Nonlinear Seismic Response of Antenna Supporting Structures 1993 Computers & Structures

8/12/2019 Nonlinear Seismic Response of Antenna Supporting Structures 1993 Computers & Structures

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NONLINEAR SEISMIC RESPONSE OFANTENNA S~PORTIN~ STRUCTURES

E. GUEVAIU and G. MCCLUREDepartment of Civil Engineering and Applied Mechanics, McGill University, Montreal, Quebec, CanadaAbstract-In the event of a severe seismic excitation, preservation of essential infrastructures, such astel~ommuni~tion facilities, is of high priority. The objective of this paper is to investigate thegeometrically nonlinear response of antenna-supporting guyed towers under earthquake loading. Twoguyed towers are analyzed: a 350 ft (107 m) tower with six stay levels and an 80 ft (24 m) mast with onlytwo stay levels. Two horizontal accelerograms are used, El Centro and Parkfield, with each record beingscaled to match the elastic design spectra of the 1990 National Building Code of Canada. Elements ofresponse analysed are: guy tensions, horizontal shears, and displacements and rotations at the tip of themast. Results indicate that although the absolute values of the dynamic amplifications are well below thelimit strength and pliability criteria for such towers, dynamic int~actions between the guywires andthe mast are important, especially in the vertical direction. Multiple support excitation of the tallest toweralso causes additional dynamic effects that are not present when only synchronous ground motion isstudied.

1. ~RODU~O~Structural designers of telecommunication towersreceive very little guidance from their national stan-dards for seismic analysis. It is generally recognizedthat wind effects, or combinations of wind and iceeffects in cold climates, are more likely to govern allaspects of design (stability, strength and serviceabil-ity) than are earthquake effects, but one must alsoconcede that the seismic behaviour of such structureshas not yet been thoroughly investigated. Also, asincreasingly tall towers are being built, more insightis needed in this area. Tall tel~mmunication towersare likely to be crucial points of a network, and maybe required to be serviceable during a major earth-quake, or at least be left undamaged in order toresume normal operations shortly after the event.

The International Association For Shell andSpatial Structures (IASS) makes only very generalrecommendations for the seismic analysis of guyedmasts (11. It states that such structures may beanalysed under a static lateral load proportional totheir weight, as is done in most building design codesfor base shears. Designers are then referred to theirnational standards for more specific guidelines ondynamic amplification factors and force dist~bution.More recommendations follow on modelling con-siderations applicable to detailed dynamic analysisfor various loads. Particular recommendations forseismic vibrations include the use of a randomvibration approach in load modelling and the as-sumption that wave propagation effects at the groundsurface are negligible (input may be assumed to besynchronous at all supports). Since earthquake loadsare already extreme events, they are assumed to becombined with dead loads only, and to occur understill air conditions. Modal superposition, valid for

linear structures, is also suggested. However, cautionin its use is recommended for very taI1 guyed mastsor for unusual towers, both of which may exhibitimportant geometric nonlinearities.

Referring to the recommendations of the CanadianStandards Association in CAN/CSA-S37 [2] forstructural design of antenna-supporting st~ctures,one finds only a general note on the possible need fora detailed dynamic analysis of seismic response forvery tall towers.

The purpose of this study is to investigate theseismic response of guyed towers using numericalsimulations on a detailed finite element model thatincludes geometric nonlinearities and that allows forpotential interactions between the mast and the guy-wires. Two guyed masts are analysed: a short towerwith only two guying levels and a taller one with six.Only lateral ground excitation is considered, andeffects of surface wave propagation are illustrated forthe tallest tower, for which the excitation at variousground anchorage points is delayed.

2. LITERATUREREVIEWPublications related to dynamic analysis of guyed

towers pertain almost exclusively to wind response.Work reported by Augusti and collaborators. [3]includes modelling of a 200 m guyed mast with threeguying levels using equivalent elastic linear springsfor the guy cables. The stiffness of the springs varieswith the frequency of oscillation, however. Inertiaeffects of the cables are not modelied and the mast isa three-dimensional (3-D) lattice structure with sevenlumped masses along its height. Although such amodel cannot account for full dynamic cable-mastinteractions, it retains the essential characteristics of

711


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712 E. GUEV R and G. MCCLUREgeometric nonlinearities. The random vibration ap-proach used for wind effects could also be adapted toa study of seismic excitation. More recently [4],detailed analyses on two guyed towers have beenreported in which the guy cables are represented by amesh of from five to twelve two-node cable elements.

Modelling aspects pertaining to geometrically non-linear effects were also investigated by Ekhande andMadugula [S]. For static analysis, they proposed aspecial cable element formulation which accounts forsagging effects by using an equivalent modulus ofelasticity. Such a formulation is not appropriate,however, if inertia effects of the cables are to bemodelled. Another numerical study by Raman andcoworkers [6] confirms the importance of geometricnonlinearities in guyed tower response underquasi-static loads.

Irvine [7] has contributed many useful discussionson the dynamic behaviour of guyed towers, namelythose presenting analytical expressions for linearizedcable vibrations. More recently, Argyris and Mlejnek[8] have briefly presented results for a 150 m transmit-ter tower subjected to idealized sinusoidal earthquakeloading. Computed displacements were of large am-plitude, indicating that serviceability conditionsmight be exceeded. Many other contributions toguyed tower dynamics were made by researchersfrom the offshore industry but are not directly rel-evant to aerial towers, and hence are not reviewedhere.

3 MODELLING OF GUYED TOWERS3.1. M odell ing of mast

Figure 1 illustrates the geometry of the two guyedtowers that were analysed. Tower A is an 80 ft (24 m)mast with two stay levels and Tower B is a taller mastwith a height of 350 ft (107 m) and six stay levels. Interms of height, Tower A represents the shortestcategory of towers use in the industry while TowerB would be classified as average-detailed data beingobtained from members of the technical committee ofCAN/CSA-S37. Both towers consist of three-leggedattice galvanized steel masts pinned on their foun-

dation and stayed by pretensioned guy wires. All guywires, except those of the lowest cluster, are con-nected to the mast by means of an outrigger orstabilizer aimed at increasing the torsional stiffness ofthe tower. A total of six guy wires are attached ateach. stabilizer to form three pairs of cables anchoredon the ground on radii oriented at a horizontal angleof 120. Due to symmetry, only one of the three setsof cables is shown in Fig. 1. Most connections arewelded and long mast sections are bolted together onsite.

Considering the large number of individual mem-bers in a lattice mast, the modelling of the mastsrequired a reduction in the number of degrees offreedom. Equivalent properties were derived for sec-

tions of the masts. Panels made of four cells as shownin Fig. 1 were analysed for shear, bending andtorsional effects. Typical panels were modelled asspace trusses, thus neglecting the additional bendingrigidity provided by the welded connections. Theresponse was then used to compute equivalent shearand bending properties using Timoshenkos beamtheory. St Venant torsion was used to derive thetorsional stiffness, thus neglecting warping effects inthe mast. This simplification is not significant, how-ever, since most of the torsional rigidity of the toweris provided by the guy wires connected at the outrig-gers. Finally, the axial stiffness was directly obtainedfrom the cross-sectional area of the legs. It wasobserved that due to the lack of symmetry in thelayout of the diagonals, a distortion of the cross-section is induced by simple lateral loading. Thiscoupled effect of bending and torsion is not ac-counted for in the formulation of the 3-D frameelement used, and thus, the equivalent beam model ofthe mast is not able to replicate the response of thedetailed space truss model. The comparison of theequivalent mast with the detailed mast in terms ofaxial, lateral and torsional loads, resulted in differ-ences of less than 3% for Tower A and less than 5%for Tower B. Special consideration was given to theoutriggers or stabilizers that were modelled with rigidlinks from the mast to the cable attachment points.

In view of mass modelling, equivalent panel den-sities were found for each typical panel. Note that noprovision was made for the mass of ancillary com-ponents and of antennas attached to the masts. Alumped mass matrix formulation was used at theelement level. The mast in Tower A was modelled bya total of 15 elements for a total of 90 degrees offreedom while the model of the mast in Tower Bincludes 31 elements for a total of 183 degreesof freedom. Gravity effects are included in the analy-sis and lumped masses are also activated in thehorizontal global directions during seismic analysis.Rotational inertia effects in individual elements areneglected. Nor does the model account for structuraldamping: note that for all welded steelwork, the IASS[l] recommends an equivalent modal viscous damp-ing ratio of 1.2%. Algorithmic damping is used,however, as discussed in Sec. 4.3, and can be con-sidered as a replacement of low structural damping.The material (structural steel) is assumed to beHookean.

The mast equivalent models were validated by afrequency analysis of the equilibrium configurationunder dead weight and cable prestressing forces. Thefirst five normal modes illustrated in Figs 2(a) and (b)represent the accuracy of the beam element mesh forthe masts of Towers A and B, respectively. Detailed3-D truss models were compared with equivalentmodels having two-node 3-D frame elements. ForTower A, there are discrepancies between thesemodels in terms of mode shapes 4 and 5 near the baseof the mast. These discrepancies occur since the


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713

Fig. I. Guy tower geometry: a) Tower A; b) Tower B.


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E. GUEVAIUnd G. MCCLURE

T-o.363 so

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Fig. 2. Lowest flexural modes of vibration: (a) Tower A; (b) Tower B.

equivalent frame model uses constant element prop-erties (constant bending rigidity) to model the taperedshape of the actual structure. Refinements would benecessary if shear and bending response near the basewas to be studied. Apart from that local effect, Fig. 2shows that the first five modes are reasonably wellrepresented by the equivalent mast models. As ex-pected, the accuracy of the prediction for the corre-sponding periods is much better: in the order of 1.5%for the fifth mode of Tower A and 3.2% for that ofTower B.3.2. Modell ing of guy cables

Guy cables are modelled with three-node trusselements with numerical integration at two Gausspoints. An initial prestress equal to approximately10% of the cable ultimate tensile strength is specifiedfor each cable element by prescribing an initial strain.Material properties are elastic, as for the mast-this

is a valid assumption since it is not expected thatcable tensions will exceed 75% of their ultimatecapacity. The stress-strain law is defined only intension, however, which allows for cable slackeningeffects to be modelled if necessary. A sufficiently finemesh, using a large kinematics formulation for thecable stiffness [ I-111, can then account for fullgeometric nonlinearities.Although a frequency analysis of the cables is notstrictly correct due to the geometric nonlinearities ofthe cables, it remains informative to decide on thenecessary degree of mesh refinement. Our objectivewas to obtain a good prediction (error below 1%) forthe sixth transverse mode, and this was achieved byusing 15 three-node cable elements. Two and four-node elements were also considered but the three-node element proved to be the best compromise interms of accuracy and numerical effort. Frequencyanalyses using both lumped and consistent cable mass


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Seismic response of antenna-supporting structures 715were carried out for Tower A and no importantdifference (less than 0.8%) was observed between theresulting fundamental periods. For the period of thefourth mode the difference is increased to 11%. Forsimplicity, and considering the exploratory nature ofthe numerical simulations to be performed, thelumped mass formulation was retained. It should benoted that the overestimation of the equivalent stiff-ness of the entire tower which is inherent to thediscretization process compensates somewhat for theeffect of the lumped mass formulation on the naturalpiOdS

Cable damping, either structural or aerodynamic,is not modelled. Unsuccessful attempts were made toinclude viscous damping as dashpot elements. Prob-lems arise with that approach mainly because discretedashpots can only be specified once along a fixeddirection [9,10] whereas we need a follower type ofdamping force, along the axial direction of each cableelement. An alternative consists of introducing Ray-leigh damping but since the dynamic analysis willproceed by direct integration, it is not a viable optionas it would require the calculation of many modeshapes to obtain proper calibration of the propor-tionality constants [1 11. In view of the difficultiesassociated with realistic modelling of cable dampingfor nonlinear analysis, it was decided to rely strictlyon algorithmic damping to filter numerically gener-ated high frequency components. Although a detaileddiscussion of cable damping is beyond the scope ofthis paper, it is recognized that research is still neededin this area to derive more appropriate dampingmodels for displacement-based finite element pro-cedures for nonlinear analysis. The main disadvan-tage of algorithmic damping induced by directintegration operators is that it cannot be calibratedwith physical damping.3.3. Comparison of model s

Modelling decisions outlined in the above para-graphs are based on the assumption that only the firstfew transverse modes of vibration of both the cablesand the masts will be excited by the ground motion.

Comparisons between the two models of the natu-ral frequencies of the entire tower are made for bothTowers A and B. For Tower A, results from thedetailed 3-D truss mast model with 1335 degrees offreedom are compared with those of the equivalentmodel having a mesh of 15 frame elements with 564degrees of freedom. For Tower B, the detailed modelwith a total of 3723 degrees of freedom is comparedwith the equivalent model having 31 frame elementsand only 2610 degrees of freedom. Note that in allcases, the finite element mesh used for the guy wiresis similar: 10-15 three-node 3-D tension-only trusselements, depending on cable length. For the TowerA comparisons, a maximum difference of the order of8% is obtained in the fundamental natural frequency.Results for Tower B comparisons show greater simi-larity between the models with a maximum difference

of the order of only 5% in the fourth frequency.Natural frequencies in the reduced model of Tower Aare consistently lower than those of the real tower,indicating greater flexibility in the equivalent model.On the contrary, for Tower B, the natural frequenciesare consistently higher in the reduced model than inthe detailed one. Referring again to Fig. 2, it can beseen that localized effects near the foundation inhigher modes of Tower A originate from the lack ofappropriate representation of the tapered mast.

4 OTHER MODELLING CONSIDERATIONS4 1 Input ground mot ion

Two ground motions were selected for the dynamicanalysis, namely the SOOEcomponent of the 1940 ElCentro earthquake and the N65E component of the1966 Parkfield earthquake. Each record represents adifferent type of seismic loading: the El Centro recordcontaining a wide range of frequencies and a longduration of strong motion, while the Parkfield recordis a good representation of a single pulse load withdominant lower frequencies. These ground motionsare used to reflect realistic frequency contents asexhibited by real earthquakes. However, their magni-tude is scaled to a level compatible with the rec-ommended design spectra of the National BuildingCode of Canada [121. For the Montreal region whichis selected as the reference for this study, the peakhorizontal ground acceleration is 0.18 g and the peakhorizontal ground velocity is 0.10 m/set. These valuescorrespond to a spectral acceleration of 0.54g and aspectral velocity of 0.20 m/set, respectively. Details ofthe scaling procedure are given by Schiff [13]. Thescaling is necessary to allow comparison of theresponse of the towers between the two accelero-grams at the same intensity. Note that only horizon-tal ground motions were simulated because itwas suspected that these would generate the largestamplifications in flexible guyed towers.4.2. Support conditions

Earthquake ground motions have high variabilityin time and space. For structures in which thedistance between supports is particularly large, thespace variability can be very important and theassumption that every point at the base of thestructure vibrates synchronously is inaccurate. Sincethe absolute velocity of the horizontal ground motioncan be determined, we can treat the motion as atravelling wave with specific velocity. Time delays forthe arrival of the wave at the base of the structure canthen be introduced at each support. This is illustratedin Fig. 3 where the ground motion first excitesanchorage point 1, then excites the foundation of themast, and lastly, excites anchorage points 2 and 3.Assuming a shear wave velocity of 3-4 km/set in arock medium [14], a total time delay of 0.045 setoccurs between extreme ground anchorage points


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716 E. GUEVAIUand G. MCCLUREwhich span 125m for Tower B. Delays are notsignificant on shorter Tower A, and hence, resultsreported for that tower are for the synchronousground excitation only.

To take different input ground excitations at vari-ous support points into account we modified theboundary conditions of the problem. The methodused is the large mass method (LMM) whose basicprinciples and numerical performance are well sum-marized by LCger et al. [15] in relation to long spanbridges. The method consists of changing the supportconditions from fixed to free in the horizontal planeand of introducing a large lumped mass in thedirection of these released degrees of freedom. Theeffect of the appropriate accelerogram, a(t), is thenintroduced directly at these large lumped masses byan external concentrated inertia force, F(t), which isequal to the product of large mass, M, and a(t). Theanalysis then proceeds as with fixed supports. Rela-tive displacements of the superstructure can readilybe obtained with respect to any support, by subtract-ing the absolute displacement at the support beingconsidered. The value of the large mass appropriatefor this particular application was determined bysensitivity analyses using a single degree of freedommodel for Tower B. Results obtained from the LMMand the fixed base method were compared using thesame undelayed sinusoidal ground excitation at allsupports. After conducting trials in the range of107-10o times the total mass of Tower B, it was foundthat a factor of lo* was the best choice to ensure

convergent and accurate results. The LMM is equiv-alent to the penalty method used in static analysis toprescribe a support degree of freedom.4.3. Numeri cal methods

Stiffness matrix updates using the BFGS method[10,111 are performed at every time step since nonlin-earities in the guy cables can be important. Thisapproach is used instead of a full reformulation of thetangent stiffness matrix at each time step, in order tosave computational effort. Equilibrium iterationswithin every time step are also performed whenevernecessary. The tolerance criterion used is based onthe Euclidean norm of the strain energy imbalancebetween consecutive time steps.

The nonlinear dynamic equations of motion aresolved by direct step-by-step integration using theNewmark+ method. Two variants of the integrationmethod are used: the first one is the common trapezoidal rule with parameters 6 = 0.5 and b = 0.25,which does not introduce any amplitude decay in thecalculated response; and the second one is the New-mark-j method with parameters 6 = 0.55 andfl = 0.3, which does introduce some amplitude decay.The second method was used to eliminate spurioushigh frequency components in the calculated re-sponse, which would normally be filtered out byphysical damping.

The time increment used in all calculations is0.005 sec. Thus, 200 time steps are necessary tocompute the response for a duration of 1 sec.

2PLAN VIEW

Fig. 3. Modelling of support conditions for asynchronous ground motion.


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Seismic response of antenna-supporting structuresTable 1. Summary of rcsponsc for Tower A

717

Cluster 1: r, = 6 kNqm/=oShear (N)Displacement (mm)Cluster 2: To = 5 kNT,,/T,Shear (N)Displacement (mm)

Parkfield El GxtroNo Numerical No Numericaldamping damping damping damping

1.43 (1.19) 1.41(1.14) l.SS(l.24) 1.48 (1.19)1166 (599) 802 (342) 1670 (750) 1340 (600)5.36 (3.09) 5.18(2.81) 6.36 (5.1) 8.72 (4.0)1.26 (1.11) 1.25 (1.10) 1.46(1.25) 1.34(1.16)1600 (750) 1041(590) 2610(1250) 2133 (1100)6.27 (3.0) 5.54 (3.0) 11.45 (6.0) 10.0 (6.0)

S RRSULlS5 1 eneral description

Calculated results for various elements of responseare summarized in Tables 1 and 2 for numericalsimulations on Towers A and B, respectively. Theseresults include ratios of the peak dynamic cabletension to the initial prestressing force (TdYo/TO),horizontal shear forces induced in the mast, andlateral mast displacements at cable attachmentpoints. Time histories are also presented for the mostrelevant response indicators.

Numerical simulations on Tower A are presentedfor the two ground accelerograms derived from theParkfield and El Centro records. In both cases, resultswith no damping and results with numerical dampingare obtained, and as mentioned previously, no timedelay is introduced between the support excitationpoints. Time histories (Figs 4and 5) are generated fora total duration of 15 set which represents 3000 timesteps-the earthquake record available has a totalduration of 2Ose.c.

Simulations on Tower B are obtained only for theParkfield ground excitation, and time delays were

Table 2. Summary of response for Tower BNo time delay Time delay

Cluster 1: To= 11.3 kNTdyn/q 1.37 1.55Shear (N) 1250 1250Cluster 2: To = 17.8 kNTdyn/& 1.31 1.32Shear (N) 3500 3200Cluster 3: To= 17.8 kNT,,,/T, 1.29 1.30Shear (N) 2800 2600Cluster 4: To = 21.3 kN

T&T, 1.34 1.36Shear (N) 2700 3000Cluster 5: To = 41 kNTdp/=a 1.37 1.33Shear (N) 1900 1800Cluster 6: To = 41 kNT,,/T, 1.67 1.51Shear (N) 1800 2060

introduced for comparison with the synchronousinput. Time histories are shown in Figs 6, 11 and 12and have a total duration of 8 sec. Note that most ofthe ground shaking takes place in the first 4sec. Itwas also desirable to reduce the total calculation timefor this model since the number of degrees of freedomis considerably larger than in Tower A.5.2. Tower A

Table 1 summarizes the dynamic amplificationsobserved for three typical elements of response: axialtension in guy cable, shear force in mast at clusterattachment point, and lateral displacement parallel toearthquake direction at the same point. Note thatcable clusters are labelled in ascending number withthe elevation of their mast attachment point beingsuch that Cluster 1 corresponds to the lowest attach-ment point. Values in parentheses represent dynamiceffects in the steady-state zone of the time histories,whereas the main values are those of the peaktransient response. This is best appreciated by look-ing at Fig. 4(a) where a peak transient tension of8.6 kN is obtained, compared with an initial prestressof 6 kN, for an amplification factor of 1.43. The rangeof tension fluctuations about the initial prestress inthe steady-state portion that follows is in the orderof 19%. Results for horizontal shears and for dis-placements at cluster attachment points are given inabsolute values.

Results for cable tensions are all given for a typicalcable aligned with the direction of the input groundmotion. Recall that this has already been illustratedschematically in Fig. 3. Time histories in Figs 4(a)and (b) show that the peak transient response occursat approximately time t = 4.5 set, which correspondsto the peak transient in the input excitation. ForCluster 1, peak amplifications are of the order of43%. Since the input excitation is rather uniformafter that transient peak, the tower reacts more or lessin a steady-state manner after that point, with maxi-mum dynamic amplifications of the order of 19%.Corresponding results are lower for Cluster 2 withrelative amplifications of 26% and 11%, respectively,for the undamped case. Note that Cluster 2 is madeof cables that are 37% longer than those of Cluster


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718 E. GUEVARA nd G. MCCLURE1 with a lower prestressing force, resulting in a moreflexible cluster. Results for the numerically dampedcase are only slightly lower with reduction in peakvalues from 2-S%. It is seen by comparing Figs 4(a)and (b) that numerical damping is efficient in filteringout the high frequency components of the responsethat are present in the undamped case during the first3 set of the time history.

The effect of numerical damping is more evident inthe reduction of the peak values of the mast shear

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Seismic response of antehna-supporting structures 719Horizontal displacements and tilting rotations are cable response were found to be linked to the inter-

given at the top of the tower in Figs 4(e) and (f). The action between axial modes of the mast, and shouldresponse is very small with frequency contents similar be filtered out by physical damping. This filtering isto those observed in shears and cable tensions. achieved by numerical damping in Fig. 5(b). Con-

The same response indicators of Fig. 4 am repeated trary to cable tension, shear response at Attachmentin Fig. 5 for the El Centro ground excitation, and the 1 exhibits higher frequency contents only after 3-4 setpulsed time histories obtained are characteristics of of ground shaking. Another interesting result is thatthis particular acceleration record. High frequencies shear forces in the mast at intermediate points,in the cable tensions are only present in the first between the cluster attachment points, had higher1.5 set as shown in Fig. 5(a). As will be discussed later frequency content than the shear forces at clusterfor Tower B, these initial high frequency effects in attachment points. This result was investigated by

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0 3 ThE s, l5 0 3 TbE s, l5Fig. 5. Elements of response for Tower A (El Centro ground motion): (a), (c) and (e) with no damping;(b), (d) and (f) with numerical damping.


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120 E. GUEVARA nd G. MCCLUREgenerating a Fast Fourier Transform (FFT) of thetime history analysis of the shear force between thefoundation and Attachment 1. It was found thatthere is frequency coincidence between the first axialmode of the mast and the fifth bending mode of thetower, at approximately 38 Hz.

In general, from Table 1, one can observe that theEl Centro excitation produces larger cable tensionamplifications, larger shear forces, and larger dis-placements, than the Parkfield.

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5.3. Tower BTable 2 summarizes the dynamic tension amplifica-

tions T,,,/T,) observed for a typical cable in theresponse of each of the six clusters. Maximum shearforces induced at the cluster attachment points arealso listed. Corresponding complete time histories ofthe cable tensions for Clusters 1, 3 and 6 are shownin Fig. 6 for both synchronous and asynchronousground excitations. Recall that guy clusters are

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Seismic response of ~tenna-supping structures 721labelled in ascending number with the elevation oftheir mast attachment point being such that Cluster1 corresponds to the lowest attachment point. Allresults were obtained using the model with numericaldamping. Results in Table 2 indicate amplifi~tions inthe cable tensions in the range of 29-37% for the fivelowest clusters, and a much larger ampiification of67% in the top cluster, for the model with syn-chronous base excitation. It is interesting to observethe effect of the time delay on the cable tensions inCluster 1. Namely, tensions are amplified from 1.37to 1.55 times the initial prestress. The amplitudes aremore or less unaffected by the delay in the otherclusters, In Cluster 6, however, the time delay tendsto reduce the peak tensions.

Note the presence of high frequency components inthe first three seconds of the time histories, especiallyin Cluster 3 (Fig. SC). To investigate the source ofthese high frequencies, we ran a Fast Fourier Trans-form analysis of the cable tension time history for allthree clusters (1, 3 and 6). Plots are given in Fig. 7.It was first thought that these high frequencies weredue to the vibration of the guy wires since some of thehigher transverse vibration modes of these cables arealso close to 11 Hz, a dominant frequency for the

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(b) 16 00i

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axial tension in Cluster 3. We then refined the cablemesh and observed no important change in the cabletensions. To get more insight into this special featureof the response, we decided to study the seismicresponse of individual ~mponents. First, the isolatedcable typical of Cluster 6 was subjected to basemotion. The tension calculated at the top attachmentpoint is plotted in Fig. 8 and indicates no highfrequency components. We then applied the verticalforce component of all cables of Cluster 6 as anexternal compressive load, P(t), on the isolatedmast-the mast was assumed to be pinned at bothends and subjected to base motion. Results for thevertical reaction in the mast are shown in Fig. 9(a)and an FFT of that time history is given in Fig. 9(b).Dominant frequencies in Fig. 9(b) match the lowesttwo axial frequencies of the mast, and clearly showthe implant cont~bution of the mast in the gener-ation of these high frequencies. In the fully coupledmodel, these high frequencies propagate through themast and in the guy wires. This result is supported bythe time histories shown in Figs 6(c) and (d) forCluster 3. Returning to the response of the completemodel, Fig. IO shows the time history of the axialforce in the mast for an intermediate point between

(4

0 00 0.006FREQUENCY (Hz) 0 FBREQI;EN& (&) Pig. 7. Fast Fourier Transform of axial tension in guys for synchronous motion.

CM 1,4,-


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7226.OE+004

5.6E+004

5.2E+004

u,z 4.8E+004Wt2 4.4E-tO04-

2 4.OE+0043.6E+004 0

E. GUEVARAnd G. MCCLURE

I I I I1 TIME2 s) 3 4Fig. 8. Axial response of guywire without mast interaction.

the foundation and the attachment point of Cluster1. In this case also, it is clear that the interaction ofthe axial modes of the mast is significant. This is animportant finding since it indicates that verticalground motion could possibly trigger large dynamicamplifications if combined with lateral excitation.

The largest shear effects are induced at the attach-ment points of Clusters 2 and 4 for which timehistories are shown in Figs II(a) and (b) for thesynchronous and asynchronous excitation, respect-ively. Table 2 indicates that shears at Attachment 2are about three times as large as those induced at the

5 - 1 SE+005dl -5 2E+0059zw -4 BE+005>

-64E+005 I0 1 TIME s) 3 I4

first stay level. Shear forces do not show a particu-larly high frequency content, however, and a transi-ent peak occurs shortly after 3 set which coincideswith the transient peak of the excitation.

Lateral displacement time histories of the displace-ment at the top of the tower are given in Figs 12(a)and (b) for the two types of excitation. As expected,the frequency content of the displacement response islower than that of the shears. It is observed that thepeak displacements are of the same order (approxi-mately 5 cm) in both the delayed and undelayedcases.

(b)1 OE+005

Fig. 9. Mast response without cable interaction: (a) vertical reaction at base of the mast; (b) FFT of thevertical reaction.


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Seismic response of antenna-supporting structures 123

9.6E+005

- 8.OE+005ww 6.4E+005FG0 4.8E+005IA-A 3 2E+005QxQ 1.6E+005

O.OE+OOO

- 1.6E+005 I I I I0 2 TIME4 6 8s)Fig. 10. Axial force in the mast at elevation 3 A.

6. CONCLUSIONIn this paper we have presented a detailed numeri-

cal investigation of the seismic behaviour of twoguyed telecommunication towers. The towers selectedrepresent current industrial practice in Canada.

Results indicate that the absolute values of thedynamic cable tensions and of the induced shearforces in the mast are well below the limit strength.Displacements obtained at cable attachment pointsand at the top of the tower are also well belowserviceability criteria for such towers. It is recognized

(0)3 OE+OOJ

2 OE+00352- 1 OE+OOJ8,,Z OOE+OOO8w -1 OE+00341 -Z.OE+OOJU-J

-4OE+003 0 1 ITIME4 s) 6 8

that seismic risk is not a serious concern in theMontreal region, and it will be interesting to studythe response of the same structures for otherlocations where the risk is higher, such as theVancouver region in British Columbia. Numericalmodelling of a taller tower is also planned in order tocover the complete range of telecommunication towercategories, from below 30 m high to over 300 m. Formulti-level guyed towers, it seems that top and bot-tom clusters are prone to the largest dynamic effects.

An important observation is that dynamic inter-actions between the guywires and the mast are

4 OE+OO3 ,b)

3 OE+OO3

z 2 OE+003

8 1 OE+OO3

; OOE+OOO

% -1 OE+OO3w5 -U,E+OOJ

-1OE+OOJ I0 TIME4 s) 6 8

Fig. 11. Shear force at the second attachment point for Tower B: (a) synchronous motion; (b)asynchronous motion.


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724 E. GUEVARA and G. MCCLURE(b)

-0 03 - -0 05-0 04 1 -0060 2 TIME4 6 8 0 TIME4 8s) s)

Fig. 12. Displacements at the top of Tower B: (a) synchronous motion; (b) asynchronous motion.

important, especially in the vertical direction. Thisneeds to be further investigated because in realearthquakes, both horizontal and vertical groundmotions are present, and the combination of the twomight adversely affect the tower.

Another interesting finding is that multiple supportexcitation of the tallest tower causes additional dy-namic effects that are not present when only syn-chronous ground motion is studied. This esult,combined with the fact that vertical accelerationsmay also trigger important dynamic amplifications,suggests that more numerical investigations areneeded to understand fully the seismic behaviour oftall, geometrically nonlinear towers.

Acknow ledgemenfs-The work reported here was carriedout with the financial support provided by the NaturalSciences and Engineering Research Council of Canada tothe second author. The assistance of Professor MurtyMaduuula of the University of Windsor (Ontario) and ofMr &mon Weisman of Weisman Con&ants Inc. ofDownsview (Ontario) is also gratefully acknowledged.

1.

2.

REFERENCESIASS (International Association For Shell and SpatialStructures), Working Group No. 4, Recommendationsfor guyed masts, IA&S, Madrid (1981).CSA (Canadian Standards Association), CAN/CSA-S37M86, Antennas, towers, and antenna-supporting

3.

4.

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structures, A National Standard of Canada, CSA,Rexdale, Toronto (1986).G. Augusti, C. Borri, L. Marradi and P. Spinelli, On thetime-domain analysis of wind response -of structures,J. W ind Emme Indusil . Aerodv n. 23. 449-463 1986).G. Augusti,-C:Borri and V. Gusella, Simulationof windloading and response of geometrically non-linear struc-tures with particular reference to large antennas, Srruc-rural Safefy 8, 161-179 (1990).S. G. Ekhande and M. K. S. Madugula, Geometricnon-linear analysis of three-dimensional guyed towers.c O??lDUt Struct 29 801-806 (1988).N. V. Raman, G. V. Surya Kumar and V. V. SreedharaRao, Large displacement analysis of guyed towers.Compur. St ruct . 28, 93-104 1988).H. M. Irvine, Cable Structures. MIT Press, Cambridge.MA (1981).J. Argyris and H. P. Mlejnek, Dynamics of Structures.Texts on Comoutational Mechanics. Vol. V. North-Holland, New kork (1991).ADINA R&D, Inc., ADINA-IN for ADINA usersmanual. Report ARD 90-4, Watertown, MA (1990).ADINA R&D, Inc., ADINA theory and modelingguide. Report ARD 87-8, Watertown, MA (1987).K. J. Bathe, Fini te Element Procedures in Engineeri ngAnalysis. Prentice-Hall, Englewood Cliffs, NJ (1982).12 National Research Council of Canada, National build-

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ing code of Canada 1990, 10th Bdn, Ottawa (1990).S. D. Schiff. Seismic desian studies of low-rise steelframes. Ph.D. thesis, University of Illinois (Urbana-Champaign) (1988).M. Wakabayashi, Design of Earthquake ResistantBuildings, pp. 6-7. McGraw-Hill, New York (1986).P. Leger, M. Ide and P. Paultre, Multiple-supportseismic analysis of large structures. Compur. Strucf. 36,1153-l 158 (1990).

Nonlinear Seismic Response of Antenna Supporting Structures 1993 Computers & Structures

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