Load assumptions for antenna structures with icing

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Staiger, F.; National Research Council of Canada. Division of Building Research

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P r e f a c e

I n many a r e a s i n Canada, i c i n g a n d wind s u b j e c t s t r u c - t u r e s s u c h a s power t r a n s m i s s i o n t o w e r s t o q u i t e s e v e r e l o a d s . The m a g n i t u d e o f t h e l o a d s d e p e n d s upon t h e s h a p e o f t h e

t o w e r , and upon t h e w e a t h e r t o which t h e t o w e r i s s u b j e c t . T h e r e i s l i t t l e i n f o r m a t i o n a v a i l a b l e t o Canadian e n g i n e e r s t h a t can b e u s e d 2s s _{g u i d e f o r s p e c i f y i n g f o r}_a. _{p a r t i c u l a r} s i t e a n 3 a s s o c i a t e d w e a t h e r c o n d i t i o n s , t h e l o a d s t o b e u s e d i n t h e d e s i g n of a t o w e r . Two s e c t i o n s w i t h i n t h e D i v i s i o n o f B u i l d i n g R e s e a r c h h a v e a n i n t e r e s t i n t h e problem o f d e t e r m i n i n g l o a d s due t o

snow and i c e . The 3 u i l d i n g S t r u c t u r e s S e c t i o n i s c o n c e r n e d w i t h t h e r e l a t i o n s h i p between t h e s t r u c t u r e and t h e l o a d ;

t h e SnoTrl and I c e S e c t i o n i s c o n c e r n e d w i t h t h e r e l a t i o n - s h i p s between t h e l o a d and t h e w e a t h e r . T h i s p a p e r by F . S t s i g e r d i s c u s s e s b o t h of t h e s e a s p e c t s o f t h e i c i n g problem a s w e l l a s t h e area i n which t h e y merge, t h a t i s , t h e r e l a t i o n s h i p between t h e s t r u c t u r e and t h e s h a p e o f t h e d e p o s i t . I t d e s c r i b e s somn, German e x p e r i e n c e s i n t h e de-

s i g n of t o w e r s a n d p r e s e n t s t e n t a t i v e recommendations con- c e r n i n g t h e specification of i c e l o a d s . The D i v i s i o n o f B u i l d i n g R e s e a r c h i s p l e a s e d t o make t h i s c o n t r i b u t i o n t o e n g i n e e r i n g p r a c t i c e by

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S t a i g e r a v a i l a b l e t o Canadian e n g i n e e r s i n t h e T e c h n i c a l T r a n s l a - t i o n s S e r i e s o f t h e N a t i o n a l R e s e a r c h C o u n c i l . The con- t r i b u t i o n o f t h e t r a n s l a t o r , [ 4 r . D . A . S i n c l a i r , i s g r a t e - f u l l y acknowledged. 0 t ta.wa O c t o b e r 1961 R.P. L e g g e t D i r e c t o r

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T i t l e :

NATIONAL RESEARCH COUNCIL OF CANADA

T e c h n i c a l T r a n s l a t i o n 9 9 1 Load a s s u m p t i o n s f o r a n t e n n a s t r u c t u r e s w i t h i c i n g (i3elastungsannahmen f u r Antennen t r a g e r i m F a l l e V e r e i s u n g ) A u t h o r : F. S t a i g e r R e f e r e n c e : Der S t a h l b a u , 30 (1) : 24-27, 1 9 6 1 T r a n s l a t o r : D.A. S i n c l a i r , T r a n s l a t i o n s S e c t i o n , N . R . C . L i b r a r y

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LORD A&SUW?TI3NS

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A N T S N N A STRTJCT1.JEE.S lJITH I C I N G

The c o n s t r u c t i o n o f t h e u l t r s s h o r t !&lave t r 2 n s m l s s i o n n e t w o r k , w h i c h was b e g u n s b o u t 1 9 5 0 3-nd I s now c o m p l e t e d , and t h e S u l l d i n g o f t e l e v i s i o n t r z i n s r n l t t e r s h a v e p r o d u c e d a w i d e v s . r i e t y o f a n t e n n a s t r u c t u r e s I n t h e f o r n o f f r s e s t , + n d i n g s t e e l l a t t i c e - w o r k t o w e r s o r z u y e d s t e e l 3 i p e a n d s t e e l l s t t l c e - w o r k masts. I n o r d e r t o s e r v e a s w i d e r e g l o n s a s - 3 o s s I b l e ~ ~ l i t h u l t r % s h o r t wave .?nd t e l e v i s i o n p r o , - ~ r s m m e s t h e s e s t r u c t u r e s , i n t h e s o u t h o f G e r m a n y , a r e u s u s l l y p l a c e d o n h i l l t o p s 2nd m o u n t a i n p e a k s i n t h e n o r t h e r n a l y l n e r e z i o n , w h e r e 1.n n o s t c a s e s s e v e r e i c i n ~ lnust S e e x p e c t e d . ldhen we cornpsre t h e s t r u c t u r : q . l c a l c l l l s t i o n s Of t h e s e a n t e n n a s t r u c t u r s s we f i n d t h a t v e r y d i f f e r e n t l o a d a s s u . n p t l o n s h a v e S e e n a d o p t e d by t h e m a n u f a c t u r e r s f o r t h e " i c i . n g l ' c a s e . The f o l l o v a i - n g a r e a few e x a m p l e s : ( a ) A v e l o c i t y p r e s s u r e f o r u n ? a v ~ u r a b l s c o n d i t i o n s o f q = 1 3 0 k Z / m 2 i s c h o s e n a c c o r d i n g t o D I N 1 0 5 5 , s h e e t 4 . The w i n d s p e e d o f 1 6 7 km/h w h l c h c o r r e s : ~ o n d s t o t h i s v e l o c i t y p r e s s u r e ( b a s e d o n t h e d e n s l t y of t h e a t m o s p h e r e a t 1 , 0 0 0 rn a b o v e s e a l e v e l ) n e v e r o c c u r s i n Germany, e x c e p t i n a few e x t r e m e l o c a t i o n s s u c h a s t h e h i g h p e a k s o f Z u g s p i t z e a n d F e l d b e r g ( 3 l a c k F ~ r e s t )

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T h i s s e l e c t e d v e l o c i t y p r e s s u r e t h e r e f o r e a u t o r n ~ ~ t l c s l l y a l l o w s f o r t h e i n c r e a s e I n l o a d d u e t o i c i n g .

( b ) Maximum I c i n g 3 n d maximum v e l o c i t y p r e s s u r e ( q = 1 3 0 k,y/m2 )

d o n o t o c c u r s i n u l t s n e o u s l y . T h e two l o a d s t h e r e f o r e n e e d n o t be s u p e r i f l p o s e d . ( c ) A v e l o c i t y p r e s s u r 5 o f q = 200 ks/m2 i s a s s u m e d . The s d - d i t i m a l l o a d 2 u e t o i c l n z i s t ~ k e n i n t o s c c o u n t S y t h e i n c r n a s e o v e r a = 1 3 0 k3/m2 a c c o r 3 I n ~ t o 3 1 N 1 0 5 5 , s h e e t 4 . ( 1 3 ) The t h i c k n e s s o f t h e i c e c c a t l n g i s a s s u i n e d t o b e 5 cm a n d a v e l o c i t y p r e s s u r e Of q = 50 kg/m2 i s u s e d - ? l i t h t h i s i n c r e a s e d w i n d imp.%ct a.re.3. ~t 1 8 0 0 a s s o v e serz l e v e l , w h e r e t h i s p - l r t i c u l s r a n t e n -

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( e ) O p s n i n g s i n t h e a n t e n n a l s t t i c e work o f l e s s t h a n 5.0 in w i d t h a r e t r e a t e d a s c l o s s d , i c e d s u r f a c e s . L a t t i c e o r t r u s s ~ n e m - b e r s I n s u r f a c e s n o t c l o s e d !?y i c i n g are i c e d t o a d i q m o t e r o f

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The a n t e n n a s t r u c t u r e i c e d i n t h i s way i s sub- j e c t t o a v e l o c l t y p r e s s u r e of q = 1 3 0 ks/rn2, c o r r e s p o n d i n g t o a wind s p e e d o f 167 km/n. ( T h i s s t i 2 u l 3 t i o n was mqde f o r a s t e e l

l a t t i c e - w o r k m a s t ) . 3 e c a u s e c o n s i d e r a b l e d i f f e r e n c e s e x i s t i n t h e a s s u r n ; ~ t i o n s re- g a r d i n g wind a n d i c e l o a d s , t e n d e r s f o r a n t e n n s s t r u c t u r e s a r e n o t cornpslmble

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F t ? v 2 u r a b l e i c i n g a s s u r n p t i o n s p r o d u c e t h e l o w e s t p r i c e s , b u t e n d q n g e r t h e s e c u r i t y o f t h e s t r u c t u r e . A s s u ; n p t i o n s ~ t h i c h SPPL-OX- imate t h e t r u e c o n d i t i o n s e n t ~ i l . ? r e : l t e r , b u t j u s t i f i e d c o s t s . W h e n t h e l o a d a s s u m j ? t i o n s a r e t o o h i s h f o r t h e i c i n g c ? s e , o v e r - d i m e n s i o n - i n s o f t h e c r o s s - s e c t i o n s p r o d u c e s e x c e s s i v e l y h e a v y c o n s t r l x c t i o n a n d h e n c e F o o r economy. A few e x a l n p l e s i h r i l l i l l u s t r s t e t h i s : I n 1 9 5 4 s n s n t e n n q s t r u c t u r e w a s b u i l t f o r r.tnse 111 t s l e v i s i o n a n d t h e US:{ n e t w o r k s t 1 8 0 0 m a b o v e sea l e v e l . S l n c e t h e r e w a s n o i n f o r m , r t i o n ~ v s i l s ' o l e on t h e i c i n g o f r a n g e I11 a n t e n n a s , t h e l o a d a s s u m p t i o n s f o r i c i n g were made 3 , c c o r d i n g t o ( 3 ) (see a b o v e ) . The

n e x t v i n t e r , h o w e v e r , i t w a s f o u n d t h a t t h e a c t u z l i c i n g f a r e x c e e d - e d t h e assumption o f 5 cm t h i c k n e s s . The r e f l e c t o r l s t t i c e - ' f i ~ o r k o f t h e r m g e 111 t e l e v i s i o n a n t 9 n n a was c o m p l e t e l y p l u g g e d by a 3 0 cm t h i c k l a y e r o f h o a r i c e * ( F i g . 1 ) . T h i s d r o p p e d t h e a c t u a l s a f e t y c o n s i d e r a b l y below t h e r e a u i r e d s : a f e t y l s v e l f o r t h e a n t e n n a s t r u c - t u r e b e c a u s e o f t h e a l m o s t tripled 10:ld f r o m t h e a n t e n n a . F o r a n a n t e n n a s t r u c t u r e o f s t e e l y n 3 l e l 3 t t i c e - w o r k stsnc7,lng a t 1 7 0 0 m a b o v e s e n l e v e l , i c i n g a s s u x ? t i o n s a c c o r d i n g t o ( e ) were

a d o p t e d i n 1 9 5 5 . It wzis _{founr? from}_{l a t ? r}_{o 3 s e r v s t l o n s , h o w e v e r ,} t h a t s t r u c t u r a l g 3 2 s o f 5 . 0 rn a r e n e v e r c o m p l g t e l y pll~gr:ed b y h o a r i c e , which o n l y h l p p e n s f o r a t o w e r ~ 1 2 t h o f 1 . 2 0 m o r l s s s . T h u s ,

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f r i 3 s t U = hor-lr i c e , ' " A ~ u h r e l f " = h o a r f r o s t , a n d t t 3 7 u l ~ e i s t ' = n n s r -

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t h e member s t r e s s e s d e t e r n i n e ? from t h i s g r e a t l y r e d u c e d wind l o n d on t h e t o w e r were c o n s i d e r a b l y l e s s t h a n t h e p e r m i s s i S l e s t r e s s , s o t h z t t h q s t r u c t u r e was d e f i n i t e l y o v e r - d e s i g n e d s n 3 t h e r e f o r e i s t o '09 r e s a r d e d 3.s uneconomic.

The l a s t example i s s 50 _mh i g h , s t e e l p i p e mast which _{w a s}

e r e c t e d a s a t e : n p o r s r y a n t e n n a s t r u c t u r e a t 1 , 0 0 0 m above s e a l e v e l .

I t Ttlas yuyed i n t h r e e p l a n e s . I t s p u r p o s e w a s t o s u p p o r t two r a n g e

I11 t e l e v i s i o n a n t e n n 3 . s a r r s n g e d laterally b e l o w t h e t o p o f t h e m r l . s t . T h i s m ~ s t f e l l , b e c s u s e o f s e v e r e i c i n g o;P t h e a n t e n n a s , i n a wind o f 1 0 0 km/h c?u5 t o t h e t e 3 r i n . z o u t o f one o f t h e guy c a b l e s . The f a i l u r e i s c l e s r l y s t t r i b u t a S l e t o n e g l e c t of i c i n g i n t h e d e s i g n .

F o r t h e s e r e a s o n s i t i s s e n e r a l l y n e c e s s a r y t o e s t s b l i s h r u l e s f o r t h e l o 2 d s due t o i c i n g which !~i11 mske i t p o s s i b l e t o put t e n d e r s on a more u n i f o r m b a s i s . To c a r r y o u t t h i s t a s k a n s w e r s must b e found t o t h e f o l l o w i n g questions: Idhat i s t h e e x t e n t o f t h e i c i n g , i . 5 . t o w h a t e x t e n t s r e t h e wind-exposed a r e a s o f 3 n t e n n a s t r u c t u r e s a n d a n t e n n a s i n c r e a s e d z s a r e s u l t of i c i n g ? What i s t h e s p e c i f i c z r s v i t y of t h e i c e ? 5Jhat i s t h e v e l o c i t y p r e s s u r e o r wind s p e e d a c t i n g on t h e i c e d a n t e n n a s t r u c t u r e ? We s h a l l now d i s c u s s t h e s e p o i n t s b r i e f l y . 2 . E x t e n t of I c i n . ~ The t e r m t l i c i n g l l r e f e r s t o a. l a y e r o f h o ~ l i r f r o s t , h o a r i c e o r n e a r - s o l i d i c e which I s d e n o s i t e d on t h e s t r u c t u r a l p a r t s o f a n t e n n a s t r u c t u r e s rind a n t e n n a s . 2 . 1 I c i n r f o f t h e y11y w i r e s o f q n t e n n a s t r u c t u r e s

Hoar f r o s t 'arms c h i e f l y on round c r o s s - s s c t i o n s o f s m a l l dimen- s i o n s which s r e s i t u a t e d i n t h e u n J i s t u r b e d s i r f l o : ~ . T h i s a p p l i e s p r i m 7 r i l y t o t h e ,guy 'rilres of z n t s n n - 7 s t r u c t u r e s . A n o t h e r con? i t ion

i s v e r y hurnid a i r a n d t e m p n r a t u r e s n r o m ? t h e f r e e z i n g p o i n t 2nd be- l o w , s u c h a s a r e f a i r l y f r e a u o n t l y o b s e r v e d on t h e Y e l d S e r g ( 3 1 z c k F a r e s t ) . S l n c e t h e guy c a b l e s c o n s i s t o f s e v e r a l s t r a n d s a n d e ~ c h

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s t r s n d i s ma.de u p o f many i n d i v i d u s l w i r e s , t h e s e p r e s e n t a r o u g h s u r f a c e a n d a r e t h u s a n e x c e l l e n t b ? . s e f o r t h ? d e p 3 s i t i n z of' i c e .

As t h e Germsn M e t e o r o l o g i c a l S e r v i c e h a s o b s e r v e d , t h o 1.Veight of i c e f o r m s d p-;r r u n n i n g metre, a n d h s n c e t h e t h i c k n e s s 0.f t h e c o s t - i n g , g e c r e s s e s w i t h i n c r e a s i n g d i a ~ n e t e r o f t h e c 2 ? 3 l e s ( F i g . 2 a n d 3 ) . This ca.n b e a t . t r i 5 u t e r l t o t h e inore f a v o u r s l ~ l e v?In? c ' 3 e f f i c l e n t w h i c h I s c = 0 . 7 f o r d

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movement o f t h e wire s o as t o s h a k e o f f t h e i c e c s , n n o t b e tau-nted o n I n eTrery c a s e . I n o r d e r t o p r o v i d e i n f o r m n t i o n on t h e amount 0.f i c i n g o n la%-

t i c e - w o r k , o:-rserv!3tions ,*Iere m.rrle o n a.nts'nnn s t r u c t u r e s msde o f s t e e l a n , z l s s s t a l t i t u 2 e s o f 1 , 0 0 0 m (Yi;?. 4 ) a n d 1 , 7 0 0 m 3 b o v e sea l e v e l

( F i g . 5 ) . It w a s Colxnr! t h a t t h e l3.t t l c e - w o r k a r e a e x p o s e d t o t h e w i n d was i n c r e a s e d u,o t o a m2.xIml1m o f 3.8 tlmes a.s a r e s u l t o f i c i n g . W i t h d 2 c r ? 2 s l n ; j w i d t h o f t h ? to7>\!er t h e I c i n ; ~ i n c r s x s e s , b s c a u s e t h e i n t ~ r v a l s b e t w e e n t h e l a t t i c e - w o r k members i s ~ r n ? ~ l l e r . F u r t h e r m o r e , a c e r t a i n j a c k p r e s s u r e d e v e l o p s f r o m t h e r e , l r f a c e of t h e t o w e r w h i c h i s noT,$ situated c l o s e r t o t h e f r a n t i r ! a 1 1 . From t h e s e o S s e r v . 3 t l o n s t h e f o l l o ! n . ~ l n g s t a t e m e n t s a p p e i r j u s t l - f l e d : (a) S t e e l a n z l e 1-tt ic e - v o r k c o n s t r u c t i o n s w i t h ~ I d t h s s ' n s . l l e r t i l i n o r e q u ~ l t o 1 . 2 0 m s h o u l d S o c s l c u l z t e d a s c o m p l e t e l y p l u g g e d i n t h e c ? . s e o f i c i n g . ( 5 ) L a t t i c e - v o r k t r i s n s l e s o f s t e e l a n s l e s ?hilth rnlnlm~xrn h e i , ; h t s o f 0 . 6 0 m o r L e s s shOl.~lrl a l s o b e t r e s t e d a s c l o s e , q s u r f a c e s f o r t h e i c i n 3 c : ? s e .

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( c ) S t e e l a n g l e l a t t i c e - w o r k members lr!hlch a r e n o t p l u g g e d by i c i n g shol.118 b e t 3 k e n a s b e l n ~ e n c a s e d i n a, c y l i n d e r of h o a r i c e w i t h s _{d i s a e t e r o f} _D ₌ _{( b}

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_{1 0 cm, where b i s t h e p r o j e c t i o n} of t h e s e c t i o n i n t h e wind d i r e c t i o n . T h e s e v s l u e s a p p l y t o ~ n t ~ n n ~ s t r u c t u r e s o f s t e e 1 a n g l e con- s t r r l c t l o n l o c q t e d between . i p p r o x l m s t e l y 809 m s n d 2 , 0 0 0 m a b o v e s e a l e v e l . Cornyare? w i t h t h e i c i n g t h i c k n e s s of 1 0 cm e s t a 3 l i s h e d u n d e r ( c ) , s m x l l e r v n l u 9 s a r e assumed i n o t h p r c o u n t r i e s , b u t w i t h d i f f e r - e n t s p e c i f i c s r : a v i t i e s ( P i g . 6 ( 2 ' 3 ) ) . I t shouL.3 i l s o b e b o r n e i n mind t h a t h i 3 h e r v e l o c i t y p r e s s u r e v s l u e s a r e employed i n t h e s e c o u n t r i e s ( F i g . 7). I c i n g of t u b u l q r l a . t t i c s - w o r k s t r u c t u r e s No i n f o r m a t i o n i s a v 3 i l s S l e on t h e i c i n g of t u b u l a r c o n s t r u c - t i o n s . I n Morava, C z e c h o s l o v a k i a , s 3 2 2 m h i g h y y e d mast of t u b u l a r c o n s t r u c t i o n w s s b u i l t two y e a r s a z o a t 600 m a b o v e s e a l e v e l . An a n t e n n a s t r u c t u r e of s i m i l a r c o n s t r u c t i o n 3 0 5 m h i g h i s t o be b u i l t t h i s y e a r i n Z a p a d n i Chechy ('?Jest 3 2 h e a i a ) . I t s l o c ~ t i o n i s 712 rn above s e a l e v e l . 3 0 t h masts h a v e b e e n c a l c u l a t e d on t h e b a s i s of an i c e c o a t i n g 6 cm t h i c k on t h e s t r u c t u r a l p a . r t s f o r a. s p e c i f i c g r a v i t y o f 0 . 6 5 kg/dm 3 0 )

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T h i s v a l u e a p p e a r s a d e q u a t e I n c o n p a r i s o n ~ i t h t h e i c i n g t h i c k n e s s o f 1 0 cm l ~ . i ? . d-own f o r s t e e l ~ n g l e l s t t i c e - w o r k m a s t s , b e c a u s e t h e :nore C?,vou m b l e a e r o - d y n a m i c form of t h e t u b u l a r c r o s s - s e c t i o n i s l e s s s u s c e p t i b l e t o i c i n s t h a n s t e e l a n g l e . The c o r n e r l e g s o p t h e t u b u l a r l s t t i c e c o n s t r u c t i o n s c o n s i s t o f p i p e s wit11 s. r n i n i r n u m ' r ? i ~ m e t e r o f 1 5 9 mrn ?.n? t h e d i 2 z o n s l s a r e of p l p e s of C O n m cllarneter2. F o r t h e c o r n e r l e g s , t h e r e r o r e , c = 0 . 7 s i n c e d , q > _-1 ?n.' f o r t h ~ c ! i ~ ~ o n a l s ln7ith d m < 1 , c = 1 . 2 i n s . c c o r d s n c e - -

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~ . : i t h DIN 1 0 5 5 , s h e e t 4 . Srnploying t h e meqn p r b ~ s u r e c o e f f i c i e n t a.nd esti.rn,=~tintz t h e t o t a l s t e e l 3 n g l e l z t t i c e - w o r k c o n s t r v c t i o n a t c = 1.1, m 3nd p u t t i n s c = 1 . 6 f o r t h b s t e e l ' 1 n g 1 ~ l 2 t t i c e - : ~ : o r k m a s t , t h e r a t i o o f c - v s l ~ s of s t e e l ~3n;le l q t t i c e - r c o r k rnssts t o t u h u l r r 1 e . t t i c e - v o r k m?.sts i s 1 . 6 : 1.1 = 1 . 4 5 . A s s u n l n g t h s t h i c k n e s s o f i c i n z t o de- p e n d on t h e c - v 3 l u e '*'e crjn c z l c u l 2 t e 3 t h i c k n e s s of 6 x 1 . 4 5 = 8.7 cm

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f o r t h e s t e e l m g l e 1 7 t t i c o - i . ~ o r k m q s t o n t h e b a s i s o f € cm f o r t h s t o f t h e t u b u l a r l a t t i c e - l r ~ o r k msst. T h i s v n l u e comes c l o s e t o t h e i c i n g t h i c k n e s s o f 1 0 cm l s l i d 3olh'n. A1thou;h i c e f i n z e r s i n t o t h e l~~inc1 r a r e l y o c c u r I n t u b u l s r l s t t i c e - w o r k c o n s t r u c t i o n s , o w i n g t o t h e g e n e r a l t u r i w l e n c e o r t h e a i r f l o w throu:h t h e l a t t i c e - ' f : o r k , t h i s i s n o t t h p c a s e f o r f r n e - s t r q n d i n g s i n z l e p i p e s . On t h e v e r t l c a l e n i t t e r of 7 t e l e v i s i o n a n t e n n a , f o r example

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w h i c h h a d a d i a r n e t ~ r o f 2 5 0 m m , 3 h o ~ r i c e f i n ; e r 6 0 cm l o n g was f3unti. T h i s i s a s u b s t ~ n t i ? l i d d i t i o n a l l o n d f o r t h e e m i t t e r i t s e l f , f o r i t s c 9 n n e c t i n g s t r u c t u r e s s n d t h e s n t e n - n a s n c h o r s 5 e J i n d must b e t a k e n i n t o a c c o u n t , i n 4 e s i g n i n g t h e a n t e n n ; l s n d t h e m t e n n a s t r u c t u r e . I n l o c ? . t i o n s w h e r e t h ~ r e i s s e v e r e h o s r i c e f o r m ? t i o n r e f l e c t o r 1 s . t t i c e s f o r t e l e v i s i o n a n t e n n a s made o t s t e e l t u b i n g become com- p l ~ t e l y p l u g g e d . The h o a r i c e l 3 y e r i s s b o u t 3 0 cm t h i c k ( F i g . - I ) . The wind l o p ? on t h e p l u g g e d r e f l e c t o r l 3 t t i c e s h o u l a b e d e t e r m i n e d

i n a c c o r f l s n c e w i t h DIN 1 0 5 5 , s h e e t 4 , u s i n g c = 1 . 2 . F o r f r o n t a l i n c i d e n c e on t h e r s n q e 111 ? n t e n n a shown :.le :;et s 'r'ind l o q ? o f 6 4 0 k g . u n d e r i c i n g c o n ? i t i o n s . ' d i t h o u t t h e i c e c o s t i n g , on t h e o t h e r h a n d , t h e wind l o a d i s o n l y 220 kg. T h i s a n t e n n q i s s u s p e n d e d from a m a s t s t 3 . n d i n g a t 1 , 8 8 0 m a.Sove s e a l e v e l . The snisll d.iet.z.nce between l s t t i c e - v : o r k members o f o n l y 2 5 cm f a v o u r s t h e f o r m a t i o n of a c l o s e d a r s a by t h e h o s r i c e . Even f o r r a n g e I s n t e n n a s , t h e r e f l e c t o r l z t t i c e s o f r ~ l h i c h h a v e s mesh ~ ! i d t h o f 4 0 cm, p l u g g e d r e f l e c t o r l q t t i c e s !.!ere f o u n d ( F i g . 3 ) . T h i s 2 n t e n n a , holvever, i s suspend-ed f r o m s s o l i d t o w e r v ~ a l l ( r e i n - f o r c e d c o n c r e t e t o w e r ) . T h e h o s r i c e blo!n~n t h r o u g h t h e o p e n i n g s o f t h e l s t t i c e p i l e s u p a t t h e t o w e r u l a l l and _ = r a . d u ~ l l y f i l l s t h e s p a c e o f 6 0 cm maximum fle:?th b e t w e e n t h e r e f l e c t o r l a t t i c e 2 n d t h e t o w e r wall ( F i g . 9 ) . 3 . T h e S p e c i f i c Gr;3v>Q.-of_Icj= The s t 3 e c i f i c s r q v i t y o f t h e I c i n g d e p e n d s on t h e ? t r n o s p h e r i c

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h u t n i 8 l t y , a i r t e m p e r a t u r e and wind s p e e d . Nearby r i v e r v a l l e y s a n d a f o r e s t e d e n v i r o n m e n t cqn h g v e a s u b s t ? n t n i s l i n f l u e n c e on t h e i c i n g of a n a n t e n n a s t r u c t u r e . M o r e o ~ r e r , t h e d e v e l o p m e n t o f ?n i c e f i n g e r can t q k e c o n s i d e r a b l e t i m e u n d e r c h s n g i n g c o n d i t i o n s . U s u a l l y t h e f o r m a t i o n o f a h o a r i c e f i n s e r b e g i n s o n l y s few d e g r e e s b e l o w f r e e z - i n g u n d e r c o n d i t i o n s o f h i g h 3 t n o s p h e r i c h u m i d i t y 2nd r n o d e r ~ t e vlind f o r c e . The p r o ~ f q f t h i s i s t h e g r ~ ? t n u m b ~ r o f i c e g r a i n s q t t h e b q s e , d e c r e ~ s i n , g s t r o n g l y t o ~ a a r d s t h e t i p o f t h e f l n g p r . T h i s a c c o u n t s f o r t h e d i f f e r e n c e i n s p e c i f i c g r a v i t y which lflss f o u n d t o b e

0.73 kg/dm3 ? t t h e bztse and 0 . 5 3 kg/dm3 a t t h e t i p . The a v e r s g e s p e c i f i c y r s v i t y o f 0 . 6 3 kg/dm3 s g r r e s w e l l w i t h o b s e r v ~ t i o n s on t h e B r q t i s l a v s t e l o v i s i o n t o l ~ ~ e r , ..rhere s = 0 . 6 5 kg/dm 3 ( 1 ) The o r l o l n a l - l y recommended s g e c i r i c z r ? v i t y o f i c i n g o f 0 . 5 0 kg/dm3

,

r e p r e s e n t - i n g a mean v a l u e f o r h o a r f r o s t ( R a u h r e i f ) a t 0 . 2 0 k;/dm3, h o a r i c e ( R a u h f r o s t ) a t 0.50 kg/dm3 a n d n e s r - s o l i d i c e ( R a u h e i s ) a t 0 . 8 0 kg/ dm3, h a s f o r t h e p r e s e n t b e e n l e f t u n c h s n g e d . Ths r e s u l t s of f u r t h e r m e a s u r e m e n t s a r e b e i n g a w a i t e d . Wind Speed D u r i n g I c i n g

The maximum wind s p e e d s f o r maximum 3 r o v t h o f I c e a c c o r d i n g t o T a b l e I were measured by t h e German M e t e o r o l o g i c a l S e r v i c e .

I n t h e s t r u c t u r a l c a l c u l . . ; l t i . o n s o f t h e C z e c h o s l o v a k i a n mast d e s c r i b e d i n s e c t i o n 2 . 3 a v e l o c i t y p r e s s u r e o f o n l y 4 5 kg/m2 w i t h 3n assumed maximum i c i n g t h i c k n e s s o f 6 cm idas u s e d . T h i s c o r r e s - ponds t o a wind s p e e d o f 27 m / s = 9 7 km/h (1)

A s t e e l a n g l e l a t t i c e - w o r k toy~ler 30 rn h i g h , which had b e e n e r e c - t e d i n s o u t h o r n G ~ r m a n y 1 0 y e a r s 2 9 0 , vas 3 l s o o y s e r v e d . I t s n l t i - t u d e , i n 9 r n y i o n v e r y s u b j e c t t o i c i n g , was 1 , 0 0 0 m s b o v e s e a l e v e l . The d e s i g n o f t h i s t o w e r ( a c c o r d i n g t o exsmple ( c ) i n t h e i n t r o d u c - t o r y p n r t of t h e p r e s e n t p a p e r ) w a s 5 s s e d on a v e l o c i t y p r e s s u r e o f 200 kg/m2. The wind a r e a o f o n e f a c e of t h e 4 - l e 5 5 e d c o n s t r u c t i o n was 1 3 . 4 5 m 2 7nd was i n c r e a s e d by i c i n g , a s o b s e r v e d , t o 4 1 . 1 r n 2 , 1 . e . T , ~ 7 ~ m u l t i p l i e d b y s p - 3 r o x i m s t e l y t h r e e . No o v e r s t r o s s i n _ = o f t h e s t m c t u r n l p? r t s o f t h e t o w e r o c c u r r e d , a s ?n i n v e s t i g s t i o n c o n f i r m e d .

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From t h i s i t msy b e c o n c l u d e d t h s t t h e l o a d a s s u m p t i o n s w e r e n o t e x c s e d e d e v e n f o r t h e c ~ s e o f i c i n g . Hence o n l y a s r n s l l v e l o c i t y p r e s s u r e c a n h a v e a c t e d on t h e s r e a t l y i n c r e a s e d wind e x p o s u r e a r e a , i . e . E 5 kg/m2 s c c o r d i n g t o a r o u ~ h c . i l c u l a t i o n . Even I f i t b e i s r a n t - e d t h ~ . t t h e p e r m l s s l b l e s t r e s s f o r s t e e l 3 7 h s s b e e n e x c e e d e d 3.nd t h e y i e l d l i m l t h a s b e e n r e a c h e d a t 1 9 2 0 kg/cm2, t h e maximum v e l o c i t y p r e s s u r e a , g a i n s t t h e I c e d t o w e r was a p p r o x i t n a t e l y q = 8 0 kg/m2, c o ~ r e s p o n c 3 i n ~ t o s wind s p e e d o f 1-30 krn/h. T h i s a s s u m e s , h o w e v e r , t'n2.t t h e h o a r I c e l a y e r w i t h s t o o d t h i s p r e s s u r e a n d n 2 s n o t blown o f f . Des:2itn t h e a'?ove o ' @ s e r v ? % i o n s , t h e p o s s i b l l l t y c a n n o t b e e n -

t i r e l y r u l e d out; t h a t maximum i c e d e p o s i t a n d maximum v e l o c i t y

p r e s s u r e may coincide, i ? o n l y b r i e f l y . It ~ v o u l d t h e r e f o r e be n e c e s - s a r y t o r e t a i n t h y a s s u m p t i o n , i n c a l c u l e t i n q s n t e n n a s t r u c t u r e s f o r c l i m a t i c a l l y ex;losed l o c s t i o n s 7tiith s t r o n g dsn:{er o f i c i n o ;

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o f a v e l o c i t y r e s s u r e q = 1 3 0 kg/m2 8 . c t i n g u n i f o r m l y o v e r t h e e n t i r e h e i , y h t o f t h e a n t ~ n n n s t r u c t u r e * o i t h rna.ximurn i c i n g . F o r t h i s c a s e , t e r m e d t h~ c s . t a s t r o p h l c c a s e , . p e r m l s s l b l e s t r e s s i n c r e a s e d t o h s l f t h e b r e a k i n g s t r e s s o f t h e m s t e r i s l e m p l o y e d c o u l d b e J u s t i f l e d . T h i s c o n t r i S u t i o n i s a n a t t e m p t t o e s t a b l i s h t h e p r i n c i p l e s by w h i c h u n i P o r m r s ~ u l n t l o n s f o r l o 3 d a z s u m 2 t l o n s o f q n t e n n ~ s t r u c t u r e s c s n Se d r ~ w n u p . The o b s e r v a t i o n s n u s t S e c o n t i n u e d 3nd t h e v q l u e s o S t a i n e d must b e v e r i f i e d 2nd c o r r e c t e d w h e r e n e c e s s z r y . A t e s t I n s t o . l l ? t i o n c o m $ r i s i n g a 1 0 0 m t a l l r e i n f o r c e d c o n c r e t e t o v e r h a s b e e n c o n s t r u c t e d 101C m q b o v e s e a l e v e l , w h e r e l t I s s u b j e c t t o e x - t r e m e i c i n z 9nd w i n d conditions. Meo s u r a i n 2 e q u i p m e n t i n s t ~ l l e d on t h i s tolrlnr w i l l e c s b l e u s t o c h e c k t h e c o r r e c t n e s s 0 7 t h e l o a d assump- t l o n e aclopted f o r t h i s t o w e r i n a c c o r d a n c e w i t h p r e v i o u s d e s i g n s . 33 c o n c l u s i o n o f t h e m e a s u r e m e n t s a f u r t h e r r e p o r t w i l l b e rnqde.

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Zwei h o h e F e r n s e h - R o h r m a s t e i n d e r T s c h e c h o s l o w . . r k e i . S t g . h l b n u , 7: 1 9 3 , 1 9 6 0 . 2 . Normen f i i r g i e 3 e l s s t u n % s s n n g . h t n e n , rl i e I n b ~ t r i e b n s h m e unc? d i e Uberr+lc=.chung d e r 3 s u t e n vom S c h w e i z e r i s c h e n I n g e n i e u r - und $ r c h i t e k t e n v e r e i n , N r . 1 C 0 , 1 9 5 6 . 3 . T r a n s m i t t i n g a n t e n n a c s . t s l o , g u e o f t h e R a d i o C o r p o r s t l o n o f A m e r i c a , 1 9 5 7 . 2nd e d i t i o n . T a b l e I

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M e a s u r e d w i n d s p e e d s a t maximum i c i n g P 1 a . c ~ o f o b s e r v a t i o n - H o h e n p e i s s e n b e r g W a s s e r k u p p e Z u g s p i t z e S r o c k e n V a r i o u s p e a k s I n t h e nips S c h n e e k o p p e Mont a l a n c F e l d b e r g

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F i g . 4 S t e e l a n g l e l a t t i c e - w o r k tower w i t h i c i n g , 1 , 0 0 0 m above s e a l e v e l F i g . 5 S t e e l a n g l e l a t t l c e - w o r k tower w i t h icing, 1 , 7 0 0 rn above sea l e v e l

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I c i n g a s s u m p t i o n s i n d i f f e r e n t c o u n t r i e s ( i c i n g t h i c k n e s s e , s p e c i f i c g r a v i t y s )

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Range I t e l e v i s i o n a n t e n n a w i t h i c i n g on r e i n f o r c e d c o n c r e t e t o w e r , 1 , 0 0 0 m above s e a l e v e l t i n g F i g . 9 Arrangement of t h e r a n g e I t e l e v i s i o n a n t e n n a on t h e r e i n f o r c e d c o n c r e t e t o w e r