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Dynamic wind loads and cladding design
Allen, D. E.; Dalgliesh, W. A.
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Dynamic Wind Loads and Cladding Design
Surcharge dynarnique due au vent et calcul du parement
Dynarnische Windbelastung und Bemessung von Gebaudeverkleidungen
D.E. ALLEN W.A. DALGLIESH
Division of Building Research National Research Council of Canada
Ottawa, Canada
W i n d s t o r m d a m a g e t o cladding ( e x t e r i o r s u r f a c e s ) of buildings often r e - s u l t s in c o n s i d e r a b l e e c o n o m i c l o s s and s o m e t i m e s p e r s o n a l i n j u r y . The s a m e c a r e should t h e r e f o r e be given t o cladding design and r e s e a r c h a s is given t o t h e s t r u c t u r e . T h i s d i s c u s s i o n looks a t two a s p e c t s of t h e d e s i g n of cladding t o r e s i s t wind loads: ( a ) how behaviour u n d e r d y n a m i c wind l o a d s a f f e c t s r e -
s i s t a n c e of both m e t a l (ductile) and g l a s s ( b r i t t l e ) p a n e l s ; (b) w h a t r i s k s of cladding f a i l u r e a r e i m p l i c i t i n N o r t h A m e r i c a n d e s i g n r u l e s . The p r o b l e m of d e t e r m i n i n g a c t u a l wind l o a d s on cladding, the g r e a t e s t unknown in t h e design p r o b l e m , i s not d i s c u s s e d .
D e s i e n of Claddine t o R e s i s t Wind L o a d s
B e c a u s e t u r b u l e n t wind i s a d y n a m i c loading, r e c e n t design a p p r o a c h e s f o r s t r u c t u r e s a r e b a s e d on a d y n a m i c component t h a t t a k e s into a c c o u n t wind t u r b u l e n c e , s i z e of building ( a v e r a g i n g e f f e c t on t u r b u l e n c e ) , a n d d y n a m i c amplification. A s i m i l a r approach i s suitable f o r cladding design ( F i g . 1)
w h e r e R i s t h e d e s i g n r e s i s t a n c e , F S t h e d e s i g n s a f e t y f a c t o r , wo t h e design wind p r e s s u r e , iG t h e m e a n wind p r e s s u r e equal t o t h e m e a n v e l o c i t y p r e s s u r e
4
t i r n e s the s h a p e f a c t o r C p , Cg the g u s t f a c t o r , IT t h e r m s ( r o o t m e a ns q u a r e ) i n t e n s i t y of wind p r e s s u r e t u r b u l e n c e and g a p e a k f a c t o r r e l a t i n g p e a k wind p r e s s u r e t o r m s i n t e n s i t y of t u r b u l e n c e . F o r a s t a t i o n a r y G a u s s i a n l o a d -
ing, the expected p e a k f a c t o r
g
i s given i n Table I, b a s e d on t h e t h e o r y given in Ref. ( 1 ) a n d a s s u m i n g t h e r e a r e 0 . 3 p e a k s p e r s e c o n d , a f i g u r e obtained f r o m f u l l - s c a l e p r e s s u r e m e a s u r e m e n t s 2 .When IT i s z e r o t h e loading i s s t a t i c a n d the r e s i s t a n c e R c o r r e s p o n d s t o t h a t f o r a s t a t i c a l l y loaded panel. Since t h e effect of d y n a m i c l o a d s on r e -
s i s t a n c e i s r e l a t e d only t o t h e t u r b u l e n t component of t h e wind, i t i s a p p r o p r i a t e t o c o n s i d e r t h i s and o t h e r s t r u c t u r a l e f f e c t s , s u c h a s d y n a m i c amplification,
280 V - DYNAMIC WIND LOADS AND CLADDING DESIGN
by a modification of the peak f a c t o r g , v l N D
in Eq. ( I ) , i. e. by multiplying g by a w m
"gust m a t e r i a l " f a c t o r , km, W o
C = 1
+
km. g o I Tg ( 2 )
The "gust m a t e r i a l " f a c t o r ,
b,
depends both on the m a t e r i a l and s t r u c t u r a l behaviour and on the nature of dynarnic loading; i t will be shown t h a t f o r cladding t h i s f a c t o r i s n e a r l y equal t o 1.The n a t u r a l frequency of m e t a l
and g l a s s panels v a r i e s f r o m about F i g u r e 1: Wind P r e s s u r e R e p r e s e n t a -
5 t o 50 Hz. In m o s t c a s e s t h i s f r e - tion f o r Cladding Design
quency i s considerably higher than
significant wind turbulence frequencies. T h u s during e l a s t i c deformations a
panel can be r e p r e s e n t e d a s a statically loaded s t r u c t u r e and dynamic ampli- f ication can be neglected. Only f o r unusual, high-f requency wind turbulence c r e a t e d locally by building c o r n e r s 4 o r by s u r f a c e i r r e g u l a r i t i e s , s u c h a s mullions, i s dynarnic magnification likely t o become significant.
I M e t a l Cladding
I
T A B L E I
-
P E A K FACTOR AND GUSTI M e t a l panels fail by yielding, FACTORS FOR GLASS
by buckling, o r by f r a c t u r e of the connections. Two a s p e c t s of m e t a l behaviour a r e d i s c u s s e d in t h i s paper: r a t e effect, i. e. change of yield strength with r a t e of loading, and the effect of p l a s - t i c deformation. Metal fatigue i s neglected in t h i s study.
According t o information on r a t e effect f o r steel, a t e n fold i n c r e a s e in r a t e of loading i n -
c r e a s e s the yield s t r e s s ,
uy,
by approximately 2 k s i . Since the s t a n d a r d ASTM t e s t i n g r a t e c o r r e s p o n d s approximately t o 10 k s i p e r second, t h e r a t e effect can be approximated by-
= 2 log(j;)
Y O (3) Duration of Load one h r . 10 m i n .where
uo
i s the yield s t r e s s according t o the standard t e s t .P l a s t i c deformation can a l s o a b s o r b an exceptional t e m p o r a r y overload; although t h e m a t e r i a l m a y yield t h e r e m a y not be sufficient permanent deforma- tion t o r e q u i r e replacement of the panel. Vickery looked into t h i s problem f o r a s t e e l building s t r u c t u r e and found that the m e a n wind speed n e c e s s a r y to p r o - duce s e v e r e damage i s about 20 p e r cent g r e a t e r than t h a t n e c e s s a r y t o just produce yielding. Expected Peak F a c t o r for Loading
t
3 . 9 3. 4Consider a simply-supported panel, undergoing p l a s t i c bending a t m i d - span. The panel i s subjected t o a half sinusoidal cycle of wind p r e s s u r e with
G l a s s (Fig. 3) km. g 4 . 0 3. 2 Mini
-
mum, 2 . 0 1 . 7D.E. ALLEN - W.A. DALGLIESH 28 1
m a x i m u m amplitude wm
-
G and forcing f r e q u e n c y n Hz (Fig. 1 ) . T h e amountof p l a s t i c deformation, b p , during an excursion of wind p r e s s u r e beyond yield p r e s s u r e wy can be calculated n u m e r i c a l l y f r o m t h e equation of motion. R a t e effect i s taken into account in accordance with Eq. ( 3 ) by e x p r e s s i n g wy in t e r m s of wo, corresponding t o the s t a n d a r d t e s t yield r e s i s t a n c e .
The following damage c r i t e r i a a r e assumed:
1 6
permanent deflection:$ =
-
and s e c t i o n failure: = 5, w h i c h e v e r o c c u r sL 50
'
6,,f i r s t . The f i r s t c r i t e r i o n c o r r e s p o n d s t o the need forYpanel r e p l a c e m e n t and the second t o reaching of m a x i m u m bending r e s i s t a n c e . Ln c o r r u g a t e d panels, local buckling o c c u r s b e f o r e v e r y l a r g e p l a s t i c deformation.
Calculations w e r e c a r r i e d out f o r 3 t y p e s of cladding spanning 10 ft: ( 1 ) sheet m e t a l (weight 1 p s f , no = 20 Hz); ( 2 ) n o r m a l roof decking o r wall cladding (weight 8 psf, no = 10 Hz); ( 3 ) r e i n f o r c e d c o n c r e t e o r m a s o n r y (weight
50 psf, no = 20 Hz). In the calculations it w a s a s s u m e d that wy = 50 psf and
-
w/wy = 0.5.
The r e s u l t s , given in F i g . 2 in t e r m s of
&,
show that f o r wind f r e q u e n c i e s l e s s than about 1 Hz, v e r y little can be gained by taking into account plasticdeformation and r a t e effect. Recalculation f o r n o r m a l cladding, C a s e
(Z),
a s s u m i n g s t r a i n hardening f a c t o r s ( r a t i o of i n e l a s t i c stiffness t o e l a s t i c stiffness) of 0.01 and 0.1 indicate that s t r a i n hardening i s no m o r e significant f o r dynamic r e s i s t a n c e t h a n it i s f o r s t a t i c r e s i s t a n c e .
Thus design wind l o a d s f o r m e t a l cladding failing p r i m a r i l y by yield c a n be d e t e r m i n e d by a s s u m i n g that the panel i s a s t a t i c s t r u c t u r e which f a i l s when the wind p r e s s u r e exceeds t h e standard p l a s
-
t i c r e s i s t a n c e . Some e x t r a r e s i s t a n c e i s available f o r r a r e l o c a l high-frequency 'm wind turbulence. Windows G l a s s i s a b r i t t l e m a t e r i a l in which f a i l u r e s t a r t s a t an invisible s u r f a c e o redge flaw. I t s s t r e n g t h i s dependent on 0 . 1 0 . 2 0 . 5 I 2 5 10
window s i z e ( i n a c c o r d a n c e with the F O R C I N G F R E Q U E N C Y n H Z
t h e o r y of weakest flaws), r a t e ( o r F i g u r e 2: Gust M a t e r i a l F a c t o r duration) of loading, and, t o a l e s s e r
k,
for One C y c l e ofextent, on t e m p e r a t u r e and r e l a t i v e Loading
humidity. Rate of loading, the only
-
-
effect of i n t e r e s t to t h i s study, can b e approximated by the following criterion:=
w h e r e w i s t h e pressgure and tf the t i m e a t failure. On the b a s i s of manufac- t u r e r s ' loading t e s t s
-
a gradually applied p r e s s u r e in which f a i l u r e o c c u r s a t about one m i n u t e , the constant CM i s d e t e r m i n e d f r o m Eq. (4) t o be282 V - DYNAMIC WIND LOADS AND CLADDING DESIGN
one peak of sine wave loading ( F i g u r e I ) , F i g . 2 shows t h a t g l a s s i s consider- ably m o r e sensitive to r a t e effect than m e t a l , although f o r a load of v e r y short duration (high n) m e t a l g a i n s on g l a s s because of i t s ductility.
Because of t h i s sensitivity to r a t e effect, one peak of loading d o e s not p r o - vide useful information f o r g l a s s . F i g u r e 3 shows the r e s u l t s of applying the damage c r i t e r i o n to a sustained random wind p r e s s u r e :
where x i s a s s u m e d to be a stationary G a u s s i a n random p r o c e s s with a mean of z e r o and a standard deviation of one. The damage will be different f o r each random p r o c e s s of duration T but the expected damage can be d e t e r m i n e d f r o m
Eq. ( 5 ) by expanding into powers of x and replacing
s',
x dt by i t s expectedvalue based on the n o r m a l distribution, 1. 3
. .
. ( n - 1 ) T . F r o m E q s . ( 1 ) and ( 3 ) , wo can be eliminated and the r e s u l t s can be e x p r e s s e d in t e r m s ofh.
g or Cg' F i g u r e 3 shows the r e s u l t s a s a
function of r m s intensity of t u r b u - l e n c e , I T , f o r 2 load durations: 10 m i n u t e s and 1 hour. The r e s u l t s
indicate constant values of
k,.
g f o rhigh intensity of turbulence and con-
stant values of
C
f o r low intensityg
of turbulence; these values a r e given in Table I. The f o r m e r
applies to m o s t windows n e a r the 0.02 0.04 0.060.080.1 D. 2 0.4 0.6 0.a1.0
ground and the l a t t e r to windows R M S I N T E N S I T Y OF T U R B U L E N C E IT
in t a l l unobstructed buildings. F i g u r e 3: Gust F a c t o r s F o r G l a s s
-
The values of km. g c o m p a r e closely t o the expected peak
S t a t i o n a r y Gaus s ian Loading f a c t o r s g, which do not c o n s i d e r dynamic s t r u c t u r a l effect. The r e s u l t s of t h i s study t h e r e f o r e indicate that, except f o r windows subject to s m a l l turbu- lence, the value of
k,
f o r g l a s s can a l s o be taken a s 1.Risk of F a i l u r e
The consequences of cladding f a i l u r e due to wind a r e not a s s e r i o u s as f o r s t r u c t u r a l collapse. North A m e r i c a n building codes allow f o r t h i s , e i t h e r by a one-third i n c r e a s e in allowable s t r e s s f o r m e t a l cladding,'' o r by a reduced r e t u r n period f o r design wind load.''
Annual f a i l u r e r i s k s implied by North A m e r i c a n de s i g i r u l e s a r e compared
in Table I1 based on the following assumptions: (1) m e t a l yield s t r e n g t h i s
distributed n o r m a l l y with a m e a n value 1 . 1 5 t i m e s the specified r e s i s t a n c e (guaranteed m i n i m u m ) and a coefficient of variation 0. 10; ( 2 ) g l a s s window strength i s distributed n o r m a l l y with a coefficient of variation 0. 25;
( 3 ) m a x i m u m annual hourly wind loads follow the e x t r e m e value Type 1 d i s t r i b u - tion with a coefficient of variation 0.30.
Annual f a i l u r e r i s k s of 0.01 to 0 . 3 p e r cent in Table I1 appear t o be con- s i d e r a b l y higher than indicated by a c t u a l damage, probably due t o conservative design assumptions. Comparative f i g u r e s in Table 11, however, indicate that
D.E. ALLEN - W.A. DALGLIESH
TABLE I1
-
ANNUAL FAILURE RISKS FOR CLADDINGa National Building Code of Canada - Sections 4. 1 , 4. 6 and 4. 7
b A m e r i c a n National S t a n d a r d s A58. 1
-
1972. S e e a l s o Ref. ( 1 0 ) CodeN B C ~ 1970 N B C ~ 1965 A N S I ~ 1972
r e c e n t Canadian design r u l e s f o r m e t a l cladding a r e too c o n s e r v a t i v e ; a safety f a c t o r of 1 . 2 5 would give a n implied f a i l u r e r a t e of 0.16 p e r cent p e r y e a r .
Recent window f a i l u r e s in t a l l buildings indicate that falling g l a s s f r o m a
b r o k e n window i n i t i a t e s f a i l u r e of a n u m b e r of o t h e r windows ( a kind of p r o - g r e s s i v e collapse). F o r t h i s and psychological r e a s o n s it i s r e c o m m e n d e d t h a t design f a i l u r e r i s k s be r e d u c e d f o r t a l l buildings. G l a s s Conclusions Safety F a c t o r 2. 5 2. 5 2. 5
A study of m e t a l f o r r a t e effect and ductility, and of g l a s s f o r r a t e effect, shows t h a t f o r turbulent wind loads, both t y p e s of cladding can be c o n s i d e r e d a s s t a t i c a l l y loaded s t r u c t u r e s in which f a i l u r e o c c u r s when wind p r e s s u r e exceeds t h e s t r u c t u r a l capacity a s d e t e r m i n e d by s t a n d a r d t e s t s . The f a c t o r
k,
in Eq. ( 2 ) , which t a k e s into account d y n a m i c behaviour u n d e r turbulent wind l o a d s , c a n be g e n e r a l l y taken a s 1. F o r g l a s s , m i n i m u m v a l u e s of the g u s t f a c t o r , C in Table I a r e r e c o m m e n d e d t o avoid f a i l u r e of windows subject t o steadyg'
winds.
Design Wind Code
Annual F a i l u r e Risk, O/o 0 . 17 0 . 21 0 . 16
Annual f a i l u r e r i s k s f o r cladding indicate that r e c e n t Canadian r u l e s f o r m e t a l cladding a r e too c o n s e r v a t i v e . E x i s t i n g s a f e t y f a c t o r s f o r windows in t a l l buildings a p p e a r t o be t o o s m a l l . R e t u r n P e r i o d , Y e a r s 10 30 50 ~ e t a ' l
T h e a r e a of g r e a t e s t u n c e r t a i n t y i n t h e design of cladding t o r e s i s t wind loads i s in t h e wind loading itself, in p a r t i c u l a r t h e intensity of t u r b u l e n c e , I T , and s h a p e f a c t o r ,
.
T h i s information should be obtained f r o m f u l l -"$
s c a l e m e a s u r e m e n t s an boundary - l a y e r wind-tunnel t e s t s . Gust F a c t o r , C g 2. 5 2. 0 2. 0 Safety F a c t o r 1. 67 1. 25 1. 25 R e f e r e n c e s Annual F a i l u r e Risk, O/o 0. 007 0. 26 0. 13( 1 ) Davenport, A.G. "Note on the D i s t r i b u t i o n of t h e L a r g e s t Values of a
Random Function with Application t o Gust Loading". P r o c . I n s t . of Civil
E n g i n e e r s , Vol. 28, 1964, p. 187.
( 2 ) Dalgliesh, W.A. "Statistical T r e a t m e n t of P e a k G u s t s on Cladding" J o u r n a l of t h e S t r u c t u r a l Division, ASCE ST9, S e p t e m b e r 1971.
V - DYNAMIC WIND LOADS AND CLADDING DESIGN
( 3 ) Standen, N.M., Dalgliesh, W.A. and Templin, R. J . "A Wind Tunnel and Full-Scale Study of Turbulent Wind P r e s s u r e s on a T a l l Building".
DME/NAE Q u a r t e r l y Bulletin No. 1971(4). National R e s e a r c h Council of Canada, J a n . 1972.
( 4 ) Ostrowski, J . S . , M a r s h a l l , R. D. and C e r m a k , J . E . "Vortex F o r m u l a t i o n and P r e s s u r e Fluctuations on Buildings1' in Wind Effects on Buildings and S t r u c t u r e s . University of Toronto P r e s s , 1968.
( 5 ) Voorhees, H.R. "A Survey of E f f e c t s on Lower-Than-Usual R a t e s of S t r a i n
in t h e Yield and T e n s i l e Strengths of M e t a l s " ASTM Data S e r i e s DS44, M a y 1969.
( 6 ) ASTM Standard A370 "Standard Methods and Definitions for Mechanical
T e s t i n g of Steel Products". ASTM Standards P a r t 4 , J a n u a r y 1970.
( 7 ) Vickery, B. J. "Wind Action on Simple Yielding S t r u c t u r e s ' ' J o u r n a l of Engineering M e c h a n i c s Division, ASCE, Vol. 96, EM2, A p r i l 1970.
( 8 ) Brown, W.G. "A Load Duration T h e o r y f o r G l a s s Design". Division of
Building R e s e a r c h , R e s e a r c h P a p e r No. 508. National R e s e a r c h Council of Canada. J a n u a r y 1972.
( 9 ) P . P . G . I n d u s t r i e s , T e c h n i c a l S e r v i c e Report No. 101, G l a s s P r o d u c t
Recommendations
-
S t r u c t u r a l .(10) A m e r i c a n I r o n and S t e e l Institute, AISI Specification f o r the D e s i g n of C o l d - F o r m e d Steel S t r u c t u r a l M e m b e r s 1968.
(11) National Building Code of Canada 1970
-
Section 4.1. S t r u c t u r a l Loadsand P r o c e d u r e s . A s s o c i a t e C o m m i t t e e on the National Building Code, National R e s e a r c h Council of Canada.
(12) Engineering News-Record. F e b r u a r y 15, 1973, p. 14.
SUMMARY
A study is made of the behaviour of ductile (metal) and brittle (glass) panels under dynamic wind loading. The results show that the effect of such factors a s dynamic amplification, rate of loading and ductility can generally be neglected. Failure risks implicit in North American codes a r e compared; some changes in design rules a r e suggested, including an increase in safety factor for glass windows in tall buildings.
RESUME
On a fait une Ctude sur le comportement des panneaux ductiles (metal) et cassants (verre) dans des conditions de chargement dynamique dO au vent. D'aprss
D.E. ALLEN - W.A. DALGLIESH
l e s r e s u l t a t s obtenus, l'effet d e f a c t e u r s c o m m e l'amplification dynamique, l a v i t e s s e d e c h a r g e m e n t e t l a ductilite e s t g e n e r a l e m e n t negligeable. L e s r i s q u e s d e r u p t u r e q u e sous-entendent l e s c o d e s n o r d - a m e r i c a i n s s o n t m i s en r e g a r d ; q u e l - q u e s modifications d a n s l e s r e g l e s d e c a l c u l s o n t s u g g e r e e s , y c o m p r i s une augmentation du f a c t e u r d e s e c u r i t e d e s f e n e t r e s v i t r e e s d a n s l e s b2timents t r & s eleves.
ZUSAMMENFASSUNG
D a s Verhalten von zahen (Metall) und s p r o d e n ( G l a s ) M a t e r i a l i e n in G e - baudeverkleidungen u n t e r d y n a m i s c h e r Windbelastung w i r d untersucht. D i e E r g e b - n i s s e deuten a n , d a s s d e r Effekt von F a k t o r e n w i e d y n a m i s c h e s Aufschaukeln, Belastungsgeschwindigkeit und Zahigkeit i m allgemeinen v e r n a c h l a s s i g t w e r d e n kann. D i e i n n o r d a m e r i k a n i s c h e n Normen enthaltenen Bruchwahrscheinlichkeiten werden verglichen. G e w i s s e V e r b e s s e r u n g e n in den Berechnungsmethoden w e r d e n vorgeschlagen, u. a. eine Erhohung d e s S i c h e r h e i t s f a k t o r s fiir G l a s in hohen G e - bauden.
