Computation of Wind Pressures on Low-rise Structures

8/3/2019 Computation of Wind Pressures on Low-rise Structures

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Journal of Wind E ngineering and Industrial Aerodynamics, 41-44 (1992) 1629-1640Elsevier 1629

C o m p u t a t i o n o f W i n d P r e s s u r e s o n Low-rise St ructuresD.A. Paterson, and J.D. Holmesb-CSIRO Division of Building, Construct ion and Engineering, P.O. Box 310, NorthRyde, N.S.W. 2113, Austra liabCSIRO Division of Building, Construction and Engineering, P.O. Box 56,Highett, Vic. 3190, AustraliaA b s t r a c t

This report describes the use of some computer programs writ ten by one of theauthors (DP) in predicting mean and peak wind pressures on arched-roofbuildings. The research was carried out because there is a lack of good wind-tunnel and full-scale data on arched-roof buildings. The programs have beenvalidated by comparing the results with wind-tunnel and full-scale dataassociated with the Texas Tech building.1. INTRODUCTION

The related problems of wind-induced pressures on building surfaces and windvelocities at pedestrian level adjacent to buildings are of great importance toengineers and architects. Over the last 20 years, these problems have usuallybeen solved by wind tunnel tests. This is a relatively expensive approach, andrequires separate models to be made for each geometrical configuration. Also, fora structure with a curved external surface, such as an arched-roof building, theflow and pressures obtained on a small scale model may differ from full scale dueto the difference in Reynolds Numbers in the two cases.

The technique of computer modelling of wind flows around structures has beendeveloped by the authors. It seems to be as accurate as wind tunnel modelling inthe determination of mean flow velocities and mean surface pressures. It ismuch less expensive than wind tunnel modelling. Mean surface pressurecoefficients, when used with peak gust wind speeds, may be sufficiently accuratefor the structural design of many structures for which resonant dynamicresponse is not expected to be important. This approach is known as the 'quasi-steady' method, and has formed the basis of many international codes and0167-6105/92/$05.00 1992 Elsevier Science Publishers B.V . All rights reserved.


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1630s t a n d a r d s f o r w i n d l o a d i n g.

T h e p r e s e n t c o m p u t e r p r o g r a m s h a v e b e e n v a l i d a t e d b y c o m p a r i n g t h e r e s u l t sw i t h th o s e o f m a n y d i f f e re n t w i n d t u n n e l a n d f u ll -s c a le e x p e r i m e n t s . O n e s u c hc o m p a r i s o n , w i t h r e s u l t s a s s o c i a t e d w i t h t h e T e x a s T e c h b u i l d i n g , i s r e p o r t e dh e r e. I n t h e f i r s t h a l f of 1 9 89 , a s e ri es o f m e a s u r e m e n t s o f p r e s s u r e s w e r e m a d eo n a n i n s t r u m e n t e d (9 .1 x 1 3. 7 x 4 .0 m ) ( 3 0 x 4 5 x 1 3 f t) e x p e r i m e n t a l b u i l d i n g a tt h e T e x a s T e c h U n i v e r s i t y [1 ]. P e o p l e w o r k i n g w i t h t h i s b u i l d i n g h a v e p r o d u c e ds o m e s e t s o f d a t a o f m e a n , r . m . s , a n d p e a k p r e s s u r e s . T h e s e a r e s o m e o f t h e b e s ts e t s o f p r e s s u r e d a t a o n lo w - r i se b u i l d i n g s c u r r e n t l y a v a i l a b l e . T h e y a r e v e r yu s e f u l in d e t e r m i n i n g w i n d l o a d s o n lo w b u i l d i n g s . T h e s e f u l l - s c a le r e s u l t s h a v ea l r e a d y b e e n c o m p a r e d w i t h so m e w i n d t u n n e l r e s u l t s m e a s u r e d a t t h eU n i v e r s i t y o f W e s t e r n O n t a r i o [2 ].

F o r t h e p r e s e n t p a p e r , w i n d f lo w s a r o u n d s t r u c t u r e s w e r e c o m p u t e d b y s o l vi n gt h e s e t of p a r t i a l d i f f e re n t i a l e q u a t io n s t h a t g o v e r n s t h e f lo w . I n t h i s i n s t a n c e,t h e t h r e e - d i m e n s i o n a l f l o w a r o u n d t h e T e x a s T e c h B u i l d i n g w a s c a l c u l a t e d a n dt h e m e a n a n d r .m . s , p r e s s u r e c o ef fi ci en ts w e r e c o m p a r e d w i t h b o t h f u l l- s c a le a n dw i n d t u n n e l r e s u l t s .T h e p r o g r a m s t e s t e d o n t h e f l o w a r o u n d t h e T e x a s T e c h B u i l d i n g h a v e b e e nu s e d t o c o m p u t e t h e f lo w s a r o u n d a l a r g e n u m b e r o f a r c h e d - r o o f b u i l d i n g s . T w oo f t h e s e c o m p u t a t i o n s a r e r e p o r t e d h e re . O n e o f t h e b u i l d i n g s i s a m o b i l e t a i l

e n c l o s u r e p r o d u c e d b y S t r a r c h I n t e r n a t i o n a l L t d o f M e l b o u r n e , A u s t r a l i a . T h em o b i le t a i l e n c lo s u r e i s a s t r u c t u r e t h a t a l lo w s e x i s t i n g h a n g a r s t o h o u s e b i g g e ra i rc r a ft . T h e f r o n t o f t h e a i r c r a ft is p u t i n t h e e x i s t i n g h a n g a r a n d a m o b i lee n c l o s u r e i s m o v e d o v e r t h e t a il o f t h e a i r c r a f t t o k e e p i t o u t o f t h e w e a t h e r a ss h o w n i n F i g u r e 1. T h e e n c l o s u r e i s s u p p o r t e d b y s e m i - c i r c u l a r p r e s t r e s s e da r c h es , e re c t e d b y t h e p a t e n t e d S t r a r c h s y s t e m . T h e e n c l o s u r e is m u c h t a l l e r a n dn a r r o w e r t h a n m o s t a r c h e d - r o o f s t r u c t u r e s b e c a u s e i t h a s t o fi t o v e r t h e t a il o fa n a i r c ra f t . T h e s t r u c t u r e o n w h i c h t h e p r e s s u r e s w e r e c a l c u l a t e d c o n s i s ts of ar o o f w i t h a r a d i u s o f 1 5 .5 m s u p p o r t e d b y v e r t i c a l w a l l s o f 1 0 m h i g h . T h e l e n g t ha l o n g t h e a x i s i s 2 0 m .

T h e o t h e r c o m p u t a t i o n r e p o r t e d h e r e is o n a n a r c h e d - r o o f b u i l d i n g . T h i sb u i l d i n g i s s el e c te d b e c a u s e i t s d i m e n s i o n s a r e t y p i c a l o f m a n y a r c h e d - r o o fb u i l d i n g s t h a t h a v e b e e n c o n s t r u c t e d b y S t r a r c h I n t e r n a t i o n a l . I t h a s a r i s e / s p a nr a t i o o f 0 .2 , a l e n g t h / s p a n r a t i o o f 1 .0 , a n d a n e a v e s h e i g h t / r i s e r a t i o o f 0 .4 5 . T h i si s o n e o f m a n y c o m p u t a t i o n s i n v o lv i n g d i f f e r e n t a r c h e d - r o o f b u i l d i n g s h a p e s ,d i f f e r e n t a p p r o a c h f l ow a n g l e s , a n d d i f f e r e n t i n l e t v el o c i ty p r o f i l es . B u i l d i n g sw e r e s t u d i e d b o t h w i t h a n d w i t h o u t m a j o r o p e n i n g s . T h e a i m o f t h e r e s e a r c hw a s t o p r o v i d e a s m u c h i n f o r m a t i o n a s p o s s i b l e o n p r e s s u r e s o n a s m a n y a r c h e d -r o o f b u i l d i n g s a s p o s s i b le u n d e r a v a r i e t y o f w i n d c o n d i ti o n s .


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F i g u r e 1 . S t r a r c h M o b i l e T a i l E n c l o s u r e .

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C o m p u t e r m o d e l l in g o f f lu i d f lo w s s t a r t s w i t h t h e e q u a t i o n s o f c o n s e r v a t io n o fm a s s a n d m o m e n t u m t h a t a r e c ol le c ti v el y k n o w n a s t h e N a v i e r - S t o k e s e q u a t io n s .T h e s e e q u a t i o n s a r e ti m e - d e p e n d e n t . I n t h e p r e s e n t a p p r o a c h th e y a r e a v e r a g e do v e r t i m e to g e t t h e R e y n o l d s e q u a t i o n s . T h e e q u a t i o n s f o r t h e c o n s e r v a t i o n o fm o m e n t u m a r e s o l v ed f or t h e m e a n ve lo c it ie s . T h e c o n s e r v a t i o n o f m a s se q u a t i o n i s c o m b i n e d w i t h t h e e q u a t i o n s f o r t h e m e a n v e l o c i ti e s to y i e l d ap r e s s u r e c o r r e c t i o n e q u a t i o n . T h i s u s e o f a p r e s s u r e c o r r e c ti o n e q u a t i o n i sk n o w n a s t h e S I M P L E m e t h o d [ 3].

T h e t i m e - a v e r a g e d e q u a t i o n s c o n t a i n s i x e x t r a t e r m s t h a t a r e r e l a t e d t o t h er .m . s , v e lo c i ti e s a n d a r e c r e a t e d w h e n t h e t i m e a v e r a g i n g i s d o ne . I n t h e p r e s e n tm e t h o d , t h e s e e x t r a t e r m s a r e d e r i v e d f r om t h e t u r b u l e n t k i n e t ic e n e r g y (k ),w h i c h i s h a l f t h e s u m o f t h e s q u a r e s o f t h e r . m . s , v e l o ci ti e s, a ~ d f r o m t h e r a t e o fd i s s i p a t i o n o f t h e t u r b u l e n t k i n e t i c e n e r g y ( z) . k a n d ~ a r e c a l c u l a t e d f r o m t w of u r t h e r e q u a t i o n s [ 4,5 ]. N o a t t e m p t h a s b e e n m a d e t o c h a n g e t h e r e s u l t s to


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1632b e t t e r f it e x p e r i m e n t a l d a t a . E a r l i e r w o r k h a s i n d i c a te d t h a t f i n e tu n i n g o f t h ec o n s t a n t s i n t h e m o d e ! i s n e i t h e r n e c e s s a r y n o r d e s i r a b l e .

T h e s e e q u a t i o n s a r e n o n - l i n e a r a n d s o a r e s o l v e d i n a n i t e r a t i v e m a n n e r .T h e y w e r e t u r n e d i n to a tr a c t a b l e f o r m b y i n t e g r a t i n g t h e m o v e r a p p r o p r i a t ev o l u m e s o n a st a g g e r e d g r id . T h e c o n v ec t io n t e r m s i n t h e e q u a t i o n s w e r ed i s c re t is e d b y u s i n g t h e f i r st - o r d e r h y b r id u p w i n d i n g s c h e m e .

C o m p u t a t i o n o f t h e f l o w o v e r a m o b i l e t a i l e n c l o s u r e p o s e s s p e c i a l p r o b l e m s .T h e r o o f i s se m i c i r c u l a r a n d t h e w a l l s a r e v e r t i c a l s o it is n e c e s s a r y t o m o d e l t h et r a n s i t i o n b e t w e e n t h e tw o c o rr e c tl y . P o l a r c o o r d i n a t e s c a n ' t e a s i l y b e u s e d a n da t t e m p t s t o u s e b o d y - f i t t e d c o o r d i n a t e m e s h e s w e r e a b a n d o n e d b e c a u s e o fc o n v er g e nc e a n d a c c u ra c y p r o b l e m s . I n t h e e n d a s i m p l e C a r t e s i a n m e s h w a sused .

A n o t h e r p r o b l e m w i t h t h e m o b i l e t a i l e n c l o s u r e i s t h a t t h e m o s t c r i ti c a l l o a dc a s e o c c u r s w h e n t h e a r c h i s o ff t h e a i r c r a f t a n d t h e w i n d i s b l o w i n g i n to t h eo p e n e n d o f t h e e n c l o s u re . I n t h i s c a se t h e r e a r e v e r y s e v e r e l i ft a n d o v e r t u r n i n gf or ce s. T h e r o o f a n d w a l l s h a v e t o b e m o d e l l e d a s z e r o t h i c k n e s s s u r f a c e s s od e r i v a t i v e b o u n d a r y c o n d i t i o n s h a v e t o b e s e t b y c h a n g i n g n o d a l c o e f f ic i en t sr a t h e r t h a n v a l u e s o v e r b o u n d a r i e s . E x t r a c a r e i s t a k e n w h e n v a l u e s o v e rb o u n d a r i e s a r e u s e d t e m p o r a r i l y t o i n c r e a s e c o m p u t a t i o n a l e f f i c i e n c y a s i nT E A C H [6 ].

T h i s a l g o r i t h m c o u l d n o t b e v e c t o r i s e d a n d s o a n e w a l g o r i t h m w a s d e v e l o p e di n w h i ch t h e S O R p a r t o f t h e a l g o r i th m w a s r e p l a c e d b y a J a c o b i a l g o r i t h m . T h i si s f u l ly v e c t o r is a b l e , a n d d o e s n o t s u b s t a n t i a l l y s lo w d o w n t h e o v e r a l lc o n v e r ge n c e b e c a u s e o f t h e u s e o f A D I . I n a d d i t i o n , s i g n i f i c a n t c h a n g e s w e r em a d e t o t h e w a y in w h i c h t h e b o u n d a r y c o n d i t i o n s a r e c a l c u l a te d . I n t h e f i n a la l g o r i th m , v e c t o r le n g t h s i n e x c e s s o f 1 0 ,0 0 0 a r e a c h i e v e d i n t h e s e t t i n g u p o f t h et r i d i a g o n a l m a t r i c e s a n d i n t h e c a l c u l a ti o n o f t h e i n i t i a l a p p r o x i m a t i o n . V e c t o rl e n g t h s a r e i n e x c e ss of 4 0 0 w h e n d o i n g t h e b lo c k T D M A s o l u ti o n . O v e r a l l , t h e r ei s a f a c t o r o f a b o u t 3 0 s p e e d - u p f r o m t h e s e c h a n g e s .I n t h e p r e s e n t p r o g r a m s , t h e l o c a ti o n s o f s o l id s u r f a c e s ( w a l l s a n d r oo f ) w e r ei n p u t a s a s i n g l e 2 -D a r r a y f r o m a d a t a f il e. T h i s a r r a y g i v e s t h e h e i g h t o f t h er o of a b o v e g r o u n d le ve l. T h e p r o g r a m s a u t o m a t i c a l l y p la c e w a l l s a t t h e e d g e s o ft h e r oo f. T h e d e c i s io n a b o u t w h i c h w a l l s a r e s o l i d a n d w h i c h a r e o p e n i s h a n d l e db y lo g ic al v a r i a b l e s w i t h i n t h e p r o g r a m s . T h i s i n p u t m e t h o d a l lo w s g e o m e t r yd a t a t o b e c r e a t e d q u i c k ly b y h a n d , w i t h o u t t h e n e e d f o r a p r e - p r o c e s s o r . I t h a sb e e n u s e d f or o t h e r p r o b l e m s i n v o lv i n g m u l t i p l e b u i ld i n g s o f ir r e g u l a r s h a p e .A la r g e a m o u n t o f e f fo r t h a s b e e n e x p e n d e d i n o p t i m i s i n g t h e p r e s e n tp r o g r a m s fo r u s e o n v e c to r p ro c e s s in g c o m p u t e r s . T h e c o m p u t e r u s e d f or t h em a i n c a l c u l a t io n s is a C r a y Y - M P 2 / 2 1 6. T h e o r i g i n a l a l g o r i t h m u s e d t h e T r i-


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D i a g o n a l M a t r i x A l g o r i t h m ( T D M A ) in o n e o f t h e t h r e e d i m e n s i o n s , c o u p l e d w i t hS u c c e s si v e O v e r - R e l a x a t i o n (S O R ) in t h e o t h e r t w o d i m e n s i o n s . T h e d i r e c t io n i nw h i c h t h e T D M A w a s t a k e n w a s v a r i e d i n t h e m a n n e r o f t h e A l t e r n a t i n gD i r e c ti o n I m p l i c i t ( A D I) m e t h o d . B u t t h e m e t h o d d i f fe r e d f ro m t h e s t a n d a r d A D Im e t h o d i n t h a t n o o p e r a t o r s p l i t ti n g w a s a p p li e d ; s o t h e n u m b e r o f s w e e p s f o re a c h e q u a t i o n d i d n o t h a v e t o b e a m u l t i p l e o f t h r e e . F a s t e s t c o n v e r g en c e w a sf o u n d t o o c cu r w h e n f o u r s w e e p s w e r e u s e d ~ br t h e p r e s s u r e c o r re c ti o n e q u a t i o na n d o n e s w e e p o n e a c h o f t h e o t h e r e q u a t i o n s .

P r e s s u r e c o e ff ic ie n ts w e r e c a l c u l a te d i n a p o s t - p r o c e s s in g p r o g r a m t h a t i sq u i t e d i s ti n c t f r o m t h e m a i n p r o g r a m s . M e a n p r e s s u r e c o e ff ic ie n ts w e r ec a l c u l a t e d f r o mmCp = 2 P / (p V2) - CP0 (1 )w h e r e P i s t h e m e a n p r e s s u r e , p i s t h e d e n s i t y , V i s t h e a p p r o a c h v e l o c i t y a tb u i l d i n g h e i g h t a n d C Po i s a r e f e r e n c e p r e s s u r e c o e ff ic ie n t. T h e r e f e r e n c ep r e s s u r e c o e f f ic i e n t w a s o b t a i n e d b y s e t t i n g t h e m e a n p r e s s u r e c o e f fi c ie n t t o ze r oa t a p o i n t w e l l a w a y f ro m t h e b u i l d i n g . R . m . s . p r e s s u r e c o e f f ic i e n ts w e r ec a l c u l a t e d f r o mc i , ff i 2 [ k / 3 + 0 . s 1 6 I C p I V o ] / v " (2 )w h e r e V 0 a n d k 0 a r e t h e v a l u e s o f v e l o c it y a n d k i n t h e a p p r o a c h f lo w a t t h eh e i g h t a t w h i c h C ~ i s r e q u i r e d .

T h e e x p r e s s i o n i n E q . 2 i s a n a p p r o x i m a t i o n c o n s i s t i n g o f t w o c o m p o n e n t s .T h e p a r t p r o p o r t i o n a l t o k i s a s s o c i a t e d w i t h s m a l l - s c a l e l o ca l p r e s s u r ef l u c t u a t i o n s i n f l o w f r e e o f m e a n v e l o c it y g r a d i e n t s a s d i s c u s s e d b y H i n z e [7 ].T h e p a r t c o n t a i n i n g V 0 i s a ' q u a s i - s t e a d y ' t e r m a s s o c i a te d w i t h t h e a m p l i f ic a t io no f u p w i n d p r e s s u r e f l u c tu a t i o n s b y v e lo c it y g r a d i e n t s i n t h e flo w .

3 . R E S U L T S3 .1 T e x a s T e c h B u i l d i n g

M e a n a n d r . m . s , p r e s s u r e c o e f f i c i e n t s , m e a n v e l o c i t i e s a n d t u r b u l e n t k i n e t i ce n e r g i e s w e r e c a l c u l a t e d f o r a p p r o a c h f lo w s a t a n g l e s o f 0 ( p a r a l l e l t o t h e l o n gs ide o f t he bu i l d ing ) t o 90 i n 10 i n t e rv a l s . A fa i r l y co a r se g r i d o f 26 x 29 x 14w i t h v a r i a b l e g r i d i n t e r v a l s is u s e d . V e l o c it y v e c t o r p l o t s a n d c o n t o u r p l o t s o fp r e s s u r e a n d k h a v e b e e n p r o d u c e d a l o n g a l a r g e n u m b e r o f s li ce s t h r o u g h a n dn e a r t h e b u i l d i n g f o r e a c h a p p r o a c h f l ow a n g le . M a n y h a v e n o t y e t b e e n


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1634p u b l i s h e d a n d a r e a v a i l a b l e f r o m t h e f ir s t a u t h o r .

C o m p u t e d m e a n a n d r . m . s , p r e s s u r e c o e ff ic i en t s o n t h e l i n e o f i n t e r s e c t io n o ft h e c e n t r a l p l a n e o f t h e b u i l d i n g w i t h t h e b u i l d i n g s u r fa c e h a v e b e e n p l o t te d f o re a c h of" t h e t e n a p p r o a c h f l ow a n g l es . T h e s e w e r e c o m p a r e d w i t h r e s u l t s f r o mf u ll s c a le a n d w i n d t u n n e l e x p e r i m e n t s f o r a p p r o a c h f lo w a n g l e s o f 0, 6 0 a n d 9 0 .T h o s e f ro m t h e 9 0 d e g r e e a p p r o a c h a n g l e a r e i n c l u d e d i n F i g u r e 2 .

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t" q

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M e a n P r e ss u re C o e f f i c ie n t , T h e t a = 9 0~, Computa t ionx Ful l Sca le W i n d T u n n e l

B C D E

~5R M . S . P r e s s u r e C o e f f i c i e n t , T h e t a = 9 0

' ~ C om puta t ionx F u l l S c a le

~ k B C D EF i g u r e 2 . P r e s s u r e c o e f f i ci e n ts f o r t h e T e x a s T e c h B u i l d i n g .


7/12

1635T h e c o m p u t e d m e a n 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 v e r y w e l l w i t h b o t h f u l l - s c a l ea n d w i n d t u n n e l d a t a , p a r t i c u l a r l y o n t h e f r o n t a n d b a c k f a c e s w h e r e t h ec o m p u t e d p r e s s u r e c o e f f i c i e n t s f a l l b e t w e e n t h o s e m e a s u r e d i n t h e w i n d t u n n e la n d f u l l s c a le . T h e a g r e e m e n t a t t h e t o p o f t h e b u i l d i n g i s a l s o g o od .T h e c o m p u t e d r . m . s , 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 f a i r l y w e l l w i t h t h e f u l l - s c a l ea n d w i n d t u n n e l r e s u l t s b u t t e n d t o b e s li g h t ly to o lo w o v er t h e w h o l e o f t h eb u i l d i n g s u r f a c e . A s i m i l a r l e v e l o f a g r e e m e n t i s f o u n d f o r f l o w s a t o t h e ra p p r o a c h a n g l e s .

3 .2 M o b i l e T a i l E n c l o s u r e

I n t h e c a l c u l at io n s , a n a p p r o a c h f lo w f or a n a t m o s p h e r i c b o u n d a r y l a y e r w i t h ar o u g h n e s s l e n g t h o f 0 .0 1 m w a s u se d . T h e J e n s e n N u m b e r ( s t r u c t u re h e i g h t /r o u g h n e s s l e n g t h ) i s a s ig n i f i c a n t s c a l i n g n u m b e r f o r w i n d l o a d s o n l o w - r i ses t r u c t u r e s ; i n t h e p r e s e n t c as e t h e J e n s e n N u m b e r i s a b o u t 2 50 0. T h e R e y n o l d sN u m b e r ( i n e r t i a l fo rces in t h e f l o w / v i s co u s fo rces ) is a l s o s i g n i f i ca n t fo r fl o wa r o u n d b o d i e s w i t h c u r v e d s u r f a c e s . F o r w i n d f lo w a r o u n d f u l l- s c a l e s t r u c t u r e sw i t h c u r v e d s u r f a c e s o f l a r g e d i a m e t e r , t h e R e y n o l d s N u m b e r i s v e r y l a r g e ( m u c hl a r g e r t h a n c a n b e o b ta i n e d w i t h w i n d t u n n e l t e st s) . F o r th e c o m p u t a t i o n s o f t h ep r e s e n t r e p o r t , t h e R e y n o l d s N u m b e r i s e ff e c ti v el y i n f i n it e , s i n c e v is c o u s s t r e s s e si n t h e f lo w a r e n e g l e c t e d i n c o m p a r i s o n w i t h t h e t u r b u l e n t s t re s s e s.

- 0 . 6 1' ~ -0.44.o . , ,

C P , ' s + X + 0 .6 i ~ I 2 0 i n t e r v a l "

- 0 . 3 2

0,17

~-0.14

F i g u r e 3 . E x t e r n a l m e a n p r e s s u r e c o ef fi ci en ts o n t h e S t r a r c h M o b i l e T a i lE n c l o s u r e


8/12

1636C a l c u l a t i o n s o f e x t e r n a l p r e s s u r e c o ef fi ci en t s w e r e m a d e f o r a s t r u c t u r e w i t hb o t h e n d s c l o s e d a n d w i t h o n e e n d o p e n , b a s e d o n t h e m e a n w i n d s p e e d a t t h et o p o f t h e s t r u c t u r e , T h o s e fo r b o t h e n d s c lo s e d a r e s h o w n i n F i g u r e 3 . T h ev a l u e s i n F i g u r e 3 w e r e c o m p u t e d a t p o i n t s a l o n g t h e c e n t r e - l in e o f t h e s t r u c t u r e .

T h e p o i n t s o f c o m p u t a t i o n w e r e a t t h e c e n t r e s o f t h e w a l l o r a n g u l a r r o o f s e c to r ss h o w n i n F i g u r e 3 .T h e m a x i m u m p o si t iv e p r e s s ur e c oe ff ic ie nt ( + 0 . 6 9) o c c u r s a b o u t h a l f w a y u p

t he s tr uc tu r e o f t he l ow er p ar t o f t he a rc h e d r oo f. T h e m i n i m u m ( m a x i m u mnegative) pressure coefficient (-0.61) occ urs at th e crest of the roof. O n theleew ard si de of the structure, the pressure coefficients ha ve fairly uni for mnegative values, as expected for a fully separated w a k e region.

T h e r e a r e n o f u ll -s c al e d a t a a v a i la b l e t o c o m p a r e t h e c o m p u t e d p r e s s u r e s w i t h.H o w e v e r , t h e c o m p u t a t i o n a l m e t h o d i s c u r r e n t l y b e i n g a p p l i e d t o o t h e r c u r v e dr o of s t r u c t u r e s fo r w h i c h s o m e f u ll -s c al e a n d w i n d t u n n e l m e a s u r e m e n t s a r ea v a i l a b l e .

3 .3 T y p i c a l A r c h e d - r o o f B u i l d i n gT h e g e o m e t r ic v a r i a b l e s t h a t a r e r e l e v a n t to t h e w i n d l o a d i n g o f a r c h e d - r o o fb u i l d i n g s a r e t h e s p a n , t h e l e n g t h , t h e ri se , a n d t h e h e i g h t o f t h e e a v e s . M a n yd i f fe r e n t g e o m e t r i c a l c o n f i g u r a t i o n s h a v e b e e n e x a m i n e d b y t h e a u t h o r s . T h e

r e s u l t s f r o m a ty p i c a l c o n f i g u r a t i o n w i t h a r i s e / s p a n r a t i o o f 0 . 2 , a l e n g t h ,' ~ p a nr a t i o o f 1 .0 , a n d a n e a v e s h e i g h t / r i s e r a t i o o f 0 . 4 5 a r e p r e s e n t e d h e r e .F o r t h e c o m p u t a t i o n t h e J e n s e n N u m b e r i s 5 0 0. F o r a s t r u c t u r e h e i g h t o f 1 0m e t r e s , a J e n s e n N u m b e r o f 5 0 0 c o r r e s p o n d s to a s u r f a c e r o u g h n e s s l e n g t h o f

0 .0 2 m e t r e s . T h i s is e q u i v a l e n t to T e r r a i n C a t e g o r y 2 i n t h e A u s t r a l i a n S t a n d a r d[8].

Figures 4a, 4b a nd 4c s h o w the co mp ut ed external pressure coefficients n theb u i l d i ng f or a p p r o a c h w i n d a n g l e s of 4 5, 0 a n d 9 0 d e g r e e s r e sp e ct i ve l y f r o m t h en o r m a l t o t h e a x i s o f t h e a r c h. B e c a u s e o f s y m m e t r y , v a l u e s o n o n e h a l f o n l y a r es h o w n f or a p p r o a c h a n g l e s o f 0 a n d 9 0 .

F o r t h e 0 c a s e, p o s i t iv e p r e s s u r e c o e f f ic i e n ts o c c u r o n t h e w i n d w a r d w a l l a n dt h e w i n~ :l w ar d e d g e o f t h e r oo f, w i t h n e g a t i v e v a l u e s o v e r t h e r e s t o f t h es t r u ct u r e . T h e h i g h e s t m a g n i t u d e n e g a t iv e v a l u e s o cc u r j u s t u p w i n d o f t h e a p e xto the r ogf .


9/12

1637

a )

-0.31

+0.07

-0.72

-1.02-0.67

- 0 . 6 0

-0.04

-0.52

-0.11

-0.65

, ~ . + 0 . 2 2

-0.20

-0.63

, ~ i - + 0 - 13

-0.28

-0.57

-0.50

+0.01

-0.29

- 0 . 6 5

+ 0 . 010 . 5 0

, ,

0 . 6 1 /-0 .50

-0,35

-0.35-0 .29

b)

F i g u r e 4 . A r e a - a v e r a g e d e x t e r n a l p r e s s u r e c o e f f ic i e n ts f o r t h e t y p ic a l a r c h e d - r o o fb u i ld in g . A p p r o ac h w in d an g le s ar e : a ) 45 , b ) 0 , c ) 90 .


10/12

1638

+0.27

+0.40

-0.39

-1.13

-0.42

-0.29

-0.26-0.29

-0.29

-0.26

-0.33

c)

Figu re 4 (Cont .)Fo r an app roach wind ang le o f 45" , pos i t ive p ress u res on ly occu r nea r t hew i n d w a rd c o rn e r o f t h e b u i ld i n g . T h e n e g a t i v e p r e s s u re s o n t h e ro o f a n d w a l lsa re gen e ra l ly h ighe r t ha n those ob ta ined fo r t he 0 case , w i th pa r t i cu l a r ly h ighsuc t ions occu r r ing a long the w indw ard en d o f t he a rch roo f.E x c e p t f o r t h e w i n d w a rd w a l l , n e g a t i v e p r e s s u re s o c c u r e v e ry w h e re fo r t h eapproach w ind ang le o f 90 Ag a in ve ry h igh suc t ions occu r a long the w indw ard

e d g e o f t h e ro of, u n d e rn e a t h t h e s e p a ra t i n g - r e a t t a c h i n g flo w .In gene ra l , fo r bu i ld ing8 wi th l en g th / span ra t io s o f un i ty o r l e s s , t he co m pu tedva lues o f ex t e rn a l p re ssu re coe ff ic ien ts a re s ign i f i can t ly l ower in m ag n i tu de t ha nt h o s e o b t a i n e d f ro m t h e c u r r e n t A u s t r a l i a n S t a n d a rd , e s p e c ia l ly fo r t h e n e g a t i v ep res su re coe ff ic ien ts . A gree m en t is much be t t e r a t ve ry la rge l eng th / spa n ra t io s .


11/12

1639CONCLU S I O N S

Th e m e t h o d o f u s i n g c o m p u t e r m o d e l l in g in p l a c e o f w i n d t u n n e l m o d e l l in g inp re d i c t i n g w i n d p re s s u re s o n b u i l d i n g s u rf a c e s h a s b e e n s h o w n t o b e v a li d . Th ea c c u rac y o f t h e p r e d i c ti o n s o f p r e s s u re s o n t h e Te x a s Te c h b u i l d i n g i s v e ry g o od .Th e u s e o f c o m p u t e r m o d e l l i n g i n p ro v i d i n g p re s s u re c o ef fi ci en ts o n a v a r i e t y o fa r c h e d - ro o f b u i l d i n g s h a s l e d t o p r e d i c ti o n s t h a t c a n a n d h a v e b e e n u s e d i n t h edes ign o f such bu i ld ings .

W e h a v e s h o w n t h a t t h e m e t h o d s a p p l i e d i n b u i l d i n g c o d e s fo r a r c h e d - ro o fb u i l d i n g s a r e g oo d w h e n t h e l e n g t h / s p a n r a t i o o f t h e b u i l d i n g is l arg e . B u t t h e ya re v e ry c o n s e rv a t i v e w h e n t h e l e n g t h / s p a n r a t io o f t h e b u i l d i n g is s m a l l .

A C K N O W L E D G E M E N TT h e a u t h or s w i s h t o a c k n o w l e d g e t h e p e r mi s s i on o f S t r a rc h I n t e r n at i o n al L t d

t o p u b l i s h s o m e r e s u lt s o f t h e c o m p u t a t i o n s c a r r i e d o u t o n b e h a l f o f th a tC o m p a n y , a n d t h e c o o p er a t i on o f D r P e t e r K e y d u r i n g t h e pro ject .

R E F E R E N C E S1. Lev i tan , M .L. , Holm es, J .D. , M ehta , K.C. and V ann , W .P. 1989, 'F ie ld-

m eas ure d p re ssu res on the Texas Tech Bu i ld ing ' , 8 th Co lloq. Indus t . Aerodyn . ,A a c h e n , W .G e rm a n y , 4 -7 S e p t.2 . S u r r y , D. 19 89 , ' P r es s u r e m e a s u r e m e n t s o n t h e T e x a s T e ch B u i l d i n g - w i n dtunne l measu remen t s and compar i sons wi th fu l l sca l e ' , 8 th Co l loq . Indus t .Aerodyn . , Aach en , W .Germ any , 4 -7 Sep t .3 . Pa tankar , S .V . , 1980 , Num erical Heat Transfer an d F luid Flow, H e m i s p h e r e ,N e w Y o rk.4 . Pate rson , D.A. 1986, Computat ion of w ind f lows ov er three.dimensionalbuildings, P h D Th e s i s , U n i v e r s i t y o f Q u e e n s l a n d , B r i s b a n e .5. P a t e rs o n , D . A . a n d A p e lt , C . J . 1 9 8 9 , ' S i m u la t i o n o f w i n d f l o w s a r o u n d t h re e -

dim ens iona l buildings', l d g & E n v i r on . , 4, 39-50.6 . Gosm an , A .D. an d Ide r i ah , F . J .K . 1976, 'TEACH-T: A gen era l com pute rp ro g ra m fo r t w o -d i m e n s i o n a l , t u rb u l e n t , r e c i r c u l a t i n g f l o w s ' , D e p a r t m e n t o fM echan ica l Eng inee r ing , Im per i a l Co l l ege , London .


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7. Hinze, J.O., 1959, T u r b u l e n c e, a n I n t r o d u c t i o n t o i t r M e c h a n i s m a n d T h e o r y,McGraw-Hill, New York.

8. Standards Australia, 1989, S A A L o a d i n g C o d e, P a r t 2 W i n d l o a d s . AustralianSta nda rd ASl170.2 - 1989.

Computation of Wind Pressures on Low-rise Structures

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