Journal of Wind Engineering and Industrial Aerodynamics, 41-44 (1992) 2035-2046 Elsevier

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Nind-induced Vibration of Transmission Line System

Y. Momomura ~, H. Marukawa b and T. Ohkuma b

Research and Development Department, Izumi Sohken Eng., Co.,Ltd. 24-2,Ginza 1-Chome, Chuo-ku, Tokyo 104, Japan

b Department of Architecture and Building Eng., Kanagawa University,3-27 Rokkakubashi,Kanagawaku,Yokohama,221,Japan

Abstract T h i s paper describes results of a full-scale measurements and

a time series analysis for the wind-induced vibration of a transmission line system. The time series analysis is based on a quasi-static assumption. The study is mainly discussed as in terms of the effects of the coupling motion between a steel tower and conductors, This is accomplished through comparing the results of measurement with calculated ones. As for the analytical response value of the coupled steel tower, the power spectrum of the response displacement has many peaks at the points that correspond to the natural frequencies of the tower, conductors and their coupling motion. Furthermore, in the frequency range which coincide with the natural frequencies of the conductors, are recognized on an interaction response between different vibration modes. Those coupling response characteristics are prominent in a longitudinal direction and are affected by the modeling manner of the supporting condition of the end of the conductors. As is explained above, the qualitative tendencies for the analytical value are in good agreement with the measured ones. However, quantitatively there were differences between their values.

I . INTRODUCTION

Past experimental and analytical studies on the structural dynamic response of a steel tower of an electric transmission line system have conclusively indicated that the characteristics are different from those of a single steel tower due to the effects exerted by the conductors (e.g., Ref. [I]). For the wind resistant design of the steel tower, it is very important to study the various vibration effects exerted upon the tower from each wind-induced vibration of the conductors. The following can be enumerated in regard to each conductor vibration: Vibration are caused by wind turbulence, vortex-induced oscillation, galloping etc. In order to evaluate accurately the effects of the each conductor vibration, and to reflect the evaluation result on the design, it is necessary to

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203b

deal with the tower as a coupled system, as well as to clarify the response characteristics of the conductors. With respect to the above, many studies (e.g., Ref. [2]) on each or the conductor vibrations have been done. However, few studies about the structural coupled behavior for the response of the steel towers and conductors have been done [~]. About the influences exerted upon the tower by the conductor vibrations, there are still problems to be solved.

An accurate estimation of the wind-induced response of the coupled steel tower and conductors is quite difficult to obtain through the use of an accustomed spectrum-- modal analysis method. It is considered alternatively that a time series analysis is useful in obtaining the response [4].

In the first place, this paper, explains the wind-induced vibration of a full-scale steel tower of transmission line system, and the results obtained from an observation of microtremors. Secondly, with the purpose of clarifying the coupled behavior of the steel tower with the conductors, a time series analysis of the response caused by along-wind turbulence is carried out. As a summary, the effects of the conductors and the validity of the analytical model are indicated. This was accomplished through comparing the result obtained from the actual measurement with calculated ones.

2. OUTLINE OF THE FULL SCALE MEASUREMENT

[Measured Transmission Line] [Measured Tower No.106]

.... ~ Measured Tower !'l-" -An4 m 6met; e { .......... i ( ' r o n s i o n t y p e ) ~& : A c c e l e r o m e t e r !

' !e : T r e m o r e m e ~ e r Susp~,,~ion No.106 Tension type !A ,__~ __,, t y p e ~ L~ ~7~L~_ ~o,Iu/ , . . . . . . . . . . . . . . . . ..........

typ No.,o, U w,.d / f 1I=106m l l=103m i1=106.5m l l = l O 0 , 5 m H=lOOm)B-b~i-ndle- d ....... 1 |

................................................ t un i :z ,_,_,!,A

Figure 1 Outline of Measured Transmission Line System and Measuring Instrument Installation Places.

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The full-scale measurement of the wind-induced vibration was carried out on an actual tension type steel tower No. !06 and conductors (See Fig. I). The data in this paper is the result obtained from a measurement on typhoon No. 7920. A wind vane and mile anemometer (made by Koshin Elect. Co. KE-500) were used for the wind velocity. An accelerometer (made by Vibration Tech. Eng. Co. STDH-3C) and a load cell (msde by Nikkei Instr. Co. LT-20TJ62) were used to measure the tower response and the fluctuating tension of the conductors respectively. Fig. I indicates the location where each of the measuring instruments were installed. The analytical data was obtained under the following conditions: an evaluation time of T=600 sec and a sampling time of dt=1.0 sec for the wind velocity fluctuation, T=600 sec and dr=0.05 sec for the acceleration and the fluctuating tension. The responsiveness of the accelerometer with frequency was limited to 0.1Hz~30.0Hz. The calculation of the power spectrum was carried out through the application of the autoregressive method.

5 . STRUCTURAL CHARACTERISTICS OF THE COUPLED STEEL TOWER AND CONDUCTORS

In order to clarify the wind-induced response of the coupled steel tower and conductors, the structural characteristics of the system must be made clear. The following results for the structural characteristics are obtained through the measurement of microtremors. Through the use of tremometers (made by Vibration Tech. Eng. Co. MTKH-IC), measurements were carried out at the observation points shown in Fig. I. The Fourier spectrum of the tower's response displacement shown in Fig. 2.

In regard to vibration in a transverse direction, two predominant peaks can be recognized in the vicinity of 1.0Hz. In additional to the peaks, several peaks are seen in the high frequency range, However, these are not so noticeable. The p e a k s a t 1 .30Hz and 3 , 1 3 H z c o r r e s p o n d t o t h e p r i m a r y and s e c o n d a r y v i b r a t i o n mode o f t h e s t e e l t o w e r . I t can be c o n s i d e r e d t h a t t h e n o t i c e a b l e p e a k a t 0 .83Hz was i n d u c e d by t h e e f f e c t o f t h e c o n d u c t o r s .

The v i b r a t i o n b e h a v i o r i n a l o n g i t u d i n a l d i r e c t i o n i s d i f f e r e n t f rom t h e one i n t h e t r a n s v e r s e d i r e c t i o n . A l a r g e number o f p r e d o m i n a n t p e a k s a r e f o u n d i n t h e low f r e q u e n c y r a n g e a t l e s s t h a n 1 . 0 H z . Many p e a k s a r e a l s o r e c o g n i z e d i n t h e h i g h f r e q u e n c y r a n g e o f 1 .0Hz o r m o r e . H o w e v e r , t h e p e a k s a r e n o t so p r o m i n e n t a s t h o s e s e e n i n t h e low f r e q u e n c y r a n g e . A number of p r e d o m i n a n t peaks i n t h e low frequency r a n g e a t l e s s t h a n 1 .0Hz a r e c o n s i d e r e d t o be i n d u c e d by t h e e f f e c t o f t h e c o n d u c t o r s . The p e a k s i n t h e p r o x i m i t y o f 1 .0Hz a r e c o n s i d e r e d t o c o r r e s p o n d i n g q u i t e w e l l w i t h t h e p r i m a r y v i b r a t i o n mode o f t h e s t e e l t o w e r .

The c r i t i c a l d a m p i n g r a t i o o f t h e t o w e r a t t h e p r i m a r y v i b r a t i o n mode i n a t r a n s v e r s e d i r e c t i o n was e s t i m a t e d t o be a p p r o x i m a t e l y 0 . 4 5 . T h i s was o b t a i n e d f rom t h e r e s u l t o f t h e m i c r o t r e m o r s .

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[ T r a n s v e r s e direction] [Longitudinal direction]

Displacement Displacement 102 (,.sec) .102(..see) (Transverse)

60.0 11.21 Top level --q'--

1 ~//M ~~ Longi- 48.0 Top level 9. G iddle udinal)

Middle ~ l e v e l

32.0 level I.I 6"41/~~~Lower level

Ig. ]~ Lower 3.

0. ' ' i''"l , . ,,,,.~ 0.0 ' '"':I ' ,'~"'l

10 0 101 i0 0 lO 1 Frequency (Hz) F r e q u e n c y (Hz)

Figure 2. Fourier Spectrum of The Tower's Response Displacement induced by Microtremors.

4. RESULT OF THE FULL-SCALE MEASUREMENT

4.1 Fluctuation of the wind velocit~ The data analyzed an wind flowing in eight different

directions. The main wind direction was close to a south-east direction (See Fig. I), and the mean wind velocity (0.) at the tower's top (H=106,Sm) was 12.0-20.5(m/sec). Under the described above condition, the turbulence intensity (Iu=4~/U.) was 12.0-20.0(~), the gust factor (G=U.,x/0.) was 1.37-1.66 (See Fig. 3), The power spectrum of the fluctuation of the wind velocity at the tower's top is shown in Fig. 4. In this figure t he Hino spec t rum i s i n d i c a t e d as w e l l . The Wave number o f t h e spectral peak for the wind velocity fluctuation was 0.0005~ 0 . 0 0 5 ( I / m ) . The s h a r p d e c r e a s e of t h e power s p e c t r u m in wave number 0 . 0 l and above , i s c aused by t h e r e s p o n s e p r o p e r t i e s o f t h e anemometer . I t can be p r o b a b l y c o n s i d e r e d t h a t t h e peak i n t he p r o x i m i t y o f 0 .01 f o r the wave number i s c a u s e d by the wake o f t h e tower . The s p e c t r a l shape f o r t he wave number o f l e s s t han 0.01 i s s i m i l a r to t h a t o f t h e Hino s p e c t r u m .

4 . 2 Response c h a r a c t e r i s t i c s o f t h e c o u p l e d s t e e l t ower a n d c o n d u c t o r s

F ig . 5 shows t h e power s p e c t r u m of t he r e s p o n s e d i s p l a c e m e n t of the tension type steel tower No. I08 at the lower level when O.=19m/sec and lu=18g at the top. The power spectrum of the fluctuating tension of the each side conductors, bot~ of which are installed on the leeward side at the upper level of the tower No. I08, is indicated in Fig. 6.

According to the power spectral shape of the tower response in the transverse direction, many peaks can be found in the high frequency range at 0.1Hz or more. The peaks at 0.THz~3.0Hz are more predominant than those at the other values. Among the

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predominant peaks, the peak in the vicinity of 1.30Hz coincide with the primary vibration mode of the tower. It is considered that the peak in the low frequency range at less than 1.30Hz, is the component induced by the conductors behavior. The pea~ in the proximity of 3.0Hz corresponds to the secondary vibration mode o£ the tower.

The power spectral shape of the tower response in a longitudinal direction indicates many peaks in the high frequency range at 0.1Hz or more. Using the structural characteristics for reference, it can be considered that several predominant peaks in the high frequency range of 0.1Hz~1.0Hz were induced by the conductors behavior. The predominant vibration component in the power spectral shape for the tower response in a longitudinal direction is different from the one in a transverse direction.

Iu G

0.5 '"2.5 0 4 O:Turbulence intensitY.2.0

• e :Gus t -- I 0 3 factor ~O O • @e I. 5

0 .2 - 1.0 CZ:Z:) 0 ~ 0,1~ 0 0.5

O0 ' ' ' I . 0 0. 5 l0 15 20 25

Bean w i n d v e l o c i t y U n ( m / s )

n . S ( n ) / a s 10 o -

t 0 - 1

10"2 ~

10 -3 ------:Hino spec t rum

1 0 - 4 , I ,I , I 1 0 - 4 10-3 10-2 i0-I

Wave number n/O'M (l/m)

Figure. 5 Hean Wind Velocity, Turbulence Intensity and Gust Factor at Top of Tower.

Figure. 4 Power Spectrum of The Wind Velocity Fluctuation at Top of Tower.

Tower pr. imaPy s e c o n d - n . S ( n ) ( L o n e) n . S ( n ) ( c,,,e )

1 l l - 2 - (T ransverse ) W • a ry

I l l" 3 = Ii - ^ I

10"4 _ ~ L ~ d i n a l ) \ j " ' "

t~,..~L I ] " 1o-5 I

f i ZZ I1=

: T r a n s v e r s e i l l - 7 I .,t I •

O-s 10=Z 10=t 10 o 101 F r e q u e n c y n (Hz)

I 0"~'~ -

1o-3 I_ ,o .L " - j " - - /

10 -5l r - - - : T o w e r No. 105 N No. 106 | L :Tower No 106 N No 107

! 0 - 6 L . - - - , J _ I I - J 10-3 10-z 10-1 100 ll} I

F r e q u e n c y n (Hz)

F i g u r e . 5 Power S p e c t r u m o f The T o w e r ' s D i s p l a c e m e n t c a u s e d by Wind.

F i g u r e . 6 Power S p e c t r u m o f The F l u c t u a t i n g T e n s i o n o f The C o n d u c t o r s .

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The power spectral shape for fluctuating tension of both conductors almost corresponds to that of the tower response in a longitudinal direction, when the difference of the noticeable vibration component in the low frequency range of less than 0.3Hz is not taken into consideration.

5 . THE CALCULATED WIND RESPONSE OF THE COUPLED STEEL TOWER AND CONDUCTORS BASED ON A TIME SERIES ANALYSIS

It has been made clear from the result of the full-scale measurement that the response characteristics of the coupled system are quite complicated due to the influence of the tower behavior on the conductors. For the purpose of clarifying the coupled system behavior, a time series analysis of the response induced by the along-wind turbulence was carried out.

5 . 1 A n a l y t i c a l o u t l i n e and t h e s t r u c t u r a l mode l f o r t h e c o u p l e d a n a l y s i s

The s u b j e c t f o r t h e a n a l y s i s w e r e t h e t o w e r o f No. 106, and t h e c o n d u c t o r s i n s t a l l e d a t e a c h l e v e l on b e t w e e n t h e t o w e r o f No. 104 and No. 108. As f o r t h e s t r u c t u r a l m o d e l o f t h e a n a l y s i s , o n l y t h e two t e n s i o n t y p e t o w e r o f N o . 1 0 6 and N o . 1 0 7 w e r e s u b s t i t u t e d f o r a beam m o d e l , e a c h o f w h i c h h a s an e q u i v a l e n t b e n d i n g s h e a r s t i f f n e s s . The o t h e r t o w e r s w e r e m o d e l e d a s r i g i d o n e s . F o r t h e c o n d u c t o r s and i n s u l a t o r s , w h i c h w e r e i n s t a l l e d a t e a c h l e v e l f o r e a c h s p a n s , and g r o u n d w i r e a t t h e t o p o f t o w e r , s u b s t i t u t e d f o r t h e m u l t i p l e m a s s m o d e l s ( S e e F i g . 7 ) . The c a t e n a r y s h a p e o f t h e c o n d u c t o r s u s e d f o r t h e r ~ s p o n s e a n a l y s i s w e r e t h e s t a t i c e q u i l i b r i u m p o s i t i o n u n d e r the ,lean wind force.

The structural models for the coupled analysis is the five- steel-tower-model and t h e four-steel-tower-model (See Fig.7). As for the flve-steel-tower-model, the end of the conductors for suspension type towers No. I04 and No. I08 were modeled as horizontal springs. The ends of the conductors fop suspension type tower No.lOS were supported with suspension. As for the four-steel-tower-model, the conductors ends of suspension type tower No. I05 and No.108 were modeled as horizontal springs. However, with both models, the wind force acted upon tower No.108 and the conductors between tower No.105 and No.107. The wind direction with respected to the longitudinal direction is 90 ° (See Fig. 7).

With respect to the natural frequency of the five-steel- tower-model, several vibration modes equivalent to the primary vibration mode of the steel tower are found in the range of 0.91-1.3Hz in the transverse direction and in the range of 0.87-2.0Hz in a longitudinal direction. The natural frequency caused by the torsional vibration is seen in the range of 1.5~2.0Hz. The natural frequency induced by the effects of the conductors is recognized in the range of 0.1~1.0Hz.

It is assumed that the da,lping was of a stiffness propor- tional type, and the damping ratio of each steel tower at the primary vibration of a single tower was fixed at 1.0~ and it

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was fixed at 0.4% for the conductors. The response calculation was conducted by means of Newmark's B method (B=I/4).

~--~ &:Simulated , -~- ~ ........ Insulators --~--~ ~-

[-_O~. ~_~ [~:Block act on ~ .... Conductors (]2-elements)

~ same simulated [Multiple mass models for lilies] wind velocity

" T e n s i o n t y p e ,() Suspension No. 106 Tension type

Tower8_elements) ~ N ° " 107 ( )( ~ ~

I. ( ) S u s p e n s i o n I t y p e No. 104 Wind 90 °

Suspens i onX~" ",~/ zn~/ type No.108 ~ / Sn,~n~ Suspension

[Beam model for support suppo~ t tension type tower] ,

/ support \

/ ~ + ........ Spring

\ ~ ~ 1[[o e case o f \ ~'~'--.~- /'four-steel-- ~ . ~ ...... \. ~ // [tower--model ~///~ .~w,; under wind force

'"-- - ' 7 / / . . . . .

~.~ ........... L ~Ive-steel- tower - model ]

Figure 7 AnalysiS.

Structural Model of Transmission Line System for

5 . ~ A s s u m p t i o n o f t h e w i n d f o r c e O n l y t h e f l u c t u a t i n g d r a g f o r c e was e m p l o y e d f o r t h e r e s p o n s e

a n a l y s i s . The f o r c e was c a l c u l a t e d t h r o u g h t h e u s e o f t h e q u a s i - s t a t i o n a r y m e t h o d . The a e r o d y n a m i c d a m p i n g was a l s o c o m p u t e d q u a s i - s t a t i o n a r i r y . The d r a g f o r c e c o e f f i c i e n t was t h e v a l u e i n d i c a t e d i n J E C - 1 2 7 [ 5 ] .

The mean wind v e l o c i t y was f i x e d a t 18m/s a t a h e i g h t o f 70% f o r t h e t o p o f t h e t o w e r ( t h i s i s c a l l e d r e f e r e n c e h e i g h t i n this paper). The vertical distribution of the mean wind velocity was followed by the power law (a=I/4). The standard deviation (o) of the fluctuation of the wind velocity, at the reference height, was fixed at 3.6m/s (turbulence intensity:

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20%), which was constant in a vertical direction. As a power spectrum of the wind velocity fluctuation ,the Hino spectrum was employed. According to the correlation of the wind velocity fluctuation, the equation proposed by Vickery [6] was aplied to the vertical plane perpendicular to mean wind direction, along- wind turbulence was perfectly correlated. The phase difference of the wind velocity fluctuation was ignored. Table I shows the details of each item for the wind velocity fluctuation.

The method presented by Iwatani [7] was employed to the time series generation for the wind velocity fluctuation. The method was based on the multidimensional autoregressive process. The simulated wind velocity fluctuation was obtained from the terms of discrete inverse Fourier transform number L=1200, and the time interval dt=O.2sec. However, in the response analysis, the simulated wind velocity fluctuation was interpolated from the time interval dt=O.2sec to dt=O.Isec.

Table. 1 Spatial Model of Fluctuation of the Wind Velocity

Item Details

Power spectrum S(n)/o e = (A/B)/{I+(n/B)z} -/-

Spatial correlation in /Coh(zi,zj,;n) = exp(-8.0.n.~IU~) a vertical direction

Spatial correlation in /Coh(xi,xj,;n) = exp(-7.0.n.[/Uz) a horizontal direction

........................................... ] ................................................................................................................................................................

Aerodynamic admittance IJxlm=2/C{l-(I/C)+(I/C)e-C}, C=7,n.B/0~

[Symbols ] A=0.238, B--0.0278 o : S t a n d a r d d e v i a t i o n n : F r e q u e n c y , zi,zj,xl,xJ:Horizontal and Vertical coordinates of the degrees -of-freedom, ~-Iz,-zMl, t=Ix,-x=l, US:Mean wind velocity at average height of the two points, 0z:Mean wind velocity at h e i g h t z, B:Width under consideration of admittance

5 . 3 The c h a r a c t e r i s t i c s o f t h e r e s p o n s e d i s p l a c e m e n t o f t h e c o u p l e d tower

The power s p e c t r u m o f t he r e s p o n s e d i s p l a c e m e n t a t t h e u p p e r l e v e l o f the s t e e l t ower No. 106 i s shown in F i g . 8. A d a t a r e f e r r i n g to the s i n g l e tower i s a l s o found in t h i s f i g u r e . The power s p e c t r u m was o b t a i n e d when t h e e v a l u a t i o n t ime T=1680 s e c , and the t ime i n t e r v a l d t = 0 . 1 s e c . F u r t h e r m o r e , t h e r e s p o n s e c h a r a c t e r i s t i c s o f t h e tower i n d i c a t e s a l m o s t t h e same t e n d e n c y a t each o f the l e v e l s ; u p p e r , m i d d l e and lower l e v e l s .

In r e g a r d to t h e power s p e c t r u m o f t h e f i v e - s t e e l - t o w e r - m o d e l in a t r a n s v e r s e d i r e c t i o n , i s s h a p e d in such a manner t h a t t h e p r e d o m i n a n t peak in t h e h igh f r e q u e n c y r a n g e o f 0 .7Hz or more i s s u p e r i m p o s e d upon t h e g e n t l e component c o r r e s p o n d i n g to t h e wind v e l o c i t y f l u c t u a t i o n . Among t h e s e p e a k s , t h e f r e q u e n c y o f

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the most predominant peak coincides with the frequency of the primary vibration mode of the tower. The peak frequency less than the frequency of the primary mode, coincides with the frequency of the conductors behavior at the seventh vibration mode. The peak recognized in the vicinity of 3.0Hz agree to the frequency of the secondary vibration mode of the tower. There is not a large difference between the spectral shape for the four-steel-tower-model and that for the five-steel-tower-model.

Concerning the longitudinal direction, the power spectrum of the five-steel-tower-model, is shaped in the following manner. The predominant peaks in the high frequency range o£ 0.1Hz or more are superimposed upon the gentle component which corresponds to the wind velocity fluctuation. The peak frequency which is seen in the frequency range of 0.1Hz~1.0Hz coincides with the natural frequency of each conductor modes. The peak frequency in the high frequency range of 1.0Hz or more coincides with the frequency of the primary mode, the secondary mode and the torsional mode of the tower The peak value at the natural frequency o£ the conductors, is more predominant than that for the natural frequency of the tower. Comparing the four-steel-tower-model with the five-steel-tower-model, some differences are recognized in the frequency of noticeable peaks which coincides with the natural frequency of the conductors in a low frequency range of less than 0.3Hz. That is the response in the longitudinal direction is influenced by the supporting condition of the end of the conductors.

[Transverse Displacement ]

n.S(n)(cm~) 10l - Tower pr~inary

Conduct:or W I(} 0 - h o r i z o n t a l l

]l}'l ~ ,Aal

11 o I 0"3 .~W

10 -4 ..... :Single tower - --=--: Fi v e - t ower ~!.'b.- .... :Four-tower

10-5 I I I ! I 0"3 lO'Z lO - ! 10 ° lO ]

Frequency n ( Hz )

[Longitudinal Displacemant]

n.S(n) (cm~) i01 -

I0 o

]0-I

10"z

10-3

10 "4- ---: Five-tower .... : Four-tower

10-5 I , 0 -3 i l l - 2 ] ( ) - I

Frequency

C o n d u c t o r vertical primary

- 1 , ' Tower

I p r i m a r y - " I V T : Tower

si onal W

~ . . t u a i n a l )

,

l(} 0 10 i

n ( H z )

Figure. 8 Analytical Value of Power Spectrum Displacement at Upper Level caused by Wind.

of Tower

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6 . C O M P A R I S O N B E T W E E N THE A N A L Y T I C A L V A L U E A N D T H E F U L L - S C A L E M E A S U R E D V A L U E

In order to investigate the validity of the model used for the time series response analysis and the points in question, a comparison between the analytical value and the measured one was carried out. The power spectrum of the response displacement of the tower at the lower level is shown in Fig. 9. The power spectrum of the fluctuating tension of the conductor at the upper level of the tower on the leeward side is indicated in Fig.lO. The measured response value is obtained when the main wind velocity is 19.0m/s and the turbulence intensity is 1 8 . 0 ~ at the top of the tower. The analytical value gained from the five-steel-tower-model.

6 . 1 R e s p o n s e characteristics of the tower As for the power spectrum of the response of the tower in the

transverse direction, comparing the analytical value with the measured value, it is found that both of the peak frequency in the high frequency range of 0.1Hz or more correspond with each other. However, about the values for the peak, the analytical value tends to be larger than the measured value in the low frequency range at less than 1.0Hz. On the other hand, in the high frequency range of 1.0Hz or more, the measured value can be seen to be larger.

Concerning the longitudinal direction, comparing the analytical value with the measured value, some differences can

[Transverse Displacement] [ L o n g i t u d i n a l Displacemant ]

If. S ( =, ) ( c,,l~ ) I()0 =

11)-I

t0-s

10-3

10 4

111-5

i(} -6

Tower C o l l d ue t o r' 1) r i , la p y

. . . , .+,- , , , . h o r i z o n t a l V " " 7 th l (l " l

~" V Tower (Transverse) "~ 2~ t seeond-

10-3

Longi - 111"3 ==~Y~tud i n a I )

= "~--W'" 11}"4

- ---: Analysis 10 -5 : Measurement

...... I I I J 111 " G 0-3 ill-,+ 10-1 if)0 l O I

t t ,S(n) (era2) It)0 +

11 "3 I 11"2

Couductor vert ical primary

V ,I il i a, 'rower

" . ~ . . . - - . . III I p r i m a r y ..-+" \ l!~1 , ,

. ~-~_ ! i i i i i T ,, .,~ i+ ~01.I i v t ! i v ill h

'+ A .i1~!tl,. " / l l i l l . 1 i T o w e r

A I VWlltJ t o t - - + U - " " . I M s i o n a l

• # - - . M e a s u r e m e n t ~ ~ l i l | , I+

I , I I | I i i l l l I

I II -I I 11 0 1 0 1

Frequency n (Hz) Frequency n (Hz)

Figure. 9 Comparison between Analysis and Full Scale Measurement of Power Spectrum of Tower Displacement at Lower Level caused by Wind.

2045

b e seen in the peak frequencies in the low frequency range at less than 0.3Hz. However, the peak frequencies in the high frequency range almost coincide with each other. When taking the result of the analytical case study indicated in clause 5.3 into consideration, it can be assumed that these differences in the low frequency range, are caused by the fact that the modeling manner for the supporting condition of the ends of the conductors differs from the actual condition. As for the peak value, the analytical value is larger than the measured one in the low frequency range at less than 1.0Hz. However, in the high frequency range the measured value is larger. This tendency was also recognized in a transverse direction.

The quantitative differences which are found in both direction can be considered to be caused by the following factors. The measured displacement value is obtained through transforming the acceleration data. Furthermore, the phase difference of the fluctuation of the wind velocity was neglected in the response analysis.

6 . 2 Fluctuating tension of t h e conductors In regard to the power spectrum of the fluctuating tension of

the conductors between the suspension type tower No.105 and the tension type tower No. 106, comparing the measured value with the analytical one, the peak frequency indicates the same tendency as that for the power spectrum of the tower response in a longitudinal direction. The peak value almost correspond to the same tendency which can be seen in the power spectrum of

[Conductors between Tower No.105 and No. I06]

z,.S(n) (ton~) I l l o

I 0-1

10-2

111-3

10-4

10 "s

! 0 - 6 1 0 - 3 lO-S

Conductor vertical p r ] m a ry

- Conduct:or V h o r i z o n t a l '

- pr imaryV 1 I [I I l l . . !

V Y I ,

- - - : A n a l y s i s tl~,i -- : Measurement ~I~,.

I I I I I 0" i I (} o I 01

F r e q u e n c y n ( Hz )

[Conductors between tower No.106 and No.107]

Conductor vertical

n. S(n) (ton z ) primary V

1 0 ° " i [

I O-! - [ , l , l . - -

" " "",, J]klAlii,.

10-4

-: AnalysJ.s ' "~I'~"~' I0-5- : Measurement ,.

lO-6 _ ~ I I ' 0 -3 I..--2 li}-] lOO i0 u

Frequency n(Hz)

F i g u r e . 10 C o m p a r i s o n b e t w e e n A n a l y s i s and M e a s u r e m e n t o f Power S p e c t r u m o f F l u c t u a t i n g C o n d u c t o r s a t Upper L e v e l c a u s e d by Wind.

Full Scale Tension of

2046

t h e tower r e s p o n s e . However, in t h e f r e q u e n c y r a n g e o f 0 .3Hz~ 1 .0Hz, t he measu red v a l u e i s l a r g e r t han t h e a n a l y t i c a l one .

Comparing the m e a s u r e d v a l u e w i t h t h e a n a l y t i c a l v a l u e o f t h e c o n d u c t o r s be tween t h e t e n s i o n t y p e s t e e l t o w e r No. 106 and Nc. 107, the peak frequencies of the power spectra in both values correspond quite well to each other. The peak value indicates the same tendency as that which is seen in the power spectrum of the tower response.

7. CONCLUSION

Through an analytical and observatory study of the wind response of a transmission line system, the following points have been clarified:

I) The power spectral shape of the tower response in a transverse direction for the analysis, corresponds quite well to that for the full scale measurement.

2) The power spectral shape of the tower response in a longitudinal direction for the analysis corresponds quite well to that for the full scale measurement, except in a low frequency range of 0.3Hz or less.

3) The power spectrum of the tower response in the longitudinal direction is affected by the modeling manner of the boundary condition at the ends of the conductors.

4) The peak frequency in the power spectrum of the fluctuating tension of the conductors, corresponds quite well to that seen in the power spectrum of the tower response in the longitudinal d i r e c t i o n .

As is explained above, the qualitative tendencies for both the measured value and the analytical value almost correspond to each other. However, quantitatively there were differences between their values,

8. REFERENCES

1 0 z o n o , S . , e t a l . , J . o f S t r u c t u r a l and C o n s t r u c t i o n Eng. ( T r a n s . of A I J ) , No. 353, 1985, p p . 4 8 - 6 1 , in J a p a n e s e .

2 Nakamura, Y., S a k a m o t o . , J . o f Wind E n g . ( T r a n s a . o f JAWE), No. 20, June , 1964, p p . 1 2 9 - 1 4 0 , i n J a p a n e s e .

3 Yamag i sh i , h . , e t a l . , P roc . o f 7 th N a t i o n a l Symposium on Wind Eng. , Tokyo, December, 1982, p p . ~ l l - 3 1 8 , in J a p a n e s e .

4 F u j i m o t o , M., Ohkuma, T . , e t a l . , J . o f Wind E n g . ( T r a n s a . o f JAWE), No. 41, O c t o b e r , 1989, p p . 6 9 - 7 4 , in J a p a n e s e .

5 The J a p a n e s e E l e c t r o t e c h n i c a l Commi t t ee , Des ign S t a n d a r d s on S t r u c t u r e s f o r T r a n s m i s s i o n , 1979, in J a p a n e s e .

6 Vickery,B,J., Civil Eng. Tras., Inst. of Eng. Australia, Vol. CEI3, N o . l , A p r i l , 1971, p p . l - 9 .

7 l w a t a n i , Y., J . o f Wind E n g . ( T r a n s a . o f JAWE), No. 11, J a n u a r y , 1982, p p . 5 - 1 8 , in J a p a n e s e .