8/13/2019 Glanville 1995

1/17

E L S E V I E R Journal of Wind Engineeringand Industrial Aerodynamics 54/55 1995) 133-149

J O U RN ~ _ O F

ONNNND

y n a m i c c h a r a c t e r i s t i c s a n d w i n d i n d u c e d r e s p o n s eo f a s t e e l f r a m e t o w e r

M . J . G l a n v i l l e , K . C . S . K w o kThe University o f Sydney School of Civil and Mining Engineering Sydney NS W 2006 Australia

bstrac t

This paper presents the results of a field measurement program which was conducted ona steel frame tower. Dynamic characteristics of the tower were measured to determine itsfrequencies of vibration, mode shapes and damp ing values. A STRAND 6 computer model wasassembled and confirmed these findings. The dynamic response of the tower unde r wind loadingwas inves t igated before and af ter the a t tachm ent of ancil laries .

1 . In tro d u ct io nA m i c r o w a v e c o m m u n i c a t i o n s s t ee l f r a m e to w e r w a s c o n s t r u c t e d i n 1 9 9 2 a m o n g s t

f ia t c a t e g o r y 2 te r r a i n a t P r o s p e c t i n t h e w e s t e rn s u b u r b s o f S y d n e y . T h e 6 7 m h i g ht o w e r h a d t o s a t is f y s t r ic t d e f le c t i o n l im i t s f o r b o t h s t a t i c a n d d y n a m i c l o a d s t o r e d u c es ig n a l t r a n s m i s s i o n i n t e r f e r e n c e a n d l o ss . T h i s w a s a c h i e v e d u s i n g a 1 26 t o n n e f r a m es y s t em c o m p r i s i n g f o u r c i rc u l a r c o l u m n s e c ti o n s r i g id l y j o i n e d t o r o l le d s e c t i o np l a tf o r m s . T o w e r g e o m e t r y a n d m a s s d i s t r i b u t io n a r e s h o w n i n F ig . 1 .

T e s t i n g c o m m e n c e d i n J u n e 1 99 2 b e f o r e a n y m i c r o w a v e d is h e s w e r e i n s ta l le d o n t h et o w e r . T h e a n c i l l a ri e s s h o w n i n F ig . 1 w e r e a t t a c h e d i n J u l y 1 9 9 3 c o n s t i t u t i n g a r o u n d5 o f t h e to w e r p r o j e c t e d a r e a o n a n y fa ce . T h e i r e ff ec t u p o n t h e d y n a m i c re s p o n s ew a s t h e n m o n i t o r e d .

2 . M e a s u r e m e n t p ro g r a mT w o a c c e l e r o m e t e r s w e r e i n st a ll e d a t t h e 5 7 m l ev e l a n d a l ig n e d o r t h o g o n a l l y a l o n g

t h e m a j o r a x e s o f t h e to w e r . A c c e l e r o m e t e r o u t p u t w a s c o n d i t i o n e d b y a p u r p o s e b u i lt

*Corresponding author.Elsevier Science B.V.S S D I 0 1 6 7 - 6 1 0 5 9 4 ) 0 0 0 3 7 - E

8/13/2019 Glanville 1995

2/17

34 M.J. Glanville, K C . E Kwok/J. Wind Eng. Ind. Aerodyn, 54/55 1995) 133-149

Y O Y1

Ngo.

Xl

a s tA n e m o m e t e r

6 7 m

59m57m54m51m48m45m42m40,5m38m35m32m29m27,5m24m20m16m12m8m

2,6mOml]m

I = X

JLQ

3 6 5 k g

4 2 8 k 93 8 k s3 8 0 0 k 93 8 0 0 k 93 8 k s3 8 k s51__00k95 5 0 0 k 95 7 5 0 k g5 7 5 0 k g5 7 5 k g6 4 ~ 9 k 99 7 5 0 k g

1 2 7 k g

I 0 2 7 0 k 9

1 0 8 7 0 k 9< ~ ] O L 7 0 k 9

6 9 0 k 9

t y

M E M B E R S I Z E So.,, . , .d457 x 9,5 C,H,S,b, , , , , .d323 x 9,5 C,H,S,c,, , , , .e '406 x 9,5 C,H,S,cL, , , .~219 x 4,8 C,H,S,e,. , , ,150 x 150 x 10 L,, , , ,150 x 75 IS9 , , , , , 360U B45h , , . , 4 6 0 U B 6 7I,. , , ,360UB57j . , , . , 8 5 0 u c 7 3k,, , , . .d75 RODL,, , ,75 x 75 x 5 Lm,,, , , ,d139 x 5,4 C,H,S,

F i g . 1. a ) G e n e r a l a r ra n g e m e n t o f t h e P r o s p e c t t o w e r . b ) M a s s d is t r ib u t i o n a s m o d e l l e d b y S T R A N D 6i n c l u d i n g i t e m s n o t l i s t e d f r o m a t o m . T h e s e i t e m s i n c l u d e s a f e t y t a il s , l e d d e r s , c a b l e t r a g s, p l a t fo r m g r a t i n g ,b o l t s a n d s o m e p l a t f o r m m e m b e r s . T h e a n c i l l a r y m a s s i s n o t i n c l u d e d .

8/13/2019 Glanville 1995

3/17

M.J. Glanville, K.C.S. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 1995) 133-149 35a m p l i f ie r a n d 1 0 H z l o w p a s s f il te r. W i n d s p e e d a n d d i r e c t io n w e r e m e a s u r e d a t t h es a m e l e v el u s in g a c u p a n e m o m e t e r a n d w i n d v a n e , re s p e ct iv e l y . T h e a n e m o m e t e r a n dv a n e s a t 1 .5 m f r o m t h e w e s t e r n f a c e o f t h e t o w e r i n o r d e r t o f i n d f re e s t r e a m f l o w s e eF i g . 1 ). W i n d w i t h y a w a n g l e b e t w e e n 2 0 a n d 1 0 0 w a s n o t a n a l y s e d t o a v o i di n t e r f e r e n c e f r o m t h e t o w e r .

A n a l o g u e d a t a w a s t r a n s m i t t e d v i a c o a x ia l c ab l e t o t h e b a s e o f t h e t o w e r w h e r e i tw a s l o g g e d b y a 4 8 6 p e r s o n a l c o m p u t e r f i tt e d w i t h a n a n a l o g u e t o d i g it a l c o n v e r t e r .D e d i c a t e d so f tw a r e d e v e l o p e d b y K w o k a n d M a c d o n a l d [ 6 ] c o n ti n u a l ly sa m p l e d t h ed a t a i n 1 4 m i n s e c t io n s a t 2 0 H z . I n v e s t i g a t i o n o f th e i d e a l i s a t io n o f w i n d s p e e ds p e c t r u m o v e r a n e x t e n d e d f r e q u e n c y ra n g e r e v e a ls a s p e c tr a l g a p b e t w e e n 1 h a n d1 0 m i n a v e r a g i n g p e r io d s . H e n c e a n a v e r a g i n g p e r i o d o f 1 4 m i n d u r a t i o n w a s c h o s e nt o p r o v i d e f a i r l y s t a b l e m e a n v a l u e s .

F o r c e v i b r a t i o n t es ts w e r e p e r f o r m e d o n t h e t o w e r in o r d e r t o o b t a i n d a m p i n gd e c a y c u r v e s f o r e a c h m o d e o f v i b r a t io n . T h e t o w e r w a s v i b r a t io n a l l y e x c it e db y o s c i l l a t i n g a b o d y w e i g h t i n t i m e w i t h a m e t r o n o m e a t e a c h n a t u r a l f r e q u e n c yo f t h e to w e r . F o r c i n g c e a s e d o n c e t h e t o w e r w a s r e s o n a t i n g a n d a t t h a t i n s t a n tt h e t o w e r w a s a l l o w e d t o v i b r a t e f r e e ly u n t i l i t c a m e t o r e s t. F o r c e v i b r a t i o n t e s t sw e r e p e r f o r m e d d u r i n g s t i l l a t m o s p h e r i c c o n d i t i o n s t o e l i m i n a t e a n y b a c k g r o u n de x c i t a t i o n .

T o w e r d e c a y d u r i n g f o r c e e x c i t a ti o n s w a s m e a s u r e d u s in g t h e i n s t a ll e d a c c e le r o -m e t e r s a n d a l as e r b e a m . A H e - N e l a s er w as p l a c e d a t th e b a s e o f t h e t o w e r a n dm a g n i f ie d t h r o u g h a z e n i t h p l u m m e t . T h e b e a m w a s p r o j e c t e d o n t o a g r id p l a c e d a tt h e t o p o f t h e t o w e r . T h e r e la t iv e m o v e m e n t o f t h e g r id t o t h e s t a t i o n a r y b e a m w a st h e n f i lm e d f o r l a t e r a n a l y s i s.

M o d e s h a p e o f t h e t o w e r w a s m e a s u r e d u s in g a n a d d i t i o n a l s e t o f a c c e l er o m e t e r s .A f t e r c a l i b r a t i o n a t t h e 5 7 m l e v e l o f t h e t o w e r , o n e p a i r o f a c c e l e r o m e t e r s w a s m o v e ds t ep b y s te p t o l o w e r l ev e ls . M o d e s h a p e w a s d e t e r m i n e d f r o m t h e r a t i o o f s i m u l ta -n e o u s l y r e c o r d e d a c c e l e r a t io n s ig n a ls . T h e p r e s e n c e o f a n y t o r s i o n a l m o d e s w a ss i m i l a r ly d e t e c t e d u s i n g a n a d d i t i o n a l p a i r o f a c c e l e r o m e t e r s e c c e n t r i c a l ly p l a c e d a tt he 57 m l eve l .

3 Com puter m ode lN a t u r a l f r e q u e n c i e s a n d m o d e s h a p e s f o r t h e t o w e r w e r e c a l c u la t e d u s i n g

S T R A N D 6 . S T R A N D 6 is a c o m m e r c i a l l y a v a i la b l e su i te o f f ul l t h r e e - d i m e n s i o n a lf in i te e l e m e n t p r o g r a m s i n c l u d in g a n a t u r a l f r e q u e n c y s ol v er . T h e n a t u r a lf r e q u e n c y s o l v e r c a l c u l a t e s t h e n a t u r a l f r e q u e n c i e s e i g e n v a l u e s 2 ) a n d v i b r a t i o nm o d e s e i g e n v e c to r s { x } ) b a s e d o n a lu m p e d m a s s a s s u m p t i o n a n d s o l v in g t h ee q u a t i o n

[ K ] { x } = 2 [ M ] { x } .[K] a n d I M] r e p r e s e n t th e b a n d e d s ti ff ne ss m a t r i x a n d t h e l u m p e d d i a g o n al ) m a s sm a t r i x , r e s p e c t i v e l y .

8/13/2019 Glanville 1995

4/17

136 M.J. Glanville , K.C S. Kwok/J. W ind Eng . Ind. Aerodyn. 54/55 1995) 13 3-1 49

2

ooo 1

z _ 1O

z - 28_

Y Y A x sr

I U F I 'l l p i , L , , , , , , , , , , , , , , , , l l , , , , , , , ,

- 3 ~ . . . . . . . . 1 2 3 4~ - p e q u e n c y H z )Fi g 2 Po w er s p ec t ra o f a cce l e r a ti o n

4 R e s u l t s

4.1. Dynamic characteristics4.1.1. Natural frequency

Power spectral density was computed for the acceleration response of the towerunder wind loading (Fig. 2). Spectral peaks indicate that mode one dominates theresponse of the tower at 1.08 Hz. The two smaller peaks represent the second andthird modes of tower vibration. The differences in natural frequencies along perpen-dicular axes are less than 2 producing strong coupling between the X X and Y Yaxis.Natural frequency values obtained through full scale measurement are compared tothose calculated by STRAND6 in Table 1. The computed results agree well with thosemeasured, particularly modes one and two.

4.1.2. Mode shapeThe mode shapes measured in full scale are compared to those calculated bySTRAND6 in Fig. 3. Fig. 4 is a STRAND6 three-dimensional representat ion of modeone vibrating along the Y Y axis.

8/13/2019 Glanville 1995

5/17

M.J. Glanvil le , K.C.S. Kwok/J. W ind Eng . Ind. Aerodyn. 54/55 1995) 133- 14 9T ab l e 1Tow er natural frequencies

137

N a t u r a l X X axis H z ) Y Y axis H z )frequencyM o d e 1 M o d e 2 M o d e 3 M o d e 1 M o d e 2 M o d e 3

Ful l s cale 1.08 1.41 3.22 1.07 1.39 3.28S T R A N D 6 1 . 1 0 1 . 4 0 3 . 5 2 1 .1 0 1 .4 0 3 . 5 4S T R A N D 6 - M A S T 1 .1 4 3 .5 3 6 . 06 1 .1 4 3 .5 4 6 . 07

M e a s u r e d M o d e S h a p eC o m p u t e d M o d e S h a p e

1

11 tI

X X Y Y

I I

. i

X l X l Y 1 Y 1

/ / /~ J

/i/ .

/ ./i

M O D E 1 M O D E 2 M O D E 3Fig . 3 . C o m p u t e d a n d m e a su r e d m o d e s h ap e s

/ ./I

M o d e o n e d i s p l a y s ty p i ca l q u a r te r si ne w a v e b e n d i n g w i t h t h e t o p m a s t d o m i n a t i n gt h e d i s p la c e m e n t o f t h e t ow e r . T h e r a t io o f m a s t d i s p l a c e m e n t t o t o w e r d i s p l a c e m e n ti s a b o u t 2 . 5: 1. T h e r a t i o o f m a s t t o t o w e r d i s p l a c e m e n t i n m o d e t w o i s a b o u t 2 4 :1s u g g e s t i n g t h a t t h is m o d e o f v ib r a t i o n i s d u e t o t h e v i b r a t io n o f th e t o p m a s t a l o n e .M o d e t h r e e d i s p l a y s t h e f ul l s i n e w a v e s h a p e w i th a s m a l l a m o u n t o f t o r s i o n t o w a r d st h e t o p o f th e t o w e r . S o m e t o r s i o n w a s m e a s u r e d i n f ul l s c a le a t m o d e t h r e e o n l y . T w oe c c e n t r ic a l ly p l a c e d c h a n n e l s e c t i o n s r u n n i n g u p o n e s id e o f th e t o p t h ir d o f t h e t o w e ra r e p r o b a b l y r e s p o n s i b l e f o r th i s b e h a v i o u r . I t s h o u l d b e n o t e d t h a t a p u r e l y to r s i o n a lm o d e w a s c a lc u l a te d b y S T R A N D 6 a t 2 .7 H z h o w e v e r n o ev i d e n ce o f t hi s m o d e w a sf o u n d d u r i n g f u l l s c a l e m e a s u r e m e n t .

S T R A N D 6 w a s u s e d to s i m u l a te r e m o v a l o f th e to p m a s t fr o m t h e to w e r. T a b le 1s u m m a r i se s t h e n e w f r eq u e n c ie s f o u n d a fte r t h e m a s t w a s r e m o v e d . T h e n a t u r a l fr e q u e n c ya n d m o d e s h a p e o f m o d e t w o w i t h o u t t h e m a s t is a lm o s t i d e n ti ca l t o t h a t o f m o d et h r e e b e f or e t h e m a s t w a s r e m o v e d . T h e n a t u r a l fr e q u e n c y o f th e m a s t a l o n e r e m o v e d

8/13/2019 Glanville 1995

6/17

138 M.J. Glanville , K.C.S. Kwok/J. Wind Eng. lnd. Aerodyn. 54/55 1995) 133-149

Fig. 4. Mode 1 Y - Y axis.

from the tower was also calculated by STRAND6 at 1.4 Hz. This confirms that thesecond mode of the tower is simply the natural frequency of the top mast. Removingthe mast would remove this mode of vibration.

4 . 1 . 3 . D a m p i n gHigh amplitude free vibration decay curves obtained from filtered accelerationrecords for mode one are shown in Fig. 5. Percentage critical damping along the Y - Yaxis is greater than that along the X - X axis. This may be attributed to the highernumber of bolted connections which offer additional damping along the Y - Y axis.Alignment of the ladders and cable trays running up the centre of the tower alsocontribute to the higher value of damping.Damping for modes two and three was similarly determined at 0.25 criticaldamping and 1.5 critical damping, respectively. A low value of damping at modetwo is expected since this mode represents vibration of the mast alone.The decay curves shown in Fig. 5 are peculiar since they exhibit lower damping athigher amplitudes. This may be explained by the large dependence of mode one uponthe vibration of the lightly damped mast which acts as an excitation mechanismduring tower decay.Fig. 6 is a plot of the peak tower displacements as mapped from the laser traceduring the free vibration decay along the X - X axis of the tower. Both methods ofdecay analysis produce the same damping values as expected.An autocorrelation analysis was employed to measure tower damping at relativelylow amplitudes under wind loading alone (less than 5 mg). One of the requirements foran autocorrelation analysis to be stable statistically is stationarity of the data on

8/13/2019 Glanville 1995

7/17

M . J . G l a n v i l l e, K .C .S . Kwok / J . W i n d Eng . I n d . Ae r o d yn . 5 4 / 5 5 1995 ) 1 3 3 - 1 4 9 1 3 9

a )c ~ 6 8 .Eo~ 5 0cO~ 4 0u 3 8@

2 @1

0_

b )0)

~ 6 8

o~ 1 2 c_e 8 83< 4@

3@

F i g

Y Y A x L s

. . . . . T o w e r d e c a y. . . . = I ~

' - - = 0 . 7 5 ~

~

8/13/2019 Glanville 1995

8/17

140 M .J . G l a n v i l l e, K .C .S . Kw ok / J . W i n d Eng . I n d . Ae r o d yn . 5 4 / 5 5 1995 ) 1 3 3 - 1 4 9

- ' 4@EX - X A x i s

3 @ ,, ,, T o w e r . d e c o y' , ( = 0 . 7 5 ~E 2 8

1@ .~ x x

2b 4b 6en f . h C y c l eF i g . 6 . F r e e v i b r a t i o n d e c a y m a p p e d f r o m l as er t r ac e .

33EcO

~

L_@6OOq- -0

o2 8

S a m p l e n u m b e rFig . 7 . R un t est for s t at ionar i t y us ing 40 sam ples .

4 8

r u n s w e r e f o u n d , s a t i s f y i n g t h e ct = 0 . 0 5 l e v e l o f s ig n i f i c a n c e s e t d o w n b y B e n d a t a n dP i e r s o l [ 1 ] . T h i s 4 6 8 s s a m p l e w a s t h e o n l y d a t a f o u n d w h i c h e x h i b i t e d s u c h s t a t io n a r -i t y i n w i n d e x c i t e d s t r u c t u r a l r e s p o n s e o v e r a s i g n i f i c a n t ti m e f r a m e . H a v i n g e f f ec t iv e l yr e m o v e d t h e f o r c in g w i n d ) n o n - s t a t i o n a r i t y fr o m t h e d a t a , w h a t r e m a i n s is th en o n - l i n e a r r e s p o n s e o f t h e t o w e r i t s e l f .

8/13/2019 Glanville 1995

9/17

M.J. G lanvil le, K.C.S. Kw ok/J. Wind Eng. Ind. Aerodyn. 54/55 1995) 133 -149 4

:;

oeO

2 e

c@

~D

8~ 'k~ ' ' ' X - X A x : ss L - L , . . . . . y - y

2bn L h C y c l e 8Fig. 8. Au tocorrelation function of first m od e acceleration.

T h e s t a t i o n a r y s et o f d a t a w a s t h e n b a n d p a s s f il te r e d a t t h e fir st m o d e a n d a na u t o c o r r e l a t i o n a n a l y s i s p e r f o r m e d . T h e r e s u l t i n g a u t o c o r r e l a t i o n c u r v e s s h o w n i nF i g. 8 i n d i c a te t h a t d a m p i n g a l o n g b o t h t o w e r a x e s is o f s i m il a r m a g n i t u d e a t l o wa m p l i t u d e s . B o t h l e v e ls o f d a m p i n g a r e t y p i c a l f o r a s te e l s t r u c t u r e u n d e r s e r v i c e a b i li t ys t ress levels 1 ,7] .4.2. Wind induced response

A t i m e h i s t o r y o f t o w e r a c c e l e r a t io n a n d w i n d v e l o c i t y o v e r a 4 0 s p e r io d is s h o w ni n F i g. 9. M o d e o n e is se e n to d o m i n a t e w h i le m o d e s t w o a n d t h r e e c o n t r i b u t e t o w a r d st h e b a c k g r o u n d r e s p o n s e o f t h e t o w e r. B e t w e e n 2 0 a n d 4 0 s a n i n c re a s e in a l o n g - w i n dY - Y ) r e s p o n s e c a n b e s e en d u e t o w i n d e n e r g y f lu c t u a t in g n e a r t h e n a t u r a l f r e q u e n c yo f t h e t o w e r . A l o c u s o f d y n a m i c r e s p o n s e o v e r a n o t h e r 5 0 s p e r i o d is s h o w n i n F i g . 1 0.

A l o n g - w i n d a n d c r o s s -w i n d c o m p o n e n t s a r e o f s i m i la r m a g n i t u d e d u e t o t h e s t r o n g -c o u p l i n g w h i c h e x i s t s b e t w e e n t h e t w o a x e s .

T h e d y n a m i c r e s p o n s e o f th e t o w e r i n th e a l o n g - w i n d d i r e c t i o n is p lo t t e d a g a i n s tt h e f l u c t u a t i o n i n w i n d s p e e d a u i n F i g . 1 1 . T h e r e i s a g e n e r a l i n c r e a s e i n t o w e rr e s p o n s e w i t h i n c r e a s e d b u f f e t i n g b y w i n d g u s t . F i g . 1 2 i l l u s t r a t e s t h e i n c r e a s e i nc r o s s - w i n d r e s p o n s e d u e t o l a t e r a l t u r b u l e n c e v ( w i n d d i r e c t i o n c h a n g e s ) .

T h e r e l a t i o n s h i p b e t w e e n t h e s t a n d a r d d e v i a t i o n o f t o w e r a c c e l e r a ti o n re s p o n s e a n dm e a n w i n d s p e e d is s h o w n i n F i gs . 1 3 a n d 1 4. T h e r e l a t i o n s h i p is p r e s e n t e d b e f o r e a n da f t e r t h e i n s t a l l a t i o n o f a n c il la r ie s . T h e a d d i t i o n o f a n c il la r i e s is s e e n t o h a v e l i tt lee ff ec t u p o n d y n a m i c r e s p o n se . I n b o t h c a se s d y n a m i c r e s p o n s e in c r e as e s in p r o p o r t i o nt o m e a n w i n d s p e e d w i t h a n e x p o n e n t o f a p p r o x i m a t e l y 2 .5 . T h i s is i n a g r e e m e n t w i thf u ll s c a le m e a s u r e m e n t s c o m p l e t e d b y G l a s s e t al. I- 2 ] a n d H i r a m a t s u a n d A k a g i I-3 ]

8/13/2019 Glanville 1995

10/17

142 M.J. Glanville, K.C.S. Kwok/J. WindEng. lnd. Aerodyn. 54/55 1995) 133-149

OE o

- 1 0

O 3E o

0 9E

1 0 x x c e e r a t o n I L

1 Y - ~ A c c e l e r a t i 0 n ] i , , A A , , t ,5 a j ~ l

' t I t t " , 7 1 v J v v l v l g l t ) t t I i t l l t l17 , W i n d s p e e d1 5 , ~ I I

1 1 r l l r9

O

W i n d d i r e c t i o n, J , , , , ~ l l . , I

, , , r , r - l O 2 0T i m e s e c o n d s )t q3 0 4 0

Fig . 9 . T ime h is to ry o f tow er acce lera t ion wind speed and d i rec t ion .

on lattice towers of varying height and more conventional design built from lighterangular steel sections

The 14 min samples have been split up in to short 60 s samples to help extrapolatethe data shown in Figs 13 and 14 The long 14 min samples display less scatter thanthe short records due to smaller statistical errors Variation in turbulence alsocontributes to the scatterA standard deviation of acceleration of 8 mg under a mean wind speed of 20 m/scorresponds to a peak resonant deflection of about 7 mm assuming sinusoidalresponse at mode one This resonant component must be added to the static deflection

8/13/2019 Glanville 1995

11/17

M.J. Glanville, K.C S. Kwok/J. W ind Eng. Ind. Aerodyn. 54/55 1995) 133-149 143

E 3I : :. 0 2

X

1 7

2

5 }6 | i J

8 6 - 4 - 2 0 2X - X A x i s A c c e l e r a t i o n r a g )F i g . 1 0 . L o c u s o f t o w e r a c c e l e r a ti o n .

33EdO.J

])