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Weak thermal points or thermal bridges
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PREFACE
The tern1 " t h e r n a l b r i d g e " i s o f t e n used t o d e s c r i b e t h o s e loca- t i o n s i n t h e e n c l o s u r e of a b u i l d i n g through which h e a t i s conducted more e a s i l y than through a d j a c e n t c o n s t r u c t i o n . In g e n e r a l t h i s occurs where m a t e r i a l s of r e l a t i v e l y high therrnal conductance provide a low r e s i s t a n c e p a t h f o r h e a t flow from i n s i d e t o o u t s i d e . I n a heated b u i l d i n g d u r i n g cold weather, t h e i n s i d e s u r f a c e temperature a t a therrnal b r i d g e i s lower than t h a t of t h e surrounding c o n s t r u c - t i o n and t h i s is u s u a l l y more s e r i o u s t h a n t h e a d d i t i o n a l h e a t l o s s . The low s u r f a c e temperature may r e s u l t i n condensation on t h e s u r f a c e , o r r e q u i r e a low i n s i d e humidity i n o r d e r t o avoid such condensation. The v a r i a t i o n s i n s u r f a c e temperature due t o t h e presence of t h e thermal b r i d g e may a l s o cause u n d e s i r a b l e d u s t marking, s i n c e t h e r a t e of d e p o s i t i o n o f d u s t on a s u r f a c e i s a f u n c t i o n of t h e d i f f e r - ence i n temperature between a i r and s u r f a c e s . Thermal b r l d g e s a r e t h u s p a r t i c u l a r l y s i g n i f i c a n t i n cold c l i m a t e s , such a s e x i s t d u r i n g t h e w i n t e r f o r most p a r t s o f Canada.
For some b u i l d i n g s thermal b r i d g e s may n o t p r e s e n t any s e r i o u s problem, b u t f o r t h e ma j o r i t y it i s important t o a t l e a s t recognize t h e l i m i t a t i o n s which t h e y impose. In b u i l d i n g s where even moderate h u m i d i t i e s must be ~ ~ a i n t a i n e d , i t i s imperative t o e l i m i n a t e thermal b r i d g e s ; t h u s a knowledge of t h e i r c h a r a c t e r i s t i c s i s r e q u i r e d .
Unfortunately, h e a t flow i n t h e v i c i n i t y o f thermal b r l d g e s i s com- p l e x and i n many c a s e s t h e most p r a c t i c a l method of o b t a i n i n g t h e r e q u i r e d information i s by d i r e c t measurement. For t h i s r e a s o n , i n f o r m a t i o n i s s t i l l inadequa+.e.
Thermal b r i d g e s may t a k e many forms. The D i v i s i o n has made e x t e n s i v e s t u d i e s of thermal b r i d g e s a s s o c i a t e d with s t u d d i n g of con- v e n t i o n a l I n s u l a t e d wood-frame c o n s t r u c t i o n and with metal frames and
s a s h of windows. Another important type of thermal b r i d g e i s a s s o c i - a t e d with s t r u c t u r a l s t e e l o r c o n c r e t e framing, and it i s mainly w i t h t h i s type t h a t t h i s paper by J. B e r t h i e r of C.S.T.B. d e a l s . The
t r a n s l a t i o n i n c l u d e s o n l y P a r t s 1 and 2 of t h e paper, d e s c r i b i n g t h e r e s u l t s of l a b o r a t o r y measurements, s i n c e t h e s e a r e of p a r t i c u l a r i n t e r e s t t o t h e D i v i s i o n . The D i v i s i o n i s g r a t e f u l t o Mr. D.A. S i n c l a i r o f t h e N.R.C. T r a n s l a t i o n s S e c t i o n f o r p r e p a r i n g t h i s t r a n s l a t i o n . Ottawa N .B. Hutcheon August 1964 A s s i s t a n t D i r e c t o r
NATIONAL RESEARCH COUNCIL OF CANADA
Technical Translation 1143
T i t l e : Weak thermal p o i n t s o r thermal bridge8
(Les p o i n t s f a i b l e s thermiquea ou ponts thermiquee) Author: J . B e r t h i e r
Reference : Cahiers d u Centre S c i e n t i f i q u e e t Technique d u ~ a t i r n e n t
,
( 3 3 4 ) :1-20, 1960
FOREWORD
The f o l l o w i n g i s
a
r e p o r t on a new s t a g e i n t h e r e s e a r c h e s undertaken by t h e Centre S c i e n t i f i q u e e t Technique du ~ g t i m e n t (C.S.T.B.) on what we c a l l t h e "hygrothermal c h a r a c t e r i s t i c s " o f e x t e r n a l w a l l s , 1 . e . t h e c h a r a c t e r i s - t i c s Involved i n problems of humidity and h e a t .The f i r s t r e s e a r c h e s d e a l t w i t h t h e r e s i s t a n c e of w a l l s t o r a i n ; t h e r e s u l t s were published i n o u r C a h i e r s (No. 178, S e c t i o n 1 9 ) : " ~ e s i s t a n c e of porous m a t e r i a l s t o r a i n " (whole b r i c k s , c o n c r e t e blocks, s o f t l i m e s t o n e ) and
(NO. 312, S e c t i o n 39): "Some r e s u l t s of r a i n t e s t s on l i g h t masonry" ( w i t h o r without c o a t i n g ) . These i n v e s t i g a t i o n s made it p o s s i b l e t o develop t e s t i n g methods: " ~ e s e a r c h and checking t e s t s approved by C.S.T.B." ( ~ a h i e r No. 312, S e c t i o n
3 9 ) ,
t o which r e f e r e n c e has been made I n t h e acceptance r e s o l u t i o n s , e s p e c i a l l y w i t h r e f e r e n c e t o t h e c a p i l l a r i t y requirements under p r e s s u r e of w a l l m a t e r i a l s .The i n v e s t i g a t i o n s were t h e n d i r e c t e d t o t h e U v a l u e s of w a l l s . The
r e s u l t s were published under t h e t i t l e : "~ecomrnendations f o r t h e use o f l i e f i t masonries'' (hollow t e r r a c o t t a bloclcs, c o n c r e t e blocks, l i g h t tamped c o n c r e t e , autoclaved c e l l u l a r c o n c r e t e ) Cahier No. 34, S e c t i o n 287. Here we f i n d f i r s t a r e p o r t on t e s t s ending w i t h t h e d e t e r m i n a t i o n of " u s e f u l U" v a l u e s , 1 . e . U
v a l u e s of w a l l s t a k i n g i n t o account t h e i r moisture c o n t e n t . We t h e n f i n d recommendations e s t a b l i s h i n g maxlrnurn a d m i s s i b l e U v a l u e s , and hence minimum t h i c k n e s s e s o f w a l l s , with s p e c i a l r e f e r e n c e t o t h e dangers o f s u r f a c e conden- s a t i o n depending on t h e r a t i n g o f t h e equipment and occupation of t h e b u i l d i n g .
The i n v e s t i g a t i o n s d e s c r i b e d h e r e concern t h e weak thermal p o i n t s , commonly h o w n a s thermal b r i d g e s . They owe t h e i r o r i g i n t o t h e d e s i r e t o combat s u r f a c e condensation. In P a r t 111 p r e c i s e , q u a n t i t a t i v e recommendations a r e made concerning means of r e d u c i n g t h e e f f e c t s o f weak thermal p o i n t s i n heavy c o n c r e t e frame w a l l s . It was p o s s i b l e t o e s t a b l i s h o n l y g e n e r a l p r i n c i - p l e s f o r t h i n l i g h t w a l l s w i t h wooden o r m e t a l framing. The p a r t i c u l a r c a s e of w a l l s w i t h a i r gaps h a s n o t been d e a l t with.
I n v e s t i g a t i o n s a r e now underway on a i r gaps i n w a l l s and r o o f s w i t h two o b j e c t i v e s : t o combat condensation i n t h e w a l l m a t e r i a l , and t o p r o v i d e pro- t e c t i o n a g a i n s t i n s o l a t i o n . The former problem has a l r e a d y been touched on in
connection with r o o f s i n Cahier No. 31, S e c t i o n
259
onde dens at ion
below s e l f s u p p o r t i n g aluminium roof i n g s ".
A summarization and s y n t h e s i s o f t h e s e v a r i o u s i n v e s t i g a t i o n s w i l l be found i n Vol. I1 of t h e R.E.E.F.-58, t h e c h a p t e r on "Hygrothermics and v e n t i l a t i o n .
M. C r o i s e t
Table of Contents
I n t r o d u c t i o n
...
5P a r t I. Q u a l i t a t i v e approach t o t h e problem by semi-natural t e a t s P r i n c i p l e of semi-natural t e s t s
...
8
R e s u l t s
...
9
P a r t 11. Q u a n t i a t i v e s t u d y
.
a r t i f i c i a l t e s t s C h a r a c t e r i s t i c s o f a thermal b r i d g e...
9T e s t method
...
10Choice of types of thermal b r i d g e s
...
12Heavy w a l l s
...
13Light w a l l s (curtain walls. fagade p a n e l s )
...
16R e s u l t s
...
17Heavy w a l l s
...
17Light w a l l s ( c u r t a i n walls. faqade p a n e l s )
...
20References
...
24Tables
...
25WEAK THERMAL POINTS OR THBRMAL BRIDGES
Summary
Uniformity of temperature on t h e i n t e r n a l s u r f a c e i s one of t h e e s s e n t i a l hygrothermal c h a r a c t e r i s t i c s of a w a l l .
The weak thermal p o i n t s , which a r e t h e cause o f uneven temperatures, c o n s t i t u t e a weakness which ought to be e l l m i - na t e d
.
The a u t h o r d e s c r i b e s a l a r g e number of t e a t s c a r r i e d o u t with v a r i o u s t y p e s of w a l l (dense w a l l s and l i g h t w e i g h t p a n e l s )
i n o r d e r t o a s s e s s t h e Importance o f thermal b r i d g e s and t o determine t h e e f f e c t i v e n e s s of p o s s i b l e remedies. He shows t h a t t h e accepted t h e o r y used in t h e c a l c u l a t i o n o f U v a l u e s i s
u n s a t i s f a c t o r y when e s t i m a t i n g s u r f a c e temperatures. The r e s u l t s obtained can be explained, however, by two simple hypotheses. From t h e s e , p r a c t i c a l r u l e s a r e d e r i v e d by which t h e e f f e c t of a thermal b r i d g e can be e s t i m a t e d , and recommendations a r e made f o r reducing t h i s e f f e c t .
I n t r o d u c t i o n
C o n s i d e r a t i o n s of comfort, econonly and h e a l t h r e q u i r e t h e U v a l u e of t h e e x t e r n a l w a l l s of a b u i l d i n g t o be k e p t s m a l l . The upper l i m i t depends on a number of f a c t o r s , f o r example:
-
t h e f u n c t i o n of t h e w a l l ( r o o f , fagade, gable, e t c . );-
t h e t y p e o f b u i l d i n g ( s c h o o l , o f f i c e , v a r i o u s c a t e g o r i e s of d w e l l i n g ) ;-
g e o g r a p h i c a l l o c a t i o n of t h e b u i l d i n g ( c l i m a t i c zone);-
t h e w a l l mass.Tables p u b l i s h e d i n C.S.T.B. C a h l e r s No.
34
and t h e b u i l d i n g r u l e scontained i n R.G.E.F.-58 ( 2 , 3 ) give maximum recommended U v a l u e s i n each c a s e . Merely t o f o l l o w t h e s e r u l e s , however, is n o t enough t o a s s u r e s a t i s f a c - t o r y hygrothermal behaviour of t h e w a l l . For t h i s t h e i d e a l would be f o r t h e temperature t o be t h e same a t e v e r y p o i n t on t h e I n t e r i o r f a c e o f t h e w a l l .
In t h e c a s e of a homogeneous w a l l s e p a r a t i n g two s p a c e s , an i n t e r i o r one o f temperature TI and a n o u t s i d e one of temperature Te, t h e t e m p e r a t u r e
e1
on t h e i n t e r i o r s u r f a c e of t h e w a l l once e q u i l i b r i u m h a s been e s t a b l i s h e d , is given by t h e e q u a t i o nwhere U i s the o v e r a l l c o e f f i c i e n t of h e a t t r a n s m i s s i o n and hi i s t h e i n s i d e s u r f a c e conductance*
.
The above e q u a t i o n shows t h a t t h e r e a r e two c a u s e s of non-uniforniity i n t h e s u r f a c e t e m p e r a t u r e s . F i r s t t h e r e i s h e t e r o g e n e i t y i n t h e w a l l , producing d i f f e r e n t l o c a l U v a l u e s . T h i s i s v e r y f r e q u e n t because m a t e r i a l s w i t h d i f - f e r e n t thermal c o e f f i c i e n t s a r e i n c r e a s i n g l y b e i n g p l a c e d s i d e by s i d e i n con- s t r u c t i o n s , f o r example:
-
a f i l l i n g of hollow b r i c k s n e x t t o a framing of r e i n f o r c e d c o n c r e t e ;-
a metal framing around a p a n e l of a faqade o r i t s i n t e r n a l framing,n e x t t o t h e i n s u l a t i o n which i t e n c l o s e s .
A l l t h o s e elements which have l e s s i n s u l a t i n g e f f e c t t h a n t h e main p a r t of t h e w a l l a r e weak p o i n t s from t h e thermal p o i n t of view. They a r e conlmonly known a s " t h e r m a l b r i d g e s " .
The second cause i s a v a r i a t i o n of s u r f a c e h e a t exchange r e s u l t i n g in a v a r i a t i o n of t h e c o e f f i c i e n t hi. These v a r i a t i o n s may be produced by a de- c r e a s e i n t h e exchanges due t o r a d i a t i o n ( o n an alunliniurn nloulding, f o r example) o r convection ( a t c o r n e r s , behind f u r n i t u r e ) .
G e n e r a l l y s p e a k i n g t h e observed phenomena a r e t h e r e s u l t s of t h e s e v a r i o u s c a u s e s and i t i s i m p o s s i b l e t o determine t h e s h a r e of each.
T r a c e s of condensation on t h e c e i l i n g of a basement apartment room on cold s p o t s produced by t h e t i e bean and t h e
j o i s t s of t h e ground f l o o r
The d i s a d v a n t a g e s of non-uniformity of s u r f a c e t e m p e r a t u r e s a r e numerous. I n sumer thermal b r i d g e s l e a d t o warmer t e m p e r a t u r e s . In a temperate c l i n i a t e t h i s i s n o t v e r y s e r i o u s and t h e w a l l does n o t s u f f e r from i t . During
cold weather, however, when t h e t e m p e r a t u r e of a thermal b r i d g e i s lower t h a n
*
The c o e f f i c i e n t c h a r a c t e r i z e s t h e t h e r m a l exchanges between t h e a i r and t h e s u r f a c e of t h e w a l l . It depends t o a s m a l l e x t e n t on s u r f a c e c o n d i t i o n and much more on t h e v e l o c i t y o f t h e a i r i n c o n t a c t w i t h i t .t h e main p a r t of t h e w a l l t h e s i t u a t i o n I s d i f f e r e n t . S e v e r a l phenomena may t h e n be observed
Condensation t r a c e s i n t h e room o f a ground f l o o r a p a r t m e n t a t t h e g a b l e end on c o l d s p o t s produced by t h e c o r n e r s
o f t h e f l o o r s and t h e e x t e r n a l w a l l s
The main one i s c o n d e n s a t i o n o f m o i s t u r e from t h e room a i r on t h e s u r f a c e of t h e w a l l . T h i s w i l l happen a s soon a s t h e dew-point of t h e humid a i r o f t h e room i s above t h e t e m p e r a t u r e of t h e t h e r m a l b r i d g e s u r f a c e . Condensation w i l l o c c u r f i r s t a t t h i s p o i n t and t h e amount o f c o n d e n s a t i o n w i l l b e g r e a t e s t e i t h e r d u r i n g a p e r i o d of h i g h h u m i d i t y o r one o f s e v e r e c o l d .
It i s n o t o u r p u r p o s e h e r e t o s t u d y t h i s phenomenon and i t s consequences i n d e t a i l , b u t we wish t o p o i n t o u t t h a t a c o l d s p o t on t h e s u r f a c e of a w a l l i s i t s p r i m a r y c a u s e . The e x t e n t of c o n d e n s a t i o n w i l l depend, o f c o u r s e , on t h e c o n d i t i o n s of o c c u p a t i o n of t h e b u l l d i n g ( p r o d u c t i o n o f m o i s t u r e , v e n t i l a t i o n , h e a t i n g , e t c . ) b u t b e f o r e a t t e m p t i n g t o p r o t e c t a g a i n s t t h e e f f e c t s o f t h i s phenomenon i t a p p e a r e d n e c e s s a r y t h a t t h e w a l l i t s e l f s h o u l d be designed t o p r e v e n t i t by p r o v l d l n g a s u f f i c i e n t l y uniform t e m p e r a t u r e on t h e I n t e r i o r f a c e . F u r t h e r m o r e , I n t h e a b s e n c e o f any h u m i d i t y i n t h e room, a c o l d s p o t g i v e s r i s e t o a n o t h e r phenomenon known a s d u s t p a t t e r n s . Even i n rooms used a s o f f i c e s , where t h e atmosphere Is always dry, t h e c o l d zones r e s u l t i n g from t h e beams, t i e s o r even j o i n t s between masonry b l o c k s e v e n t u a l l y become
o u t l i n e d by a c o n s i d e r a b l e d e p o s i t of d u s t . T h i s phenornenorl can a p p a r e n t l y be explalned a s f o l l o w s :
The d u s t p a r t i c l e s a r e kept i n suspension I n t h e a i r by molecular a g i t a t i o n and t h e shocks r e s u l t l n g from i t . T h i s a g i t a t i o n i n c r e a s e s w i t h i n c r e a s i n g temperature. In t h e v i c i n i t y of a cold s p o t a d i s e q u i l i b r i u m occurs I n t h e i n t e r a c t i o n , and t h e d u s t p a r t i c l e s a r e thrown a g a i n s t t h e cold s p o t . Since t h e l a t t e r i s g e n e r a l l y moist a s a r e s u l t of even very s l i g h t condensa- t i o n , t h e d u s t p a r t i c l e s c l i n g b e t t e r t o i t .
Although t h i s phenomenon i s n o t a s s e r i o u s a s condensation, i t i n d i c a t e s t h a t whatever t h e type of c o n s t r u c t i o n , a thermal b r i d g e i s always a d e f e c t .
The purpose of t h e p r e s e n t a r t i c l e i s t o r e p o r t on t h e s t u d i e s made by C.S.T.B. w i t h a view t o i n v e s t i g a t i n g p r a c t i c a l methods of o b t a i n i n g s a t i s - f a c t o r y u n i f o r m i t y o f temperatures on i n t e r i o r s u r f a c e s . P a r t I w i l l be devoted t o a q u a l i t a t i v e s t u d y of t h e phenomena. P a r t I1 w i l l r e p o r t on some a r t i f i c i a l q u a n t i t a t i v e t e s t s c a r r i e d o u t on a number of s p e c i a l c a s e s . P a r t I11 w i l l a t t e m p t t o e x p l a i n t h e r e s u l t s on t h e b a s i s of a s i m p l i f i e d t h e o r y . From t h i s we s h a l l be a b l e t o g e n e r a l i z e I n a number of simple c a s e s .
F i n a l l y , i n P a r t N , drawing c o n c l u s i o n s from o u r s t u d y , we s h a l l g i v e p r a c t i c a l r u l e s f o r e s t i m a t i n g t h e e f f e c t of a thermal b r i d g e and c o r r e c t i n g
i t .
P a r t I
Q u a l i t a t i v e Approach t o t h e Problem by Semi-Natural T e s t s
P r i n c i p l e of s e m i - n a t u r a l t e s t s
The p r i n c i p l e u n d e r l y i n g t h e s e t e s t s i s a s f o l l o w s .
I n a b u i l d i n g , whose e x t e r n a l w a l l s a r e t h e w a l l s t o be s t u d i e d , a warm and humid atmosphere i s produced d u r i n g t h e w i n t e r in t h e i n t e r i o r c l o s e t o t h e I n s i d e s u r f a c e of t h e w a l l . The e x t e r n a l c o n d i t i o n s a r e n a t u r a l .
These t e s t s were c a r r i e d o u t o n l y on w a l l s of t h e r e l n f o r c e d c o n c r e t e frame type f i l l e d w i t h l i g h t w e i g h t masonry.
To f a c i l i t a t e o u r s t u d y we have chosen f o r t h e f i l l i n g c e l l u l a r c o n c r e t e of d e n s i t y
0.6
kg/dm3 ( k = 0.3 kcal/mh0c) which i s d e c i d e d l y more i n s u l a t i n g t h a n t h e mass c o n c r e t e of t h e framework (d = 2.2; k = 1 . 5 ) .Three t y p e s of thermal weak p o i n t s have been c o n s i d e r e d .
-
t o t a l b r i d g e , with framework t r a v e r s i n g t h e w a l l completely;-
p a r t l a l b r i d g e w i t h i n t e r n a l o r e x t e r n a l i n s u l a t i o n ;-
b r i d g e and i n t e r n a l c o n c r e t e s l a b d i f f u s i n g t h e h e a t f l u x .In t h e second c a s e t h e width of t h e thermal b r i d g e was v a r i e d a s w e l l a s t h e thickness of t h e i n s u l a t i o n .
These w a l l s had a n e x t e r n a l c o a t i n g of lime-cement mortar and an i n t e r i o r c o a t i n g of p l a s t e r 1 cm t h i c k . A r e a c t i v e p a i n t was applied over t h e p l a s t e r i n o r d e r t o emphasize t h e condensation and t o permit a rough e s t i m a t i o n o f i t s
e x t e n t . R e s u l t s
Figure 1 shows both the c o n s t r u c t i o n of the d i f f e r e n t bridges and t h e r e s u l t s obtained.
In t h e case of t h e t o t a l bridge, 1 . e . t h e framework t r a v e r s i n g t h e e n t i r e t h i c k n e s s of the wall, whether t h i s bridge was wide ( v e r t i c a l framing member
in t h e c e n t r e of the f i g u r e ) o r narrow ( h o r i z o n t a l frame member t o t h e l e f t ) very considerable t r a c e s of condensation appear.
A t t h e extreme l e f t , on the thermal bridge with d i f f u s e d h e a t f l u x t h e mildews a r e def i n i t e l y l e s s apparent.
A t t h e r i g h t , on t h e various p a r t i a l cold b r i d g e s with i n t e r i o r Insula- t i o n , t h e t r a c e s of condensation a r e p r a c t i c a l l y non-existent. No d i f f e r e n c e can be discerned between t h e wide and narrow ones on t h e one hand and t h e more o r l e s s i n s u l a t e d ones on t h e o t h e r .
However, t o the l e f t , on t h e two p a r t i a l cold b r i d g e s with e x t e r n a l i n s u l a t i o n t h e condensation t r a c e s a r e very marked, p r a c t i c a l l y s i m i l a r t o those obtained on t h e t o t a l cold b r i d g e s .
A t first glance t h i s appears t o be
a
s u r p r i s i n g r e s u l t . Actually, t h e c a l c u l a t e d thermal conductance of t h e wall a t t h e thermal bridge i s t h e o r e t i - c a l l y t h e same whether t h e i n s u l a t i o n i s placed i n s i d e o r o u t s i d e . S i m i l a r l y t h e thermal bridge with d i f f u s e d h e a t f l u x has t h e same U value a s t h e t o t a l bridge.In f a c t , t h e s e r e s u l t s 'show t h a t t h e problem i s much more complex, and t h a t merely conlparing wall U values a t t h e thermal b r i d g e s with c o e f f i c i e n t s a t r i g h t a n g l e s t o t h e U v a l u e s i n t h e main p a r t of t h e wall i s by no means s u f f i c i e n t t o s o l v e i t o r even t o p r e d i c t t h e form t h a t t h e phenomena w i l l
t a k e .
It is because of t h e s e d i f f i c u l t i e s t h a t we have undertaken much more
p r e c i s e a r t i f i c i a l t e s t s which w i l l enable us t o d e a l q u a n t i t a t i v e l y with t h e s e phenomena.
P a r t I1 7
Q u a n t i t a t i v e Study
-
A r t i f i c i a l T e s t s C h a r a c t e r i s t i c s of a thermal bridgeThe problems presented by thermal b r i d g e s can be reduced t o t h e d e t e r - mination o f t h e temperatures on t h e I n t e r i o r f a c e of t h e heterogeneous
wall
when t h e l a t t e r i s s i t u a t e d i n a cold e x t e r n a l and warm i n t e r n a l environment. The curve g i v i n g t h e temperature d i s t r i b u t i o r l on t h e i n t e r n a l s u r f a c e , a s shown f o r example i n F i g . 2, then e n a b l e s us t o c h a r a c t e r i z e t h e thermal
bridge. Two elements must be considered, f i r s t t h e spreading o u t of t h e curve which e n a b l e s u s t o determine t h e width of t h e zone where condensation i s t o be f e a r e d , and second t h e temperature of t h e c o l d e s t s p o t . The a b s o l u t e value of t h i s temperature i s n o t s o important because i t depends e s s e n t i a l l y on t h e i n t e r i o r and e x t e r i o r temperatures. We t h e r e f o r e i n t r o d u c e a c o e f f i c i e n t which c h a r a c t e r i z e s t h e h e t e r o g e n e i t y of i n t e r i o r s u r f a c e temperature:
where Ti i s t h e i n t e r i o r a i r temperature, 8 t h e I n t e r i o r s u r f a c e temperature of a p o i n t i n t h e thermal bridge zone and., 0, t h e i n t e r i o r s u r f a c e t e n ~ p e r a t u r e a t a p o i n t remote from t h e thermal b r i d g e i n t h e main p a r t of t h e w a l l .
In P a r t I11 i t w i l l be shown t h a t t h i s r a t i o i s p r a c t i c a l l y independent of t h e i n t e r i o r and e x t e r i o r temperatures. Denoting t h e maximum value of p
by P,, then
where Qm i s t h e temperature of t h e c o l d e s t p o i n t on t h e thermal b r i d g e .
T h i s c o e f f i c i e n t , which we s h a l l c a l l t h e c o e f f i c i e n t of i n t e r i o r s u r f a c e temperature h e t e r o g e n e i t y i n d i c a t e s t o a c e r t a i n e x t e n t by how much t h e
c o l d e s t p o i n t i s c o l d e r i n r e l a t i o n t o t h e i n t e r n a l a i r temperature t h a n t h e main p a r t of t h e w a l l .
We s h a l l wish t o compare t h i s c o e f f i c i e n t t o t h e c o e f f i c i e n t pc ( t h e o r e t - i c a l c a l c u l a t e d c o e f f i c i e n t ) which i s determined from t h e w a l l U value a t t h e thermal b r i d g e ( U ) and t h e w a l l U value away from t h e thermal bridge* ( u c )
P a s f o l l o w s : T e s t method Exact d e t e r m i n a t i o n of t h e curve of p v a l u e s by c a l c u l a t i o n i s i m p r a c t i c - a b l e .
*
T r a n s l a t o r ' s n o t e : There i s no e x a c t r e n d e r i n g f o r " l a p a r t i e c o u r a n t e du mur". It means b a s i c a l l y any p a r t of t h e w a l l n o t c l o s e t o the edges.The method of d i r e c t o b s e r v a t i o n i s d e l i c a t e , because t h e measurement of a s u r f a c e temperature i s d i f f i c u l t t o c a r r y o u t with p r e c i s i o n . However, i t
i s t h e o n l y way i n which t h e v a r i o u s f a c t o r s which may i n f l u e n c e p can be taken I n t o account.
The t e s t s were c a r r i e d o u t i n t h e thermal roorn of t h e Champs-sur-Marne experimental s t a t i o n ( ' ) ( F i g .
3 ) .
The w a l l c o n t a i n i n g t h e thermal b r i d g e s t o be s t u d i e d divided t h e room i n t o two s p a c e s . The i n t e r i o r warm space was k e p t a t a c o n t r o l l e d temperature of approximately 30°C while t h e e x t e r i o r cold space was kept a t about - 5 O C .
The i n t e r i o r temperature was placed i n t e n t i o n a l l y h i g h e r t h a n average room ter;lperature i n o r d e r t o i n c r e a s e t h e d i f f e r e n c e between t h e two environments, t h e r e b y enhancing t h e accuracy of t h e measured i n t e r i o r s u r f a c e temperature. T h i s w i l l n o t a f f e c t t h e r e s u l t s because t h e values of p a r e p r a c t i c a l l y
Independent of temperature. A i r teniperatures were recorded c o n t i n u o u s l y d u r i n g t h e t e s t by means of r e s i s t a n c e thermometers connected t o a r e c o r d i n g p o t e n t i - ometer. Furthermore, s i n c e t h e purpose of t h e s t u d y was t o e l i m i n a t e condensa- t i o n , m a t t e r s were arranged s o t h a t t h e thermal c h a r a c t e r i s t i c s of t h e
m a t e r i a l s and t h e i r temperature would n o t be a f f e c t e d by condensation. The atmosphere of t h e i n t e r i o r room was d r y (approximately
35%
r e l a t i v e humidity) s o t h a t no condensation would t a k e p l a c e on t h e cold s p o t s .The w a l l s u r f a c e tenrperaturee were measured w i t h Iron-constantan thermo- couples 1/10 rnm i n diameter. These thermocouples were connected t o a 12-point r e c o r d i n g potentiomneter. Temperatures were t h u s recorded s i m u l t a n e o u s l y a t 12 p o i n t s on t h e zone in q u e s t i o n . We t h u s obtained an a c c u r a t e summary of t h e s u r f a c e temperature curve ( F i g . 2 )
.
Note I:
Glc wish t o r e c a l l one of t h e c h a r a c t e r i s t i c s of t h e room which i s
e s s e n t i a l t o t h e s t u d y . This has t o do with t h e s u r f a c e h e a t exchanges between * t h e a i r and t h e w a l l . A c e r t a i n number of measurements c a r r i e d o u t on homoge-
neous w a l l s have shown t h a t t h e convection c o n d i t i o n s c r e a t e d I n t h e two rooms, f o r w a l l s with U values of approximately 1.2 kcal/(m2hoc), gave s u r f a c e con- ductances of approximately 7 kcal/(m2hoc) f o r t h e i n t e r i o r environment and 1 8 kcal/(m2h0c) f o r t h e e x t e r i o r . It was very Important t h a t t h e I n s i d e s u r - f a c e h e a t exchanges d u r l n g t h e t e s t s were s i m i l a r t o p r a c t i c a l s u r f a c e h e a t f o r t h e t e s t w a l l o r a t l e a s t t o t h e o r e t i c a l l y determined v a l u e ( 1 . e . hi =
7 kcal/(m2h0c). It may then be assumed t h a t s u r f a c e temperature v a r i a t i o n s
Note I1
Some i n v e s t i g a t o r s have t a k e n advantage of t h e s i m i l a r i t y between t h e e q u a t i o n s o f e l e c t r i c a l t r a n s m i s s i o n and those of h e a t t r a n s m i s s i o n i n o r d e r t o c o n s t r u c t e l e c t r i c roodels of w a l l s ( 9 ) . Thus a continuous model can be
obtained with e l e c t r o l y t e s . The d e t e r m i n a t i o n of t e m p e r a t u r e s i s t h e n replaced by a d e t e r m i n a t i o n of v o l t a g e , which i s rrruch more a c c u r a t e .
However, t h e s e provide o n l y approximate s o l u t i o n s , f o r t h e f o l l o w i n g two r e a s o n s :
Surface conductance, which i s r e p r e s e n t e d by f i x e d r e s i s t a n c e s i n such a model, i s a f u n c t i o n o f t h e temperature d i f f e r e n c e b e t ~ e e n t h e environment and t h e w a l l , t h u s o f what we a r e t r y i n g t o determine. A method i n v o l v i n g succes- s i v e approximations should enable us t o t a k e t h e v a r i a t i o n o f s u r f a c e conduc- t a n c e i n t o account. Accuracy may be decreased, however, s i n c e t h e way in
which s u r f a c e conductance v a r i e s with temperature i s n o t v e r y w e l l known.
The second reason i s much more s e r i o u s , because t h e r e i s no simple way of a v o i d l n g i t . T h i s has t o do with t h e f a c t t h a t h e a t exchange between two m a t e r i a l s i n c o n t a c t i s dependent n o t o n l y on t h e i r c o n d u c t i v i t y c o e f f i c i e n t b u t a l s o on t h e i r s p e c i f i c h e a t and d e n s i t y . E l e c t r i c a l analogy methods
cannot reproduce c o n d u c t i v i t y r a t i o s and do n o t t a k e i n t o account thermal c a p a c i t y .
Choice of t y p e s of thermal b r i d g e s
The t e s t method used i s n o t v e r y quick. It i s n e c e s s a r y t o w a i t f o r t h e e s t a b l i s h m e n t of s t e a d y s t a t e h e a t flow c o n d i t i o n s f o r each w a l l . T h i s may
t a k e t e n o r more hours f o r l i g h t p a n e l s and a s much a s f o r t y - e i g h t h o u r s f o r heavy masonry w a l l s .
Once s t e a d y s t a t e h a s been e s t a b l i s h e d w i t h t h e thermocouples i n p l a c e from t h e beginning o f t h e t e s t , a i r and s u r f a c e temperatures can be recorded i n f i f t e e n minutes. The a c t u a l measuring time i s t h u s very s m a l l compared w i t h t h e time r e q u i r e d t o r e a c h s t e a d y s t a t e . A s a r e s u l t s e v e r a l t e s t models, g e n e r a l l y f o u r , a r e grouped i n
a
s i n g l e w a l l . Only t h e most c h a r a c t e r i s t i c t y p e s a r e s t u d i e d .Our choice was guided by one prime c o n s i d e r a t i o n . W c l a s s i f i e d t h e w a l l s e i n t h r e e c a t e g o r i e s a c c o r d i n g t o t h e thermal c h a r a c t e r i s t i c s of t h e m a t e r i a l s from which t h e y a r e made:
F i r s t we have pure masonry w a l l s , i n which r e i n f o r c e d c o n c r e t e i s n e x t t o
l i g h t masonry (hollow b r i c k , a r t i f i c i a l s t o n e , l i g h t - w e i g h t c o n c r e t e , e t c . ) . These w a l l s may be c o n s t r u c t e d i n t h e t r a d i t i o n a l manner o r may c o n s i s t o f l a r g e p r e f a b r i c a t e d p a n e l s c o n t a i n i n g t h e s e elements. The t h i c k n e s s o f t h e s e w a l l s v a r i e s between 20 and 30 cm, t h e r a t i o of d e n s i t i e s of t h e m a t e r i a l s
p r e s e n t i s between 2 and 4 and t h a t of t h e thermal c o n d u c t l v i t l e s between
3
and 5.Next, we have mixed w a l l s i n which r e i n f o r c e d c o n c r e t e and very l i g h t i n s u l a t i n g m a t e r i a l s a r e used s i d e by s i d e ; t h e s e a r e g e n e r a l l y l a r g e p r e f a b - r i c a t e d p a n e l s . They have about t h e same t h i c k n e s s a s t h e above w a l l s , b u t t h e r a t i o of d e n s i t i e s of t h e m a t e r i a l s v a r i e s between 20 and 100 and t h e r a t i o of c o n d u c t i v i t l e s between 3 0 and 50.
F i n a l l y , we have l i g h t w a l l s , of t h i c k n e s s between
3
and5
cm, which c o n s i s t of very l i g h t i n s u l a t i n g m a t e r i a . 1 ~ s t a n d i n g n e x t t o wood o r m e t a l s .The c h a r a c t e r i s t i c s of t h e m a t e r i a l s c o n s t i t u t i n g t h e d i f f e r e n t t y p e s o f w a l l s a r e summarized i n t h e f o l l o w i n g t a b l e :
Heavy w a l l s
Reinforced c o n c r e t e framework with l i g h t - w e i ~ h t masonry f i l l i n g o r l a r ~ e , l i y h t - w e i a h t nlasonry p a n e l s
We have adopted t h e same t y p e s of t h e r m a l b r i d g e s t h a t had been s t u d i e d C o n d u c t i v i t y k i n kcal/(mhoc) 1 . 5 0.3 t o 0.6 1 . 5 0 . 0 3 t o 0 . 0 5 0 . 1 t o
0.15
50 t o 170 0 . 0 3 t o 0 . 0 5p r e v i o u s l y i n t h e s e m i - n a t u r a l t e s t s . For convenience t h e models c o n s i s t e d of blocks of c e l l u l a r c o n c r e t e (d = 600 k d m 3 , k = 0 . 3 ) i n t e r r u p t e d by a dense c o n c r e t e framing ( d = 2,200, k = 1 . 5 ) .
T o t a l b r i d g e . In a d d i t i o n t o t h e t o t a l thermal b r i d g e ( F i g . 4, models
A , and A , ) f o r which we took t h e same two widths a s s t u d i e d i n t h e s e m i - n a t u r a l t e s t s , namely 7 . 5 and 22.5 cm, we s t u d i e d v a r i o u s arrangements i n which, a p r i o r i , i t was p o s s i b l e t o o b t a i n more uniform i n t e r i o r s u r f a c e temperatures.
The d i f f e r e n t arrangements s t u d i e d can be reduced t o two.
F i r s t 2,rrangement: Thermal b r i d g e with i n t e r i o r d i f f u s i o n l a y e r ( F i g . 5 ) . One s o l u t i o n c o n s i s t s i n d i f f u s i n g t h e s u r f a c e t e m p e r a t u r e s by p l a c i n g a comparatively conductive m a t e r i a l o v e r t h e e n t i r e i n t e r i o r s u r f a c e of t h e w a l l . D e n s i t y In 2200 600 t o 1000 2200 2 0 t o 1 0 0 400 t o 700 3000 t o
8000
2 0 t o 1 0 0 Types of w a l l m rl 3 .5
g
4 rl +.r a63
c-lReinforced CONCRETE frame and
.
.
...
LIGHT \EIGHT IIASONRY f i l l i n g...
Large p r e f a b r i c a t e d c o n c r e t e p a n e l i n c o r p o r a t i n g very l i g h t INS ULAT I O N...
C u r t a i n o r p a n e l fagade w a l l s...
with a framing of WOOD...
o r PETAL...
and very l i g h t INSULATIONThe e f f e c t i v e n e s s of t h i s method had been demonstrated i n t h e semi- n a t u r a l t e s t s . I n t h e a r t i f i c i a l t e s t s we attempted t o c a l c u l a t e i t .
S t a r t i n g with a b r i d g e comprising a framework of compact c o n c r e t e i n t e r - s e c t i n g a c e l l u l a r c o n c r e t e block w a l l 20 cm t h i c k , we s t u d i e d t h e e f f e c t of
a
compact s l a b of c o n c r e t e 5 cm i n t h i c k n e s s ( B , ) f o r frame widths of 7.5 and 22.5 cn. W thought e i t would be i n t e r e s t i n g t o i n c r e a s e t h e c o n d u c t i v i t y of t h i s s l a b i n t h e l a t e r a l d i r e c t i o n , p e r p e n d i c u l a r t o t h e framing. For t h i s purpose, a d d i t i o n a l s l a b s , i d e n t i c a l t o t h e p r e c e d i n g ones except t h a t t h e y were s t r o n g l y r e i n f o r c e d viith i r o n rods running p e r p e n d i c u l a r t o t h e framework(B,), were a p p l i e d t o t h e i n t e r i o r s u r f a c e .
S i m i l a r l y , we t r i e d t o i n c r e a s e t h e e f f e c t i v e n e s s of a p l a s t e r c o a t i n g (of r e l a t i v e l y low c o n d u c t i v i t y ) by r e i n f o r c i n g i t s t r o n g l y with two l a y e r s of g r i l l w o r k
(B,)
.
S t i l l o t h e r specimens were c o n s t r u c t e d t o determine t h e e f f e c t of v a r i o u s degrees of f l a r i n g of t h e framework.
F i n a l l y we sought t o determine t h e e f f e c t of a framing which by p r o j e c t - i n g g r e a t l y on t h e e x t e r i o r forms a cordon, and hence a kind of c o o l i n g f i n , by i n c r e a s i n g t h e a r e a of t h e e x t e r i o r s u r f a c e .
Second arrangement: I n s u l a t i o n of thermal b r i d g e . Rio s o l u t i o n s have been s t u d i e d :
(1) P a r t i a l b r i d g e s (Fig. 6 ) . I n t h i s s o l u t i o n t h e framing does n o t go a l l t h e way through t h e w a l l and i s t h u s i n s u l a t e d by a c e r t a i n t h i c k n e s s of t h e m a t e r i a l * v~hich c o n s t i t u t e s t h e main p a r t of t h e w a l l .
The s e m i - n a t u r a l t e s t s demonstrated t h a t t h e r e was a g r e a t d i f f e r e n c e I n
e f f e c t i v e n e s s depending on whether t h e i n s u l a t i o n was placed i n s i d e o r o u t s i d e . With a view t o determining t h e s e e f f e c t s more a c c u r a t e l y we s t u d i e d t h e same types of thermal b r i d g e s i n t h e a r t i f i c i a l t e s t s .
For t h i s purpose a c e l l u l a r c o n c r e t e w a l l 20 cm t h i c k was c o n s t r u c t e d . This w a l l was p a r t i a l l y i n t e r s e c t e d by two dense c o n c r e t e frameworks, one
7 . 5 cm wide and t h e o t h e r 22.5 cn wide. The r e s i d u a l t h i c k n e s s of t h e c e l l u l a r c o n c r e t e was
5
cm and7.5
cm, r e s p e c t i v e l y . Four specimens were t h u s a v a i l - a b l e . T h l s w a l l was t e s t e d on both s i d e s s o t h a t t h e i n s u l a t i o n could be placed s u c c e s s i v e l y on t h e i n s i d e and on t h e o u t s i d e .( 2 ) Corrected b r l d ~ e s ( F i g . 7 ) . This term r e f e r s t o a b r i d g e i n s u l a t e d by very e f f e c t i v e i n s u l a t i n g n a t e r i a 1 , t h e t h i c l m c s s of which was c a l c u l a t e d s o t h a t t h e U value a t r i g h t a n g l e s t o t h e i n s u l a t e d framework would be e q u a l t o t h a t c a l c u l a t e d f o r t h e main p a r t of t h e w a l l . (We then have pc = 1.) We
a g a i n took t h e c a s e of w a l l A, where t h e t h e r m a l b r i d g e c o n s i s t e d of a dense c o n c r e t e framework i n t e r l s c c t i n g a 20 cm t h i c k w a l l of c e l l u l a r c o n c r e t e covered by a p l a s t e r c o a t i n g 2.5 cm t h i c k . In t h e f i r s t t e s t t h e p l a s t e r was removed o p p o s i t e t h e frames which were 7.5 and 2P.5 cm widc, and r e p l a c e d w i t h 2 cm of a e r a t e d p o l y s t y r e n e
.
One t e s t was c a r r i e d o u t w i t h p o l y s t y r e n e on t h e i n t e r i o r and one w i t h p o l y s t y r e n e on t h e e x t e r i o r .
The 2 cm thlclcness was chosen i n such a way t h a t U = Uc, 1 . e . pc = 1. P
Large c o n c r e t e p a n e l w i t h v e r y l i g h t i n s u l a t i n g m a t e r i a l s i n c o r p o r a t e d i n i t
I n g e n e r a l , t h c s e p a n e l s a r e b u i l t i n sandwich f a s h i o n ; a v e r y good i n s u l a t i n g m a t e r i a l , vrliich p r o v i d e s good t h e r ~ r ~ a l i n s u l a t i o n , i s sandwiched
between two c o n c r e t e s l a b s of v a r i o u s t h i c k n e s s e s which perform t h e o t h e r func- t i o n s of t h e w a l l ( n ~ e c h a n i c a l s t r e n g t h , p e r m e a b i l i t y , t h e r m a l I n e r t i a , e t c
.
).
Very f r e q u e n t l y , t h e n , t h e r m a l b r i d g e s a r e formed by t h e c o n c r e t e J o i n i n g s t r i p s between t h e o u t e r and i n n e r s l a b s o r by t h e j o i n t s between two p a n e l s . The d i f f e r e n c e between t h e c o n d u c t i v i t i e s and s p e c i f i c g r a v i t i e s of t h e d i f - f e r e n t m a t e r i a l s involved ( k = 1 . 5 kcal/(mhoc); d = 2,200 kg/rn3 f o r t h e con- c r e t e and k = 0.03 t o 0.05; d = 20 t o 100 f o r t h e insulation) r e s u l t s i n v e r y s u b s t a n t i a l t h e r m a l b r i d g e s . I n t h i s c a s e w e t r i e d t o d e t e r m i n e p r e c i s e l y t h e r e s p e c t i v e r o l e of t h e two c o n c r e t e s l a b s , e s p e c i a l l y t h a t o f t h e I n t e r i o r one. The w a l l s s t u d i e d had t h e f o l l o w i n g t h i c k n e s s e s : A c o n c r e t e s l a b o f 5 cm; a s l a b of p o l y s t y r e n e 3 cm t h i c k ( g i v i n g a u s e f u l t h l c k r ~ e s s of a b o u t 2 . 5 cm, s i n c e t h e c o n c r e t e p e n e t r a t e d s l i g h t l y i n t o t h e p o l y s t y r e n e on both i t s f a c e s ) ; and a c o n c r e t e s l a b 1 5 cm t h i c k . Openings
7.5 cm, 1 5 cni, 22.5 crn and 45 cm wide were provided i n t h e p o l y s t y r e n e , t h u s c o n s t l t u t l n g a l i n k between t h e two s l a b s , and a t h e r l r ~ a l b r i d g e .
These w a l l s were t e s t e d w i t h t h e
5
cm s l a b and t h e 1 5 cm s l a b s u c c e s s i v e l y on t h e ;rarm s i d e .S p e c i a l t h c r ~ t a l b r i d r e s
;:e a l s o I n i t i a t e d a s t u d y of therrnal b r i d g e s e x i s t i n g a t c o r n e r s . The s t u d y Is evcn more con,plex, because i t i s n e c e s s a r y t o d i s t i n g u i s h between t h e c o r n e r where ttro i d e n t i c a l e x t e r n a l w a l l s J o i n ( ~ 1 . g .
8 )
and t h e c o r n e r where an e x t e r n a l w a l l is joined by a partition o r f l o o r (I?ig. 9 ) .T h e r c a l bridr;es a t t h e c o r n e r between two e x t c r n a l w a l l s . In t h i s c a s e , even k ~ i t h two w a l l s h a v i n g t h e same U v a l u e , t h e t e m p e r a t u r e s a t t h e c o r n e r t r i l l be d i f f e r e n t from t h e terirperatures e l s e w h e r e on t h e w a l l s . There a r e two r e a s o n s f o l h t h i s :
F i r s t t h e s u r f a c e a r e a of t h e e x t e r n a l w a l l Is g r e a t e r t h a n t h a t of t h e i n t e r n a l w a l l . Thc car;& f l o w of c o l d fro1-1 t h e e x t e r i o r w i l l t h u s l e a d t o
lower t e n ~ p e r a t u r c s th a n on a w a l l w i t h p a r a l l e l f a c e s .
Then, t h e r e i s a r e d u c t i o n i n t h e r a d i a t i o n and c o n v e c t i o n s u r f a c e h e a t exchanges. T h i s f u r t h e r c o n t r i b u t e s t o t h e l o w e r i n g o f t h e t e m p e r a t u r e on t h e i n s i d e s u r f a c e .
A r t i f i c i a l t e s t s on t h i s t y p e of t h e r m a l b r i d g e a r e r a t h e r u n c e r t a i n and
i t i s d o u b t f u l whether o r n o t t h e s u r f a c e h e a t exchanges can be e x a c t l y r e p r o - duced. On t h e o t h e r hand, we p o s s e s s t h e r e s u l t s o f n a t u r a l t e s t s c a r r i e d o u t i n Geriany a t t h e Holzkirchen ~ t a t l o n ( ~ ) , where t e m p e r a t u r e s were measured on t h e i n t e r i o r surfac'e of t h e n o r t h w e s t c o r n e r of more t h a n 20 houses w i t h d i f f e r e n t k i n d s o f w a l l s .
P a r t i t i o n s and f l o o r s . Where an e x t e r n a l w a l l meets a p a r t i t i o n o r f l o o r t h e problem I s v e r y d i f f e r e n t . The p a r t i t i o n o r f l o o r i s a t t h e i n t e r i o r room t e m p e r a t u r e (we assume t h a t t h e w a l l o r f l o o r s e p a r a t e s two e q u a l l y h e a t e d s p a c e s ) . The e x t e r i o r s u r f a c e a r e a i s n o t a s l a r g e a s t h e i n t e r i o r s u r f a c e a r e a . Thus t h e two e f f e c t s mentioned p r e v i o u s l y oppose one a n o t h e r . F u r t h e r - more, t h e p a r t i t i o n o r f l o o r o f t e n d i f f e r s g r e a t l y i n i t s therrnal c h a r a c t e r i s - t i c s from t h e e x t e r i o r w a l l .
F i n a l l y , b o t h p a r t i t i o n s and f l o o r s can t e r m i n a t e f l u s h w i t h t h e faqade, o r b e f o r e r e a c h i n g t h e fagade, o r can even extend beyond i t , forming a cordon. Only t h e c o r n e r between t h e e x t e r i o r w a l l and t h e p a r t i t i o n h a s been s t u d i e d . For t h i s purpose a s t r u c t u r e r e p r e s e n t i n g t h e p a r t i t i o n was joined a t r i g h t a n g l e s t o t h e 2 2 . 5 cm wide frames of w a l l s A, B and C. T h i s s t r u c t u r e was con- s t r u c t e d from s o l i d b l o c k s i d e n t i c a l w i t h t h e c o n c r e t e of t h e frame.
I n t h e c a s e of w a l l B we a l s o s t u d i e d t h e i n f l u e n c e of a n e x t e r i o r s t r u c - t u r e for*ming a cordon and c o o l i n g f i n .
L i g h t w a l l s ( c u r t a i n r r a l l s , fagade p a n e l s )
One of t h e e s s e n t i a l f e a t u r e s of t h i s kind o f c o n s t r u c t i o n i s t h e v e r y s m a l l t h i c k n e s s of t h e v:all which i s nade p o s s i b l e by t h e u s e of good i n s u l a - t i o n : t h e sane U v a l u e can be o b t a i n e d w i t h a w a l l u s i n g a 2 cm t h i c k n e s s of good i n s u l a t i o n ( k = 0.03 t o 0 . 0 5 ) a s w i t h one 20 cm t h i c k i n l i g h t masonry.
In o r d e r t o cornpensate f o r t h e i r l a c k of thermal c a p a c i t y t h e s e w a l l s must have v e r y good U v a l u e s (around 1 . 0 ) . Such c o e f f i c i e n t s a r e e a s i l y o b t a i n e d w i t h srnall t h i c k n e s s e s o f i n s u l a t i n g m a t e r i a l .
I.Shen t h i s i n s u l a t i o n i s i n t e r r u p t e d by a frame which i s a l s o v e r y t h i n , s i g n i f i c a n t therrnal b r i d g e s a r e formcd
.
b!e s h a l l d i s t i n g u i s h between t h e r n a l b r i d g e s produced by wooden menbers which g e n e r a l l y m ~ k e up t h e I n t e r n a l frzrning o f p a n e l s and t h o s e produced by m e t a l franics, whether t h e y a r e i n t e r n a l frames, a s a r e f r e q u e n t l y used i n t h i s
t-ype of c o n s t r u c t i o n t o ensure r i g i d i t y and e a s e of a s s e ~ ~ l b l y , o r a r e e x t e r n a l frar~ie:: i n which t h c kzo~r~o,o;encous p a n e l i s y1acc.d.
Wooden o r s i i : ~ i l a r franiin:
T o t a l brid,yc. The main p a r t of t h e models was c o n s t r u c t e d of
3
cm t h i c k expanded p o l y s t y r e n e(I<
= 0.03 kcal/(nlh°C); d = 20 k d 1 n 3 ) .W s t u d i e d t h e e f f e c t of t h e width of t h e frame. e For t h i s purpose t h e i n s u l a t i o n was i n t e r r u p t e d by members having t h e same t h i c k n e s s a s t h e p a n e l ( 3 cm) b u t of d i f f e r e n t widths ( 0 . 6 , 1,
3
and 6 cm).
In 01-der t o e s t i m a t e t h e e f f e c t of changing t h e r a t i o of thermal charac- t e r i s t i c s of t h e m a t e r i a l s , models i d e n t i c a l w i t h t h e above were b u i l t , b u t i n which t h e wood was r e p l a c e d by pressed wood t h a t was more i n s u l a t i n g and
l i g h t e r ( k = 0.06 and d = 500 kg/m3) t h a n t h e v~ood used i n t h e p r e v i o u s t e s t . Bridge with i n t e r i o r d i f f u s i o n l a y e r . Me a g a i n wished t o determine t h e e f f e c t of a conducting l a y e r on t h e i n t e r i o r s u r f a c e . Some p a n e l s use alumin- ium f o i l under t h e i n t e r i o r l a y e r a s vapour b a r r i e r s . It i s q u i t e p o s s i b l e t h a t t h i s h i g h l y conductive m a t e r i a l s i g n i f i c a n t l y d i f f u s e s t h e temperatures d e s p i t e t h e small t h i c l m e s s e s employed. . In o r d e r t o c a l c u l a t e t h i s phenomenon
we cemented f i r s t a s h e e t of aluminium
1/10
mm
t h i c k on t o t h e models ( k =170 k c a l / l n h O ~ ) and t h e n a s h e e t of copper 2/10 nm t h i c k ( k = 350 kcal/rnhOc). These s h e e t s had been p a i n t e d g r e y t o rilaintain t h e sane s u r f a c e h e a t exchange a s b e f o r e .
Metal framing
T o t a l b r i d g e . To begin with we s t u d i e d t o t a l b r i d g e s formed with v a r i o u s s t e e l s e c t i o n s i n t e r s e c t i n g a p o l y s t y r e n e p a n e l
3
cm t h i c k .7Jc t h e n sought t o determine t h e i n f l u e n c e of i n c r e a s i n g o r d e c r e a s i n g t h e p r o j e c t i o n of an e x t e r i o r cordon c o n s t i t u t i n g a c o o l i n g f i n .
I n t e r r u p t e d b r i d g e . Seeking a remedy t o t h i s type of thermal b r i d g e we s t u d i e d , f o r a simple t h e o r e t i c a l case, t h e e f f e c t of an i n t e r r u p t i o n i n t h e thermal b r i d g e , o r more e x a c t l y a d e c r e a s e i n t h e metal c r o s s - s e c t i o n a l a r e a and an i n c r e a s e i n t h e thermal p a t h l e n g t h .
P r a c t i c a l e x a ~ i p l e s
.
F i n z l l y , we s t u d i e d some p r a c t i c a l examples of thermal b r i d g e s a t t h e j o i n t between two p a n e l s . Again, s e e k i n g t o c o r r e c t t h e thermal b r i d ~ c , we s t u d i e d t h e e f f e c t of i n t e r r u p t i n g t h e framing and i t si n s u l a t i o n with various t y p e s of I n t e r i o r and e x t e r i o r mouldings. R e s u l t s
Valls w i t h r e l n f orced c o n c r e t e framing and l i g h t masonry f i l l i n q
The r e s u l t s obtained a r e shown i n Table I., where we g i v e t h e v a l u e s of
P
, deterrnincd from tlie rneasu~>ed tenlperaturcs arld t h o s e of p c a l c u l a t e d from
C
T o t a l b r i d g e . A c t u a l l y a t r u e t o t a l b r i d g e was not t e s t e d s i n c e no such b r i d g e e x i s t s i n p r a c t i c e . There a r e always i n t e r i o r and e x t e r i o r c o a t i n g s . The f i r s t t e s t s c a r r i e d o u t on w a l l s A (A,
-
A S ) enabled us t o o b t a i n t h e r e a l value of t h e t o t a l b r i d g e i n a w a l l with c o a t i n g s and we found t h a t :pm = 2 . 1 f o r t h e 7 . 5 cm width;
pm = 2.3 f o r t h e 22.5 cm width.
kle n o t e t h a t t h e narrower t h e framing t h e s m a l l e r pm, and t h a t i n both c a s e s i t i s l e s s than pc : pc = 2.4.
Thermal b r i d g e w i t h i n t e r i o r d i f f u s i o n l a y e r . The e f f e c t of t h e c o n c r e t e s l a b placed on t h e i n t e r i o r s u r f a c e i s t o f l a t t e n t h e curve of i n t e r i o r s u r f a c e temperatures. The important improvement o b t a i n e d w i t h a simple s l a b ( B , ) must be noted:
pm changes from 2 . 1 t o 1.4 f o r t h e 7 . 5 cm width; and from 2.3 t o 1.7 f o r t h e 22.5 cm width.
These v a l u e s a r e f a r l e s s than p c
'
which i s s t i l l e q u a l t o 2.4:-
The f l a r i n g of t h e framework (B,-
B,) makes i t p o s s i b l e t o o b t a i n s t i l l s m a l l e r pm v a l u e s . I n t h l s way w e achieved v a l u e s of1.3
f o r 1 = 7.5, and 1.45 f o r 1 = 22.5;-
P u t t i n g reinforcement (B,) i n t h e s l a b makes very l i t t l e d i f f e r e n c e . Depending on t h e width, pm changes from 1.4 t o1.35
and from 1.7 t o1 . 6 5 .
We a l s o t e s t e d t h e e f f e c t of reinforcement i n t h e p l a s t e r s l a b i n s t a l l e d i n such a way a s t o make t h e r e l a t i v e l y i n s u l a t i n g p l a s t e r more conductive in
t h e l a t e r a l d i r e c t i o n . Again (B,) t h e r e s u l t s were i n c o n c l u s i v e ; p, changes, depending on t h e width, from 1.95 t o 1.9 and from 2 . 2 t o 2.15. The e f f e c t i s
t h u s n e g l i g i b l e .
Generally speaking pm d e c r e a s e s a s 1 d e c r e a s e s and i t i s always l e s s p c .
Note. The e f f e c t of a n e x t e r i o r f i n (B) i s a l s o comparatively s l i g h t i n t h i s case; i t causes pm t o change from 1 . 7 t o 1.8 ( B compared t o B, ).
P a r t i a l b r i d g e s . The r e a d e r w i l l n o t e t h e l a r g e d i f f e r e n c e i n t h e shape of t h e curves obtailied when t h e i n s u l a t i o n i s on t h e i n s i d e ( C , and C,) and when i t i s on t h e o u t s i d e ( C , and C,).
( a ) In t h e c a s e of i n t e r i o r i n s u l a t i o n a v e r j good c o r r e c t i o n of t h e t h e r n a l b r i d g e i s o b t a i n e d , and t h e narrower t h e fraine t o be p r o t e c t e d , t h e b e t t e r t h e c o r r e c t i o n . The c o l d e s t p o i n t i s d i r e c t l y o p p o s i t e t h e c e n t r e of
t h e frame. Tne s n a l l d i f f e r e n c e obtalncd with d i f f e r e n t t h l c k n e s s e s of i n s u l a t i o n should be noted (C
,
conlpared t o C 2 ).
Note ay;ain t h a t pm < pc.
( b ) \!hen t h e i n s u l a t i o n i s p l a c e d on t h e c x t e r i o r t h e r e i s no inlprovement and now i t secns a s though t h e s i : ~ a l l e r t h e width of t h e frame, t h e more pro- nounced i s t h e e f f e c t of t h e thermal b r i d g e . The t h i c k n e s s of t h e i n s u l a t i o n
i s more s i g n i f i c a n t
.
We a ~ a i n n o t e t h a t t h e p o s i t i o n of t h e c o l d e s t p o i n t i s s t i u a t e d o p p o s i t e t o t h e f r a n e , b u t n e a r t h e edge. Note a l s o t h e e x i s t e n c e of a warm s p o t n e a r t h e frame. The temperature t h e r e i s h i g h e r than i n t h e main p a r t o f t h e w a l l .
F i n a l l y i t must be emphasized t h a t prfl i s d e c i d e d l y g r e a t e r t h a n p c . It
is t h u s a n e r r o r t o suppose t h a t t h e c l a s s i c a l c a l c u l a t i o n always y i e l d s a
margin of s a f e t y . These r e s u l t s a r e a b s o l u t e l y o p p o s i t e t o t h o s e o b t a i n e d f o r i n t e r i o r i n s u l a t i o n .
We s h a l l e x p l a i n t h i s i n P a r t 111.
Corrected b r i d g e s . ( a ) The above r e s p l t s , i n t h e c a s e of e x t e r i o r i n s u l a - t i o n , a r e r a t h e r s u r p r i s i n g ; t h e t e s t s c a r r i e d o u t on w a l l D with e x t e r i o r c o r r e c t i o n have confirriled them. Although c o n d i t i o n s were chosen s o t h a t t h e U
v a l u e of t h e w a l l a t t h e frame would be t h e same a s i n t h e main p a r t of t h e w a l l ( p c = l ) , very d i f f e r e n t temperatures a r e observed on t h e i n t e r i o r s u r f a c e .
I n p a r t i c u l a r , f o r t h e 7.5 cm width r e p l a c i n g t h e e x t e r i o r p l a s t e r c o a t i n g w i t h 2 cn of p o l y s t y r e n e has p r a c t i c a l l y no e f f e c t on t h e telnperatures and
g i v e s s u b s t a n t i a l l y t h e same v a l u e f o r pm.
An improvement of t h e t h e r m a l b r i d g e can be o b t a i n e d by having t h e
insulation o v e r l a p t h e frame c o n s i d e r a b l y on both s i d e s , b u t t h e r e s u l t s remain u n s p e c t a c u l a r . For a narrow b r i d g e a n o v e r l a p p i n g on b o t h s i d e s of 7 . 5 cm e q u a l t o 1 s t i l l g i v e s a hip& pin v a l u e ( 1 . 1 5 ) . F o r a wider b r i d g e a n o v e r l a p p i n g on b o t h s i d e s of 22.5 crn ( e q u a l t o 1 ) g i v e s pm =
1.5.
( b ) I n t h e c a s c of i n t e r i o r c o r r e c t i o n , t h e temperature o p p o s i t e t h e frame i s h i g h e r than on t h e main p a r t of t h e w a l l ; t h e c o l d e s t s p o t , however, i s
d i s p l a c e d o u t s i d e t h e frafilc. The t h e frame, t h e c o l d e r t h i s s p o t w i l l b e .
I n t e s t s
D,,
rcherc t h e i n s u l a t i o n o v e r l a p s t h e frame, good improvement can be observed. Horxver, i t does n o t appear t h a t t h e width o f t h e i n s u l a t i o n r e q u i r e d t o o b t a i n a given pm i s a l i l l e a r f u n c t i o n o f t h e width o f t h e frame. An o v e r l a p p i n g of7.5
c n f o r a frame width of 7.5 cm i s s u f f i c i e n t (pm = 1 . 2 5 ) ~ while an o v e r l a p p i n j of 22.5 C I , ~ f o r a 22.5 v i d e fra~lie i s e x c e s s i v e ( p m = 0.87).F i n a l l y , :.re ~ o t e t h c d i f f e r e n c e of form? i n t h e temperature curves
o b t a i n e d betrveel? t h e c a s c lrherc t h e i n s u l a t i o n i s i n s i d e , and t h a t where i t i s
o u t s i d e . To sho:.; t h i s r e z u l t rnorc c l e a r l y we have p l o t t e d t h e v a l u e s of p f o r both of t h e s e c a s e s on t h e sar3e graph ( P i g . 1 0 )
-
t e s t s D , andD3.
Althou& t h e pm v a l u e s a r e n o t very d i f f e r e n t t h e curve of p f o r i n t e r i o r i n s u l a t i o n i s~iluch l e s s f l a t i n t h c zonc of p > 1 . 5 than t h c curvc obtained f o r e x t e r i o r i n s u l a t i o n .
Lar.qc concre tc panel i n c o r p o r a t i n g l i ~ h t i n s u l a t i o n The p e s u l t s are ziven i n Table 11.
The very h i g h value of P , obtained when t h e framing Is very wide (pm = 3 . 2 ) should be noted.
l l i t h t h e
15
c m s l a b on t h e i n s i d e , t h e b e s t c o r r e c t i o n i s obtained with t h e narrow thermal b r i d g e . A width of7.5
crn s t i l l g i v e s a h i g h pm value(1.8).
With t h e
15
cm s l a b on t h e o u t s i d e , t h e v a l u e s of pm rcrnaln very high (above3 ) .
For t h e l a r g e r b r i d g e widths (15 and 22.5 cm) t h e y a r e s l i g h t l y above p c ( p c = 3.Ll).S p e c i a l thermal b r i d ~ c s
P a r t i t i o n s and f l o o r s . Table I11 shows t h e r e s u l t s obtained i n t h e f o u r c a s e s s t u d i e d .
The c o l d e s t p o i n t i s found on t h e p a r t i t i o n a few c e n t i m e t r e s away from t h e c o r n e r .
Ln
t h e l a s t c o l r n i of Table I11 a r e given v a l u e s of pill obtained on thermal b r i d g e s a t w a l l s without p a r t i t i o n s . Those obtained with p a r t i t i o n s a r e alwayslower. T h i s i s due t o t h e f a c t t h a t tile c o n c r e t e p a r t i t i o n , away from t h e corner, i s a t tenipellature Ti throu&h i t s e n t i r e mass s o t h a t t h e r e i s a con- s i e e r a b l e flow of h e a t i n t h e d i r e c t i o n of t h e c o r n e r .
The t o t a l bridge ( A ) now g i v e s a pm value of o n l y 1 . 9 i n s t e a d of 2.4.
Wc again f i n d t h a t good d i f f u s i o n i s obtained w i t h t h e i n t e r n a l c o n c r e t e s l a b , e n a b l i n g t h c a t t a i n m e n t of p, =
1.5
without a cordon and p,= 1 . 5 5d e s p i t e a l a r z e cordon. E x t e r n a l i n s u l a t i o n c o n t i n u e s t o be i n e f f e c t i v e (pm =
Corner b e t w e n two o u t s i d e v a l l s . A t a c o r n e r betwecn two e x t e r n a l w a l l s v a l u e s of pm, which can be derived from Gcrman t e s t s ( 7 ) a r e h i m e r . For w a l l s with U v a l u e s of 1.2 t o
1.5
t h e y a r e i n t h e v i c i n i t y of 1.8, while f o r w a l l s with U valucs of l c s s t h a n 1 t h e y reach 2.5.Thc shape of the curvc i s t h e n d i f f e r e n t .
Figure 1 2 shov~s th e temperatures obtained a t t h e c o r n e r between t h e west and n o r t h v:alls, v;hicii were s o l i d b r i c k
38
cm t h i c k . The curve shotvs a s h a r p peak; t h e r e s u l t i s a c o l d e r b u t l c s s extensive a r e a . Thus t h e e f f e c t o f t h e maximurn p In uhich i s obtained con be l e s s s e v e r e .~ i y h t w a l l s ( c u r t a i n w a l l s , fc?.$ade p a n e l s )
llooden _fra:ninz
T o c . Thc r e s u l t s a r e given i n Table
