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Wind loads on buildings
Schoemaker, R. L. A.; Wouters, I.
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NATIONAL RESE-ARCH COUNCIL OF CANADA
Technical T r a n s l a t i o n TT-488
Wind Loads on Buildings
.
(Windbelasting op ~ouwerken)
.
R. L. A. Schoemaker and I. Wouters.
Het Bouwbedri j f ,
9
(22) : 275-283, 1932.PREFACE
I n t h e course of t h e work of t h e Building Design S e c t i o n of t h i s Division, a s well a s work undertaken i n t h e r e v i s i o n of t h e National Build- i n g Code of Canada, i n f o r m a t i o n on wind l o a d s on b u i l d i n g s i s v e r y important. A s such l i t e r a t u r e i s r e l a t i v e l y s c a r c e , t h e Division welcomes t h e t r a n s l a t i o n of t h i s e x p l a n a t i o n of t h e t e n t a t i v e s t a n d a r d s h e e t
V789 i s s u e d by t h e Main O f f i c e of
t h e Dutch Standards Association.The Division of Building Research wishes t o thank M r . H. A. G. Nathan of t h e National Research Council L i b r a r y S t a f f f o r t r a n s l a t i n g t h i s a r t i c l e .
Ottawa, J u l y , 1954
Robert F. Legget, Director.
WIND LOADS ON BUILDINGS
E x p l a n a t i o n of t h e t e n t a t i v e s t a n d a r d s h e e t V 785% i s s u e d by t h e Raain O f f i c e of t h e Dutch S t a n d a r d s Association.
( c f . Het Bouwbedrijf, no, 1 8 , p. 230 ( 2 6 t h Aug- u s t 1932) and Bouwk, Weekblad k c h i t e c t u r a , no,
39,
p, 350, 2 4 t h September, 1932). I n t r o d u c t i o n
-
One of t h e t a s k s of Commission F ( f o r t h e S t a n d a r d i z a t i o n of T e c h n i c a l D a t a f o r B u i l d i n g ~ e g u l a t f o n s ) was t o d r a f t a new s t a n d a r d s h e e t w i t h r e g u l a t i o n s r e g a r d i n g t h e e f f e c t o f wind on b u i l d i n g s , S i n c e i n t h i s d r a f t (V 789) t h e m a t t e r i s t r e a t e d i n a manner which d i f f e r s from p r e v i o u s p r a c t i c eit
seems d e s i r a b l e t o throw some l i g h t on t h e u n d e r l y i n g p r i n c i p l e s o f t h e new r e g u l a t f o n s .The c a l c u l a t i o n of t h e f o r c e s and p r e s s u r e s ( f o r c e s p e r u n i t of a r e a ) e x e r t e d by moving a i r on s t a t i o n a r y o b j e c t s , f e e . , t h e f o r c e s and p r e s s u r e s r e l a t e d t o t h e c o n d i t i o n s o f flow a b o u t t h e o b j e c t , p r e s e n t s g r e a t d i f f i c u l t i e s , Even t h e l o a d c o n d i t i o n s f o r t h e s i m p l e c a s e , where a f l a t , c i r c u l a r p l a t e i s exposed normal t o t h e d i r e c t i o n o f a n a i r flow of c o n s t a n t v e l o c i t y , can only be determined experiment all^,
*
P o s s i b l e o b s e r v a t i o n s r e g a r d i n g t h i s e x p l a n a t i o n o f t h e t e n t a t i v e s t a n d a r d s h e e t a r e i n v i t e d by t h e C e n t r a l Normalisatie Bureau, Koningskade 23, f s - Gravenhage o r t h e S e c r e t a r i a a t van den Normal- i s a t i eraad, Bragaweg38,
Bandoen No 0. I.53 Fnclc'
+x The r e l a t i o n ; f o r c e
=
&
x d e n s i t yx
( v e l o c i t y ) ' i s a b s o l u t e l y c o r r e c t as i s known from t h e b a s i c p r i n c i p l e s o f dynamics, i f by s u r - f a c e i s meant t h e p r o f i l e of a f l u i d o r gas stream o f f i n i t e width which a t c o n s t a n t v e l o c i t y i s normal t o t h e d i r e c t i o n o f a s t a t i o n a r y , f l a t p l a t e , The s u r f a c e of t h e p l a t e i s much g r e a t e r t h a n t h e p r o f i l e of t h e stream s o t h a t t h e v e l o c i t y i n t h e i n i t i a l d i r e c t i o n vanishes. The c a s e o f a p l a t e i n a n a i r stream o f i n f i n i t e widthi s
e n t i r e l y d i f f e r e n t ,It i s evident from Fig, 1 t h a t with r e s p e c t t o t h e s t , i t i c
pressur* p o s i t i v e p e s u r e s form i n f r o n t of t h e p l a t e and negative p r e s s - u r e s form behind
it,
b
7
Of t h e s e p o s i t i v e and negative pressures only one p o s i t i v e pressure, i.e., t h a t a t t h e c e n t r e of t h e p l a t e , where t h e v e l o c i t y of t h e a i r becomes zero, can be determined without having t o r e s o r t t o experiments,
A s i s known from physics,* t h i s p o s i t i v e p r e s s u r e ( a l s o c a l l e d v e l o c i t y pressure) i s
fr
x d e n s i t y x (velocity)2.Since t h e weight of 1 cu,m,
(1
e u , f t , ) of a i r a t a temperature of 150C. ( 5 9 0 ~ ~ ) and an atmospheric pressure of 760mm.
(29.9") Hg i s 1,23kgm.
(. 07651 l b . )
-
a value which i n Holland may always be maintained with some approximation-
t h e d e n s i t y i s?eight i n km. of 1 cu.m, of a i r ( l b e / l
)
a c c e l e r a t i o n due t o g r a v i t y i nm,
per s e c O d 32.2 f t , sec,2=
LZ!
o r approximately1 kgmo sece2/n.4
9a
8 18
K 3 z O 2 ) 1b. x sec.2/ft0i]*
By s t a t i c pressure i s meant t h e p r e s s u r e which t h e a i r should have e x e r t e d on a p l a t e ( t h e p r e s s u r e s a t t h e f r o n t and a t t h e back of t h e p l a t e a r e i d e n t i c a l ) when t h e p l a t e moved a t t h e same v e l o c i t y a s t h e surrounding a i r and thus was a t r e s t ( s t a t i c ) with r e s p e c t t o t h e a i r ,This atmospheric pressure i s i n d i c a t e d by a barometer, which likewise changes p o s i t f o n a t t h e same v e l o c i t y a s the a i r , Suppose t h i s barometer i n d i c a t e s 760
mm,
(29.9") Hg then t h e s t a t i c pressure i s 0,76 x13-6
x 103
=
10336 kgm, per sq,mo(U,7 l b , per sq. i n ,
). This s t a t i c p r e s s u r e i s a l s o present a t t h e point of t h e so-called t t s t a t f c w opening of as t s t i o n a r y P i t o t tube ( c f , Fig, 6 ) .
*
This v e l o c i t y p r s s s u r e i s derived from B e r n o u l l i g s theorem, which s t a t e s t h a t a t steady flow:pressure -k
4
x d e n s i t yx
( v e l o c i t y ) 2 = constant. I n aerodynamic l i t e r a t u r e t h e following d e f i n i t i o n i s given: "The press- u r e head i s t h e p o t e n t f a r energy of motion of t h e u n i t ~ o l u m e . ' ~ Since t h e mass of t h e u n i t volumeis
t h e density, t h e values f n t h e t e x t a r e obtained d i r e c t l y , The point where t h e v e l o c i t y becomes zero and where t h e p o s i t i v e p r e s s u r e becomes equal t o t h e pressure head f s c a l l e d n s t a g n a t i o n p o i n t w ,I f t h e v e l o c i t y f s v i n m. per sec., (miles per hr. ) then t h e v e l o c i t y pressure i s
Next, t h e f o r c e exerted by t h e a i r stream on t h e c i r c u l a r p l a t e , shown i n Fig. 1, must be found as t h e r e s u l t a n t of t h e p o s i t i v e and nega- t i v e pressures, It i s simpler, of course, t o determine t h i s f o r c e
K
d i r e c t l y by measurement,
I f t h e value of t h i s force i s divided by t h e s u r f a c e of t h e p l a t e , then t h e q u a n t i t y which i s dencted i n t h e present r e g u l a t i o n s a s "wind p r e s s u r e H i s obtained*,
Moreover, experiments have shown t h a t f o r a square p l a t e t h e wind p r e s s u r e i s the same a s f o r a c i r c u l a r one, But f o r r e c t a n g u l a r p l a t e s t h e wind pressure i n c r e a s e s a s t h e s e p l a t e s becone more oblong, Further- more s i n c e "wind p r e s s u r e N must always be i n t e r p r e t e d a s t h e r e s u l t a n t of ~ o s i t i v e and negative pressures, t h e Dutch Standards Association
-
i n order t o prevent confusion-
p r e f e r s " v e l o c i t y pressure1' a s a u n i t , This i s a well-defined term and i s always used a s such i n t h e r e l e v a n t l i t e r a t u r e .I f , a s mentioned above, t h e v e l o c i t y pressure i s denoted by q i n kgm. per sq,m,, ( l b , per s q , f t . ) then t h e force K i n
kgm,
( l b , ) ex- e r t e d on a p l a t e having t h e s u r f a c ef
i n sq,m. ( s q o f t , ) i swhere c i s a c o e f f i c i e n t which depends on the shape of t h e p l a t e and which must be determined experimentally,
I n r e c e n t experiments with c i r c u l a r and square p l a t e s ( 2 )
it
was found t h a t c=1,16,
This shows t h a t t h e f r e q u e n t l y used value c=
1 0 2i s
a very good approximation and t h a t t h a l u e obtained by E i f f e l , L e o ,?3J
c
=
1,28,i s
t h e r e f o r e s l i g h t l y t o o high*
The municipal b u i l d i n g r e g u l a t i o n s of t h e City of Amsterdam provide f o r a wind pressure of 100 t o 200 kgm, p e r sq,m.,
(20.5 t o41,O
l b , pers q . f t , ) dependfng on t h e more o r l e s s exposed p o s i t i o n of t h e building. The Prussian r u l e s of 24th December,
1919,
s p e c i f y a wind pressure of75
t o 225 kgm, per sq.rn.
(15,4 t o 46.1 l b o per s q o f t o ) depending on shielding, geographical p o s i t i o n and height above t h e ground.For a r e c t a n g l e whose l e n g t h t o breadth r a t i o i s 581 t h e value f o r
c
obtained i n t h e above experiments was 1.20, FOP i n f i n i t e l y long r e c t - a n g l e s t h i s value becomes 1.96.I f a p l a t e i s exposed t o t h e a i r stream not a t a r i g h t angle (900) but a t an a n g l e o ( t h e n , t h e f r i c t i o n a l o n g t h e p l a t e , a s experiments have shown, may be neglected s o t h a t i n t h i s case a f o r c e Kq a c t i n g a t r i g h t a n g l e on t h e p l a t e may be used i n c a l c u l a t i o n s ,
The r e l a t i o n between t h i s f o r c e Kt,and t h e f o r c e
Kg0
e x e r t e d on t h e same p l a t e normal t o t h e d i r e c t i o n of t h e wind, L e o ,does not seem t o a g r e e w i t h a c t u a l c o n d i t i o n s a t a l l ,
h his
formula i s f r e q u e n t l y used and has even been included i n t h e P r u s s i a n r e g u l a t i o n s . ) For a square p l a t e and6 =
350 K35 i s appreciably g r e a t e r t h a n $0.I f t h e p l a t e P (Fig. 2b) i s n o t f r e e l y exposed t o t h e wind but i s p a r t of a system of planes (Figs, 2b, c, d, e, e t c , ) , t h e c o n d i t i o n s of flow a r e e n t i r e l y d i f f e r e n t , Therefore, t h e f o r c e and t h e pressure d i s - t r i b u t i o n on t h e p l a t e a l s o change and t h e use of one s i n g l e formula would t h u s give i n c o r r e c t r e s u l t s .
If t h e p l a t e i s replaced by a s o l i d , e,g, a cube standing on t h e ground, then a t t h e d i r e c t i o n of t h e wind a s shown i n Fig.
3
p o s i t i v e p r e s s u r e i s only e x e r t e d on t h e f a c e 1, 2,3,
4
and negative pressure on t h e back, s u r f a c e and s i d e s ,The occurrence of negative ppessure ( s u c t i o n ) i n b u i l d i n g s
i s
s u f f i c i e n t l y known from p r a c t i c e (roof covering being r a i s e d , wall covering forced outward). Although t h i s phenomenon
i s
f r e q u e n t l y d i s - cussed i n t h e l i t e r a t u r e ,it
has not y e t been taken i n t o account i n e x i s t i n g r e g u l a t i o n s , However, t h e Dutch Standards Association i s going t o t a k e t h i s problem i n t o account.2, Model T e s t s i n mind Tunnels
Of t h e o l d e r t e s t s with models of b u i l d i n g s E i f f e l f s t e s t s ( j ) should be e s p e c i a l l y mentione FOP o r e pecent model t e s t s t h e reader
i s
r e f e r r e d t o t h e l i t e r a t u r e t i ,4-117.
Naturally t h e r e s u l t s obtained from t h e s e t e s t s proved t o be val- uable m a t e r i a l , b u t a t t h e same time
it
was found necessary t o make a number of supplementary experiments, F a c i l i t i e s were extended through t h e c o u r t e s y of t h e Aerodynamics Laboratory, Delft, and, among o t h e r t h i n g s , t e s t s were conducted on t y p e s of r o o f s which had not been i n - v e s t i g a t e d previously. The e f f e c t of wind on groups of b u i l d i n g s was i n v e s t i g a t e d and t h e e f f e c t of s h i e l d i n g was a l s o s t u d i e d , These t e s t s , a s well a s t h e i n v e s t i g a t i o n s i n Amsterdam mentioned below, were per-F i g .
4
shows t h e shape o f t h e s e models, which were made of t h i n s h e e t i r o n , I n o r d e r t o conform w i t h t h e s e t - u p i n t h e wind t u n n e l t h e lower walls were n o t p u t up, Small h o l e s wepe c u t i n t h e f r o n t and back walls as w e l l as t h e r o o f s u r f a c e p fa F i g o5 )
c o r r e s p o n d i n g w i t h t u b e ss o l d e r e d t o t h e i n s i d e , Rubber h o s e s connected t o manometers were a t t a c h e d t o t h e t u b e s , as can be s e e n from F i g ,
6,
The p r e s s u r e d i f f e r e n c e , f e e , , t h e d i f f e r e n c e between t h e p r e s s u r e a t t h e c e n t r e of t h e c f r c u l a r o u t e r end of t h e P i t - o t t u b e (where t h e v e l - o c i t y becomes z e r o ) and t h e s t a t i c p r e s s u r e a t t h e It s t a t i c n opening a
(whose e x a c t p o s i t f on i s determined e m p i r i c a l l y ) i s measured by manometer
q.
T h i s p r e s s u r e d i f f e r e n c e i s t h e 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 , t h e v e l o c i t yi s
o b t a i n e d from t h i s measured d i f f e r e n t i a l p r e s s u r e , Thed i f f e r e n c e between t h e p r e s s u r e i n one of t h e h o l e s b and t h e s t a t i c p r e s s u r e i s measured by manometep
M2,
i n d i c a t i n g whether t h e p r e s s u r e a t t h e o u t e r w a l l of t h e model i s p o s i t i v e o r n e g a t i v e ,I n t h e t e s t s t h e wind v e l o c i t y was s e t a t 12m,per s e c , (27 m i l e s / h o u r ) a f t e r
it
had become a p n a r e n t t h a t t h e p r s s s u r e d i s t r i b u t i o ni s
n o t a p p r e c i - a b l y a f f e c t e d by t h e wind v e l o c i t y , The modeis were always mounted i n such a way t h a t t h e f a c e was exposed nom,al t o t h e wind,The p e s u l t s o f t h e model tests i n t h e D e l f t wind tunnel* a r e shown i n Figs. 7 t o 21, The numerals on t h e p r e s s u r e - d i s t r i b u t i o n c u r v e s r e - p r e s e n t t h e rounded-off c o e f f i c i e n t s by which t h e v e l o c i t y p r e s s u r e head must be m u l t i p l i e d i n o r d e r t o o b t a i n t h e p o s i t i v e p r e s s u r e (+) o r n e g a t i v e p r e s s u r e (-) a t t h e o u t e ~ w a l l o f t h e model,
I n c a s e s where t h e d i f f e r e n c e between t h e c o e f f i c i e n t s a t t h e p e r i - phery o f t h e model and t h o s e a t t h e c e n t r e was a p p r e c i a b l e , t h i s has been i n d i c a t e d i n t h e f i g u r e s by broken dash l i n e s a t t h e edge o f t h e p r e s s u r e - d i s t r i b u t i o n curve, Furthermore, t h e c o e f f i c i e n t s a r e mean v a l u e s ,
The g e n e r a l t r e n d o f t h e p o s i t i v e and n e g a t i v e D r e s s u r e s o b t a i n e d from t h e s e t e s t s a g r e e s wfth t h a t o f t h e r e s u l t s o b t a i n e d from o t h e r i n - v e s t i g a t i o n s . The n e g a t i v e p r e s s u r e s were marked i n t h e D e l f t model t e s t s as w e l l , The f a c t t h a t t h e y were h i g h e ~ t h a r ~ t h o s e found elsewhere must
small dimensions
sf
t h e wind t u n n e l , i , e o ,*
Measurements were a l s o c a r r i e d o u t a t t h e Power s u r f a c e o f t h e eaves o f t h e models B andD
andi t
was found t h a t t h e p o s i t i v e and n e g a t i v e p r e s s - u r e s a t t h e e a v e s and a t t h e a d j a c e n t v e r t i c a l walls were i d e n t i c a l , I n a d d i t i o n , a n i n v e s t i g a t i o n was made t o determine whetherit
would make a d i f f e r e n c e i f i n s t e a d o f smooth s h e e t i r o n a r o o f i n g m a t e r i a l w i t h a r o u g h e r s u r f a c e ( w a f f l e aluminium) was used, The r e s u l t wa.s n e g a t i v e .T e s t s were a l s o c a r r i e d o u t i n t h e Amsterdam wind t u n n e l t h ~ o u g h t h e c o u r t e s y of t h e R f j k s s t u d i e d i e n s t voor de l u c h t v a a r t , AmsterdaM, T h i s wind t u n n e l i s much l a r g e r t h a n that i n D e l f t , It i s c i r c u l a r and had a diameter of 1 6 0 em, The n e g a t i v e p r e s s u r e s were much lower h e r e as can be seen from F i g s , 22 t o 26,
A s mentioned above t h e t e s t s i n D e l f t and Amsterdam were i n t e n d e d t o supplement t h e d a t a o b t a i n e d from experimental work elsewhere, p r i n c i p - a l l y t o determine t h e e f f e c t of t y p e s of r o o f s which had n o t been previous- l y i n v e s t i g a t e d , Groups of r o o f s were a l s o i n v e s t i g a t e d i n o r d e r t o s t u d y
t h e s h i e l d i n g e f f e c t , It was c o n s i d e r e d s u f f i c i e n t t o mount t h e model o n l y i n such a way that t h e f a c e was always exposed normal t o t h e d i r e c t i o n of t h e windmc. T e s t s w i t h wind a t i n c l i n e d i n c i d e n c e were c a r r i e d o u t elsewhere on a l a r g e scale(2g11)e A d e s c r i p t i o n of t h e s e t e s t s has been o m i t t e d here, Fig, 27 c l e a r l y shows t h a t t h e p r e s s u r e d i s t r i b u t i o n v a r i e s
g r e a t l y i n t h i s case. T h i s f i g u r e was t a k e n from a paper by
Dr,
~ l a c h s b a r t ( l 2 ) ~ The a n g l e of i n c i d e n c e i n Fig, 27 i s 90, 45, and 0 degrees, r e s p e c t i v e l y .The d i s t r i b u t i o n of t h e p o s i t i v e and n e g a t i v e p r e s s u r e s i s g i v e n f o r s e c t i o n s I, I1 and 111. The high v a l u e f o r t h e n e g a t i v e c o e f f i c i e n t i s d i s c u s s e d i n S e c t i o n 9,
3,
Models and Actual ConditionsFrom t e s t s w i t h models of i d e n t i c a l shape b u t of d ' f f e r e n t s i z e
3
i iff el
mentions, among o t h e r s , a l i n e a r r a t i o 1 : 5 0 ) ( ~ ~ , 3i t
i s e v i d e n t t h a t t h e p r e s s u r e d i s t r i b u t i o n remains unchanged as l o n g a s t h e s u r f a c e s o f w a l l s and r o o f do n o t j o i n smoothly b u t do i n t e r s e c t sharpl-,I n v e s t i g a t i o n s by ~ m i t h ( l 3 ) w i t h l a r g e models ( 6 f e e t i n width) exposed t o n a t u r a l wind showed s i m f l a p r e s u l t s and t h e r e i s no i n d i c a t i o n t h a t t h i s i s d i f f e r e n t from a c t u a l b u i l d i n g s ,
S i n c e t h e same c o n s t a n t v e l o c i t y i s produced throughout t h e e n t f p e wind t u n n e l , t h e q u e s t i o n a r i s e s whether a r e d u c t i o n s h o u l d n o t be made
f o r l a r g e s u r f a c e s of w a l l s and r o o f s , F o r ,
i t
seems unreasonable t o assume simultaneously t h e same maximum v e l o c i t y throughout a l a r g e volumeof a i r o
*
I n t h i s wind t u n n e l t h e model was mounted on a s u p p o ~ t ,*
Therefore, no measurements were made w i t h r e s p e c t t o t h e d e c r e a s e i n wind v e l o c i t y r i g h t above t h e p l a t e on which t h e model was mounted( c f . Fig. 6 ) -
-)HHC F o r round o b j e c t s , such a s w i r e s , p o l e s , chimneys and gas t a n k s , t h e
flow, and t h u s t h e p r e s s u r e d i s t r i b u t i o n , change w i t h t h e diameter. T h i s i s d e s c r i b e d i n d e t a i l i n S e c t i o n 12.
T e s t s c a r r i e d o u t wh n t h e F o r t h Bridge was under c o n s t r u c t i o n p o i n t i n t h e same d i r e c t i o n f l 4 , l 5 ) . During a p e r i o d of
s i x
y e a r sit
became e v i d e n t h e r e t h a t t h e maximum wind p r e s s u r e on a n a r e a o f 0,14 sq,m. ( 1 , 5 s q , f t , ) was 200 kgm, p e r aq,m, (41 l b , p e r sq, f t , ) and on a n a d j a c e n t a r e a of 28 sq.m. (300 s q , f t . ) t h e maximum wind p r e s s u r e was 132 kgm, p e r
sq,m. (27 l b . p e r s q . f t , ) , I n g e n e r a l , t h e wind p r e s s u r e on a l a r g e a r e a was from 50 t o 70% ( i n a s f 1 c a s e 80%) o f t h a t on a n a r e a 200 times a s small. However, S t a n t o n
4f63
a d v i s e s a g a i n s t t h e a p p l i c a t i o n of a r e d u c t i o n ,However, a r e d u c t i o n has been allowed f o r i n S t a n d a r d Sheet V
789,
F o r , as a r u l e , i n l a r g e a r e a s o n l y one of t h e dimensions i s p a r t i c u l a r l y l a r g e ( l o n g w a l l s and r o o f s u r f a c e s , h i g h chimneys) s o t h a t f o r such
oblong s u r f a c e s t h e c o e f f i c i e n t c i n c r e a s e s ( c f . S e c t i o n I ) , T h i s i n c r e a s e was d i s r e g a r d e d i n t h e t e n t a t i v e s t a n d a r d s h e e t , compensating f o r t h e
above r e d u c t i o n ,
4.
V e l o c i t y P r e s s u r e sThe d a t a on maximum wind v e l o c i t i e s , from which t h e v e l o c i t y p r e s s -
&
(,00256 v2) were d e r i v e d , had been o b t a i n e d from t h e Kon. Ned..Z~:J?
l o g i s c h I n s t i t u u t ( ~ o y a l Dutch Meteorological ~ n s t i t u t e ) , De B i l t ZCf0177~ Of course, t h e s e v a l u e s v a r y w i t h t h e geographical p o s i t i o n ( d i s t a n c e from t h e c o a s t ) and w i t h t h e h e i g h t above t h e g ~ o u n d . The small map i n V 789 was prepared from t h e s e d a t a , FOP s i m p l i c i t y t h e c o u n t r y i s d i v i d e d i n t o t h r e e r e g i o n s , i n which t h e maximum v e l o c i t y p r e s s u r e s a r e s p e c i f i e d as 120 (24,6), PO0 (20,5), and 80 kgm. p e r sq,m,(16.4 l b , p e r s q , f t ,
)?
I n t h i s manner a h i g h e r value, f . e., 60 kgm. p e r sq,m, (12,3 l b , p e r s q . f t , ) t h a n would have been expected from t h e De B i l t d a t a i s recommended f o r t h e i n t e r i o r of t h e country, T h i s w i l l improve t h e s a f e t y , These v a l u e s c a n be maintained f o r a i r stratas near t h e ground, f o e , , up t o and i n c l u d i n g 1 5 m, (49 f t , ) above t h e ground, whereas, a c c o r d i n g t o t h e De B f l t d a t a , between 1 5 (49) and 35
m,
(115 f t , ) above t h e ground a n i n c r e a s e i n v e l o c i t y p r e s s u r e must be expected a t t h e r a t e of 2kgm,
p e r sq.m. p e r metre of h e i g h t (.125 l b , p e r s q , f t . p e r f o o t of h e i g h t ) , Hence a t a h e i g h t o f 35m,
(I15 f t , ) t h i s i n c r e a s e i s 4 0 kgm. p e r sq,m,(8,2 l b , p e r sq, f t , ), But above 35
m,
(115 f t o ) up t o 50 m o (164 f t o ) no f u r t h e r i n c p e a s e i s r e q u i r e d .*
The i n c r e a s e s i n t h e minimum v a l u e of 80 kgm, p e r sq,m. by 25 and 50 p e r c e n t a g r e e w i t h t h e r e s p e c t i v e pepcentages i n t h e P r u s s i a n r u l e s mentioned above,Since it i s s c a r c e l y r e q u i r e d t o know t h e v a l u e s f o r t h e v e l o c i t y p r e s s u r e a t h e i g h t s exceeding 50
m.
(164 f t , ) r e s p e c t i v e d a t a have been omitted i n t h e t e n t a t i v e s t a n d a r d s h e e t , I n such a c a s e f u r t h e r informa- t i o n should be r e q u e s t e d from t h e l d e t e o r o l o g i c a ~ In s t i t u t e , De B i l t ,F o r an Amsterdam c o n s t r u c t i o n of 50
rn,
(164 f t . ) h e i g h t (e,g. t h e chimney shown i n F i g , 28a) t h e v a l u e s f o r t h e v e l o c i t y p r e s s u r e i n Fig. 28b should apply, For s i m p l i c i t y t h e t e n t a t i v e s t a n d a r d s h e e t spec- i f i e s t h a t i n t h i s c a s e a mean v a l u e f o r t h e v e l o c i t y p r e s s u r e may be maintained from t h e bottom upward merely by i n c r e a s i n g t h e b a s i c v a l u e f o r t h e v e l o c i t y p r e s s w e by 1kgm.
p e r sq,m, f o r each metre by which t h e c o n s t r u c t i o n i s h l g b e r t h a n 1 5 a, The v e l o c i t y p r e s s u r e v a l u e s shown i n Fig. 28e were o b t a i n e d i n t h i s manner,Whenever a comparative c a l c u l a t i o n i s made f o r d i f f e r e n t h e i g h t s and S e c t i o n s I I B and I I C of t h e t e n t a t i v e s t a n d a r d s h e e t ape s p u l i e d , i d - e n t i c a l r e s u l t s a r e n o t obtained, of course, but t h e r e s u l t s show s a t i s - f a c t o r y agreement, However, t h e d i f f e r e n c e s a r e c o n s i d e r a b l e f o r v e r y g r e a t h e f g h t s , F o r example, S e c t i o n I I B s p e c i f i e s a v e l o c i t y p r e s s u r e of
l 4 O kgm.
p e r sq,m, (28,7 l b . p e r sq, f t , ) f o r a constructl.on i n Amsterdam, whereas S e c t i o n I I C a p p l i e d t o a chimney of PO0me
(328 f t , ) h e i g h t i nt h e same c i t y would g i v e
185
kgm, per sq,rn. (38 l b , per sq, f t , )But, a s was shown above, a t h e i g h t s exceeding 50 m. a f u r t h e r i n c r e a s e i n t h e l o c a l v e l o c i t y p r e s s u r e must be expected, Moreover, i n t h e c a s e under consSderation t h e high v a l u e of 185 kgm, p e r sq.m, (38 l b . p e r s q . f t , ) i n c l u d e s a s a f e t y f a c t o r as w e l l , High, s l e n d e r c o n s t r u c t i o n s , such a s chimneys, have c o n s i d e r a b l e n a t u r a l p e r i o d s of o s c i l l a t i o n . There- f o r e , t h e fntroduc%forn of a n impact f a c t o ~ should be considered, ( c f , f o l l - owing s e c t i o n ) .
5.
GustsThe q u e s t i o n whether o r not. t h e e f f e c t of g u s t s i s s m a l l e r t h a n tkst of a c o n s t a n t wind which h a s t h e same v e l o c i t y a s a g u s t on a t t a i n i n g i t s
m a x i m u m
f o r c e i s d e a l t w i t h below.A s i s known from t h e law of e l a s t i c i t y , t h e time d u r i n g which t h e f o r c e a c t s must be s h o r t and must spproxfmaLely correspond t o one-third of t h e b u i l d i n g v s n a t . w a l p e r i o d of o s c i l l a t i o n , *
*
The l o n g e s t p e r i o d of o s c i l l a t i o n recorded i n t h e l i t e r a t u r e i s 7.2 sec. f o r a sky serape^(E,
Ne
Record 1 9 February, 1931). FOP a chimney 70m.
According t o t h e De B i l t data
it
d e f i n i t e l y t a k e s a g u s t of wind two seconds t o a t t a i n i t s maximum v e l o c i t y , whichit
maintains f o r f i v e seconds, Thenit
decreases again i n t h e same manner, No reduction can be made f o r t h e f o r c e of t h e g u s t s because of t h e i r s h o r t duration, But,a s
suggested i n t h e previous section, t h e use of an impact f a c t o r seeins t o be more reasonable, p a r t i c u l a r l y i n view of t h i s r a p i d i n c r e a s e i n v e l o c i t y ,Fortunately, t h e r e has never been any evidence of successive g u s t s c o i n c i d i n g with t h e n a t u r a l period of o s c i l l a t i o n of buildings, This would be c r i t i c a l indeed,
S t i l l another c o n d i t i o n which l e a d s t o t h e increase i n f o r c e dur- i n g t h e a c c e l e r a t i o n of t h e wind should be noted, According t o t h e t h e o r y t h e e f f e c t of a c c e l e r a t i o n i s proportional t o t h e volume of t h e body
s t r u c k , whereas according t o t h e p r e s e n t authors the e f f e c t of v e l o c i t y i s wroportional t o t h e surface exposed t o t h e wind, However, f o r a mean value of t h e v e l o c i t y t h e a c c e l e r a t i o n i s a t i t s maximum; when t h e velo- c i t y a t t a i n s i t s maximum, t h e a c c e l e r a t i o n becomes zero.
Only f o r very l a r g e bodies do c o n d i t i o n s become more unfavourable a t mean v e l o c i t y than a t mximum v e l o c i t y ,
6.
CyclonesThe values f o r t h e v e l o c i t y p r e s s u r e s l i s t e d i n V
789
t a k e t h e s t r o n g e s t g a l e s i n t o aeeount*.The values obtained f o r cyclones may e a s i l y be considerabl higher and a v e l o c i t y pressure of 600 kgm. per sq.a. (123 i b . per sq.ft.S i s by no means a n exaggerated f i g u r e ,
1% i s economfeally unreasonable t o take such high values i n t o account since i n t h e Netherlands cyclones s c a r c e l y ever occur over a l i m i t e d area. The f a c t t h a t i n 1925 ( ~ o r c u l o ) and 1927 cyclones d i d occur i n two adjacent places must be considered a coincidence.
7.
I n c l i n a t i o n of Wind t o t h e HorizontalThe present Dutch r u l e s (e.ge t h e Amsterdam r u l e s ) s p e c i f y t h e i n c l i n a t i o n of t h e wind from 1 0 degrees above t o 1 0 degrees below h o r i - z o n t a l , However, t h e Prussfan r u l e s assume h o r i z o n t a l wind,
*
A v e l o c i t y of 29m,
per sec, ( f e e , , no 1 2 of t h e Beaufort s c a l e ) r e s u l t s i n a v e l o c i t y pressure of only&=
53 kgm, per sqemoThe model t e s t s i n t h e wind t u n n e l were conducted w i t h h o r i z o n t a l wind, but i n Amsterdam a t e s t was conducted with t h e wind i n c l i n e d above t h e h o r i z o n t a l ( c f . Fig.
26).
There i s very l i t t l e d i f f e r e n c e between Fig.26
and Fig. 25 (horf z o n t a l wind),Recently t h e r e g u l a t i o n s were amended s p e c i f y i n g t h a t t h e wind may d e v i a t e from t h e h o r i z o n t a l d i r e c t i o n . F o r g a f r e e h o r i z o n t a l roof should only be a f f e c t e d by t h e f r i c t i o n and t h e f o r c e on t h e small v e r t i c a l pro- j e c t i o n , both of which a r e n e g l i g i b l e ,
It i s evident from t e s t s t h a t when t h e a i r flow i s not e x a c t l y p a r a l l e l with a p l a t e b u t only d e v i a t e s a few degrees from t h i s d i r e c t i o n , t h e p l a t e i s subjected t o a considerable f o r c e , Since t h e wind can d e v i a t e above and below t h e h o r i z n t a l t h e new Dutch r e g u l a t i o n s
(VC
of V 789) s p e c i f y a c o e f f i c i e n t of 0,6 f o r f r e e h o r i z o n t a l roofs, With r e s p e c t t o a i r flows i n c l i n e d v e r t i c a l l y downwards ( s q u a l l s )-
no matter howunpleasant t h e y nay be when t h e y come i n c o n t a c t with t h e smoke i n chimneys, o r f o r a i r c r a f t
-
t h e r e i s no need f o r a n x i e t y because t h e v e l o c i t y i s t o o low t o have any e f f e c t on buildings,8, Wind with Respect t o t h e Comuass Bearinq
Although no d a t a regarding t h e c a r d i n a l p o i n t of t h e wind a r e given i n V 789
it
may be u s e f u l t o know i n s p e c i a l c a s e s (e,g, with a view t o f i x i n g t h e ~ o s i t i o n of a grandstand open a% one s i d e ) t h a t t h e v e l o c i t y p r e s s u r e s quoted by t h e M e t e o ~ o l o g i c a l I n s t i t u t e De B i l t apply t o winds from t h e following d i r e c t i o n s : South, South J e s t , Xes-c and North Vest. For winds from North o r South ?Gist 90% of t h e values f o r t h e v e l o c i t y p r e s s u r e w i l l s u f f i c e , and f o r winds from North East OP E a s t 70%,9 0
C o e f f i c i e n t sThe p o s i t i v e and negative p r e s s u r e s e x e r t e d on t h e s u r f a c e s of a b u i l d i n g a r e derived from t h e v e l o c i t y p r e s s u r e by multiplying t h e l a t t e r by t h e c o e f f i c i e n t s obtained experimentally, From t h i s
it
i s evident t h a t t h e s e c o e f f i c i e n t s vary a t d i f f e r e n t p o i n t s of t h e same s u r f a c e (roof o r wall). Moreover, t h e y depend on t h e angle a t whish t h e wind s t r i k e s t h e surface. I n p r a c t i c eit
i s d i f f i c u l t t o t a k e t h e s e d i f f e r e n t c o e f f i c i e n t s i n t o account and t h e r e f o r e a mean value must be used,The c o e f f i c i e n t s l f s t e d i n V 789 were determined a me n values from
7 9 7
a v a i l a b l e data, c h i e f l y obtained from t h e Gbttingen t e s t s
4
5
A s explained below, these c o e f f i c i e n t s d i f f e r from t h o s e obtained experimentally.
( i ) The c o e f f i c i e n t r e t a i n e d f o ~ t h e maximum p o s i t i v e pressure i s 0.8 times t h e v e l o c i t y prassure; a c t u a l l y t h e p o s i t i v e pressure i s equsl t o t h e v e l o c i t y pressure, However,
it
occurs only f o c a l l y , e.g, on wind- ows. These a r e capableaf
r e s i s t i n g pressure, of course,( i i ) The c o e f f i c i e n t f o r t h e maximum s u c t i o n i s 0,6 times t h e v e l - o c i t y pressure, Actually much g r e a t e r s u c t i o n s o c c w l o c a l l y , p a r t i c u l a r - l y a t t h e i n t e r s e c t i o n s of s u r f a c e s , a s
i s
evident from Fig, 27. However,t h e s e high l o c a l s u c t i o n s cannot be used a s a b a s i s fop c a l c u l a t i o n ; they may serve a s a guide f o r properly securing t h e roofing m a t e r i a l and wall covering a t t h e p o i n t s i n question, For
a
t y p i c a l xa p l e of t h e e f f e c t'il8T of s u c t i o n the r e a d e r i s r e f e r r e d t o t h e l i t e r a t u r e
( i i i ) Regarding r o o f s
it
i s a well-known f a c t t h a t p o s i t i v e pressure i s e x e r t e d on t h e lower s i d e of a roof and negative pressure on t h e upper part. However, t h e height of t h e roof from t h e ground a l s o has some e f f - e c t ( c f . Fig, 299, The p o s i t i v e pressurei s
shown i n Fig, 29a and t h e negative i n 29b, Thisi s
a l s o evident from t h e curved shape of t h e flow l i n e s , Owing t o t h e c e n t r i p e t a l f o r c e t h e pressure i s g r e a t e s t a t t h e convex side.It had f i r s t been intended t o i n c l u d e t h e s e d i f f e r e n c e s i n t h e t e n t a t i v e standard s h e e t , b u t t h i s would have made t h e standard sheet t o o complex and t o o d i f f i c u l t t o handle, Therefore, only mean rough values have been f i s t e d ,
PO, L n t e r i o r Pressure
in
BufldinagThe d i f f e r e n c e between t h e p r e s s u r e a t one point of t h e e x t e r n a l wall of t h e model and t h e s t a t i c p r e s s u r e i n t h e tunnel was obtained a s t h e r e s u l t of t h e model t e s t s (Fig, 6). This d i f f e r e n c e i s expressed by t h e v e l o c i t y pressure, m u l t i p l i e d by a c o e f f i c i e n t , with the s i g n
+
f o r p o s i t i v e pressure and-
f o r negative pressure, A s s t a t e d i nSection
3 ,
t h e same c o e f f i c i e n t s apply f o r a buildfng having a form s i m i l a r t o t h e model, However, it i s not t h e d i f f e r e n c e between t h e e x t e r n a l pressure and t h e s t a t i c pressure which must be known f o r prac- t i c a l purposes, but r a t h e r t h e d i f f e r e n c e between the e x t e r n a l and i n t e r - n a l pressures i n a building. I f t h i s i n t e r n a l pressurei s
lower than t h e s t a t i c pressure, o r i n o t h e r fiords, i f " t h e r e i s negative p r e s s u r e i n a building, then t h i s i s i n agreement with t h e assumption t h a t although t h e r e i s s t a t i c ppessure i n t h e b u i l d i n g t h e p o s i t i v e p r e s s u r e s a t t h e o u t s i d e a r e nevertheless g ~ e a t e r by a s much a s t h e pressure i n t h eb u i l d i n g i s lower than t h e s t a t i c p r e s s u r e , while t h e negative pressures a t t h e o u t s i d e a r e lower by a s much a s t h e pressure d i f f e r e n c e nentioned.
If t h e i n t e r i o r p r e s s u r e i n t h e b u i l d i n g should be g r e a t e r t h a n t h e s t a t i c p r e s s u r e , f o e . , g r e a t e r t h a n t h e p o s i t i v e p r e s s u r e i n t h e b u i l d - i n g , t h e same reasoning a p p l i e s .
However, t h e i n t e r n a l p r e s s u r e i s g e n e r a l l y n o t e q u a l t o t h e s t a t i c p r e s s u r e . Irming r and PBkkentved s t u d i e d t h i s problem and published a n i n t e r e s t i n g papery6)o They assume t h a t a b u i l d i n g always has some gaps even though windows and doors may be c l o s e d ; t h e j o i n t s a r e n o t t i g h t and t h e r o o f i s seldom completely t i g h t e i t h e r , Through t h e s e gaps a i r flows inwards and outwards, depending on whether t h e p r e s s u r e a t t h e o u t s i d e i s h i g h e r o r lower t h a n a t t h e i n s i d e . S i n c e under s t e a d y - s t s t e c o n d i t i o n s a s much a i r must flow inwards a s outwards and s i n c e t h e amount of a i r flow- i n g through a gap i s p r o p o r t i o n a l t o t h e s i z e of t h e gap and t h e r o o t of t h e p r e s s u r e d i f f e r e n c e , t h e i n t e r n a l p r e s s u r e may be o b t a i n e d by c a l c u l a - t i o n , i f t h e gaps a r e known.
I n t h e Danish t e s t s such c a l c u l a t i o n s were made f o r models i n which t h e gaps were uniformly d i s t r i b u t e d over a l l t h e a d j o i n i n g s u r f a c e s . The i n t e r n a l p r e s s u r e t h y s o b t a i n e d was cheeked by measurelnents and u s e f u l d a t a were obtained. I m i n g e r and mkkentved t h u s found t h a t t h e r e was n e g a t i v e p r e s s u r e i n a detached model i n which t h e gaps ( s m a l l h o l e s ) had been uniformly d i s t r i b u t e d over a l l t h e a d j o i n i n g s u r f a c e s , T h i s i s a l s o t h e c a s e i n a s i m i l a r b u i l d i n g under i d e n t i c a l c o n d i t i o n s .
If t h e gaps a r e n o t uniformly d i s t r i b u t e d , and i f , f o r example, a window o r door i s open, o r blown open, t h a t i s t o s a y , t h e r e a r e openings f o r v e n t i l a t i o n , c o n d i t i o n s change.
F o r t h e c o e f f i c i e n t s i n Subsection I11 of V 789 s t a t i c p r e s s u r e i n t h e b u i l d f n g has been assumed, T h i s i s considered a good approximation.
However, i f a gap becomes s o l a r g e t h a t
it
a f f e c t s t h e i n t e r i o r p r e s s u r e a sit
does i n p a r t i a l l y open sheds,it
i s a d v i s a b l e t o take t h e v a r i a t i o n from t h e i n t e r i o r and s t a t i c p r e s s u r e s i n t o account (cf.S e c t i o n
N
ofV
789).11. S h i e l d i n g
The c o e f f i c i e n t s a p p l y t o i s o l a t e d buildings. The s h i e l d i n g e f f e c t was i n v e s t i g a t e d a t D e l f t . A t e s t was made on a model e p l a c e d a t v a r i o u s d i s t a n c e s from a model g ( ~ i g . 30). I n Fig, 3 1 t h e r e s u l t s obtained a t t h e c e n t r e of t h e model have been p l o t t e d f o r d i s t a n c e s of 20, 40 and 8 0 cm. and f o r i n f i n i t e d i s t a n c e (no s h i e l d i n g ) a s well. I n o r d e r t o a v o i d crowding t h e diagram o n l y t h e c o e f f i c i e n t s f o r m h a v e been e n t e r e d ,
It should be pointed o u t t h a t a t a d i s t a n c e of 20 em. negative
p r e s s u r e i s exerted on t h e face. got u n t i l t h e d i s t a n c e i s 40 cm, i s posi- t i v e p r e s s u r e exepted, A t t h e l e e s i d e d i s t a n c e does not a p p r e c i a b l y a f f e c t t h e negative p r e s s u r e ,
I f t h e roof i s s l a n t i n g a t t h e l e e s i d e , then a l l t h e p r e s s u r e curves coincide, while a t t h e back w a l l t h e p r e s s u r e curves f o r 20, 40 and 80 cm, coincide,
From Figs, 1 5 up t o and i n c l u d i n g 21, 25 and 26 t h e e f f e c t of s h i e l d i n g on t h e roof a l s o i s evident,
A l l t h e s e t e s t s were made with t h e wind normal t o t h e f a c e i n t h e d i r e c t i o n ,
we
If t h e d i re c t i o n of t h e wind i s w l , t h e n s e c t i o n a ( ~ i g , 30) can no longer be considered shielded, of course, No d e f i n i t i o n of s h i e l d - i n g could be given i n t h e r e g u l a t i o n s , However, t h i s f a c t o r should not be d i s r e g a r d e d a l t o g e t h e r and each c a s e must be l e f t t o t h e d i s c r e t i o n of t h e a u t h o r i t i e s concerned.12, C y l i n d r i c a l S t r u c t u r e s
A s mentioned above, f o r angular o b j e c t s of v a r i o u s s i z e s t h e co- e f f i c i e n t c remains unchanged, provided t h e s e o b j e c t s have t h e same shape, even i f t h e wind v e l o c i t y changes,
Conditions a r e d i f f e r e n t f o r round o b j e c t s whose diameter may d i f f e r g r e a t l y and whose f o r n v a r i e s from wires a m i l l i m e t r e s i n diameter t o gas t a n k s s e v e r a l t e n s of metres i n diameter,
The general t r e r d of t h e p o s i t i v e and negative p r e s s u r e s i s always a s shown i n Fig, 32 (vihere a p o s i t i v e p r e s s u r e
=
v e l o c i t y p r e s s u r e a t t h e c e n t r e of t h e viindlvard s i d e ] , However, t h e values of t h e p o s i t i v e and n e g a t i v e p r e s s u r e s and t h e p o s i t i o n of t h e p o i n t 0 v a r y g r e a t l y and t h u s t h e r e s u l t a n t f o r c e e x e r t e d on t h e c y l i n d e r v a r i e s a l s o ,T h i s f o r c e
may
a g a i n be denoted a s c,q,
f , , where f i s assumed t o be t h e plane of t h e p r o j e c t i o n , t h u s diameter x length.A paper t i t l e d IVinddruk op c y l i n d e r s N (Wind p r e s s u r e on c y l i n d e r s ) by Engineer Professor
DP,
F, KO
The van I t e r s o H c o n t a i n s a diagram( ~ i g ,
3 )
i n which, ont
e sis of t e s t s conducted i n GBttingen withi n -
f i n i t e l y long c y l i n d e r s f 1 9 r t h e value f o r e has been p l o t t e d a s a f u n c t i o n
of t h e ReynoldsB number,
The
l a t t e r means v e l o c i t y x diameter,
kinematic v i s c o s i t yo r f o r a i r , approximately 7 x v e l o c i t y
x
diameter,if
t h e v e l o c i t y i sex-
pressed i n cm, per second and t h e diameter En em,
A t a v e l o c i t y of 40
m.,
o r 4,000 em,, pep second ( v e l o c i t y p r e s s u r e 100 kg-. p e r sq,m, ) t h e Reynolds number t h u si s
28,000x
diameter ( e x p r e s s e d i n crn. ).A t t h i s wind v e l o c f t y a Reynolds number of 105 corresponds t o a diameter of 100,000 =
3,6
cm. and f o r t h i s a c o e f f i c i e n t e o f 1.2 a p p l i e s .28,000
I n t h e d i a g ~ a r n r e f e r r e d t o t h i s c o e f f i c i e n t c
=
1 , 2 f i r s t remains unchanged a s t h e d i a m e t e r i n c r e a . s e s and drops r a p i d l y t o 0,3 when t h e d i a - meter i s 18 em, But t h e c o e f f i c i e n t s l i g h t l y i n c r e a s e s a g a i n a s t h e d i a - meter i n c r e a s e s up t o36
cm. The Gbttingen t e s t s d i d n o t go beyond t h i s .I n
o t h e r t e s t s t h e maximum v a l u e obtained f o r c a l s o was 1.2*,T h e r e f o r e , this v a l u e should be r e t a i n e d f o r wire, F o r c y E i d r i c a l o b j e c t s w i t h s t i l l l a r g e r d i a m e t e r s t h e c o e f f i c i e n t s sometimes d i f f e r completely
(lower o r h i g h e r ) from t h o s e based on t h e GBttingen t e s t s , and t h e c o n d i t i o n o f t h e flow (more OP l e s s uniform) and t h e degree of roughness of t h e
sur-
f a c e seems t o have a m e a t e f f e c t .
F o r a n o r d i n a r chimney exposed t o n a t u r a l wind t h e v a l u e f o r
a
c
ob- t a i n e d i n washington( 0 ) was 0.67. The f a c t t h a t up t o t h e second decimal t h i s f i g u r e a g r e e s w i t h a f i g u r e from t h e s i n e squared r u l e must be c o n s i d e r - ed p u r e l y i n c i d e n t a l . T h i s f i g u r e (rounded o f f t o 0,7) h a s s i n c e proved i t s u s e f u l n e s s i n p r a c t i c e and has t h e r e f o r e been r e t a i n e d ,F o r s t i l l highep s t r u c t u r e s o f c i r c u l a r p r o f i l e , e,g. gas t a n k s , t h e e x i s t i n g p r a c t i c e may be followed, i f d a t a a r e n o t a v a i l a b l e .
F o r curved r o o f s t h e coefficients of V
789
may be r e t a i n e d ,13,
P o i n t by P o i n t E x p l a n a t i o n of V782
Although on t h e whole r e f e r e n c e can be made t o t h e preceding pages a nunber of d e t a i l s a r e e x p l a i n e d below,
I. The word " s i m u l t a n e o u s l y ~ has been i n s e r t e d i n t h e t e x t i n o r d e r t o p r e v e n t m i s i n t e p p r e t a t i o n , f e e . , t h a t p o s i t i v e p r e s s u r e i s e x e r t e d when t h e wind comes from one d i p e c t i o n and n e g a t i v e p r e s s u r e when it comes from another.
11, See S e c t i o n
4.
*
For s t i l l s m a l l e ~ d i a m e t e r s t h e c o e f f i c i e n t i n c r e a s e s a p p r e c i a b l y a f t e r dropping f o p a s h o r t time, However, t h e s e small diameters a r e unimportant f o r t h e p r e s e n t purpose,111.
A.
B. C, A s s t a t e d above, t h i s i s a case of nean values here. Henceit
i s not claimed t h a t t h e y a r e a b s o l u t e l y c o r r e c t . Nor i s t h i s required, p a r t i c u l a r l y i n view of t h e wind l o a d under considera- t i o n which cannot be a c c u r a t e l y defined l i k e o t h e r loads,I n order t o o b t a i n in. a given c a s e t h e exact p r e s s u r e d i s t r i b u t i o n f o r various d i r e c t i o n s of t h e wind, t h e r e l e v a n t l i t e ~ a t u r e should be con- s u l t e d f o r cases which agree s a t i s f a c t o r i l y with the case i n question. Wind tunnel t e s t s should then s e t t l e t h e questicn. However, t h i s means t h a t i n most c a s e s t h e c o e f f i c i e n t s ~ r o v i d e a s a t i s f a c t o r y b a s i s f o r c a l - c u l a t i o n . The i n c l u s i o n of negative c o e f f i c i e n t s ( s u c t i o n ) i n t h e t e n t a - t i v e standard s h e e t i s nrob:ibly t h e most r a d i c a l improvement with r e s p e c t t o e x i s t i n g r e g u l a t i o n s .
The f a c t t h a t highep p o s i t i v e pressures ( c o e f f i c i e n t up t o 1.0) and much higher negative pressures nay occur l o c a l l y has been s t a t e d above.
111.
D,
The c o e f f i c i e n t s r e f e r r e d t o i n 12, B and C a r e intended f o r s p e c i a l j o i s t s . For wind bracfngs and anchorages of end gables alower mean value w i l l s u f f i c e , Therefore, a reduction of 10% i s admiss- i b l e . This i s
a n
approximate value obtained from a v a i l a b l e data.Observation 1 (belonging t o 111): This observation, a s well a s observations
3,
4,
5,
6 and7,
i s merely intended as a n i l l u s t r a t i o n .Observation 2 (belongi ng t o 111) ; This note was necessary be-
cause i n case of l i t e r a l a p p l i c a t i o n of t h e r u l e e i t h e r t o o low a nega- t i v e pressure ao111.d be a p p l i e d t o a low roof o r none a t a l l . In Fig, 33 t h e flow curve i n d i c a t e s t h a t f n the hatched region t h e p o s i t i v e press- ure exerted on t h e roof i s equal t o t h a t on t h e high viall.
TV. See S e c t i ~ n 10: S t r i c t l y speaking, f o r sheds (e.g. hangars) a p o s i t i v e pressure of +O,8 and a negative pressure of -0.6 should have been a s s m e d . However, +0,6 and -0.4, respec
t i
vely, have been r e t a i n e d because t h e s i d e s whfch a r e not open a r e p r a c t i c a l l y never q u i t e t i g h t .V. The c a s e of overhanging r o o f s (double c a n t i l e v e r construc- t i o n ) i s somewhat s i m i l a r t o tha.t of a e r o f o i l s a s long a s t h e p i t c h i s low. I n case a of Fig.
34
an upward f o r c e ( l i f t f o r a i r c r a f t ) i s e x e r t e d which i n case b becomes a downward f o r c e , of course.I n case c ( c f . Section 7 ) , i f t h e wind i s h o r i z o n t a l and i f t h e f r i c t i o n and t h e Force on t h e small v e ~ . t l c a l p r o j e c t i o n a r e neglected, no f o r c e a t a l l should be exerted but a f o r c e w i l l be exerted i f t h e i n - c l i n a t i o n of t h e nind changes s l i g h t l y (e.g.
5
degrees). Cases a and b a r e s e n s i t i v e t o such changes i n t h e i n c l i n a t i o n of t h e wind and s i n c e t h e s e changes occur a t t h e s i d e of t h e h o ~ i z o n t a l exposed t o t h e windi t
i s s p e c i f i e d t h a t t h e c a l c u l a t i o n be c a r r i e d out i n two d i f f e r e n tA s t o t h e q u e s t i o n w h e t b r t h e method of e a l e u l a t i o n i n V. A , l e , i s redundant, it should be p o i n t e d o u t t h a t where t h e l o a d has been reacved from t h e p o s t this method nay be r e q u i r e d i n order t o t a k e i n t o account a n upward f o r c e a t t h e anchorage of t h e p o s t . Furthermore, t h i s method i s a l s o
d e s i r a b l e s i n c e S t i s e s s e n t i a l t o a t t a ~ h t h e r o o f i n g m a t e r i s l p r o p e r l y , p a r t i c u l a r l y i n view of t h e c o n s f d e ~ a b l y h i g h e r s u c t i o n s which may occur l o c a l l y .
It i s p o i n t e d o u t that t h e l i m i t i n g c a s e of V, A, B and C, i . e . , a h o r i z o n t a l overhanging r o o f , r e q u i r e s i d e n t i c a l p o s i t i v e and n e g a t i v e p r e s s u r e s ( 0 , 6 ) a t t h e upper s i d e , I n t h i s e a s e no h o r i z o n t a l f o r c e has been s t i p u l a t e d , Sueh a f o ~ e e may a c t u a l l y OCCLW, of c o u r s e , b u t
it
w i l lbe small. I n g e n e r a l , a b u i l d i n g s h o u l d be capable of w i t h s t a n d i n g t h i s f o r c e and
it
need n o t be t a k e n i n t o account,V I , For detached w a l l s o r s u r f a c e s ( e , g o b i l l b o a r d s ) a v a l u e of
1.4
f o r t h e c o e f f i c i e n t i s c o n s i d e r e d s a t i s f a c t o r y , FOP a square board normal t o t h e viind a a o e f f i e i e n t of 1.,6 should s u f f i c e , u n l e s s t h e co- e f f i c i e n t i s i n c r e a s e d f o r wind a t o b l i q u e i n c i d e n c e ( e f . S e c t i o n I),V I I . The r e g u l a t i o n f o r framework f e b s e d on data i n t h e l i t e r a - t u r e (21,22)o S t r i c t l y speaking, t h e c o e f f i c i e n t f o r g i r d e r s a t t h e wind- ward s i d e should be g r e a t e r t h a n t h a t f o r g i r d e r s a t t h e Tee s i d e , b u t f o r
s i m p l i c i t y o n l y one mean coeffic.Sent has been r e t a i n e d ,
V I I I , (See S e c t i o n 1 2 ) : No c o e f f i c i e n t has been l i s t e d f o r r e c t - a n g u l a r chimneys, which a r e r a r e anywa.yo The c o e f f i c i e n t should be
I.&*.
I X . The reduction p e r m i t t e d f o r s h i e l d e d p o s i t i o n s h a s been e s t i m a t e d . S i n c e t h e c o e f f i c i e n t s
under B
a r e reduced t h i s r e d u c t i o n a l s o i s a p p l i c a b l e t o a l l t h e c o e f f i c i e n t s of s u b s e c t i o n I11 which a r e a p p l i e d i n s u b s e e t i o n s I V andV,
X,
Observation l. It h a s been e s t a b l i s h e d by t h e Meteorological I n s t i t u t e , De B i l t , t h a t wind l o a d s and snow l o a d s need n o t be t a k e n i n t o a c c o u n t simultaneously, It i s thought t h a t a t t e m p e r a t u r e s a t whichit
snows and a t which i c e i s l i k e l y t o form t h e r e a r e no s e v e r e storms,
X.
Observation 2, T h i s c l a u s e has been adopted from t h e pre- l i m i n a r y r u l e s of t h e t e n t a t i v e s t a n d a r d s h e e t f o r s t e e l b r i d g e s (VOSB 1932 o f t h e committee ~ 1 s t ) ~ The elatrse i s Intended t o t a k e i n t o a c c o u n t t h e f a c t t h a t t h e a c t u a l dead weight of a b r l d g e may d i f f e r from t h a t assumed i n t h e c a Z c u l a t i o n , Then t h e u n p l e a s a n t s i t u a t i o n may a r i s e t h a t p r e s s u r e forms i n t h e g i r d e r s of t h e franeviork which had been cal- c u l a t e d f o r t e n s f on,*
For t h e c a l c u l a t i o n of chimneys t h e r e a d e r i s r e f e r r e d t o D I N S h e e t 1056 and t o t h e paper byW,
van Teylingen i n de Ingenfeur, no, 21, 1927.14.
NotesF i n a l l y t h e r e a d e r ' s a t t e n t i o n i s drawn t o t h e f o l l o w i n g n o t e s : (1) The P r u s s i a n r e g u l a t i o n s c o n t a i n t h e f o l l o w i n g passage: "Buildings which a r e s u f f i c i e n t l y s t i f f e n e d by walls and c e i l i n g s need n o t be examined f o r wind p r e s s u r e a s a r u l e , l t
No such c l a u s e was i n c l u d e d i n V
789
because t h i s s t a n d a r d s h e e ti s
i n t e n d e d merely t o g i v e d a t a f o r t h e magnitude of t h e f o r c e s o c c u r r i n g and when t h e s e d a t a a r e a p n l i e di t
becomes immediately c l e a r whether OPn o t a case r e q u i r e s calcul_ation.
The q u e s t i o n a s t o what e x t e n t t h e dependence of t h e wind on t h e dead weight o f t h e m a t e r i a l (e. g. c o n c r e t e o r s t e e l ) s h o u l d be con- s i d e r e d has been d i s r e g a r d e d s i n c e
i t
i s always d e s i r a b l e t o t a k e t h e e f f e c t of wind i n t o account.( 2 ) I n t h e c a s e of n e g a t i v e p r e s s u r e ( o r s u c t i o n ) on r o o f s i n - v o l v i n g upward f o r c e s , t h e s e may exceed t h e dead weight and a l o a d i s t h u s a p p l i e d on a main g i r d e r i n t h e manner shown i n F i g ,
35.
T h i s i s d i s t i n c t from t h e u s u a l assumution o f continuous downward f o r c e s ,While in t h e l a t t e r assumption t h e r e i s e x c l u s i v e l y t e n s i o n i n t h e bottom boom member o f t h e main g i r d e r , t h e upward f o r c e s may b r i n g a b o u t p r e s s u r e i n t h e members.
If t h e members have n o t been c a l c u l a t e d f o r p r e s s u r e , t h e compressive f o r c e must be taken i n t o a c c o u n t i n some o t h e r way, e.g. by v e r t i c a l r o d s which r e s i s t bending. However, t h i s i s r e q u i r e d i n p r i n c i p l e i n o r d e r t o t a k e i n t o account t h e compressive f o r c e s p r e s e n t i n t h e bottom bocm members ( a s w e l l as i n t h e d i a g o n a l and v e r t i c a l r o d s , which me s u c h i n t h e same p o s i t i o n i n t h i s c a s e ) .
Since V
789
i s confined t o d a t a on t h e magnitude of t h e f o r c e s t h e r e i s no need t o pay a t t e n t i o n t o cornpressive f o r c e s p o s s i b l y occur- r i n g i n t h e lower boom members, e t c ,( 3 )
For a e o e f f i c i e n t of0.6
uniformly a p p l y i n g t o t h e e n t i r e roof t h e f o r c e s a t t h e c e n t r e d i a g o n a l ( ~ i g ,35)
become z e r o because t h e dead weight i s assumed t o be a uniform l o a d , However, t h e assump- t i o n of a uniform e o e f f i c i e n t over t h e e n t i r e roof i s o n l y a rough one, and a t t h e windward s i d e t h e s u c t i o n s a c t u a l l y have h i g h e r values. Therefore, t h e f o r c e s a t t h e diagonal i n q u e s t i o n a r e n o t zero.However, when a t r u s s i s designed t h e u s e o f l i g h t - w e i g h t and weak s e c t i o n s a r e avoided, T h e r e f o r e , t h e s e members s h o u l d be s u f f i c i e n t - l y s t r o n g t o w i t h s t a n d f o r c e s .
( 4 )
A t t e n t i o n s h o u l d a l s o be p a i d t o o s c i l l a t i o n s a t c o n s t a n t v e l - o c i t y normal t o t h e d i r e c t i o n of t h e win& ( c f , American C i v i l E n g i n e e r s Bndbook. iderriman, 1930. p. 295).Model t e s t s w i t h c y l i n d e r s showed t h a t v o r t i c e s (SD-called Karmants v o r t i c e s ) a r e r e l e a s e d a t t h e l e e s i d e , a l t e r n a t e l y a t t h e l e f t - h a n d a n d r i g h t - h a n d s i d e s and t h a t t h e p e r i o d of r e l e a s e of two v o r t i c e s a t t h e same s i d e was a p p r o x i m a t e l y 0.2
8
sec. (v=
v e l o c i t y i n m. p e r sec. a n d d=
d i a m e t e r i n m. ).
S i n c e t h i s n e r i o d i s t h e same as t h a t of t h e n a t u r a l o s c i l l a t i o n , c o n s i d e r a b l e v i b r a t i o n s , which r e q u i r e s p e c i a l p r e c a u t i o n s , may be brought about.
w It i s a well-known phenomenon t h a t when a s t i c k i s p l a c e d p a r a l l e l t o t h e d i r e c t i o n o f flow of w a t e r t h e s t i c k w i l l o s c i l l a t e normal t o t h e d i r e c t i o n o f t h e flow.
References
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z u r
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16,
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