ST057Ghodrati

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DYNAMIC RESPONSE OF ANTENNA-SUPPORTING STRUCTURES

G. Ghodrati AmiriA

, A. BoostanB

A Department of Civil Engineering, Iran University of Science & Technology, IranB Department of Civil Engineering, Islamic Azad University of Tehran, Iran

ABSTRACT: The subject of this paper is the investigation of the dynamic behavior of self- supportingtowers with four legs. In this regard, 10 existing self-supporting telecommunication towers with heightsvarying from 18 to 67 m have been studied under Tabas, Naghan and Manjil earthquake spectra, whichare among the important and major earthquakes in Iran. These spectra were scaled to the baseacceleration of 0.35g in order to be compared with the design spectrum of the Iranian 2800 seismic codeof practice. The seismicity level of Iran is one of the high seismicity levels in the world. The results arestudied in parallel to the concepts of the seismic national code for buildings. Also, since in most cases, thewind force is taken as the controlling force for designing these structures, a comparison is made betweenthe results of wind and earthquake loading. These comparisons result the necessity of consideringearthquake loads in tower analysis and design. Their dynamic analyses are performed by SAP2000program.

1. INTRODUCTION

Communication industry has a unique situation in the history of human life. In the current century, this fieldhas become significantly important and has been named communication era. Telecommunication towershave essential role in this industry. They support radio, television, and telephone antennas to transmittelecommunication signals over long distances. In the emergency situation, these towers play animportant role for transmitting news from damaged area to the rescue centers (medical services, firefighting and police stations). Therefore damage to them can significantly increase loses due to naturaldisasters. Also, infrastructures such as dams, electricity power stations, gas and fuel stations, etc. for theiroperation need these masts for transmitting their data and these towers are very important for suchfacilities. Therefore, the protection of these masts during severe events is of major importance andaccordingly the performance of such structures under these loadings should be properly evaluated. Due tothe relative small weight of the structure of these towers and having wide-area components at the top of

them like dishes, the main and considerable load in them is generally wind load. Also in most code ofpractices for telecommunication towers, the wind load combined with the ice load is considered to be thedesign load of the structure. But with the increase of the height and therefore the increase in weight andalso taking into account the slenderness of the structure, the seismic load can be considerable in thesestructures. Therefore in the last research developments of the advanced countries, earthquake and itsdynamic effects on these structures (with three legs) are also considered. The purpose of this study isinvestigating the dynamic behavior of self- supporting towers with four legs.

4e Confrence spcialise en gnie des structures

de la Socit canadienne de gnie civil

4thStructural Specialty Conferenceof the Canadian Society for Civil Engineering

Montral, Qubec, Canada

5-8 juin 2002 /June 5-8, 2002


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2. BACKGROUND

Mikus (1994) did one of the first studies performed on the seismic analysis of the self-supportingtelecommunication towers and it was about the superposition of modes. Considering 6 towers with heightsbetween 20 to 90 meters and 3 earthquake records, he concluded that the initial 4 modes of the towergive the required precision in the modal analysis.

In 1995, Galvez performed some researches about the equivalent static analysis. He considered 3 towerswith heights of 90, 103 and 121 meters and 45 earthquake records. In 1996, sackmann also followingGalvaz studies, he studied 10 towers with heights between 30 and 120 meters and offered some tablesfor the determination of base shear factor.

Khedr and McClure in 1999, in continuation of the studies performed by Galvez and Sackmann,developed a function for the profile of acceleration distribution along the height of the tower.

The valid codes of practice also offered some relationships for seismic analyses of the self-supportingtowers. The NEHRP Guideline-TS13 offered some relationships for the determination of the base shearbased on the design acceleration spectrum, importance factor, weight, behavior modification factor andthe period of the principal mode of vibration of the tower.

The Canadian standard CSA-S37 code of practice, in the latest edition, has offered somerecommendations for the investigation of the dynamic behavior of the towers based on the position andheight of them.

The Australian standard AS 3995-95 code of practice, considers the wind loading effect as the controllingfactor for towers with height less than 100 meters and only obligates the consideration of seismic loadingfor towers with heights more than 100 meters.

The Euro code 8 part 3 (En7 1998-3) code of practice also obligates the study of the behavior of towersunder elastic response spectrum and 8 time histories of existing records. This code has offered somerelationships for determining the base shear and its distribution along the height supposing that the massdistribution of the tower along the height is concentrated.

Considering the results obtained from these researches, the necessity of dynamic study of the self-supporting telecommunication towers is revealed more.

3. DESCRIPTION OF TOWERS

Towers under study are self-supporting towers with four legs, different heights and capacities, which aredesigned and installed, based on the wind load as the controlling design factor. The samples selected forthis research are from 10 different heights, which were constructed in Iran. These towers are tetrahedronswith different types of restraints even at the same height with the sample. In Table 1, the specifications ofthe selected samples are given. In this table, Ltotalis the total height, Wtotalis the total weight, DL is the freeend wide, DOis the fixed base wide and Ltaperis the height up to where the constant section begins.Single equal leg angles are generally being used in the members of the tower. The used steel in towersections L100*100*10 and larger ones is ST52 with yield stress of 3600 kg/cm

2and for smaller ones is

ST37 with yield stress of 2400 kg/cm2. The elastic modulus of the used leg angles is 2.1E6 kg/cm2andtheir unit weight is 7850 kg/m

3. The connections are generally composed of nuts and bolts and plates are

used as an interface member. The general shape of the towers can be seen in Figure 1.

4. MODELLINGOFTOWERS

SAP2000 software is used for analyzing the structures. The display environment of SAP2000 is anappropriate environment for modeling structures like towers that have several members with different


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Table 1. Towers used for numerical simulation

Ltotal(m)

Wtotal(kg)

DL(m)

DO(m)

Ltaper(m)

18 4072 2 3.4 10

22 5651 2 3.9 14

25 6791 2 4.3 17

30 8670 2 5 22

35 10721 2 5.7 27

42 13366 2 6.7 34

48 16700 2 7.6 40

54 20271 2 8.4 46

60 24627 2 9.3 52

67 29513 2 10.3 59

specifications. With regard to the existing connections between members based on the position andnumber of used bolts, these connections are classified into 2 types of fixed and joint connections andaccordingly, the members are classified into beam and truss. After determination of the coordinates ofnodes of the towers and their members, the geometric properties of tower sections are given to thesoftware. The 3D distributed mass of the tower is automatically considered along the members byspecifying the density of the used materials and geometric properties of the sections. In order to considerthe mass of nuts and bolts, ladder and other installed equipment on the tower, since their weights areknown, by modifying the density, this mass is distributed along the height of the structure. Its important tonote that this weight is very considerable and ignoring it, has a very substantial effect in the results.Structure damping is modeled with a value of 2% of critical viscous damping.

5. EARTHQUAKE EFFECTS

The effects of the earth movement are considered in the form of acceleration response spectrum. In thisresearch, the design spectrum of the Iranian 2800 seismic code of practice has been used and thecorresponding parameters are:

-Base design acceleration A=0.35g (region with relative high risk of seismic activity)-Ground type II (T0= 0.5)-Importance factor I=1.2 (Important Structures)-Structural behavior factor R=1 (Due to the vitality of towers and the need for their stability andserviceability after occurrence of earthquake)

In addition to the above spectrum, 3 spectra including Manjil, Tabas and Naghan, which are among thefamous and major earthquakes in Iran, were employed. These spectra were scaled to the baseacceleration of 0.35g in order to be compared with the design spectrum of the Iranian 2800 seismic codeof practice.

According to the EIA code of practice, if in a record, the ratio of maximum earthquake acceleration tomaximum earthquake velocity exceeds 0.3, controlling the tower with that record is obligatory. Theseratios for the 3 records are 1.034, 0.972 and 0.8324 for Manjil, Tabas and Naghan respectively. Accordingto the mentioned limit of the EIA, in all the 3 records, the dynamic calculations are necessary.


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6. WIND & ICE LOADINGS

Wind loading has been chosen based on EIA Standard with the base wind velocity of 160 km/h. For iceloading, the thickness of the ice is considered to be 1 inch. In order to consider it in the program, the unitweight of the ice is calculated and after the determination of the total weight of the structure, by modifyingthe initial material density, this extra weight is distributed along the whole structure.

7. RESULTS

7.1 Natural Frequency Analysis

Using the natural frequency analysis, the first few frequencies of the modeled structures are determined.Figure 1 show the lowest three flexural mode shapes of 67-m tower.

Figure 1. The lowest three flexural mode shapes of 67-m tower

The following empirical relationship is offered for determining the first natural period of vibration in terms ofthe total height.

T1= 0.0086H 0.0068 [1]

In this relationship, T1 is the natural period of the principal mode of vibration in second and H is the towerheight in meter.

Also, the following functions are offered for determining the periods of the second and third modes ofvibration.


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T2= 0.003H 0.003 [2]

T3= 0.0017H 0.0066 [3]

7.2 Dynamic Spectrum Analysis

Using the modal analysis option in SAP2000, the first few frequencies of the modeled structures aredetermined and using the Iranian code 2800 of practice design spectrum, the spectrum analysis is beingperformed on the towers. Since there is no limitation in the program, the first 20 modes of vibration areconsidered in the spectrum analysis. Also to perform a dynamic analysis of towers, 3 spectra includingManjil, Tabas and Naghan, which are among the famous and major earthquakes in Iran, were employed.

The ratio of the base shear (V) to total weight (W) resulting from the spectrum analysis with all spectrumsis calculated for all the samples. Figure 2 shows the percentage ratio of the base shear to the total towerweight versus tower height. Because of the values of the Iranian code 2800 of practice design spectrumare maximum for most of the samples, the following relationship can be offered for all the towers. Thisrelationship is the same as the Khedr and McClure s (1999) relationship that offered for their towersunder 45 earthquake records with three legs.

Vh= M Ah(1.8573 - 0.6617 Tf) [4]

In this relationship Vhis the base shear, M is the total tower mass in kg, Ahis the peak horizontal groundacceleration for the site in m/s

2and Tfis the fundamental flexural period of vibration of tower in second.

0

10

20

30

40

50

60

70

80

0 20 40 60 80

(Base Shear / Total Wieght) %

TowerHieght,m

Spec2800 Manjil Tabas Naghan

Figure 2. Percentage ratio of the base shear to the total tower weight versus tower height

Also, the maximum horizontal displacement of the highest point of the towers resulting from the spectrumanalysis with Iranian 2800 standard design spectrum can be expressed by the following formula.

dmax= 0.0032H - 0.0584 [5]


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dmaxis in meter and H is the height of tower in meter.

The amount of allowable deformation and rotation of the towers are controlled in terms of the installedequipment. Therefore one of the important criteria for design is serviceability limit.

7.3 Distribution of Shear Loads along the Height of Tower resulting from the 2800 IranianStandard Design Spectrum

Figures 3 to 5 show the distribution of shear load along the height of tower resulting from the 2800 Iranianstandard design spectrum for some towers. Based on the EIA Standard the horizontal forces shall bedistributed vertically as the following relationship. In this relationship, Wiand Wxare the portion of W at orassigned to level i or x, hiand hxare the height above to level i or x, V is the total design lateral force. Sothis formula was used for sample towers to compare with the real values. The result show that Eq.6 canbe used for the distribution of shear load along the height of the tower.

=

ii

xxx

hW

hVWF [6]

0

5

10

15

20

0 1 2 3

Shear Force ,T

TowerHieght,m

Spec 2800 Eq.6

Figure 3. Distribution of shear load along the height of 18-m tower

0

10

20

30

40

50

0 2 4 6 8 10

Shear Force ,T

T

owerHieght,m

Spec 2800 Eq.6



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0

10

20

30

40

50

60

70

80

0 5 10 15 20

Shear Force ,T

TowerHieght,m

Spec 2800 Eq.6


7.4 Static Wind Analysis

In order to perform static analysis of towers, the wind and ice load combination considering the dead loadof structure and 75 % of wind load applied to freezing elements of the structure, was considered. After thedetermination of the resistant areas against wind and the wind load applied to towers and the modificationof it with 0.75 factor, we reached to a distribution very near to wind loading without considering the iceloading. But since in the wind and ice load combination, the dead load of ice is also considered, thereforethe ice and wind load combination is the predominant factor in determining the forces in tower elementscompared to wind loading. Of course, this conclusion is reached with considering 1inch thickness for iceloading. Its clear that by decreasing thickness of the ice, the predominant factor is wind load and byincreasing thickness, the predominant factor is wind and ice load combination in the towers under study.

7.5 Comparison between Results obtained from Wind and Earthquake Loading

In this section, a comparison shall be made between the results obtained from the static linear analysisresulting from ice and wind loading under the effect of EIA code of practice loading and output resultsobtained from dynamic analysis under the effect of 2800 Iranian standard design spectrum. All of thetowers are modeled bare with no antennas, ladders, ice guards and other eccentrically attached devices.

Figures 6 to 8 show maximum base shear, maximum moment and maximum horizontal displacementversus tower height resulting from the wind and earthquake loadings. Studying these graphs indicates thatthe values obtained from wind load exceed from earthquake load. Of course with increase in the numberof antennas and weight of tower the effect of earthquake load is increased.

0

20

40

60

80

0 10 20 30

Base Shear ,T

TowerHieght,m

Spec2800 Wind

Figure 6. Maximum base shear versus tower height


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0

20

40

60

80

0 200 400 600 800 1000

Base Moment ,T.m

To

werHieght,m

Spec2800 Wind

Figure7. Maximum moment versus tower height

0

20

40

60

80

0 0.05 0.1 0.15 0.2 0.25

Max. Horizontal Displacement ,m

TowerHieght,m

Spec2800 Wind

Figure 8. Maximum horizontal displacement versus tower height

8. CONCLUTIONS

In this research, a study of dynamic behavior of self-supporting towers with four legs under seismicconditions in Iran was performed and it was compared to the EIA wind loading. The results summarizedas follows :

1-The following relationships are offered for determining the lowest three first periods of vibration (s) interms of total height in meter.

T1= 0.0086H 0.0068, T2= 0.003H 0.003, T3= 0.0017H 0.0066

2-The following relationship is offered for determining the base shear in terms of the total tower mass (kg),the peak horizontal ground acceleration (m/s

2) and the fundamental flexural period (s) of vibration of tower

under the Iranian 2800 standard design spectrum.

Vh= M Ah(1.8573 - 0.6617 Tf)

3-The maximum horizontal displacement of the highest point of the tower (m) resulting from the spectrumanalysis with the Iranian 2800 standard design spectrum can be expressed by the following formula.

dmax= 0.0032H - 0.0584

4-Based on the EIA Standard the horizontal forces shall be distributed vertically as the following


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relationship. In this relationship, Wiand Wxare the portion of W at or assigned to level i or x, h iand hxarethe height above to level i or x, V is the total design lateral force. The result shows that this equation canbe used for the distribution of shear load along the height of the tower.

=

ii

xxx

hW

hVWF

5- A comparison between the results obtained from the static linear analysis resulting from ice and windloading under the effect of the EIA code of practice loading and output results obtained from dynamicanalysis under the effect of the 2800 Iranian standard design spectrum show that the values obtainedfrom wind load exceed from earthquake load. It should be noted that all of the towers are modeled barewith no antennas, ladders, ice guards and other eccentrically attached devices. Of course with increase inthe number of antennas and weight of tower the effect of earthquake load is increased.

9. REFERENCES

Australian Standard AS 3995 (1994) Design of Steel Lattice Towers and Masts, Australia StandardsAssociation, Sydney, Australia.

CSA (1994) Antennas, Towers, and Antenna-Supporting Structures, CSA S37-94, Canadian StandardsAssociation, Toronto, Ontario, Canada.

European Pre-Standard ENV 1998-3 (1998) Design Provisions for Earthquake Resistance of Structures,part3: Towers, Masts and Chimneys, Brussels, Belgium.

FEMA (1998) NEHRP Recommended Provisions for Seismic Regulations for New Buildings and otherStructures, Building Seismic Safety Council.

Galvez, C. (1995) Static Method for Aseismic Design of Self-Supporting Towers, M. Eng. Project ReportG95-08, Department of Civil Engineering and Applied Mechanics, McGill University, Montreal,Quebec, Canada.

Galvez, C. and McClure, G. (1995) A Simplified Method for Aseismic Design of Self-Supporting LatticeTelecommunication Towers, Proc. of the 7

th Canadian Conference on Earthquake Engineering,

Montreal, Quebec, Canada, 5-7 June, 541-548.Khedr, M.A. (1998) Seismic Analysis of Lattice Towers, Ph.D. Thesis, Department of Civil Engineering

and Applied Mechanics, McGill University, Montreal, Canada.Khedr, M. A. and McClure, G. (1999) Earthquake Amplification Factors for Self-SupportingTelecommunication Towers, Canadian Journal of Civil Engineering, 26(2), 208-215.

Mikus, J. (1994) Seismic Analysis of Self-Supporting Telecommunication Towers, M. Eng. Project ReportG94-10, Department of Civil Engineering and Applied Mechanics, McGill University, Montreal,Quebec, Canada.

Permanent Committee for Revising the Iranian Code of Practice for Seismic Resistant Design of Buildings(1999), Iranian Code of Practice for Seismic Resistant Design of Buildings, Standard No. 2800, 2

nd

edition, Building & Housing Research Center, Tehran, Iran.Sackmann, V. (1996) Prediction of Natural Frequencies and Mode Shapes of Self-Supporting Lattice

Telecommunication Towers, Department of Civil Engineering and Applied Mechanics, McGillUniversity, Montreal, Quebec, Canada.

Computers & Structures, Inc. (1995) SAP2000 Users Manual, Berkeley, California.TIA/EIA-222-F (1996) Structural Standard for Steel Antenna Towers and Antenna Supporting Structures ,

American National Standard.

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