Publisher’s version / Version de l'éditeur:
Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.
Questions? Contact the NRC Publications Archive team at
PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.
https://publications-cnrc.canada.ca/fra/droits
L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site
LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.
Proceedings of the 5th International Conference on Wind Engineering, 1, pp.
553-565, 1980
READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE. https://nrc-publications.canada.ca/eng/copyright
NRC Publications Archive Record / Notice des Archives des publications du CNRC :
https://nrc-publications.canada.ca/eng/view/object/?id=ed51ef44-4f7c-4ea0-be33-3f0a5abcbf3b
https://publications-cnrc.canada.ca/fra/voir/objet/?id=ed51ef44-4f7c-4ea0-be33-3f0a5abcbf3b
NRC Publications Archive
Archives des publications du CNRC
This publication could be one of several versions: author’s original, accepted manuscript or the publisher’s version. / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur.
Access and use of this website and the material on it are subject to the Terms and Conditions set forth at
Comparisons of wind tunnel and full-scale building surface pressures
with emphasis on peaks
-
- ,
-
r -4rj
National Research
Conseil national
ler
k
Council Canada
de recherches Canada
H1
A
I
COMPARISONS OF WIND TUNNEL A N D
I
FULL
-
SCALE BUILDING SURFACE PRESSURES
WITH EMPHASIS O N
PEAKS
by
W.A. Dalgliesh,
J.T.
Templin and
K.R
Cooper
A!+d
ALYZED
Reprinted from
Wind Engineering
Proceedings, 5th Int. Conf. on Wind Engineering
Fort
Collins, Colorado, 8
14 July 1979
ANALYZED
p. 553
-
565NRC
-
CIS'I'1BLDG. RES.
L I B R A R Y
DBR
Paper No.
961
Division of Building Research
RESUME
Les a u t e u r s comparent l e s c o e f f i c i e n t s de p r e s s i o n en grandeur r 6 e l l e obtenus pour un B d i f i c e de 5 7 6 t a g e s 1 Toronto a v e c ceux obtenus d a m l a s o u f f l e r i e d e 9 m s u r 9 m du C o n s e i l n a t i o n a l de r e c h e r c h e s du Canada. Les r B s u l t a t s s' a c c o r d e n t l o r s q u ' i l e x i s t e s u f fisam- ment de donnees e n grandeur r 6 e l l e .
11s
proposent une m6thode q u i permet d e t r a i t e r les p r e s s i o n s maximales grPce 1 l ' a j u s tement d'une d i s t r i b u t i o n e x p o n e n t i e l l e 1 u n e p o p u l a t i o n I'd' GvBnemen t ss i g n i f i c a t i f s i n d e p e n d a n t s " a p p e l e s p o i n t e s de p r e s s i o n . C e t t e d i s t r i b u t i o n s ' a j u s t e b i e n aux r g s u l t a t s e n s o u f f l e r i e e t e n grandeur r E e l l e q u i
Reprinted from
WMD
ENGINEERING
Edited
byJ.
E
CERMAK
COMPARISONS OF WIND TUNNEL AND
FULL-SCALE BUILDING SURFACE
PRESSURES WITH EMPHASIS ON -PEAKS
W. A. DALGLIESH,
J.
T. TEMPLIN
and
K. R. COOPER
National Research Council of Canada, Ottawa, Ontario, Canada
F u l l - s c a l e p r e s s u r e c o e f f i c i e n t s o b t a i n e d from a 57-storey b u i l d i n g i n Toronto and wind t u n n e l r e s u l t s from t e s t s i n t h e 9 m by 9 m wind t u n n e l a t t h e N a t i o n a l Research C o u n c i l of Canada a r e compared and d e m o n s t r a t e good agreement where s u f f i c i e n t f u l l - s c a l e d a t a e x i s t . A method of t r e a t i n g peak p r e s s u r e s i s proposed based on t h e f i t of a n e x p o n e n t i a l d i s t r i b u t i o n t o a p o p u l a t i o n of " s i g n i f i c a n t independent e v e n t s , " c a l l e d p r e s s u r e s p i k e s . T h i s d i s t r i b u t i o n p r o v i d e s a good
f i t t o b o t h f u l l - s c a l e and wind t u n n e l r e s u l t s , which g e n e r a l l y a g r e e .
I
INTRODUCTIONAn i m p o r t a n t a p p l i c a t i o n of wind t u n n e l t e s t i n g is t h e p r o v i s i o n of t h e s u r f a c e p r e s s u r e l o a d s t h a t a r e r e q u i r e d f o r t h e d e s i g n of c l a d d i n g of t a l l b u i l d i n g s . There i s a growing c o n f i d e n c e t h a t c a r e f u l s i m u l a t i o n of t h e f l o w - f i e l d and nearby s t r u c t u r e s w i l l produce i n f o r m a t i o n t h a t a c c u r a t e l y r e f l e c t s t h e f u l l - s c a l e
s i t u a t i o n . Recent comparisons of model and f u l l - s c a l e p r e s s u r e measurements have shown t h a t t h i s c a n b e s a i d about t h e mean v a l u e and t h e s t a n d a r d d e v i a t i o n of s u r f a c e p r e s s u r e f l u c t u a t i o n s ( l ' 2 f 3 ) , b u t n o t w i t h e q u a l c o n f i d e n c e a b o u t t h e peak p r e s s u r e s because i t i s d i f f i c u l t t o f i n d a r e p r e s e n t a t i v e v a l u e ( 4 ) and 5 e c a u s e u n u s u a l l y h i g h peaks, o c c a s i o n a l l y found i n f u l l s c a l e ( 5 ) , might n o t b e reproduced o r d e t e c t e d a t model s c a l e .
T h i s p a p e r e x p l o r e s two s u b j e c t s :
(1) The d i f f i c u l t i e s i n o b t a i n i n g f u l l - s c a l e p r e s s u r e measurements f o r t h e comparison w i t h wind t u n n e l f i n d i n g s a r e d i s c u s s e d based on r e c e n t
f u l l - s c a l e o b s e r v a t i o n s and t h e r e s u l t s of a new wind t u n n e l t e s t . The f u l l - s c a l e measurements were made on t h e Commerce Court b u i l d i n g i n downtown Toronto; t h e model experiments were performed on a 1:200 s c a l e model mounted i n t h e 9 m by 9 m
wind t u n n e l of t h e N a t i o n a l A e r o n a u t i c a l E s t a b l i s h m e n t i n Ottawa. The d i s c u s s i o n emphasizes t h e v a r i a b i l i t y i n f u l l - s c a l e p r e s s u r e measurements t h a t does n o t a r i s e i n t h e wind t u n n e l .
( 2 ) An approach t o t h e s t u d y of peak p r e s s u r e s i s i n t r o d u c e d based on f i t t i n g a n e x p o n e n t i a l d i s t r i b u t i o n t o a p o p u l a t i o n of " s i g n i f i c a n t independent e v e n t s " c a l l e d s p i k e s . A d i s c u s s i o n of time s c a l i n g i s p r e s e n t e d which e n a b l e s comparison of model and f u l l - s c a l e o b s e r v a t i o n s .
554 W . A . D a l g l i e s h , J . T. Templin and K . R. Cooper
F i g u r e 1 Commerce C o u r t Tower (arrow) F i g u r e 2 Commerce Court Model i n NRC i n downtown Toronto viewed from ct=330° 9 m x 9 m Wind Tunnel viewed from a=1O0
MODELIFULL-SCALE BUILDING GEOMETRY
The 57-storey (239 m) Commerce Court Tower i s s i t u a t e d i n t h e c o r e of Toronto and i s surrounded on t h r e e s i d e s by b u i l d i n g s of comparable h e i g h t ( F i g u r e 1 ) . The n e a r b y t a l l b u i l d i n g s c o v e r a n a r e a of 1 km2; a s t r i p of t a l l b u i l d i n g s , % km wide, e x t e n d s s e v e r a l k i l o m e t r e s t o t h e n o r t h . Surrounding t h e s e a r e a s a r e s e v e r a l k i l o m e t r e s of r e l a t i v e l y low b u i l d i n g s . Lake O n t a r i o p r o v i d e s a smooth f e t c h beyond one k i l o m e t r e t o t h e s o u t h .
A 1:200 s c a l e model of t h e Tower and i t s e n v i r o n s , i n c l u d i n g a l l a d j a c e n t t a l l b u i l d i n g s , was c o n s t r u c t e d ( F i g u r e 2 ) . A power law p r o f i l e of 0.33 was e s t a b l i s h e d o u t s i d e t h e c e n t r a l c o r e f o r a p p r o a c h e s o v e r t h e c i t y from t h e west, n o r t h and e a s t w h i l e a p r o f i l e exponent of 0.15 was used f o r t h e l a k e exposure t o t h e s o u t h . A t h i r d p r o f i l e was provided f o r winds coming from n e a r n o r t h by a d d i n g l a r g e r b l o c k s t o t h e urban roughness t o s i m u l a t e t h e s t r i p of t a l l b u i l d i n g s . Each boundary l a y e r was developed u s i n g s p i r e s a t t h e i n l e t t o t h e t e s t s e c t i o n followed by r o u g h n e s s b l o c k s . The d e t a i l e d p r o x i m i t y model was mounted 18.3 m downstream of
t h e s p i r e s on a 7 . 3 m d i a m e t e r t u r n t a b l e . MODEL--SCALE PRESSURE MEASUREMENTS
The mean and t h e root-mean-square-about-the-mean (rnsm) of t h e s u r f a c e p r e s s u r e f l u c t u a t i o n s of t h e model a s w e l l a s t h e a s s o c i a t e d minima and maxima weremeasured t h r o u g h a 360° wind d i r e c t i o n r a n g e u s i n g i n c r e m e n t s of no g r e a t e r t h a n 10'. The Commerce Court p r e s s u r e model had 96 s u r f a c e p r e s s u r e t a p s on f o u r l e v e l s , 32 of which corresponded t o l o c a t i o n s on t h e f u l l - s c a l e b u i l d i n g . Measurements were made w i t h a c a l i b r a t e d pressure-tube-scanivalve-transducer system developed a t t h e N a t i o n a l A e r o n a u t i c a l ~ s t a b l i s h m e n t c ~ ) , w i t h a f l a t frequency r e s p o n s e t o 135 Hz. Each t a p was s e q u e n t i a l l y sampled a t 200 samples p e r second (200 s - l ) f o r 20 s . The mean p r e s s u r e c o e f f i c i e n t i s d e f i n e d a s
Wind Tunnel and F u l l - S c a l e ~ u i l d i n g S u r f a c e P r e s s u r e s 555
where t h e b a r i n d i c a t e s a n a v e r a g e over time, p i s t h e measured p r e s s c r e , pref i s t h e r e f e r e n c e s t a t i c p r e s s u r e and q =
tpv2
5.s t h e r e f e r e n c e dynamic p r e s s u r e a t t h e h e i g h t of t h e anemometer l o c a t i o n . ( p i s t h e d e n s i t y of a i r c o r r e c t e d f o ra t m o s p h e r i c t e m p e r a t u r e and p r e s s u r e and
v
i s t h e mean speed from t h e anemometer.) The rmsm s u r f a c e p r e s s u r e c o e f f i c i e n t i s.
'Time-series d i g i t a l d a t a from s e l e c t e d t a p s were r e c o r d e d f o r s e v e r a l wind d i r e c t i o n s , a t 500 s - l f o r 200 s . These were used f o r t h e d e t a i l e d s t u d i e s of peak p r e s s u r e s .
FULL-SCALE PRESSURE MEASUREMENTS
The p r e s s u r e s were measured a t 3 2 l o c a t i o n s around t h e e x t e r i o r of t h e b u i l d i n g on f o u r l e v e l s ( F i g u r e 3 ) . Measurements were made r e l a t i v e t o a common i n t e r n a l r e f e r e n c e p r e s s u r e . An anemometer and wind vane mounted on a mast ou t h e roof 285 m above ground were used f o r t h e r e f e r e n c e wind v e l o c i t y measurements. The mean and rmsm of t h e f u l l - s c a l e p r e s s u r e f l u c t u a t i o n s , wind speeds and d i r e c t i o n s have been r e c o r d e d f o r 5-min p e r i o d s every hour f o r 6 y e a r s . O n l y t h e m o s t r e c e n t 2 y e a r s of d a t a (February 1976 t o June 1978) a r e a n a l y z e d i n t h i s paper because new b u i l d i n g s were b e i n g e r e c t e d i n t h e v i c i n i t y p r i o r t o t h i s p e r i o d . Beginning i n A p r i l 1977, maximum and minimum p r e s s u r e s were a l s o r e c o r d e d f o r each 5-min
sampling i n t e r v a l . The s i g n a l s were f i l t e r e d w i t h a 2-pole, 1 5 Hz low-pass f i l t e r and t h e n sampled d i g i t a l l y a t 20 s - l . I n a d d i t i o n t o t h e s e srmmary d a t a , time- s e r i e s d a t a sampled a t 20 s-l were recorded f o r l o n g e r p e r i o d s d u r i n g h i g h winds.
e . g . , TAP 3 0 4 3
-
L E V E L 0 4-
T A P N U M B E R-
L E V E L A N E M O M E T E R R O O F 3 4 5 7I
F i g u r e 3 L o c a t i o n of p r e s s u r e t a p s common t o model and f u l l - s c a l e b u i l d i n g COMPARISON OF MEAN AND RMSM PRESSURESE L E V . rn 2 8 5 239 202 1 6 6 138 102
Because f u l l - s c a l e p r e s s u r e s a r e a f f e c t e d n o t o n l y by wind speed and d i r e c t i o n , b u t
1
a l s o by t h e i n t e r n a l p r e s s u r e due t o b u i l d i n g p e r m e a b i l i t y , v e n t i l a t i o n andt e m p e r a t u r e e f f e c t s , a m u l t i p l e l i n e a r r e g r e s s i o n must b e performed t o o b t a i n mean
'
p r e s s u r e c o e f f i c i e n t s . The measured p r e s s u r e s a r e assumed t o b e d e s c r i b e d by- -
556 W. A. D a l g l i e s h , J. T. Templin and K. R. Cooper
- -
- -
1 1P = Po
-
Pi ( 3 )where po and p i a r e o u t s i d e and i n s i d e p r e s s u r e s r e s p e c t i v e l y , pb is b a r o m e t r i c p r e s s u r e , To and T i a r e o u t s i d e and i n s i d e a b s o l u t e t e m p e r a t u r e s r e s p e c t i v e l y and A, and
rT
a r e c o e f f i c i e n t s determined by t h e l e a s t s q u a r e s f i t . Thec o e f i i c i e n t A r e p r e s e n t s t h e f i x e d p r e s s u r e d i f f e r e n c e a c r o s s t h e w a l l r e s u l t i n g from p r e s s u r i z a t i o n of t h e b u i l d i n g w i t h no wind a n d no t e m p e r a t u r e d i f f e r e n c e . The l a s t term i n t h e e q u a t i o n r e p r e s e n t s t h e p r e s s u r e a c r o s s t h e w a l l due t o a t e m p e r a t u r e d i f f e r e n c e between i n s i d e and o u t s i d e ( s t a c k e f f e c t )
.
The wind p r e s s u r e c o e f f i c i e n t(5)
r e p r e s e n t s t h e p r e s s u r e d i f f e r e n c e t h a t changes w i t h v i n d v e l o c i t y due t o aerodynamic e f f e c t s and c a n b e r e p r e s e n t e d by- - -
C = C - C
P t P p i ( 4 )
where is t h e e x t e r n a l p r e s s u r e c o e f f i c i e n t and i s t h e mean i n t e r n a l p r e s s u r e c o e f f i c i e n t r e p r e s e n t i n g wind-induced v a r i a t i o n s i n i n s i d e p r e s s u r e due t o b u i l d i n g p e r m e a b i l i t y . A m u l t i p l e l i n e a r r e g r e s s i o n performed on t h e mean p r e s s u r e d a t a r e v e a l s t h a t t h e p r e s s u r e i s h i g h l y c o r r e l a t e d w i t h t h e s t a c k e f f e c t s o has a l a r g e p a r t i a l c o r r e l a t i o n c o e f f i c i e n t ( r p T l q ) t y p i c a l l y g r e a t e r t h a n 0.85. On t h e o t h e r hand, t h e p a r t i a l c o r r e l a t i o n c o e f f i c i e n t ( r g,lT) of p r e s s u r e w i t h r e s p e c t t o dynamic r e f e r e n c e p r e s s u r e , q, r a n g e s from 0.8 t o 0.15 depending on wind d i r e c t i o n .
Large v a l u e s of rpq/T a r e a s s o c i a t e d w i t h r e l a t i v e l y w e l l - d e f i n e d v a l u e s o f
C
; small v a l u e s o f re,/, s h o u l d b e r e g a r d e d a s a warning t h a t d e r i v e d iromtiEt
p a r t i c u l a r d a t a s e t i s u n r e l i a b l e .The p r o c e s s of d e r i v i n g from f u l l - s c a l e d a t a i s shown g r a p h i c a l l y i n F i g u r e 4. The l i n e on e a c h mean p r e s s u r e p l o t ( l e f t s i d e ) h a s t h e e q u a t i o n 7 = A + q s o that A i s t h e y - i n t e r c e p t and
C
3 s t:le s l o p e . L i n e a r r e g r e s s i o n w i t h dynamicP t
p r e s s u r e o n l y p r o v i d e s rmsm p r e s s u r e c o e f f i c i e n t s (C;) a s s l o p e s of t h e g r a p h s on t h e r i g h t s i d e of F i g u r e 4. I n g e n e r a l , t h e c o r r e l a t i o n c o e f f i c i e n t s !rpq) f o r C; a r e g r e a t e r t h a n t h e p a r t i a l c o r r e l a t i o n c o e f f i c i e n t s f o r
.
The 225 d a t a p o i n t s p l o t t e d i n F i g u r e s 4 ( a ) and (b) were a l l o b t a i n e d a t n e a r l y t h e same wind d i r e c t i o n and extend t o a maximum speed of 26 m / s . These f e a t u r e s , p a r t i c u l a r l y t h e wide wind-speed range, r e s u l t i n l a r g e v a l u e s f o r rpq/T and, c o n s e q u e n t l y , r e l i a b l e e s t i m a t e s f o r Cz.
Examples of d a t a sets n o t p o s s e s s i n g such d e s i r a b l ef e a t u r e s a r e g i v e n i n F i g u r e s 4 ( c ) and ( d ) ; o n l y 83 p o i n t s were o b t a i n e d w i t h i n a 10' s e c t o r (253' t o 263') and, what i s more i m p o r t a n t , t h e r e were no wind s p e e d s o v e r 12 m/s. Although a l e a s t - s q u a r e s f i t c a n always b e d e r i v e d , t h e low v a l u e s of rpq/T i n d i c a t e t h a t l i t t l e c o n f i d e n c e should b e p l a c e d i n t h e s l o p e s o b t a i n e d . Another problem a s s o c i a t e d w i t h low wind s p e e d s i n f u l l - s c a l e measurements i s t h a t
t h e r m a l e f f e c t s a r e more l i k e l y t o produce a d i f f e r e n t flow t h a n t h e n e u t r a l boundary l a y e r s i m u l a t e d i n t h e wind t u n n e l .
The d i f f i c u l t y i n g e n e r a t i n g f u l l - s c a l e p r e s s u r e c o e f f i c i e n t s t o compare w i t h wind t u n n e l r e s u l t s i s i l l u s t r a t e d by t h e s c a t t e r i n F i g u r e 4 , f o r which t h e r e i s no wind t u n n e l e q u i v a l e n t . I n t h e wind t u n n e l , a mean p r e s s u r e c o e f f i c i e n t can b e o b t a i n e d a t a f i x e d v a l u e of dynamic p r e s s u r e and wind d i r e c t i o n , w i t h a
r e p e a t a b i l i t y of 20.04 f o r
5
and k0.01 f o r C i , even when t h e t e s t s a r e performed one y e a r a p a r t . MUCH of t h i s v a r i a t i o n i s due t o minor d i f f e r e n c e s i n t h e model I and boundary l a y e r s e t u p . I f two r u n s of 20 s a r e made one a f t e r t h e o t h e r , t h er e p e a t a b i l i t y improves t o k0.01 and 0.005 f o r C- and C' r e s p e c t i v e l y .
Wind Tunnel and F u l l - s c a l e B u i l d i n g S u r f a c e P r e s s u r e s
Sn
a ) T A P 3 0 8 2 2 5 P O I N T S F R O M
a
=1 7 0 " T O 1 7 6 "
=1 7 3 "
MODEL C ' = 0.13 P vl I I" -100-
150 0b )
T A P 3 1 2 2 2 5 P O I N T S F R O M
a
=1 7 0 " T O 1 7 6 "
Z
=1 7 3 "
100 I 10. -300 0-
C )T A P 3 0 8 8 8 P O I N T S F R O M
a
=2 5 3 " TO 2 6 3 "
a
=2 5 8 "
200 FULL-SCALE C ' = 0,02 P9 q, Po q, Po F i g u r e 4 Measured f u l l - s c a l e s u r f a c e p r e s s u r e s v s dynamic r e f e r e n c e p r e s s u r e558 W. A. D a l g l i e s h ,
J.
T. Templin and K. R. CooperS i n c e t h e p r e s s u r e s measured i n f u l l s c a l e a r e d i f f e r e n c e s between i n s i d e and out- s i d e , p a r t of t h e s c a t t e r may b e due t o v a r i a t i o n s from hour t o hour of t h e I i n t e r n a l p r e s s u r e due t o b u i l d i n g v e n t i l a t i o n . Some of t h i s e f f e c t was removed by d i v i d i n g t h e d a t a i n t o day and n i g h t sets s i n c e t h e p r e s s u r i z a t i o n of t h e b u i l d i n g
,
i s reduced a t n i g h t , changing t h e v a l u e s o f A and
Z5i;
.
T h i s a l s o gave two independent sets of p r e s s u r e c o e f f i c i e n t s .-
-
Cpt c o i n c i d e s w i t h o n l y i f happens t o b e z e r o (Eq. 4 ) ; u n f o r t u n a t e l y , C p i c a n n o t b e e x t r a c t e d u s i n g o n l y t h e f u l l - s c a l e d a t a . F o r any g i v e n wind d i r e c t i o n , t h e r e s h o u l d be a common o f f s e t between wind t u n n e l Cp and f u l l - s c a l e
Cpt
f o r t h e32 p a i r s of c o r r e s p o n d i n g t a p s , even though t h e o f f s e t w i l l b e somewhat obscured by random v a r i a t i o n s i n t h e m o d e l / f u l l - s c a l e t a p - p a i r d i f f e r e n c e s . T h i s common o f f s e t , t a k e n t o b e t h e mean of t h e d i f f e r e n c e s f o r t h e 3 2 t a p - p a i r s , was removed from t h e r e s u l t s shown i n F i g u r e 5 . The f u l l - s c a l e p o i n t s i n F i g u r e 5 ( a ) a r e o f f s e t upwards by a n e g l i g i b l e amount, 0.01, b u t i n F i g u r e 5 ( b ) t h e o f f s e t downwards i s 0.67. N e v e r t h e l e s s , t h e remaining d i f f e r e n c e s between wind t u n n e l and f u l l s c a l e a r e i n e a c h c a s e r o u g h l y s i m i l a r i n c h a r a c t e r , w i t h t h o s e of
F i g u r e 5 ( a ) c o n s i s t e n t l y s m a l l e r . I n F i g u r e 5 ( b ) t h e s o u t h w a l l t a p on l e v e l s e v e n
i s t h e o n l y t a p f o r which comparison w i t h wind t u n n e l r e s u l t s s u f f e r s b a d l y
b e c a u s e of t h e l a r g e o f f s e t . Taking a l l 5 1 w i n e e c t o r s i n t o account, t h e a v e r a g e o f f s e t i s -0.12, n o t a n u n r e a s o n a b l e v a l u e f o r C p i averaged o v e r a l l wind
d i r e c t i o n s
.
The a u t h o r s have r e s e r v a t i o n s , however, a b o u t e q u a t i n g t h e s e o f f s e t s t oCpi
.
For some wind s e c t o r s w i t h i n s u f f i c i e n t d s and low p a r t i a l c o r r e l a t i o n c o e f f i c i e n t s , t h e o f f s e t s g i v e u n l i k e l y v a l u e s f o r C p i.
Even where t h e p a r t i a l c o r r e l a t i o n c o e f f i c i e n t s a r e h i g h , t h e r e remains a n element of u n c e r t a i n t y i n t h e comparisons of mean p r e s s u r e c o e f f i c i e n t s b e c a u s e t h e r e was no independente v a l u a t i o n o f
.
T h i s i s n o t a problem when comparing r m s m p r e s s u r ea )
a
=1 7 3 "
1.0 ,"a 0.0-
-
1. I N D TlJNNEL TAPS12-
LEVEL 3 10 J8 04 -1.0 0.0 7 -03 CI/ 09-
02 1.0 1210 C& 0 4 0 2 03 07 W-
--
I"
!
0.4-
0 o FULL-SCALE FULL-SCALE LEVEL LEVEL 3 7
-
3 .. , 3 ,
-+L
b )
a
=2 5 8 "
-
a 0.0 I U -1.0 0.0NORTH EAST SOUTH WEST NORTH EAST SOUTH WEST
F i g u r e 5 Level p l o t s comparing model a n d f u l l - s c a l e p r e s s u r e s f o r two l e v e l s a t 2 wind d i r e c t i o n s
-
0.4 ,,
-
7 Lg";\Z
Ta.z5s* 7-
u
.' 3 02 03 07 09 - 3 0 TAPS 12 10 Pa 04Wind Tunnel and F u l l - s c a l e B u i l d i n g S u r f a c e P r e s s u r e s 559 1
.o
I 0.4 lua 0.0-
P U 0 . 2 -1.a
0.0a ,
DEGREESa ,
DEGREESF i g u r e 6 P r e s s u r e p l o t s comparing model and f u l l - s c a l e r e s u l t s f o r two t a p s a t a l l wind d i r s c t i o n s
c o e f f i c i e n t s because t h e y a r e c a l c u l a t e d on t h e same b a s i s i n wind t u n n e l and f u l l - s c a l e
.
F i g u r e 6 shows g e n e r a l agreement between wind t u n n e l and f u l l - s c a l e p r e s s u r e c o e f f i c i e n t s f o r two t y p i c a l t a p s a t a l l wind d i r e c t i o n s . The f u l l - s c a l e mean p r e s s u r e c o e f f i c i e n t s ( l e f t ) have t h e o f f s e t removed b u t t h e rmsm p r e s s u r e c o e f f i c i e n t s ( r i g h t ) a r e d i r e c t l y from t h e l i n e a r r e g r e s s i o n .PEAK PRESSURES
The peak p r e s s u r e c o e f f i c i e n t r e q u i r e d f o r c l a d d i n g d e s i g n c a n b e r e l a t e d t o t h e mean and r m s m p r e s s u r e c o e f f i c i e n t s by i n t r o d u c i n g a d e s i g n peak f a c t o r , gd:
The symbol d e n o t e s a p o s i t i v e extreme v a l u e ; t o s i m p l i f y t h e d i s c u s s i o n a l l peak f a c t o r s w i l l b e t r e a t e d a s i f p o s i t i v e . The assignment of a v a l u e f o r gd i s n o t a s s t r a i g h t f o r w a r d a s f o r and C b because t h e peak f a c t o r must a c c o u n t f o r t h e randomness i n h e r e n t i n p r e s s u r e f l u c t u a t i o n s . Although, f o r a g i v e n f l o w s i t u a t i o n and b u i l d i n g geometry,
5
and C b a r e n e a r l y c o n s t a n t from one sampling i n t e r v a l t o a n o t h e r , t h e maximum p r e s s u r e observed w i l l v a r y i n a random f a s h i o n .1
A r e a s o n a b l e way of choosing a r e p r e s e n t a t i v e v a l u e f o r gd might b e t o p i c k one of t h e f o l l o w i n g : t h e v a l u e t h a t o c c u r s most f r e q u e n t l y ( t h e mode), t h e a v e r a g e v a l u e ( t h e mean), o r t h e v a l u e w i t h a n a c c e p t a b l y s m a l l p r o b a b i l i t y of b e i n g, exceeded. Whatever t h e c h o i c e , i n f o r m a t i o n i s r e q u i r e d a b o u t t h e extreme v a l u e d i s t r i b u t i o n of peak f a c t o r s .
Peak f a c t o r p a r a m e t e r s do n o t a p p l y t o t h e c o l l e c t i o n of v a l u e s making up t h e
,
sampling i n t e r v a l . Each sampling i n t e r v a l p r o v i d e s only one maximum; t h e extremev a l u e d i s t r i b u t i o n p a r a m e t e r s a p p l y t o a c o l l e c t i o n of maxima d e r i v e d from many such i n t e r v a l s . T h i s does n o t mean t h a t t h e s t a t i s t i c s of t h e p a r e n t p o p u l a t i o n of p o i n t s i n t h e sampling i n t e r v a l a r e u n r e l a t e d t o t h o s e of t h e extremes; on t h e
560 W. A . D a l g l i e s h , J . T. Templin and K . R. Cooper
c o n t r a r y , a n e x p r e s s i o n f o r t h e extreme v a l u e d i s t r i b u t i o n c a n b e d e r i v e d from t h e p a r e n t p o p u l a t i o n . I f t h e p a r e n t p o p u l a t i o n i s Gaussian, a t y p e I double
e x p o n e n t i a l d i s t r i b u t i o n h a s been shown t o a p p l y t o p e a k s ( 8 ) and f o r p r e s s u r e s on windward f a c e s of a b u i l d i n g r e a s o n a b l e agreement was found('r
.
I n s t r o n g l yt u r b u l e n t n e g a t i v e p r e s s u r e r e g i o n s t h e t a i l of t h e p a r e n t p o p u l a t i o n i s much h i g h e r t h a n t h e Gaussian, however, and p r e d i c t i o n s based on t h i s assumption f a l l f a r s h o r t of o b s e r v a t i o n s .
PARENT
POPULATION OFSPIKES
One s o l u t i o n t o t h e d i f f i c u l t y of a p p l y i n g a Gaussian d i s t r i b u t i o n t o t h e p o i n t s making up c e r t a i n time r e c o r d s of f l u c t u a t i n g p r e s s u r e s i s t o s a y t h a t i n t e r m i t t e n t
" b u r s t s " of t u r b u l e n c e a r e superimposed on a r e c o r d t h a t i s o t h e r w i s e Gaussian i n n a t u r e . I n o t h e r words, a t random i n t e r v a l s throughout t h e sampling p e r i o d , s t r o n g " s p i k e s " of p r e s s u r e o c c u r , o f t e n w i t h v e r y s h o r t r i s e t i m e s . Because of t h e i r l a r g e v a l u e s , a l l t h e s e s p i k e s end up i n t h e t a i l of t h e p r o b a b i l i t y d i s t r i b u t i o n and u s u a l l y t h i s i s t h e o n l y p a r t of t h e d i s t r i b u t i o n t h a t i s
d i s t F n c t l y non-Gaussian. Of c o u r s e , t h e t a i l of t h e d i s t r i b u t i o n i s t h e o n l y p a r t t h a t i s of i n t e r e s t f o r extreme v a l u e p r e d i c t i o n .
T h i s o b s e r v a t i o n prompted a new l i n e o f i n v e s t i g a t i o n , aimed a t t h e s p i k e s r a t h e r t h a n t h e e n t i r e p o p u l a t i o n of p o i n t s i n t h e sampling i n t e r v a l . ' h o r u l e s were d e v i s e d , one t o r e s t r i c t c o n s i d e r a t i o n t o e v e n t s t h a t would b e s i g n i f i c a n t from t h e s t a n d p o i n t of l o c a t i n g t h e extreme, and t h e second t o e n s u r e t h a t t h e e v e n t s were independent of one a n o t h e r . Each e v e n t i s d e s c r i b e d by a s i n g l e number c a l l e d t h e s p i k e v a l u e :
1 ) A s p i k e v a l u e must b e away from t h e mean by a t h r e s h o l d v a l u e a t l e a s t t w i c e t h e r m s m . Both mean and r m s m a r e measured o v e r t h e e n t i r e sampling i n t e r v a l .
2) A s p i k e must b e s e p a r a t e d from a d j a c e n t s p i k e s by r e t u r n s toward t h e mean t h a t e x t e n d a t l e a s t t h e t h r e s h o l d v a l u e from t h e s p i k e v a l u e .
F i g u r e 7 shows a s h o r t segment of r e c o r d c o n t a i n i n g t h r e e s p i k e s . The r e a d i n g s have been normalized by s u b t r a c t i n g t h e mean v a l u e , t h e n d i v i d i n g by t h e rmsm v a l u e . Note t h a t t h e second r u l e makes s m a l l e r " j i g g l e s " i n t h e r e c o r d i n e l i g i b l e a s s p i k e s , even though t h e y may b e beyond t h e t h r e s h o l d l e v e l .
T I M E , s
Wind Tunnel and F u l l - s c a l e B u i l d i n g S u r f a c e P r e s s u r e s 561
The s i m p l e s t d i s t r i b u t i o n t o a p p l y t o t h i s new p a r e n t p o p u l a t i o n , t h a t of t h e s p i k e s , i s t h e n e g a t i v e e x p o n e n t i a l ( 9 )
.
The cumulative d i s t r i b u t i o n is:~ ( g ) = 1
-
exp [-(g-
8 ) / ( g-
811The s p i k e v a l u e g i s normalized a s
I p
-
p l / p v . 8 i s t h e t h r e s h o l d v a l u e , chosen t o b e 2, mentioned i n t h e f i r s t r u l e , andg
i s t h e mean of t h e s p i k e v a l u e s i n t h e i n t e r v a l . The extreme v a l u e d i s t r i b u t i o n of peaks,8,
where each peak i n t h e d i s t r i b u t i o n i s t h e maximum s p i k e v a l u e from a sampling i n t e r v a l , i s c l o s e l y r e l a t e d t o t h e above e x p r e s s i o n and r e q u i r e s o n l y one more parameter:~ ~ ( 2 ) = {i
-
exp [-(8-
8 )/(s
-
8)lIn
The new parameter n i s t h e a v e r a g e number of s p i k e s p e r i n t e r v a l . A s one might e x p e c t , t h e l o n g e r t h e sampling i n t e r v a l , t h e l a r g e r t h e maximum s p i k e v a l u e
( p e a k ) . The v a l u e of t h e most p r o b a b l e peak ( t h e mode ^g) i n c r e a s e s l i n e a r l y w i t h t h e n a t u r a l l o g a r i t h m of n a s f o l l o w s :
For a p r o p e r comparison of peak p r e s s u r e s , t h e model sampling p e r i o d must b e t h e p r o p e r l y s c a l e d e q u i v a l e n t of t h e f u l l - s c a l e p e r i o d . The time s c a l i n g parameter i s T = t VIE, where t and
P.
a r e a c h a r a c t e r i s t i c time and l e n g t h . I f t i s chosen t o b e t h e sampling p e r i o d ( t s ) and R i s thought of a s a n a v e r a g e "spacing between s p i k e s " (lls), t h e n t h e a v e r a g e number of s p i k e s p e r i n t e r v a l would b e g i v e n by:INVESTIGATION OF PRESSURE SPIKES AND PEAK FACTORS
Nine s e l e c t e d wind t u n n e l t a p s were sampled a t 500 s-I a t a r e f e r e n c e s p e e d of
7 = 15 m / s t o p r o v i d e one hundred 2 s sampling i n t e r v a l s . Four h i s t o g r a m s of p r e s s u r e s p i k e s were developed from groupings of two o r t h r e e t a p s a t a time u s i n g t h e two r u l e s p r e v i o u s l y d e f i n e d . The grouping was n e c e s s a r y t o p r o v i d e a n a c c e p t a b l y l a r g e sample of peak f a c t o r s .
One of t h e f u l l - s c a l e h i s t o g r a m s was o b t a i n e d by sampling e i g h t p r e s s u r e t a p s on t h e windward f a c e of t h e b u i l d i n g a t 20 s - I f o r 160 min when t h e wind had a d i r e c t l o n of 350° and a mean speed of 23 m / s . T h i s provided 256 5-min sampling i n t e r v a l s from which n and
g
could be e s t a b l i s h e d . The o t h e r t h r e e f u l l - s c a l e d i s t r i b u t i o n s were o b t a i n e d from t h e peak v a l u e s r e c o r d e d f o r t h e h o u r l y o b s e r v a t i o n s of 5-min p e r i o d s sampled a t 20 s - I when t h e mean speed was, on average, 1 7 m / s . Histograms of peaks were f i t t e d by extreme v a l u e d i s t r i b u t i o n s i n o r d e r t o o b t a i n n andg
f o r comparison w i t h model s c a l e . T h i s method of ' b a c k - c a l c u l a t i n g " t o d e t e r m i n e n andg
gave r e a s o n a b l e agreement when compared w i t h d i r e c t l y measured v a l u e s of n andg .
T a b l e 1 sumnarizes t h e e x p o n e n t i a l p a r a m e t e r s found f o r b o t h model and f u l l s c a l e . The h i s t o g r a m s and t h e c o r r e s p o n d i n g e x p o n e n t i a l c u r v e s a r e shown i n F i g u r e s 8 ( a ) t o 8 ( d ) . Except f o r t h e t h r e e f u l l - s c a l e c a s e s j u s t mentioned, t h e e x p o n e n t i a l c u r v e s a r e d e f i n e d by t h e observed v a l u e s of n and
g
o b t a i n e d from t h e time s e r i e sW. A . D a l g l i e s h , J. T. Templin and K. R. Cooper W I N D T U N N E L 1 . 6 1 1 1 1
- ( a )
-
I I A P S 2 9 9 P E A K S 1 5 0 I F U L L - S C A L E T I , ' , I I 8 T A P S ? 5 5 P E A K S 8 4 I I I I I d T A P S 1 5 8 P E A K S l B 5-
-
, I , , ,- ( d '
I T A P bO 1 0 0 P E A K SI
-
a l A P S 7 4 P E A K S n = l O F i g u r e 8 Peak p r e s s u r e h i s t o g r a m s and e x p o n e n t i a l c u r v e s r e c o r d s d e f i n i n g t h e p a r e n t p o p u l a t i o n of p r e s s u r e s p i k e s , and a r e n o t " f i t s " t o t h e h i s t o g r a m s . The f a c t that agreement i s good even though most of t h e c u r v e s a r e d e r i v e d from t h e p a r e n t p o p u l a t i o n and n o t d i r e c t l y from t h e h i s t o g r a m s of peaks i n d i c a t e s t h e u s e f u l n e s s of t h e concept of a p a r e n t p o p u l a t i o n of s p i k e s . F u r t h e r , comparison of t h e model and f u l l - s c a l e d i s t r i b u t i o n shows them t o b e i n r e a s o n a b l e agreement, e x c e p t f o r F i g u r e 8 ( d ) f o r which t h e model p r e s s u r e s were measured a t a f i x e d wind d i r e c t i o n of 60°, i n t h e wake of a b u i l d i n g 285 m h i g h . To o b t a i n s u f f i c i e n t d a t a p o i n t s a t f u l l s c a l e f o r a h i s t o g r a m , d a t a from a band between 30 and 90' had t o be used, and even t h e n on1.y 74 p o i n t s were found. Because of t h e l o c a l i z e d v a r i a t i o n s of flow i n a wake i t i s a n t i c i p a t e d t h a t t h eWind Tunnel and F u l l - s c a l e B u i l d i n g S u r f a c e P r e s s u r e s 563
T a b l e 1. P r o p e r t i e s of p r e s s u r e s p i k e s and peaks from wind t u n n e l and f u l l s c a l e
*
no p a r e n t d i s t r i b u t i o n a v a i l a b l e : n andg
o b t a i n e d from e x t r e e v a l u e d i s t r i b u t i o n f i t t e d t o match t h e mean and s t a n d a r d d e v i a t i o n , g" and2'
( ) p a r e n t h e s e s i n d i c a t e wind t u n n e l v a l u e s of n a d j u s t e d t o r e p r e s e n ta model sampling p e r i o d e q u i v a l e n t t o 5 min i n f u l l s c a l e S i g n F.S. I t e s of Speed Peak m / s a pos 23 a ' pos 23 b pos 17 c neg 17 d neg 17
u n u s u a l d a t a a t 60' i n t h e wind t u n n e l would b e masked i n f u l l s c a l e by d a t a from t h e r e s t of t h e s e c t o r .
Extreme Values (peaks)
Time s c a l i n g must b e t a k e n i n t o account i n a p r o p e r comparison of model and f u l l - s c a l e r e s u l t s . According t o Eq. (9), v a l u e s of n o b t a i n e d from t h e 2 s r e c o r d s i n t h e wind t u n n e l a t a r e f e r e n c e speed of 15 m / s correspond t o t h o s e from t h e 5-min r e c o r d s i n F u l l s c a l e o n l y i f t h e f u l l - s c a l e r e f e r e n c e speed is 20 m / s , assuming t h e s c a l e of mean "spike s p a c i n g " ks i s t h e same a s t h e geometric s c a l e . Values of n a d j u s t e d t o c o r r e s p o n d t o t h e f u l l - s c a l e 5-min r e c o r d a r e shown i n p a r e n t h e s e s b e s i d e t h e measured wind t u n n e l v a l u e s i n T a b l e 1.
P a r e n t P o p u l a t i o n ( s p i k e s )
F u r t h e r i n v e s t i g a t i o n of t h e e f f e c t s of time s c a l i n g i n d i c a t e s t h a t sampling a t 500 s - l i n t h e wind t u n n e l i s e q u i v a l e n t t o sampling a t 3.8 s-' f o r Item a (Table 1) a n d 2.8 s-l f o r Items b t o d . One might e x p e c t lower v a l u e s a t t h e s e lower model sampling r a t e s compared t o 20 s-l which was used i n f u l l s c a l e , b u t i n f a c t t h e wind t u n n e l r e s u l t s a r e e q u a l t o o r g r e a t e r t h a n t h e f u l l s c a l e i n a l l b u t one c a s e . The c o n t i n u o u s r e c o r d from f u l l s c a l e used f o r I t e m a was d i g i t a l l y f i l t e r e d t o s i m u l a t e a s i n g l e p o l e f i l t e r a t 1 . 5 Hz and sampled a t 4 s-l. The p r o p e r t i e s of t h e f i l t e r e d r e c o r d , I t e m a', range from 4 t o 10 p e r c e n t below t h o s e f o r I t e m a e x c e p t f o r n which dropped from 6.3 t o 4.8. The f i l t e r c h a r a c t e r i s t i c s of t h e model sampling system were n o t w e l l r e p r e s e n t e d by a s i n g l e p o l e f i l t e r , however, and t h e half-power p o i n t w a s c l o s e r t o 5 Hz ( f u l l s c a l e ) t h a n t o 1 . 5 Hz. I n any c a s e , f i l t e r c h a r a c t e r i s t i c s and sampling r a t e s of t h e measuring system e v i d e n t l y i n f l u e n c e t h e magnitude of t h e p r e s s u r e s p i k e s r e c o r d e d , and even l a r g e r
9^'
W.T. F.S. 0.9 1 . 0 d.9 0.4 0.4 1.9 1 . 5 1.1 1 . 5-
2
W.T. F.S. 3.5 3.4 3.2 2.2 2.2 3.6 3.3 5 . 1 3.4 nW.T.
F.S. 5.6(6.4) 6.3 4.8 Z.O(l.7) 1.6* 3.3(2.8) 2.6* l l . O ( g . 4 ) 3.0* e f f e c t s may b e s e e n i n t h e i r s h a p e s .-
2
W.T. F.S. 3.9 3.8 3.5 2.5 2.5 4.5 4.2 5.4 4.3-
g W.T. F.S. 2.9 2.8 2.7 2.3 2.4* 3.3 3.3" 3.3 3.3*SLOPES OF PRESSURE SPIKES
Spikes come i n a v a r i e t y of s h a p e s . Although on a compressed t i m e s c a l e t h e y may l o o k l i k e v e r t i c a l l i n e s , on an expanded s c a l e l i k e t h a t i n F i g u r e 7 t h e y c a n o f t e n b e roughly d e s c r i b e d a s a t r i a n g u l a r p u l s e w i t h a b a s e w i d t h (extended back t o t h e mean l e v e l ) v a r y i n g from 1 t o 10 s . The s l o p e s of 29 of t h e l a r g e s t s p i k e s of t h e
564 W. A . D a l g l i e s h , J . T. Templin and K . R. Cooper
f u l l - s c a l e r e c o r d s f o r Item a of T a b l e 1 were found t o a v e r a g e 7 . 3 C;/s w i t h a c o e f f i c i e n t of v a r i a t i o n ( c .c.v. = s t a n d a r d d e v i a t i o n
+
mean v a l u e ) of 0.7. On t h e o t h e r hand, 56 of t h e l a r g e s t s p i k e s from t h e wind t u n n e l s t u d y gave a n a v e r a g e of 3.0 C i / s (C.O.V. = 0 . 6 ) . The l a r g e d i s c r e p a n c y may b e due t o t h e d i f f e r e n c e s i n h i g h f r e q u e n c y f i l t e r i n g and sampling r a t e s . When t h e f i l t e r e d f u l l - s c a l e r e c o r d sampled a t 4 s-' was examined, t h e r a t e was found t o b e2 . 7 C$/s ( c .o.v. = 0 . 7 ) . The s l o p e s d i s c u s s e d s o f a r have been f o r p o s i t i v e peaks; t h e a v e r a g e s l o p e f o r 98 n e g a t i v e s l o p e s from 19 t a p l o c a t i o n s sampled a t 20 s-l e i t h e r i n t h e wake o r i n g l a n c i n g s i d e - f a c e f l o w w a s n e a r l y d o u b l e
(14.2 C 1 / s w i t h C.O.V. = 0 . 9 ) . The f u l l - s c a l e s l o p e s r e f e r t o a mean r e f e r e n c e speed
OF
23 m l s , and would presumably b e even s t e e p e r f o r h i g h e r s p e e d s .CONCLUDING REMARKS
The wind t u n n e l and f u l l - s c a l e mean and r m s m p r e s s u r e c o e f f i c i e n t s a g r e e w e l l where t h e r e a r e s u f f i c i e n t f u l l - s c a l e d a t a a t h i g h wind s p e e d s . Wind s p e e d s of a t
l e a s t 20 m / s a r e r e q u i r e d t o o b t a i n r e l i a b l e e s t i m a t e s of p r e s s u r e c o e f f i c i e n t s f o r a p a r t i c u l a r wind d i r e c t i o n a t f u l l s c a l e . Otherwise, t h e f u l l - s c a l e d a t a have t o o much random v a r i a t i o n t o be of u s e . P a r t of t h e p r e s s u r e v a r i a t i o n c o u l d b e e l i m i n a t e d by o b t a i n i n g a r e f e r e n c e p r e s s u r e independent of i n t e r n a l b u i l d i n g p r e s s u r e , a s would b e provided by a s t a t i c p r e s s u r e t a p away from t h e i n f l u e n c e of t h e b u i l d i n g .
A scheme h a s been proposed f o r i d e n t i f y i n g s i g n i f i c a n t independent peak e v e n t s , p r e s s u r e s p i k e s , a s t h e y o c c u r a t random i n t e r v a l s i n a t i m e s e r i e s , t h e s t a t i s t i c a l p r o p e r t i e s of which c a n b e a d e q u a t e l y d e s c r i b e d by a n e x p o n e n t i a l d i s t r i b u t i o n . Two p a r a m e t e r s , t h e number of s p i k e s i n t h e i n t e r ~ r a l and t h e a v e r a g e s p i k e v a l u e , d e s c r i b e t h e extreme v a l u e d i s t r i b u t i o n of peaks a t a p a r t i c u l a r p r e s s u r e t a p o r group of t a p s , a l l o w i n g t h e peak a t a n y d e s i r e d p r o b a b i l i t y l e v e l t o b e p r e d i c t e d f o r any storm d u r a t i o n . P o s i t i v e p r e s s u r e r e g i o n s , f o r which p o s i t i v e peaks a r e of i n t e r e s t , t y p i c a l l y h a v e narrow p r o b a b i l i t y d e n s i t y f u n c t i o n s c e n t r e d a t peak f a c t o r s lower t h a n r e g i o n s of p o s i t i v e p r e s s u r e t h a t a r e i n f l u e n c e d by wakes. Negative p r e s s u r e r e g i o n s , p a r t i c u l a r l y o n s i d e w a l l s n e a r u p s t r e a m c o r n e r s , e x h i b i t b r o a d e r d i s t r i b u t i o n s e x t e n d i n g t o l a r g e r peak f a c t o r s t h a n f o r p o s i t i v e p r e s s u r e s .
C o n s i d e r i n g t h e d i f f e r e n c e s i n t h e model and f u l l - s c a l e measuring s y s t e m s , t h e agreement found between peak d i s t r i b u t i o n p a r a m e t e r s i s e n c o u r a g i n g . A d d i t i o n a l e x p e r i m e n t s a r e planned i n which g r e a t e r a t t e n t i o n w i l l be p a i d t o a p r o p e r matching of sampling r a t e s and f i l t e r c h a r a c t e r i s t i c s of wind t u n n e l and f u l l -
s c a l e measuring s y s t e m s . Changing t h e f i l t e r and sample r a t e f o r one f u l l - s c a l e r e c o r d gave h i g h e r peaks f o r t h e l a r g e r r a t e , a t r e n d t h a t may c o n t i n u e even beyond 20 s - l . I n view o f t h e d i f f i c u l t y and expense of r a i s i n g sampling c a p a b i l i t i e s , i t i s w o r t h examining t h e r e s p o n s e of t h e c l a d d i n g t o p e a k s . Annealed f l o a t g l a s s o f f i c e windows p r o v i d e a p a r t i c u l a r l y i n t e r e s t i n g example
b e c a u s e t h e i r c a p a c i t y t o w i t h s t a n d peak p r e s s u r e s i s thought t o i n c r e a s e a p p r o x i m a t e l y a s t h e 1 / 1 3 t h power of t h e pgak s l o p e [ l 0 ) . T h i s would mean t h a t t h e 9 p e r c e n t i n c r e a s e i n peak magnitude
(g)
a t t h e h i g h e r sampling r a t e i s a l m o s t matched by a n 8 p e r c e n t i n c r e a s e i n c a p a c i t y r e s u l t i n g from t h e i n c r e a s e i n peak s l o p e from 2.7 C; s-I t o 7.3 C+ s - l . T h i s example, a l t h o u g h over- s i m p l i f i e d and based on i n s u f f i c i e n t d a t a , i l l u s t r a t e s some of t h e c o n s i d e r a t i o n s i n a s s e s s i n g t h e adequacy of d e s i g n d a t a . Each c l a d d i n g a p p l i c a t i o n may h a v e somewhat d i f f e r e n t r e q u i r e m e n t s , depending on m a t e r i a l p r o p e r t i e s , s i z e , and n a t u r a l f r e q u e n c y . The need f o r more i n f o r m a t i o n on t h e r e s p o n s e of c l a d d i n g a s w e l l a s t h e c h a r a c t e r i s t i c s of t h e l o a d i n g i s a p p a r e n t . N e v e r t h e l e s s , t h eWind T u n n e l and F u l l - s c a l e B u i l d i n g S u r f a c e P r e s s u r e s 565 a u t h o r s s u g g e s t t h a t wind t u n n e l p r o c e d u r e s of t h e s o r t d e s c r i b e d c a n p r o v i d e a d e q u a t e d a t a f o r c l a d d i n g d e s i g n f o r h i g h - r i s e b u i l d i n g s . U n l e s s t h e e f f e c t s of s c a l e ( s a m p l i n g r a t e , s a m p l e l e n g t h , r e f e r e n c e s p e e d ) a r e a c c o u n t e d f o r , however, s y s t e m t i c p e a k p r e d i c t i o n e r r o r s w i l l r e s u l t , a n d t h e p r a c t i c e o f o b s e r v i n g o n l y a s i n g l e p e a k t o d e t e r m i n e t h e d e s i g n p r e s s u r e c o e f f i c i e n t w i l l o c c a s i o n a l l y y i e l d u n r e p r e s e n t a t i v e v a l u e s . The a u t h o r s recommend t h a t p e a k s b e s e l e c t e d f r o m a t least 1 0 s u b s e t s of a n e x t e n d e d s a m p l i n g i n t e r v a l , t o p e r m i t ' t a c k - c a l c u l a t i o n " o f n a n d
g
a n d a more s o u n d l y b a s e d p r e d i c t i o n of peak p r e s s u r e c o e f f i c i e n t s . ACKNOWLEDGEMENTS The a u t h o r s w i s h t o e x p r e s s t h e i r s i n c e r e a p p r e c i a t i o n t o t h e f o l l o w i n g o r g a n i z a - t i o n s a n d i n d i v i d u a l s f o r t h e i r c o n t r i b u t i o n s t o t h i s p a p e r : C a n a d i a n I m p e r i a l Bank of Commerce, owners of t h e b u i l d i n g ; members of t h e Low Speed Aerodynamics S e c t i o n , N a t i o n a l A e r o n a u t i c a l E s t a b l i s h m e n t ; and c o l l e a g u e s , p a r t i c u l a r l yP . J . Daly and F.W.K. Hummel, of 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 . T h i s p a p e r i s a j o i n t c o n t r i b u t i o n of two D i v i s i o n s of 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 o f Canada:
t h e N a t i o n a l A e r o n a u t i c a l E s t a b l i s h m e n t a n d 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 . It i s p u b l i s h e d w i t h t h e a p p r o v a l of t h e D i r e c t o r s of t h e s e D i v i s i o n s .
REFERENCES:
1. K . J . E a t o n and J . R . Mayne, The measurement of wind p r e s s u r e s on t w o - s t o r e y h o u s e s a t A y l e s b u r y , J. I n d . Aerodynamics, 1, 67 ( 1 9 7 5 ) .
2. R.D. M a r s h a l l , A s t u d y of wind p r e s s u r e s o n a s i n g l e - f a m i l y d w e l l i n g i n model and f u l l - s c a l e , J . I n d . Aerodynamics, 1, 177 (1975)
.
3 . W.A. D a l g l i e s h , Comparison of m o d e l / f u l l - s c a l e wind p r e s s u r e s on a h i g h - r i s e
b u i l d i n g , J . I n d . Aerodynamics, 1, 5 5 (1975)
.
4. J . A . P e t e r k a and J . E . Cermak, Wind p r e s s u r e s o n b u i l d i n g s
-
p r o b a b i l i t y d e n s i t i e s , P r o c . ASCE, Vol. 101, No. ST6, p . 1255-1267 ( 1 9 7 5 ) .5. K . J . E a t o n , C l a d d i n g a n d t h e wind, P r o c . ASCE, Vol. 1 0 2 , No. ST5, p. 1043-1053 (1976)
.
6 . H.P.A.H. I r w i n and K.R. Cooper, C o r r e c t i o n of d i s t o r t i o n e f f e c t s c a u s e d by t u b i n g s y s t e m s i n measurement of f l u c t u a t i n g p r e s s u r e s , N a t i o n a l R e s e a r c h C o u n c i l of Canada, LTR-LA-222 (1979)
.
7. W.A. D a l g l i e s h , S t a t i s t i c a l t r e a t m e n t o f peak g u s t s on c l a d d i n g , P r o c . ASCE, Vol. 97, No. ST9, September 1971, p. 2173-2187 ( 1 9 7 1 ) .
8 . A.G. D a v e n p o r t , Note on t h e d i s t r i b u t i o n of t h e l a r g e s t v a l u e of a random f u n c t i o n w i t h a p p l i c a t i o n t o g u s t l o a d i n g , P r o c . I n s t . C i v . Eng. 28, 187 ( 1 9 6 4 ) .
' 9 . E. J . Gumbel, S t a t i s t i c s of e x t r e m e s , Columbia U n i v e r s i t y P r e s s , New York, 1958, p . 113-118.
1 0 . W.G. Brown, A l o a d d u r a t i o n t h e o r y f o r g l a s s d e s i g n , N a t i o n a l R e s e a r c h C o u n c i l of Canada, 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 , R e s . P a p e r 508 ( 1 9 7 2 ) .
I
I
This publication is being distributed by the Division of Building R e s e a r c h of the National R e s e a r c h Council of Canada. I t should not be reproduced in whole o r in p a r t without p e r m i s s i o n of the original publisher. The Di- vision would be glad to b e of a s s i s t a n c e in obtaining s u c h p e r m i s s i o n .
Publications of the Division m a y be obtained by m a i l - ing the a p p r o p r i a t e r e m i t t a n c e ( a Bank, E x p r e s s , o r P o s t Office Money O r d e r , o r a cheque, m a d e payable to the R e c e i v e r G e n e r a l of Canada, c r e d i t NRC) to the National R e s e a r c h Council of Canada. Ottawa. K1A OR6. Stamps a r e not acceptable.
A l i s t of a l l publications of the Division i s available and m a y be obtained f r o m the Publications Section, Division of Building R e s e a r c h , National R e s e a r c h Council of Canada, Ottawa. KIA OR 6.
