitudedistance (MR) scenarios considered for Montral, Quebec, Canada.

where Vx is the shear force distribution along the tower;

[2] M V x x m x a x x xxll

base d d

( ) ( )00

Prediction of tower acceleration profiles, a(x)In most cases studied, a strong correspondence was found

between the tower acceleration amplification profile andits fundamental sway mode shape. The graphs shown inFigs. 724 represent the average acceleration amplificationprofiles along the height of the towers mounted on eachbuilding. These profiles are calculated for each of the sixseries of earthquake records applied separately to both prin-cipal horizontal directions of the buildings, U1 and U2. Alsoadded to the graphs is the proposed acceleration amplifica-tion profile corresponding to the fundamental sway modeshape of each tower mounted on a rigid base, adjusted tomatch the maximum acceleration amplification at the towertop.

Figures 716 show that the proposed shape of the acceler-ation profile is generally conservative, especially at highertower elevations. The only significant exceptions are shownat low elevations in Figs. 17 and 18 for tower TC3 mounted

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Fig. 6. Concept of the proposed simplified method. Mbase, overturning moment at the base of the telecommunication tower calculatedaccording to the proposed simplified method; SRSS, modal combination method using the square root of sum of squares; Vbase, baseshear force at the base of the telecommunication tower calculated according to the proposed simplified method; x, position of towersection along elevation.

Fig. 7. Acceleration amplification profiles of tower TC1 mountedon building CHYBA9, U1 direction. The prefixes H, M, and Lin Figs. 724 denote high, medium, and low a/v ratios, respec-tively; and 2%, 10%, and 50% denote probabilities of exceedanceof 2%, 10%, and 50% in 50 years.

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Fig. 8. Acceleration amplification profiles of tower TC1 mountedon building CHYBA9, U2 direction.

Fig. 9. Acceleration amplification profiles of tower TC2 mountedon building CHYBA9, U1 direction.

Fig. 10. Acceleration amplification profiles of tower TC2mounted on building CHYBA9, U2 direction.

Fig. 11. Acceleration amplification profiles of tower TC3mounted on building CHYBA9, U1 direction.

Fig. 12. Acceleration amplification profiles of tower TC3mounted on building CHYBA9, U2 direction.

Fig. 13. Acceleration amplification profiles of tower TC1mounted on building CHYBA4, U1 direction.

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Fig. 14. Acceleration amplification profiles of tower TC1mounted on building CHYBA4, U2 direction.

Fig. 15. Acceleration amplification profiles of tower TC2mounted on building CHYBA4, U1 direction.

Fig. 16. Acceleration amplification profiles of tower TC2mounted building CHYBA4, U2 direction.

Fig. 17. Acceleration amplification profiles of tower TC3mounted on building CHYBA4, U1 direction.

Fig. 18. Acceleration amplification profiles of tower TC3mounted on building CHYBA4, U2 direction.

Fig. 19. Acceleration amplification profiles of tower TC1mounted on building 2020 University, U1 direction.

on building CHYBA4: these localized effects are largelycompensated by the overprediction of the amplifications athigher elevations, and the global effects at the tower baseusing the proposed method are conservative.

When the tower is more flexible than the building (seeFigs. 7 and 8), the former does not always experiencedynamic amplification along the complete height. This behavioris not reflected in current code provisions, which tend topropose a larger component force amplification factor forflexible components without specific reference to the sup-porting structure. The proposed method also provides con-servative estimates of seismic forces in such a case. It isfurther observed that this 30 m tower (TC1) is very flexibleand represents an upper limit case of towers mounted onbuilding rooftops.

The unusual behavior of tower TC1 mounted on the 2020University building (Fig. 20) reflects the contribution of somehigher modes of the tower attributed to the influence of thehigher modes of the supporting building. This result is shownto illustrate a case where the simplified acceleration profilepredicted by the fundamental tower sway mode is not appro-

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Fig. 20. Acceleration amplification profiles of tower TC1mounted on building 2020 University, U2 direction.

Fig. 21. Acceleration amplification profiles of tower TC2mounted on building 2020 University, U1 direction.

Fig. 22. Acceleration amplification profiles of tower TC2mounted on building 2020 University, U2 direction.

Fig. 23. Acceleration amplification profiles of tower TC3mounted on building 2020 University, U1 direction.

Fig. 24. Acceleration amplification profiles of tower TC3mounted on building 2020 University, U2 direction.

priate. It is recommended to perform detailed dynamicanalysis for similar buildingtower combinations.

The adjustment factors calculated for the acceleration pro-files of the buildingtower combinations studied are pre-sented in Tables 79, where T and Tp are the fundamentalperiods of the building and supported tower mounted on arigid base, respectively. These adjustment factors simplymultiply the building horizontal acceleration at rooftop levelto yield the value of the acceleration at the tower top, andthe shape of the acceleration profile fits the fundamentalsway mode calculated for the tower on a rigid base.

Following this study, amplification factors were proposedas listed in Table 10 and illustrated in Fig. 25 to estimate thetower acceleration profile when mounted on a stiff building(T < 0.5 s).

The limit of 0.5 s was selected to match the limit of appli-cability of the simplified static force procedure for buildingsrecommended in NBCC 2005 (NRCC 2006). This limitrelates to the assumption that the seismic response of thebuilding can be approximated by its fundamental sway moderesponse. Figure 25 shows that the proposed factors are

generally conservative, in particular when the Tp /T ratioexceeds 1.2.

For a tower mounted on a flexible building (T 0.5 s) it isproposed to amplify the rooftop acceleration by a factor of 3to obtain the tower acceleration profile. As discussed previ-ously in reference to Fig. 20, a flexible tower mounted onthe rooftop of a flexible building would require a dynamicanalysis of the buildingtower system to obtain more realisticseismic tower loads.

Parametric study to verify the proposedsimplified method

Using eqs. [1] and [2] for each buildingtower combina-tion, the values of equivalent base shear forces and overturningmoments at the buildingtower interfaces were calculated asshown schematically in Fig. 6. The shear force diagram wasobtained by multiplying the mass profile and the accelera-tion profile; and the base overturning moment was obtainedby integrating the mass profile, acceleration profile, momentarm. Results were compared with the values obtained fromthe detailed SAP2000 models using the square root of sumof squares (SRSS) modal combination method. The averageresults for all sets of records are presented in Table 1113.Detailed calculations can be found in the complete study byAssi (2006). In these tables, Vf and Mf are the base reactionscalculated in the numerical simulations, and Vbase and Mbase

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U1 U2

Building Tp /TAmplificationfactor Tp /T

Amplificationfactor

CHYBA9 1.43 0.40 1.24 0.80CHYBA4 0.92 3.32 1.21 1.432020 University 0.19 1.25 0.20 3.21

Note: T, fundamental period of the building; Tp, fundamental period ofthe tower mounted on a rigid base.

Table 7. Calculated tower acceleration amplification factors inprincipal horizontal directions U1 and U2 for tower TC1 onthree buildings.

U1 U2

Building Tp /TAmplificationfactor Tp /T

Amplificationfactor

CHYBA9 0.72 1.09 0.62 0.60CHYBA4 0.46 1.00 0.61 0.912020 University 0.09 2.12 0.10 2.75

Table 8. Calculated tower acceleration amplification factors inprincipal horizontal directions U1 and U2 for TC2 on threebuildings.

U1 U2

Building Tp /TAmplificationfactor Tp /T

Amplificationfactor

CHYBA9 0.97 2.70 0.84 1.31CHYBA4 0.62 1.34 0.82 0.882020 University 0.13 1.59 0.13 1.96

Table 9. Calculated tower acceleration amplification factors inprincipal horizontal directions U1 and U2 for TC3 on threebuildings.

Tp /T Amplification factor00.6 1.00.91.1 4.0

1.2 1.0

Table 10. Proposed tower accel-eration amplification factors fortowers mounted on stiff buildings(T < 0.5 s).

Fig. 25. Proposed and calculated tower acceleration amplificationfactors versus Tp /T for towers mounted on stiff buildings (T