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REFERENCE

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Hi" 5! "ECHNICAL NOTE 710-7

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BUILDING

RESEARCH TRANSLATION

Weak Thermal Points

Or Thermal Bridges
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards1 was established by an act of Congress March 3,

1 901 . The Bureau's overall goal is to strengthen and advance the Nation's science and

technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Computer Sciences and

Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates

that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics —

Linac Radiation 2 — Nuclear Radiation '- — Applied Radiation 2 — Quantum

Electronics :| — Electromagnetics :! — Time and Frequency 3 — Laboratory

Astrophysics •"• — Cryogenics 3

. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research lead- ing to improved methods of measurement, standards, and data on the properties of

well-characterized materials needed by industry, commerce, educational institutions, and Government; provides advisory and research services to other Government agencies;

and develops, produces, and distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials and the following divisions: Analytical Chemistry—Polymers—Metallurgy—Inorganic Materials—Reactor

Radiation—Physical Chemistry.

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upon request. The Institute also monitors NBS engineering standards activities and

provides liaison between NBS and national and international engineering standards

bodies. The Institute consists of a Center for Building Technology and the following

divisions and offices: Engineering and Product Standards—Weights and Measures—Invention and

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consists of the following offices and divisions: Information Processing Standards—Computer Information—Computer Services —Systems Development—Information Processing Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS and other agencies of

the Federal Government; promotes the development of the National Standard Reference Data System and a system of information analysis centers dealing with the broader

aspects of the National Measurement System; provides appropriate services to ensure

that the NBS staff has optimum accessibility to the scientific information of the world,

and directs the public information activities of the Bureau. The Office consists of the following organizational units: Office of Standard Reference Data—Office of Technical Information and

Publications—Library—Office of International Relations.

1 Headquarters and Laboratories at Galthersburg, Maryland, unless otherwise noted ; mailing address Vashington, D.C. 20234.

2 i art of the Center for Radiation Research.

8 Located at Boulder, Colorado 80302.

4

1.J art of the Center for Building Technology.
BUILDING RESEARCH TRANSLATION

Weak Thermal Points or Thermal Bridges

J. Berthier

Centre Scientifique et Technique du Batiment

Paris, France

Translated by National Science Library

National Research Council

Ottowa, Ontario, Canada

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of

transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

'**»e,uof*

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued May 1973
National Bureau of Standards Technical Note 710-7

Nat. Bur. Stand. (U.S.), Tech. Note 710-7, 96 pages (May 1973) CODEN: NBTNAE

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. 03.46:710-7).

Price $1.25 domestic postpaid or $1.00 G.P.O. Bookstore
FOREWORD

The United States/French Cooperative Program on Building

Technology entails an exchange of personnel between the

National Bureau of Standards (Center for Building Technology)

and the Centre Scientifique et Technique du Batiment

(CSTB) of France. The program also involves the exchange

of information between the two research organizations.

It is felt that some of the documented information can

be usefully shared with the U.S. building industry; and,

therefore, certain papers were selected for reproduction

in media on sale to the public by the Government Printing

Office. It should be understood that the CSTB documents

made public through such media as this TECHNICAL NOTE

do not necessarily represent the views of the National

Bureau of Standards on either policy or technical levels.

At the same time, building researchers at the National

Bureau of Standards consider it a public service to share

with the U.S. building industry certain insights into

French building technology.

7? &J^£f

ames R. Wright, Director

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

xix

WEAK THERMAL POINTS OR THERMAL BRIDGES

by

1/

J. Berthier

Uniformity of temperature on the internal face is one of the

essential hygro-thermal qualities for a wall.

Cold bridges, which are the cause of uneven temperatures, constitute

a weakness which ought to be corrected.

The author describes a large number of tests carried out with

various types of wall (dense walls and lightweight panels) in order to assess the importance of cold bridges and to determine the effectiveness

of possible remedies; he shows that the accepted theory used in the

calculations of U-coeff icients is unsatisfactory when estimating surface

temperatures. The results obtained can be explained, however, by means

of two simple hypotheses; on the basis of these there are practical

rules which can be used in establishing the importance of cold bridges,

and recommendations for reducing them.

Key words: Floors and panels; moisture condensation: thermal bridges;

thermal insulation; U-values of walls.

—This paper is translated from the French original and is published

under the Center for Building Technology, Centre Scientifique et

Technique du Batiment information exchange program.
INTRODUCTION

Considerations of comfort, economy and health require the U value

of the external walls of a building to be kept small. The upper limit

depends on a number of factors, for example: —the function of the wall (roof, facade, gable, etc.); —the type of building (school, office, various categories of

dwelling)

;

—geographical location of the building (climatic zone)

;

—the wall mass.

Tables published in C.S.T.B. Cahiers No. 34 and the building rules

contained in R.E.E.F.-58 (Bib. 2, 3) give maximum recommended U values in

each case.

Merely to follow these rules, however, is not enough to assure

satisfactory hygrothermal behavior of the wall. For this the ideal

would be for the temperature to be the same at every point an the

interior face of the wall. In the case of a homogeneous wall separating

two spaces, when the interior temperature is T. and the outside temperature is T , the temperature on the interior surface of the wall under

e i a steady state condition, is given by the equation

>i = T± - -jL(T

£

- T

e

)

where U is the overall heat transmission coefficient and h^ is the

inside surface conductance .

The coefficient characterizes the thermal exchanges between the air and

the surface of the wall. It depends to a small extent on surface condition and much more on the velocity of the air in contact with it.
The above equation shows that there are two causes of non-uniformity

in the surface temperatures. First there is heterogeneity in the wall,

producing different local U values. This is very frequent because

materials with different thermal coefficients are increasingly being

placed side by side in constructions, for example: —a filling of hollow bricks next to a framing of reinforced

concrete; —a metal framing around a panel of a facade or its internal

framing, next to the insulation which it encloses.

All those elements which have less insulating effect than the main

part of the wall are weak points from the thermal point of view. They

are commonly known as "thermal bridges".

The second cause is a variation of surface heat exchange resulting

in a variation of the coefficient h.. These variations may be produced

by a decrease in the heat transfer due to radiation (on an aluminium

moulding, for example) or convection (at corners, behind furniture).

Generally speaking, the observed phenomena are the results of these

various causes and it is impossible to determine the share of each.

The disadvantages of non-uniformity of surface temperatures are

numerous.

In summer thermal bridges lead to warmer interior temperatures. In

a temperate climate this is not very serious and the wall does not suffer

from it. During cold weather, however, when the temperature of a thermal

bridge is lower than the main part of the wall the situation is different.

Several phenomena may then be observed.
The main one is condensation of moisture from the room air on the

surface of the wall. This will happen as soon as the dew-point of the

humid air of the room is above the temperature of the thermal bridge surface.

Condensation will occur first at this point and the amount of condensation

will be greatest either during a period of high humidity or one of severe

cold.

It is not our purpose here to study this phenomenon and its

consequences in detail, but we wish to point out that a cold spot on the

surface of a wall is its primary cause. The extent of condensation will

depend, of course, on the conditions of the building occupancy (production

of moisture, ventilation, heating, etc.) but before attempting to protect

against the effects of this phenomenon it appeared necessary that the

wall itself should be designed to prevent condensation by providing a

sufficiently uniform temperature on the interior face.

furthermore, in the absence of any humidity in the room, a cold

spot gives rise to another phenomenon known as dust patterns. Even in

rooms used as offices, where the atmosphere is always dry, the cold zones

resulting from the beams, ties or even joints between masonry blocks eventually become stained by a considerable deposit of dust. This phenomenon

can apparently be explained as follows

:

The dust particles are kept in suspension in the air by molecular

agitation and the shocks resulting from it. This agitation increases

with increasing temperature. In the vicinity of a cold spot a turbulence

occurs in the interaction, and the dust particles are thrown against the

cold spot. Since the latter is generally moist as a result of even very

slight condensation, the dust particles readily cling to the surface.

4
Photo 1 Traces of condensation on the ceiling of a basement

apartment room on cold spots produced by the tie beam and the joists of the ground floor.

Photo 2 Condensation traces in the room of a ground floor apartment at the gable end on cold spots produced by

the corners of the floors and the external walls.
Although this phenomenon is not as serious as condensation, it

indicates that whatever the type of construction, a thermal bridge is

always a defect.

The purpose of the present article is to report on the studies made

by C.S.T.B. with a view to investigating practical methods of obtaining

satisfactory uniformity of temperatures on interior surfaces.

Part I will be devoted to a qualitative study of the phenomena

Part II will report on some artificial quantitative tests carried

out on a number of special cases.

Part III will attempt to explain the results on the basis of a

simplified theory. From this we shall be able to generalize in a number

of simple cases.

Finally, in Part IV, drawing conclusions from our study, we shall

give practical rules for estimating the effect of a thermal bridge and

correcting it.

PART I: QUALITATIVE APPROACH TO THE

PROBLEM BY SEMI-NATURAL TESTS

PRINCIPLE OF SEMI-NATURAL TESTS

The principle underlying these tests is as follows.

In a building, whose external walls are to be studied, a warm and

humid atmosphere is produced during the winter in the interior close to

the inside surface of the wall. The external conditions are natural.

These tests were carried out only on walls of the reinforced

concrete frame type filled with lightweight masonry.
To facilitate our study we have chosen for the filling cellular

concrete of density 0.6 kg/dm3 (k = 0.3 kcal/mh°C) which is decidedly

more insulating than the mass concrete of the framework (d = 2.2; k = 1.5).

Three types of thermal weak points have been considered. —total bridge, with framework traversing the wall completely; —partial bridge with internal or external insulation; —bridge and internal concrete slab diffusing the heat flux.

In the second case the width of the thermal bridge was varied as

well as the thickness of the insulation.

These walls had an external coating of lime-cement mortar and an

interior coating of plaster 1 cm thick. A water reactive paint was

applied over the plaster in order to emphasize the condensation and to

permit a rough estimation of its extent.

TEST RESULTS .

Figure 1, shows the construction of the different bridges, and the

results obtained by testing follow:

In the case of the total bridge, i.e. the framework traversing the

entire thickness of the wall, either for the wide bridge (vertical framing

member in the center of the figure) or the narrow bridge (horizontal frame

member to the left), very considerable traces of condensation appeared.

At the extreme left, on the thermal bridge with diffused heat flux

the mildews are definitely less apparent.

At the right, on the various partial cold bridges with interior

insulation, the traces of condensation are practically non-existent. No

difference can be discerned between the wide and narrow ones on the one

hand and the more or less insulated ones on the other.
However, to the left, on the two partial cold bridges with external

insulation the condensation traces are very marked, practically similar to

those obtained on the total cold bridges

At first glance this appears to be a surprising result. Actually,

the calculated thermal conductance of the wall at the thermal bridge is

theoretically the same whether the insulation is placed inside or outside.

Similarly the thermal bridge with diffused heat flux has the same U value

as the total bridge.

Actually, these results show that the problem is much more complicated. They also indicate that the problem definitely cannot be solved by

considering solely the ratio of U factors at right angles to the thermal

bridge and in the main ("running") part of the wall. Moreover, such

limited consideration even precludes predicting what form or direction the

phenomena will take.

Because of these difficulties we conducted much more accurate and

detailed artificial tests enabling us to quantify these phenomena.*

PART II: QUANTITATIVE STUDY - ARTIFICIAL TESTS

CHARACTERISTICS OF A THERMAL BRIDGE

The problems presented by thermal bridges can be reduced to the

determination of the temperatures on the interior face of the heterogeneous

wall when the latter is situated in a cold external and warm internal

environment. The curve giving the temperature distribution on the internal

surface, as shown for example in fig. 2, then enables us to characterize

the thermal bridge. Two elements must be considered, first the spreading

* Translated by the Joint Publication Research Service, U.S. Department

of Commerce, Washington, D.C.

8
out of the curve which enables us to determine the width of the zone where

condensation is to be anticipated, and second, the temperature of the

coldest spot. The absolute value of this temperature is not so important

because it depends essentially on the interior and exterior temperatures.

We, therefore, introduce a coefficient which characterizes the heterogeneity

of the interior surface temperature:

T± - 6 P = Ti - e c

where T. is the interior air temperature, 6 the interior surface temperature of a point in the thermal bridge zone and, 6 the interior surface

temperature at a point remote from the thermal bridge in the main part of

the wall.

In part III it will be shown that this ratio is practically independent of the interior and exterior temperatures. Denoting the maximum

value of p by p , then

Ptti "

Ti - 9m

'm T-L - 6 i °c

where 8 m

is the temperature of the coldest point on the thermal bridge.

This coefficient, which we shall call the coefficient of interior

surface temperature heterogeneity, indicates to a certain extent by how

much the coldest point is colder in relation to the internal air temperature than the main part of the wall.

We shall wish to compare this coefficient to the coefficient p

(theoretical calculated coefficient) which is determined from the wall U

value at the thermal bridge (U ) and the wall U value away from the thermal
bridge (U) as follows:

Test Method

U

P

The exact determination for the calculation of the curve of p is

impractical.

The method of direct observation is delicate, because the measurement of a surface temperature is difficult to carry out with precision.

However, it is the only way in which the various factors which may

influence p can be taken into account

.

The tests were carried out in the thermal test chamber of the

Champs-sur-Marne experimental station^-*-' (Fig. 3) .

The wall containing the thermal bridges to be studied divided the

room into two spaces. The interior warm space was kept at a controlled

temperature of approximately 30°C while the exterior cold space was kept

at about -5°C. The interior temperature was placed intentionally higher

than average room temperature in order to increase the difference between

the two environments, thereby enhancing the accuracy of the measured

interior surface temperature. This will not affect the results because

the values of p are practically independent of temperature. Air temperatures were recorded continuously during the test by means of resistance

thermometers connected to a recording potentiometer. Furthermore, since

the purpose of the study was to eliminate condensation, experiments were

designed so that the thermal characteristics of the materials and their

temperature would not be affected by condensation. The atmosphere of the

interior room was dry (approximately 35% relative humidity) so that no

condensation would take place on the cold spots.

10
The wall surface temperatures were measured with iron-constantan

thermocouples 1/10 mm in diameter. These thermocouples were connected

to a 12-point recording potentiometer. Temperatures were thus recorded

simultaneously at 12 points on the zone in question. We thus obtained an

accurate profile of the surface temperature curve (Fig. 2)

.

Note 1 ;

We should like to recall one of the heat-chamber characteristics essential to the study in question. This characteristic involves surface

heat transfers between environments and wall. A certain number of measurements taken on homogeneous walls revealed that ventilation conditions

created in both chambers, enabled us to obtain, for walls with a U factor

of approximately 1.2 kcal/(m h C) , surface heat transfers of close to

7kcal/(m h°C) for the outside environment. It was most important that

during our tests, inside surface transfers for the test wall be close to

the actual transfers, or at least to theoretically determined transfer

values (i.e., hi=7kcal/(m h C) . It may, in fact, be assumed that the

secondary phenomena acting upon them will cause them thus to vary in accordance with their real law of variation.

Note 2 ; Some investigators have taken advantage of the similarity between

the equations of electrical transmission and those of heat transmission

in order to construct electric models of walls (Bibliography 9) . Thus a

continuous model can be obtained with electrolytes. The determination of

temperatures is then replaced by a determination of voltage, which is much

more accurate.

* Translated by the Joint Publication Research Service, U.S.. Department

of Commerce, Washington, D.C.

11
However, these provide only approximate solutions, for the following

two reasons

:

Surface conductance, represented by fixed resistances in such a

model, is a function of the temperature difference between the environment and the wall, which is precisely what we are trying to determine.

A method involving successive approximations should enable us to take

the variation of surface conductance into account. Accuracy may be

decreased, however, since the way in which surface conductance varies

with temperature is not very well known.

The second reason is much more serious, because there is no simple

way of avoiding it. This has to do with the fact that heat exchange between two materials in contact is dependent not only on their conductivity

coefficient but also on their specific heat and density. Electrical

analogy methods cannot reproduce conductivity ratios and do not take

into account thermal capacity.

Choice of types of thermal bridges

The test method used is not very quick. It is necessary to wait for

the establishment of steady state heat flow conditions for each wall.

This may take ten or more hours for light panels and as much as fortyeight hours for heavy masonry walls.

Once steady state has been established with the thermocouples in

place from the beginning of the test, air and surface temperatures can be

recorded in fifteen minutes. The actual measuring time is thus very

small compared with the time required to reach steady state. As a result

several test models, generally four, are grouped in a single wall. Only

the most characteristic types are studied.

12
Our choice was guided by one prime consideration. We classified the

walls in three categories according to the thermal characteristics of the

materials from which they are made:

First, we have pure masonry walls, in which reinforced concrete is

next to light masonry (hollow brick, artificial stone, light-weight concrete, etc.). These walls may be constructed in the traditional manner or

may consist of large prefabricated panels containing these elements. The

thickness of these walls varies between 20 and 30 cm, the ratio of densities of the materials present is between 2 and 4 and that of the thermal

conductivities between 3 and 5.

Next, we have mixed walls in which reinforced concrete and very light

insulating materials are used side by side; these are generally large

prefabricated panels. They have about the same thickness as the above

walls, but the ratio of densities of the materials varies between 20 and

100 and the ratio of conductivities between 30 and 50.

Finally, we have light walls, of thickness between 3 and 5 cm, which

consist of very light insulating materials standing next to wood or metals,

The cahracteristics of the materials constituting the different types

of walls are summarized in the following table:

Types of wall Density

in kg/m

Conductivity

k in. kcal/(mh°C)

CO

CD

>->

CO

CD X

Reinforced CONCRETE frame and. .

.

LIGHT WEIGHT MASONRY f Jl 1 ing . .

.

2200

600 to 1000

1.5 0.3 to 0.6

Large prefabricated concrete .......

panel incorporating very lignt

INSULATION ................

2200

20 to 1 00

1.5

0.03 to 0.05

C/5

CO Curtain or panel facade walls

with a framing of WOOD. ......

or METAL.

and very light INSULATION.......

400 to 700

3000 to 8000

20 to 100

0.1 to 0.1 5 50 to 170

0.03 to 0.05

13
HEAVY WALLS

Reinforced concrete framework with light-weight masonry filling or large , light weight masonry panels

We have adopted the same types of thermal bridges that had been

studied previously in the semi-natural tests. For convenience the models

consisted of blocks of cellular concrete (d = 600 kg/m , k = 0.3) interrupted by a dense concrete framing (d = 2,200, k = 1.5).

Total bridge . In addition to the total thermal bridge (Fig. 4)

,

for which we took the same two widths as studied in the semi-natural

tests, namely 7.5 and 22.5 cm, (Table I, models Ai and A,,)*, we studied

various arrangements in which, a priori, it was possible to obtain more

uniform interior surface temperatures. The different arrangements studied

can be reduced to two.

First arrangement : Thermal bridge with interior diffusion layer (Fig. 5).

One solution consists in diffusing the surface temperatures by placing a

comparatively conductive material over the entire interior surface of the

wall.

Figure 4 Total bridge Figure 5 Thermal bridge with interior diffusion layer

The effectiveness of this method had been demonstrated in the seminatural tests. In the artificial tests we attempted to calculate it.

Starting with a bridge comprising a framework of compact concrete

intersecting a cellular concrete block wall 20 cm thick, we studied the

effect of a compact slab of concrete 5 cm in thickness (B-^) for frame

*Table I contains models Aj and A2

, B-B^, Cj-C^ , D^-D^ , as referred to

throughout the following pages.

14
widths of 7.5 and 22.5 cm. We thought it would be interesting to increase

the conductivity of this slab in the lateral direction, perpendicular to

the framing. For this purpose, additional slabs, identical to the preceeding ones except that they were strongly reinforced with iron rods running

perpendicular to the framework (Ba) , were applied to the interior surface.

Similarly, we tried to increase the effectiveness of a plaster coating

(of relatively low conductivity) by reinforcing it strongly with two layers

of grillwork (B5)

.

Still other specimens were constructed to determine the effect of

various degrees of flaring of the framework.

Finally we sought to determine the effect of a framing which by

projecting greatly on the exterior forms a cordon, and hence a kind of

cooling fin, by increasing the area of the exterior surface.

Second arrangement : Insulation of thermal bridge.

Two solutions have been studied:

(1) Partial bridges (Fig. 6). In this solution the framing does not

go all the way through the wall and is thus insulated by a certain thickness

of the material which constitutes the main part of the wall.

r

j

(a) (b)

Figure 6 Partial bridge

(a) Exterior insulation

(b) Interior insulation

The semi-natural tests demonstrated that there was a great difference

in effectiveness depending on whether the insulation was placed inside or

outside. With a view to determining these effects more accurately we

15
studied the same types of thermal bridges in the artificial tests.

For this purpose a cellular concrete wall 20 cm thick was constructed.

This wall was partially intersected by two dense concrete frameworks, one

7.5 cm wide and the other 22.5 cm wide. The residual thickness of the

cellular concrete was 5 cm and 7.5 cm, respectively. Four specimens were

thus available. This wall was tested on both sides so that the insulation

could be placed successively on the inside and on the outside.

(2) Corrected bridges (Fig. 7). This term refers to a bridge

insulated by very effective insulating material, the thickness of which

was calculated so that the U value at right angles to the insulated framework would be equal to that calculated for the main part of the wall. (We

then have p =1.) We again took the case of wall A, where the thermal

bridge consisted of a dense concrete framework intersecting a 20 cm thick

wall of cellular concrete covered by a plaster coating 2.5 cm thick. In

the first test the plaster was removed opposite the frames which were 7.5

and 22.5 cm wide, and replaced with 2 cm of aerated polystyrene.

=

(a) (b)

Figure 7 Corrected bridge

(a) Exterior insulation

(b) Interior insulation

One test was carried out with polystyrene on the interior and one

with polystyrene on the exterior.

The 2 cm thickness was chosen in such a way that U = U , i.e. P =1.

p c c Large concrete panel with very light insulating materials incorporated in it.

In general, these panels are built in sandwich fashion; a very good

insulating material, which provides good thermal insulation, is sandwiched

16
between two concrete slabs of various thicknesses which perform the other

functions of the wall (mechanical strength, permeability, thermal inertia,

etc.)

.

Very frequently, then, thermal bridges are formed by the concrete

joining strips between the outer and inner slabs or by the joints between

two panels. The difference between the conductivities and specific gravities

of the different materials involved (k = 1.5 kcal/(mh°C); d = 2,200 kg/m3

for the concrete and k = 0.03 to 0.05; d = 20 to 100 for the insulation)

results in very substantial thermal bridges.

In this case we tried to determine precisely the respective role of

the two concrete slabs, especially that of the interior one.

The walls studied had the following thicknesses:

A concrete slab of 5 cm; a slab of polystyrene 3 cm thick (giving a

useful thickness of about 2.5 cm, since the concrete penetrated slightly

into the polystyrene on both its faces) ; and a concrete slab 15 cm thick.

Openings 7.5 cm, 15 cm, 22.5 cm and 45 cm wide were provided in the polystyrene, thus constituting a link between the two slabs, and a thermal

bridge. These walls were tested with the 5 cm slab and the 15 cm slab

successively on the warm side.

Special thermal bridges

We also initiated a study of thermal bridges existing at corners.

The study is even more complex, because it is necessary to distinguish

between the corner where two identical external walls join (Fig. 8) and

the corner where an external wall is joined by a partition or floor

(Fig. 9).

17
Figure 8 Corner between Figure 9 Partition or floor two external walls

Thermal bridges at the corner between two external walls . In this

case, even with two walls having the same U value, the temperatures at

the corner will be different from the temperatures elsewhere on the walls.

There are two reasons for this

:

First the surface area of the external wall is greater than that of

the internal wall. The same flow of cold from the exterior will thus

lead to lower temperatures than on a wall with parallel faces.

Then, there is a reduction in the radiation and convection surface

heat exchanges. This further contributes to the lowering of the temperature on the inside surface.

Artificial tests on this type of thermal bridge are rather uncertain

and it is doubtful whether or not the surface heat exchanges can be

exactly reproduced. On the other hand, we possess the results of natural

tests carried out in Germany at the Holzkirchen Station (Bibliography 7)

,

where temperatures were measured on the interior surface of the northwest

corner of more than 20 houses with different kinds of walls.

Partitions and floors . Where an external wall meets a partition or

floor the problem is very different. The partition or floor is at the

interior room temperature (we assume that the wall or floor separates two

equally heated spaces) . The exterior surface area is not as large as the

18
interior surface area. Thus the two effects mentioned previously oppose

one another. Furthermore, the partition or floor often differs greatly

in its thermal characteristics from the exterior wall.

Finally, both partitions and floors can terminate flush with the

facade, or before reaching the facade, or can even extend beyond it,

forming a cordon. Only the corner between the exterior wall and the

partition has been studied. For this purpose a structure representing

the partition was joined at right angles to the 22.5 cm wide frames of

walls A, B and C. This structure was constructed from solid blocks

identical with the concrete of the frame.

In the case of wall B we also studied the influence of an exterior

structure forming a cordon and cooling fin.

Light walls (curtain wall, facade panels)

One of the essential features of this kind of construction is the

very small thickness of the wall which is made possible by the use of good

insulation: the same U value can be obtained with a wall using a 2 cm

thickness of good insulation (k = 0.03 to 0.05) as with one 20 cm thick

in light masonry.

In order to compensate for their lack of thermal capacity these walls

must have very good U values (around 1.0). Such coefficients are easily

obtained with small thicknesses of insulating material.

When this insulation is interrupted by a frame which is also very

thin, significant thermal bridges are formed.

We shall distinguish between thermal bridges produced by wooden

members which generally make up the internal framing of panels and those

produced by metal frames, whether they are internal frames, as are

19
frequently used in this type of construction to ensure rigidity and ease

of assembly, or are external frames in which the homogeneous panel is

placed.

Wooden or similar framing

Total bridge . The main part of the models was constructed of 3 cm

thick expanded polystyrene (k = 0.03 kcal/(mh°C); d = 20 kg/m3

)

.

We studied the effect of the width of the frame. For this purpose

the insulation was interrupted by members having the same thickness as

the panel (3 cm) but of different widths (0.6, 1, 3 and 6 cm).

In order to estimate the effect of changing the ratio of thermal

characteristics of the materials, models identical with the above were

built, but in which the wood was replaced by pressed wood that was more

insulating and lighter (k = 0.06 and d = 500 kg/m3) than the wood used in

the previous test.

Bridge with interior diffusion layer . We again wished to determine

the effect of a conducting layer on the interior surface. Some panels use

aluminium foil under the interior layer as vapor barriers. It is quite

possible that this highly conductive material significantly diffuses the

temperatures despite the small thicknesses employed. In order to calculate

this phenomenon we cemented first a sheet of aluminium 1/10 mm thick on to

the models (k = 170 kcal/mh°C) and then a sheet of copper 2/10 mm thick

(k = 350 kcal/mh°C)

.

These sheets had been painted grey to maintain the same surface heat

transfer coefficient as before.

Metal framing

Total bridge. To begin with we studied total bridges formed with

20
various steel sections intersecting a polystyrene panel 3 cm thick.

We then sought to determine the influence of increasing or decreasing the projection of an exterior cordon constituting a cooling fin.

Interrupted bridge . Seeking a remedy to this type of thermal bridge

we studied, for a simple theoretical case, the effect of an interruption

in the thermal bridge, or more exactly a decrease in the metal crosssectional area and an increase in the thermal path length.

Practical examples . Finally, we studied some practical examples of

thermal bridges at the joint between two panels. Again, seeking to correct

the thermal bridge, we studied the effect of interrupting the framing and

its insulation with various types of interior and exterior mouldings.

RESULTS

Heavy walls

Walls with reinforced concrete framing and light masonry filling

The results obtained are shown in Table I, where we give the values

of p determined from the measured temperatures and those of p calculated

from the ratio U /U . P c Total bridge . Actually a true total bridge was not tested since no

such bridge exists in practice. There are always interior and exterior

finish. The first tests carried out on walls A (A^^A?) enabled us to

obtain the real value of the total bridge in a wall with coatings and we

found that

:

p =2.1 for the 7.5 cm width;

m

p = 2.3 for the 22.5 cm width, m

21
We note that the narrower the framing the smaller p and that in

both cases it is less than p c

: p c = 2.4.

Thermal bridge with interior diffusion layer . The effect of the

concrete slab placed on the interior surface is to flatten the curve of

interior surface temperatures. The important improvement obtained with a

simple slab (B ) must be noted:

p changes from 2.1 to 1.4 for the 7.5 cm width;

and from 2.3 to 1.7 for the 22.5 cm width.

These values are far less than p , which is still equal to 2.4:

c —The flaring of the framework (B„ - B~) makes it possible to obtain

still smaller p m

values. In this way we achieved values of 1.3

for I = 7.5, and 1.45 for I = 22.5; —Putting reinforcement (B^) in the slab makes very little difference. Depending on the width, Pm

changes from 1.4 to 1.35 and

from 1.7 to 1.65.

We also tested the effect of reinforcement in the plaster slab installed in such a way as to make the relatively insulating plaster more

conductive in the lateral direction. Again (Br) the results were inconclusive; p changes, depending on the width, from 1.95 to 1.9 and from

2.2 to 2.15. The effect is thus negligible.

Generally speaking Pm

decreases as I decreases and it is always

less P . cNote . The effect of an exterior fin (B) is also comparatively slight

in this case; it causes p to change from 1.7 to 1.8 (B compared to B-^) .

22
Partial bridges . The reader will note the large difference in the

shape of the curves obtained when the insulation is on the inside

(C-^ and C2) and when it is on the outside (C~ and C, ) .

(a) In the case of interior insulation a very good correction of the

thermal bridge is obtained, and the narrower the frame to be protected,

the better the correction. The coldest point is directly opposite the

center of the frame. The small difference obtained with different thicknesses of insulation should be noted (Ci compared to Co)

.

Note again that p m

< P c

(b) When the insulation is placed on the exterior there is no improvement and now it seems as though the smaller the width of the frame,

the more pronounced is the effect of the thermal bridge. The thickness

of the insulation is more significant.

We again note that the position of the coldest point is situated

opposite to the frame, but near the edge. Note also the existence of a

warm spot near the frame . The temperature there is higher than in the

main part of the wall.

Finally it must be emphasized that p is decidedly greater than p .

It is thus an error to suppose that the classical calculation always yields

a margin of safety. These results are absolutely opposite to those obtained

for interior insulation.

We shall explain this in Part III

Corrected bridges . (a) The above results, in the case of exterior

insulation, are rather surprising; the tests carried out on wall D with

exterior correction have confirmed them. Although conditions were chosen

so that the U value of the wall at the frame would be the same as in the

23
main part of the wall ( p =1), very different temperatures are observed

on the interior surface.

In particular, for the 7.5 cm width replacing the exterior plaster

coating with 2 cm of polystyrene has practically no effect on the temperatures and gives substantially the same value for p .

An improvement of the thermal bridge can be obtained by having the

insulation overlap the frame considerably on both sides, but the results

remain unspectacular. For a narrow bridge an overlapping on both sides

of 7.5 cm equal to t still gives a high p m

value (1.65). For a wider

bridge an overlapping on both sides of 22.5 cm (equal to t ) gives P =1.5.

(b) In the case of interior correction, the temperature opposite

the frame is higher than on the main part of the wall; the coldest spot,

however, is displaced outside the frame. The wider the frame, the colder

this spot will be.

In tests D, , where the insulation overlaps the frame, good improvement can be observed. However, it does not appear that the width of the

insulation required to obtain a given P is a linear function of the width ° m

of the frame. An overlapping of 7.5 cm for a frame width of 7.5 cm is

sufficient (Pm

= 1.25), while an overlapping of 22.5 cm for a 22.5 wide

frame is excessive (Pm

= 0.87).

Finally, we note the difference of form in the temperature curves

obtained between the case where the insulation is inside, and that where

it is outside. To show this result more clearly we have plotted the

values of P for both of these cases on the same graph (Fig. 10) - tests

D-l and D . Although the P m

values are not very different the curve of p

for interior insulation is much less flat in the zone of p > 1.5 than the

24
curve obtained for exterior insulation.

Large concrete panel incorporating light insulation

The results are given in Table II.

The very high value of P m

obtained when the framing is very wide

(p m

= 3.2) should be noted.

With the 15 cm slab on the inside, the best correction is obtained

with the narrow thermal bridge. A width of 7.5 cm still gives a high P

value (1.8).

With the 15 cm slab on the outside, the values of p m

remain very

high (above 3). For the larger bridge widths (15 and 22.5 cm) they are

slightly above p c

(p Q = 3.4).

Special thermal bridges

Partitions and floors . Table III shows the results obtained in the

four cases studied.

The coldest point is found on the partition a few centimeters away

from the corner.

In the last column of Table III are given values of p obtained on

thermal bridges at walls without partitions. Those obtained with partitions are always lower. This is due to the fact that the concrete

partition, away from the corner, is at temperature T. through its entire

mass so that there is a considerable flow of heat in the direction of the

corner.

The total bridge (A) now gives a Pm

value of only 1.9 instead of

2.4.

We again find that good diffusion is obtained with the internal

concrete slab, enabling the attainment of P m

= 1.5 without a cordon and

25
p m

- 1.55 despite a large cordon. External insulation continues to be

ineffective (P =1.7).

Corner between two outside walls . At a corner between two external

walls values of P m , which can be derived from German tests (Bibliography 7)

.

are higher. For walls with U values of 1.2 to 1.5 they are in the vicinity

of 1.8, while for walls with U values of less than 1 they reach 2.5.

The shape of the curve is then different.

Figure 12 shows the temperatures obtained at the corner between

the west and north walls, which were solid brick 38 cm thick. The curve

shows a sharp peak; the result is a colder but less extensive area. Thus

the effect of the maximum P which is obtained can be less severe.

Light walls (curtain walls, facade panels)

Wooden framing

Total bridge . The results are given in Table IV. The narrower

the framing, the smaller the P m

values. They are always smaller than P

, which for wood is equal to 2.8 and for pressed wood 1.7.

For wooden framing the surface temperature curve shows a rather

sharp drop at the edges of the framing.

In the case of pressed wood framing, however, the curve is flatter.

Thermal bridge with interior diffusion layer . The technical

difficulty of obtaining a perfect thermal contact between the metal foil

and the wall without an intervening cushion of air made it impossible to

determine accurately the effectiveness of diffusing the heat flux. On the

other hand, foils are generally put underneath the interior plaster,

which adds an effect of its own. Our tests indicate, however, that for

the wooden framing it seems possible to diffuse the heat flux sufficiently

26
in this way in order to obtain acceptable surface temperatures. Thus it

should be possible to obtain p = 1.5 with a 1/10 mm aluminium foil under

a covering of plaster board or plywood on a wooden framework less than

2 cm wide for the hardwood (oak) used in the tests, or 3 cm for soft wood

(fir)

.

Metal frameworks

Theoretical cases . The main part of the wall consisted of 3 cm

expanded polystyrene framed with steel sections of various shapes.

The tests showed that the temperature on the metal part was practically uniform, with a sudden drop occurring at the edge of the section

(Fig. 13).

The results are collected in Table V. We have included at the same

time values of p m = * m and of y = i ° m . In part 3 it will

T± - 6 C T i"T

e be shown that for this case 6 m

is practically independent of , so that

the ratio y will remain essentially constant regardless of the U value of

the main part of the wall. This is why y is of interest here.

This ratio establishes the surface temperature of the framework in

relation to the internal and external temperatures.

Thus y = 0.5 indicates that the surface temperature on a framework

is the arithmetic mean of T. and T . l e If y < 0.5, this temperature is closer to T. than T ; if y > 0.5,

it is closer to T than T..

e i

Two types of thermal bridges may be distinguished.

(1) Total bridge (top of Table V) . The smallest value of y is obtained for the T-section with the flange on the interior. What we get,

27
in effect, is a diffusion by the flange. If the flange were wider the

value of y would certainly be smaller.

When the flange of the T is to the outside the situation is reversed,

with the result that y = 0.8. The wider the flange, the greater this

effect would be. The I-section gives a y which is practically an average

of the two preceding ones.

(2) Thermal bridge with fin (center of Table V). The value of y

is decidedly higher, corresponding to a lower temperature than for the

same test without a fin. The larger the fin the more pronounced this

effect.

(3) Interrupted thermal bridge (bottom of Table V) . Decreasing

the area of metallic section between the two iron plates helps to decrease

the value of y . The curve of Fig. 16 shows that in the last test, which

corresponds to an area of 1 cm per m of the section, the ratio y has practically attained its limiting value, given by the heat exchange through the

layer of air between the two iron plates. However, a layer of air in this

kind of panel is itself a thermal bridge. In order to obtain a satisfactory effect the joining member between the two plates should pass through

the insulation.

Practical Examples . The results obtained in the following three

examples have confirmed and supplemented the results previously obtained

in the theoretical cases.

(1) Example of a total bridge with fin. We first studied the thermal

bridge produced by a large metal framework containing homogeneous panels.

The panel had a U value of approximately 1 kcal/m2h°C. The framing, which

28
projected considerably on the outside, forms a definite cooling fin.

Figure 17 shows a plan section of the framing and the temperature curve

obtained . From this we calculate

Pm= 5 ' 7

and y = 0.75,

very high values from which we may deduce that for T. = 18 °C and T = -6°C

the temperature on the framing will be 0°C.

This very high y value is due largely to the fin, but probably also

to an appreciable decrease in the radiation exchange between the metal

surface and the interior.

(2) Examples of improvement of a total bridge by interruption and

by interior mouldings.

Another, more classical example is the facade panel bounded by an

omega-shaped frame (Fig. 18)

.

The test panel had a U value of approximately 0.9 kcal/ (mz h°C)

.

Several tests have been carried out on the joint between two panels.

First the thickness of the framing head was varied; then an attempt was

made to reduce the heat flow area by providing holes or slots and to

lengthen the thermal path or to interrupt the thermal bridge in one way

or another.

Finally the effecc of an internal moulding either or wood or polystyrene (which insulated the interior side of the thermal bridge) was

studied.

The results are shown in the curves of Fig. 18.

(a) Interrupted thermal bridge

29
The circular perforations are relatively ineffective since the

reduction in heat flow area and the increase in path length is slight.

On the other hand three rows of slots in staggered array reduce

p from 4 to 2.7, which, however, is still a very high value.

(b) Interior moulding

The application of a moulding has the effect of moving the coldest

spot to the edge. The result is the same as for the case of the thermal

bridge corrected by an interior insulation. It is important to note that

the diffusions obtained with the wooden moulding is better than that obtained with the expanded polystyrene moulding. The latter slightly decreases the temperature variation opposite the frame, but the variation

is increased at the edge of the moulding. The width of the moulding seems

to be more important than its insulating power. To obtain satisfactory

results it should be quite wide.

(3) Example of improvement by an exterior moulding.

In the third example exterior insulation was the chief subject of

investigation. The panel was again bounded by a metal frame of a rather

elaborate form shown diagrammatically in Fig. 19. The main part of the

panel had a U value of 1 kcal/(m h°C).

The joint between the two panels was covered with an exterior steel

moulding and an interior plastic moulding.

We decided to test this joint, as just described, after filling the

space between the exterior moulding and the panels with glass wool, and

finally with an additional filling of light insulation between the exterior

moulding and the panels.

The results obtained are shown in Fig. 19. Again we find the relative

ineffectiveness of exterior insulation and of too narrow an interior moulding.

30
Part III

Theoretical Considerations - Practical Rules

Theor etical Considerations

We shall briefly consider the elementary theory currently accepted

for the determination of U values and will show where it is inadequate;

with the aid of supplementary hypotheses we shall attempt to explain the

phenomena observed in our tests. The latter will enable us in a few simple

cases to generalize the results obtained and to provide rules by which the

effectiveness of the systems employed to reduce the heterogeneity of

surface temperatures can be estimated.

Elementary Theory

We assume that the heat flow is perpendicular to the parallel faces

of the wall.

This is tantamount to neglecting the lateral heat exchange between

materials placed next to each other.

We then consider that both parts of the wall - the main part (C)

and the part consisting of the thermal bridge (P) are two independent

walls and to each we apply the equations of a homogeneous flat wall or of

a wall consisting of homogeneous parallel sheets.

The U value of each of these walls is given by the equations:

<°> i/°c - 4r +2$c + -k (p) 1/u

» -\ + 2MP

+ 1

and the temperature of their interior surface by the equations:

Uc U

P , Ti - e c " "hf <*i " T e) Ti " e p = ~hT < Ti " Te)

31
In the case of a homogeneous wall traversed by a total bridge we

obtain, for example, the temperature profile of Fig. 20.

We have seen that the thermal bridge is characterized by the

coefficient: TMi ~ 9m

p m

== T± - 6 C

Elementary calculation leads us to take

Up

P = —L~

Uc over the entire width of the thermal bridge.

p is thus independent of the interior and exterior temperatures;

it is a characteristic of the wall.

Note :

This further assumes that the surface conductance h. is the same

1

opposite the main part of the wall as opposite the thermal bridge; since

this coefficient depends on T. - 6 it will vary. In fact the variation

is very slight and can be neglected here at least as far as masonry walls

are concerned.

Graphical Representation

The temperature profiles for the two parts of the wall can be drawn.

Taking the example of the homogeneous wall traversed by a total bridge we

obtain the diagram of Fig. 21.

Note that the two curves obtained intersect inside the wall at an

abscissa point x measured from the interior surface. In this plane the

temperature is the same both in the main part of the wall and in the

thermal bridge. This is an isothermal plane for the wall, x may easily

be calculated:

he 18 x = r— e ; x = * Q , -, e = 0.72e

h-£ + he 18 + 7

32
a value independent of k and k .

Let us take another example. Fig. 22 represents a wall composed of

three materials: C, P and I.

These materials are chosen such that k > k > k-,-

.

P c x

In practice this may represent a wall of cellular concrete interrupted by a dense concrete frame and carrying on this frame an insulating

material of very low conductivity such as polystyrene.

The thickness of most insulating materials (I) may always be chosen

such that the Uc value in the main part of the wall and U_ opposite the

cold bridge are the same when calculated by elementary theory.

In the case of a 20 cm wall of cellular concrete interrupted by a

dense concrete frame, e (insulation thickness) would be of the order of

2 cm.

The elementary calculation then gives the same surface temperatures

at C and at P and does not differentiate between the cas.es, where the

material (I) is placed on the exterior surface, and on the interior surface

of the wall, or even in the middle.

The graphical representation serves to distinguish between the

different cases.

If a sign be applied to the areas bounded by the temperature profiles

- positive if the profile traced in the main part of the wall is above

that in the thermal bridge, otherwise negative - then the algebraic sum

of the areas in question will vary. It will be positive when the insulation is placed inside and negative when it is placed outside. It will be

zero when it is put in the center of the wall.

33
Supplementary Hypotheses

The elementary theory assumes that the heat flux lines are perpendicular to the parallel faces of the wall.

In reality, near the plane of contact of the two materials the

flux lines are deformed (Fig. 23).

If we take the flux vector 9 to be tangent to a flux line, it

can be divided according to two axes into 9 T perpendicular to the wall

faces and <p- parallel thereto.

The sum of all the vectors ? = $ will be called the transverse

T t

flux and that of the vectors * = *L the lateral flux.

It is very difficult to determine the exact values of $ and *rj,

and it is not the aim of the present paper to make them explicit.

With the aid of certain simplifying hypotheses, however, approximate

values can be attained.

1, $ : consider the part of the wall forming the thermal bridge.

T

For $ we shall take the value given by the elementary theory, namely

$T

= U

p

S (T± - Te )

where S is the area of the material (P) for 1 meter of length,

S = I x 1 and $ T = £U

p

(T±

- Te)

2

.

$T

: the graphical representation gives us a picture of $ . L L" In the preceding examples, if S and S are the area of the triangles

formed by the temperature profiles, $L

is a function of S and S2

•

$T could be evaluated more accurately if we knew the temperature

profile in the plane of contact, T, between the two materials. In fact,

these temperatures depend not only on the conductivities of the materials

involved, but also on their density and specific heat, or more exactly

34
on the relative product of these three values k, c, d, known as the

coefficient of thermal contact. The heaviest material (highest k c d)

tends to impose its temperature in some manner.

In the particular case of two semi-infinite materials in contact

with mass temperatures at 9

p

and 9

r the temperature of the plane of

contact is given by Oc ~ e T / ( kcd )p

6 T

- 6 p

~ ^ (kcd)

c The actual case of the wall is not exactly this theoretical case,

but we will assume that the temperature profile in the plane of contact

(T) can be deduced from the temperature profile in the planes (P) and

(C) . The wider the thermal bridge the more accurate this will be.

The lateral flux can then be evaluated from curves C and T in

Fig. 24. It will have the following form for 1 meter of wall:

\d t with

$L = -J~\ k (°P " e T)c&

<K L

= -|- Eka

where a is the area bounded by the two temperature profiles in the

planes T and P on one hand and the faces of the material on the other

hand, and k is the conductivity of the corresponding material.

In fact a is an increasing function of L so that $t is not inversely

proportional to t.

Sign Convention

We consider as positive the areas bounded by the temperature profiles

where the profile traced in the plane (P) is below that traced in the plane

T and as negative the areas where the temperature profile traced in the

plane (P) is above that traced in the plane T (Fig. 24).

35
T • — ft Let p be the maximum real value of the ratio ±J — in the zone

p p i c of the thermal bridge. We shall put a = m , P c - 1 a represents the percentage by which the real value of p m

departs

from the value p„ equal to the ratio U„/U . *- Pc

Having stated this we shall now make the following two hypotheses:

1. a is an increasing function of $-r/$ T

.

2. p pm

has the same sign as $ T /$^, i.e., the same as $L#

These two hypotheses are logical: as the absolute value of $T /$ ,

increases, i.e., as the lateral heat transfer increases compared with

$ , the greater will be the difference between the calculated value which

T

neglects lateral heat transfer and the true value . The absolute value

P^ P c m

of the ratio will therefore increase.

Pc " 1

If $ /$ is positive, i.e., if $ > 0, the direction of lateral heat

L T L

transfer, neglected in the calculation of p , is from the main part of

the wall towards the thermal bridge. The true value of p must therefore

be less than that of p . The opposite will be true if the direction of

lateral heat transfer is away from the thermal bridge towards the main

part of the wall ($ < 0); then p c

< p m

.

These supplementary hypotheses will enable us to explain the results

of our tests.

Application to certain types of thermal bridges that have been studied

Total bridge

The temperature profiles in the planes (C) , (T) and (P) form two

triangles with the faces of the wall (Fig. 25)

.

he

We have seen that x = , —

;— e hl + he The fact that h

e

> hi means that a-, > a

2

36
Now, $ = r kp(a-, -02).

Hence $ / > 0.

From this we deduce pr > p. c tn On the other hand $

T /$ T

is a decreasing function of p, hence the

larger the value of t the closer p will be to p .

To determine the role of the thermal characteristics of the

materials in question we take the example of a pressed wood frame, a

wooden frame and an iron frame interrupting polystyrene. The characteristics of these materials are given in the following table:

k

kcal/m- h°C

d kg/m°c kcal/m3 Ikted

Polystyrene 0.03 20 0.33 0.2

Pressed wood 0.06 500 0.35 10 Wood 0.15 650 0.35 34

Iron 50 7 700 0.12 46,200

We thus have the following ratios of the coefficients of thermal

contact—pressed wood/polystyrene = 50 —wood/polysytrene = 170 —iron/polystyrene = 231,000

As this ratio increases 0TM approaches and $T decreases. Thus

for constant t the greater the difference between the coefficients of

thermal contact of the materials, the greater will be p .

In conclusion, in a total thermal bridge the wider the bridge the

closer p is to p„, and for a constant bridge width, the greater the

m c

difference between the coefficients of thermal contact of the materials,

the closer p m is to p c

. 37
In other words the narrower the thermal bridge and the more

similar the materials are with respect to their thermal characteristics ,

the smaller will be p . m

Thermal Bridge with Interior Diffusion

The presence on the interior surface of the wall of an additional

thickness of conductive material will appreciably reduce the value of

ek $ and considerably increase that of $L

in which the term —j is

contained. The ratio ®-il§rv will thus increase with decreasing £ (width

of thermal bridge) , increasing e (thickness of slab) and increasing k

(conductivity of materials) . The flaring of the thermal bridge can be

compared to a slab of variable thickness, which increases e still further

in comparison with the simple slab.

Reinforcement of the slab also helps to increase $

T without changing $£. Comparing the products ek for a concrete slab and for reinforcement respectively, we obtain ek = 0.075 for a 5 cm concrete slab. To

obtain the same product with reinforcement would require a cross-sectioned

area of 0.075/50 = 0.0015 m , corresponding to a reinforcement weight of

2

almost 12 kg per m of slab, which is difficult to imagine. We had at our

disposal only 6 kg per m^ , which can be considered a maximum. The effect

was insignificant.

Note: Thermal bridge with exterior diffusion

In the case of an exterior concrete slab $ T is always appreciably

decreased, but the same also is true of $ , which becomes negative as

-Li soon as the slab exceeds a certain thickness. At this moment $

T /$ T is

negative and must result in p_ > p . m c

38
We did not test this type of thermal bridge unless we consider the

test on the insulated concrete wall with the 15 cm slab is on the outside. The above note explains why the values of p are noticeably

greater than p .

When the wall has an exterior coating this coating acts as an

exterior diffusion layer. However, the k value of a mortar coating is

less than that of dense concrete, so that in comparison to the total

bridge $ decreases more than in the case of a slab of concrete, and <£>

decreases less. The ratio *-r/$rp taen remains essentially the same as

for a total bridge.

Partial Thermal Bridge

This is the case where the elementary theory is most at fault. It

is, in fact, incapable of explaining the differences obtained for different

positions of the insulation.

The supplementary hypotheses which we have formulated lead to

surprising results, but these conform to the experimental evidence.

We shall examine this case in greater detail in order to explain

the results obtained in the tests.

The tested wall was constructed of cellular concrete blocks (k = 0.3;

d = 600), the frames of dense concrete (k = 1.5; d = 2,200); its thickness

e = 0.2 m.

Interior Insulation

We shall try to determine the shape of the curves representing the

function a (e,£)

.

39
Our tests give us four pairs of points:

t- 7.5 cm e= 5 cm and e= 7.5 cm t= 22.5 cm e= 5 cm and e= 7.5 cm

When e= we have a total thermal bridge and when e= e we have a

homogeneous wall. In this latter case a =

when H —> a —* 1

when £ —* a a —*-

We can draw the curves of Fig. 26. Note that a is always positive

and is a maximum at approximately 5 cm.

The shape of these curves can be found with the aid of our hypotheses

and a consideration of the ratio $ /$„.

If we draw the temperature profile in the planes (P) and (T) we

conclude that $, is positive, resulting in a > 0.

$ T decreases with increasing e.

It may be shown that <!> passes through a maximum so that $l/$ t

passes through a maximum, resulting in a maximum for a.

Finally for e = constant Q-^/QTM decreases as £ increases and hence

a must decrease.

Consideration of the ratio $, /$^ enables us to extrapolate the two

curves obtained for other values of p (Fig. 26). From these curves we

shall deduce the graphs of Part 4.

Exterior Insulation

Once more we obtained 4 pairs of values of the function a (e, £)

.

The values found experimentally are negative, that is to say

K mr c

40
Following the curves of Fig. 26, a, starting from a positive

value (for e =0), decreases, passes through at e approximately

2 cm, then through a negative minimum at e approximately 10 cm, after

which it increases to for e = e.

The shapes of these curves can be found again by consideration of

the ratio $ L

/$ T

. The temperature profiles in the planes (P) and (T)

show that §-^ > for e = 0, becomes for a particular value of e(e = 2),

and then becomes negative. When e increases the absolute value of $l

passes through a maximum and decreases to become when e = e.

From this we derive a similar variation for a. This shows that

in the case where e > 2 cm the value of p given by elementary theory is

too small. As the width of the thermal bridge decreases P deviates

further from the real value. These conclusions are exactly the opposite

to what we obtain when the insulation is placed inside.

Note ; Thermal bridge corrected by exterior insulation. The conclusions

of the theory are the same as in the preceding case: pm

> p , the

difference increases as the thermal bridge becomes narrower. This is

substantially what we have found, but this theory predicts that for even

smaller widths we can find a thickness of insulation which will obtain

pm

values greater than those obtained without insulation.

We tried to confirm this result experimentally. We measured the

interior temperature on a joint approximately 2 cm wide between two cellular

concrete blocks. Then, scraping the outside of the joint we successively

insulated it with thicknesses of 0.6, 1 and 1.4 cm of polystyrene.

41
The results of the following table show that the ratio y passes

through a maximum, which confirms our predictions.

£ T.

i ®m T T T{ -em

19.5 10.5 25 9 0.360

0.6 20.0 10.7 25.5 9.3 0.365

1 19.5 10.1 25 9.4 0.376 maximum

1.4 19.6 11.1 35.1 8.5 0.338

42
Part IV

Practical Rules - Conclusion

We shall now draw conclusions from our tests in the light of the

study which we have just outlined. For this purpose we shall classify

thermal bridges according to the kinds of walls and their types and we

shall try in each case to provide simple rules by which the effect of the

thermal bridge or the effectiveness of its correction can be judged.

It will be noted in what follows that the effect of thermal bridges

will be judged in relation to the value p = 1.5. That is to say, without prejudicing eventual rules which may be drawn up with respect to

materials, we acknowledge that this value appears to be a reasonable limit.

It will be shown specifically on all the graphs.

Heavy walls

Reinforced concrete frame walls with masonry filling or light masonry

panels

All our tests dealt with walls consisting of cellular concrete

blocks 20 cm thick.

It is of little practical interest to try to extrapolate the results

for other thicknesses of this type of wall, since the U value requirements

impose a minimum thickness (which is 20 cm for cellular concrete)

.

On the other hand it would be more useful to be able to extend the

results obtained to filling materials other than cellular concrete. When

we consider on the one hand that by using a less insulating material than,

for example, cellular concrete as a filling, smaller values of p are

obtained, since the materials in contact are thermally closer to each other,

43
whereas on the other hand, in order to retain an acceptable U value it

is necessary to increase the thickness of the wall, resulting in an

increase in p

ffi , then in first approximation it may be assumed that the

results we have obtained and the rules which we shall deduce from them

will be applicable to all light masonry fillings, that is to say: —hollow and perforated terra cotta blocks; —hollow heavy and light concrete artificial stone; —veneered light concrete; —cellular concrete blocks

intersected by concrete frames, and having a U value corresponding to our

requirements.

Total bridge

Fig. 27 gives the variation of pm

with width £ of the thermal bridge.

It will be noted that in order to have p m smaller than 1.5, t must

be less than 2 cm, i.e., approximately the width of a joint between masonry

blocks. Generally speaking these will be the only acceptable total thermal

bridges.

Before considering the various remedies for the total bridge, let

us note that interior diffusion and insulation are two good solutions.

Exterior insulation is a poor solution, while correction of the thermal

bridge is fairly good with interior insulation but mediocre with exterior.

Bridge with interior diffusion coating

Fig. 28 gives a chart by which it is possible to determine the supplementary thickness of an interior slab of dense concrete as a function of

the width £ of the frame, in order to obtain the desired p .

44
For example, a frame of 15 cm width will give p < 1.5 if the

interior face of the wall is furnished with a slab of concrete of thickness e > 6 cm.

Partial bridge

Interior insulation

Fig. 29 is a chart from which we can find the thickness of the

material e to be left in front of the frame in order to obtain the desired

p as a function of the width Z of the frame.

*m

For example, for a frame 15 cm wide it will be sufficient to place

in front of it a thickness of material greater than 5 cm in order to have

a p„ less than 1.5. m

Exterior insulation

The results obtained and the explanations deduced from our

hypotheses indicate that this solution in practice cannot provide a

satisfactory result.

Corrected bridges

It may be recalled that this is a thermal bridge which has been

insulated with a calculated thickness of insulation so that the U value

opposite to the insulated frame shall be equal to that calculated for

the middle of the wall.

Interior correction

While our hypotheses may enable us to predict the existence of a

higher temperature opposite the frame than at mid -wall, they do not enable

us to determine the value of p , since the cold point has been displaced

outside the frame. The values of p m

found where the insulation does not

45
overlap the frame are rather high. This solution is therefore ineffective

and we shall not give any curves for it.

It is necessary, therefore, to overlap the insulation. Several

factors are involved in determining the width: the thickness of the

wall, the width of the thermal bridge, the conductivity of the insulation

being applied.

Extrapolation of the results obtained in the course of our tests

makes it possible to indicate approximately the width of insulation

required in order to have P m

< 1.5. These are :

Narrow bridge : I < e; x > 1.5 £

Wide bridge : I > e; x > 2 I

for an insulation having a k value equal to 0.03 or 0.04 kcal/(mh°C;.

For higher k values (less insulating materials require a greater thickness)

the width to be applied will be slightly less.

It is not necessary, in fact, to apply a thickness of insulation

such that the U values will be equal. A better diffusion of temperatures

will probably be obtained by using a somewhat smaller thickness of

insulation.

Exterior correction

The conclusions are completely opposite. The narrower the thermal

bridge, the larger and more important must be the overlap. In order to

have p m< 1.5 with an insulation of k = 0.03 or 0.04 it is necessary to

take:

Narrow bridge : £ < e ; x > 4 I

Wide bridge : £ > e; x > 3 ^

For higher k values the width of the insulation would be even greater

46
Finally, it would be advantageous to apply an insulation of

greater thickness, giving a smaller U value opposite to the thermal

bridge.

NB: Plastered walls.

Outside mortar coating :

We saw at the end of the paragraph relating to "Thermal bridge with

interior diffusion" (page 39) that the two effects of an exterior coating

on the inside surface temperature of the wall cancel each other out

(increasing the insulation opposite to the thermal bridge tends to decrease

p while the flux on the outside tends to increase it) . The preceding

m

charts can therefore be directly applied.

Interior plaster coating ;

Plaster coating is generally used on walls which do not have an

interior concrete cover (partial bridge with interior insulation: Fig. 29)-

Since the thermal characteristics of plaster are similar to those of

light masonry, we could deduce from the thickness given by the chart for

an uncoated wall, the imaginary thickness given by the expression—^—2—

k

e where k and k are respective conductivities of the material and of the

plaster (ke

= 0.5) and eg is the thickness of the plaster coating.

Large concrete panel incorporating a light insulation

a) Thick interior slab

The values of p depend essentially on the thickness of the incorporated

insulation. Fig. 30 gives a chart for the case where the useful thickness

of the insulation is 2.5 cm, which corresponds to an initial thickness of

approximately 3_ cm for rigid and relatively non-porous materials. The

concrete always penetrates slightly into both faces of the materials.

47
This is a thickness that can be recommended. It leads to U values

at midwall of the order of 0.9 to 1, depending on the thickness of the

concrete slabs.

For walls having an exterior concrete slab 5 cm thick and a useful

insulation thickness of 2.5 cm this chart gives values of e (thickness

of interior slab) as a function of t (width of frame) in order to get a

desired p . Actually e is generally determined by structural considerations, since the interior concrete cover frequently has a load bearing

function. A thickness of 20 cm is normal; in order to get p m

< 1.5 it is

then necessary to have <£. < 7.5 cm.

This width is adequate for "ladder" joints between slabs, but the

joints between two panels result in much wider thermal bridges.

A satisfactory solution can, however, be reached by applying an equal

thickness of insulation in the joint (Fig. 31).

This assembly is roughly equivalent to two thermal bridges of width

-c with a diffusion slab of thickness e .

Finally, let us note that a greater thickness of the exterior slab

would have an unfavorable effect

.

If this thickness was substantially greater than 5 cm e would have

to be appreciably increased in order to achieve the same result.

b) Thick exterior slab

When the thickness of the exterior slab is much greater than that

of the interior (approximately twice as thick) , the diffusion effect

obtained by the thin interior slab is cancelled out by the external one,

which channels the heat flow into the bridge, with the result that the

P m

value is close to that of the total bridge calculated by the elementary

48
theory. It can even be greater than this if the exterior slab is still

thicker. Any concrete joint, however thin, results in an unacceptable

cold spot.

Special thermal bridges

Corner between two exterior walls

Although no test has been made on this type of thermal bridge, it

is well known, and the German experiments show, that the corner between

two external walls forms an important thermal bridge.

However, although p is large, the p curve is favorable inasmuch

as it is peaked in the zone where pm > 1.5, i.e., the zone where p > 1.5

is a narrow band.

The quantities of water condensing will thus be smaller than on a

wall where the curve is spread out. This must result in a higher admissible

pm. p < 2 appears to be a reasonable limit, m

The problem changes when a post is located in the corner (Fig. 32)

.

To the effect of the corner itself, resulting in a p m

= 1.8, is added

that of the thermal bridge produced by the post. Note that this is a

bridge partially insulated inside by a layer of material of variable

o width (approximately e = — , corresponding to p m

= 1.4.)

It may be shown that in first approximation

p total = p corner x p thermal bridge

i.e. pm

= 1.8 x 1.4 = 2.5

Hence this is an unacceptable thermal bridge. Its correction is

difficult. One solution consists in cutting off the corner in such a way

as to reduce the factor 1.8 (Fig. 33).

49
Corner between partition or floor and exterior wall

Because of the small number of tests available and the lack of

precision in the calculations we are as yet unable to give precise rules

for this case. The conclusions which follow should be regarded only as

orders of magnitude. To begin with a distinction should be made between

the partition and the floor, since the surface heat exchanges are different

in the two cases. The tests have dealt with partitions. The case of the

floor is less favorable. There are fewer remedies than for the wall.

Only interior diffusion and exterior correction are really effective.

Exterior insulation (case of the partial thermal bridge) requires

a considerable thickness in order to be really effective.

It has been shown that the values of pm

found for a partition are

less than those obtained for the same thermal bridge in a wall.

1. In the case of floors (less favorable than partitions) the

same rules can be applied as given for walls, namely:

Interior diffusion :

- light masonry (fig. 28);

- concrete and light insulation incorporated in it (Fig. 30, leading

to division of the thermal bridge - Fig. 34)

.

Exterior correction : x > 3 t

- the thermal bridges being wide (Fig. 35)

.

2. In the case of partitions somewhat less severe rules can be adopted

- Interior diffusion: the values of e as a function of I given by

Fig. 28 for light masonry and Fig. 30 for concrete walls incorporating

light insulation, can be reduced by 30%.

- Exterior correction: we may take: x > 2£(Fig. 35).

50
The general observations of page 5 3 are still valid.

N.B. A solution often used is that of forming a partial thermal

bridge with exterior insulation, so that the floor or partition does not

extend to the bare exterior of the wall. Despite its thermal ineffectiveness this method has the advantage of providing a homogeneous wall section

on the outside, which is advantageous from various points of view,

especially for the adhesion of coatings.

Insulation 1/3 of the wall thickness must be considered a minimum

(Fig. 36a).

To the exterior insulation can be added interior diffusion (Fig. ;5bb)

in order to obtain a satisfactory solution. At the limit (Fig. 36c) the

thermal bridge disappears.

Light walls - curtain walls - facade panels

Wooden frame

The curve of Fig. 37 gives the values of p as a function of the

width of the wood frame.

We find that in order to get p < 1.5 ,t must be the order of ° m

a millimeter ; the total bridge is thus always unacceptable.

In this connection note that the ratio of the coefficient of

thermal contact between the wood and the very 1 ight insulation is greater

than that between the concrete and the light masonry (8 times on the

average) . The latter two materials are more similar in their thermal

properties than wood and light insulations. In addition, the k values

are roughly only 1/10 as much and therefore the same applies in general

to the thicknesses of the walls. Thus even when we divide the width of

the frame by 10 we have a p mvalue greater than that obtained in masonry

51
walls. In the latter, In order to have p < 1.5 it would be necessary m

J

to have t < 2 cm. In the case of wood with light insulation t would have

to be of the order of a millimeter.

Actually, while the total bridge does not exist in practice as far

as masonry walls are concerned because of the coatings applied, we are

even less concerned with them in curtain or facade panel walls with

internal wood framing. The interior finish generally has an appreciable

thickness relative to the thickness of the panel and this finish acts

as an interior insulation or diffusion layer.

Because of the variety of finish used (plasterboard, cement asbestos » plywood, sheet metal) we are unable to give any general rule,

but a framing width of 2 cm must be considered a maximum in order to

obtain p < 1.5. The interposition of a thick aluminium foil (0.1 or m r

0.2 mm) beneath the finish to act simultaneously as a vapor barrier

would make it possible to use widths up to 3 cm.

One solution would consist in placing under the finish another

continuous material that is sufficiently rigid and insulating (k = 0.06

to 0.1) and a thickness - 1 to 2 cm depending on the width of the framing

member and the k of the material used (Fig. 38).

Metal framing

The p values found in the case where the framing passes through

m

the whole panel are always very high (4 to 6) and the proposed remedies

are few.

The most effective remedy seems to be interrupting the thermal

bridge, e.g. by using two frames separated by a good insulator and joined

here and there by bolts passing through the insulation. A bolt cross

52
section smaller than 1 cm^/m of section length seems to be acceptable.

The other solution consists of correcting the thermal bridge by

insulating mouldings.

We have seen that an interior moulding need not be too insulating,

but must be wide. The width depends, of course, on the framing width,

and in general this solution results in very wide, unattractive mouldings

A complete covering would be preferable.

The exterior moulding, on the other hand, must be very insulating

and still wider.

Without interruption of the thermal bridge it appears difficult to

obtain a satisfactory result without using both exterior and interior

moulding.

Conclusion

In closing we must refer again to an important point which our

tests brought out, namely the discrepancy between the values of the

coefficient p as calculated by the classical method and those of pm

obtained by measurement.

Although it is true that for a total thermal bridge pm

is always

less than p c

, the discrepancy increasing with decreasing width of the

bridge and increasing similarity in the thermal characteristics of the

materials in contact, this is not a general rule. As soon as we try to

correct the thermal bridge, whether by insulating it or diffusing it, we

change completely the form of the flux lines and of the isotherms, and

adhering to elementary theory may lead to ineffective solutions and even

to a worsening of matters.

53
We believe we have sufficiently emphasized the basic differences

between interior and exterior insulation, both for partial and corrected

thermal bridges.

We would nevertheless mention once more the good results obtained

when there is a layer of homogeneous material on the interior face of

the wall. Whether this material is insulating or conducting is a matter

of little importance. The essential point is that it should be continuous

and sufficiently thick. Thus the two solutions represented in Fig. 39

both give ° a coefficient p =1.5.

m

In addition to the lower values of pm obtained there is another

advantage in having a layer of homogeneous material on the interior face .

That is that the moisture absorbed during temporary condensations, which

are always possible, will be distributed more uniformly.

From this point of view interior correction, which introduces a

third material, creates a new discontinuity. Although it provides a

satisfactory result from the thermal point of view it should be avoided

as far as possible.

It thus appears that for heavy walls it is relatively easy to

obtain by these methods a wall which, although heterogeneous, has on its

interior face a surface temperature which is uniform enough to avoid

serious risks of condensation.

For light walls our study has not enabled us to give precise and

directly usable information as for the case of heavy walls. It has,

however, brought the problem into sharp focus. The thinness of the good

insulating materials used means that a piece of wood, or even an air gap

constitute thermal bridges that are at least as severe as a concrete

54
frame in a traditional wall for which the wood and air gaps had an insulating effect. As far as metal framing is concerned, without thermal interruption its correction is very difficult. The solution using two mouldings

remains very uncertain.

However, structural devices should render such thermal bridges

acceptable. For example panel joints may be put opposite to partitions

and floors, or else the thermal bridge can be accepted and the panel thus

treated as a problem in carpentry involving condensation gutters.

Every case is separate and can only be judged as a unit: panel,

joint, fastening.

This, together with the wide diversity of finishes used, makes it

impossible for us to give precise rules here for these cases.

55
Appendix

Effect of Thermal Bridges on the Overall U-Value

It was not the aim of our study to determine experimentally the

overall U values of walls containing frames and thereby to check the

values that can be obtained by the elementary theory; we shall however

conclude with a few remarks on this subject because it appears necessary

to recall the limitations of this therory.

We assume that the flow of heat is perpendicular to the faces of

the wall so that the wall may be divided perpendicularly to its faces

into slices containing the same layers of material. The thermal resistance

of these slices, calculated by taking into account their areas, are

assembled in parallel, and from the equivalent resistance obtained the

U value of the wall can be derived.

In conventional walls where the materials used do not possess very

different thermal characteristics the value thus obtained seems accurate

enough for heat loss calculations.

However, the same does not necessarily hold for more complex walls

in which good insulating materials such as the very light ones are used

side by side with conducting materials such as concrete or even highly

conducting ones like the metals.

Actually U value tests carried out on very theoretical cases for

demonstration purposes have shown substantial differences between measured

and calculated values.

We measured the U value of a sandwich panel having a core of 3 cm

polystyrene between two slabs of insulating fibreboard. This panel was

first tested by itself and then interrupted by flat iron bars 5 mm thick

56
spaced 20 cm apart then by iron T bars with the flanges on the interior

face, and finally by I bars.

The Table" shows the results obtained by measurement and by calculation using the elementary method. The calculated results are almost the

same for the three types of reinforcement but the measured results are

very different.

In particular, placing the flange as the inside for either the T or

the I bars provides a considerable increase.

It is probable that the diffusion of the flux produced by a conducting interior slab provides, in the case where the frame members are

near to each other, a considerable increase in the flux traversing the

wall. It may be noted, moreover, that in our tests the temperature differences between the ambient air and the main part of the wall are systematically higher in tests B than in tests C, although the differences between

the interior and exterior temperatures are substantially the same, and

that wall B containing 5 cm more concrete has a lower calculated U value.

This probably results in a considerable increase in U value due to the

fact that the slab of concrete diffuses the flow of cold from the frames

and from each of the joints separating the blocks of cellular concrete.

The case of the large heavy concrete panels with incorporated

insulation raises the same problem. Having a thick slab of concrete on

the inside makes the temperatures of the interior surface more uniform

but certainly leads to a substantial increase in the overall U value.

The closer the bridges are together and the thicker the interior slab,

the greater this increase will be.

See Table page58

57
The phenomenon would be even more evident in the case of a wall , using metal sheets for its interior and exterior finishes and an internal

metallic frame . The losses through such a panel depend more on the separation between the frames than on the filling insulation and calculation by

the classical method has no significance.

Panel Calculated U—value

0.8

0.9

0.9

0.9

58
BIBLIOGRAPHY

France "La Chambre thermique de la Station experimentale de

Champs-sur-Marne" (The thermal chamber of the Experimental Station of Champs-sur-Marne) , Cahier du C.S.T.B . ,

( C.S.T.B . Official Report ) , no. 24-25 (Section 216).

"Recommandations pour l'emploi des maconneries legeres

en consideration de leurs caracteristiques thermiques

utiles" (Recommendations for the use of light-weight

masonry with respect to their thermal characteristic

uses.), Cahier du C.S.T.B. no. 34 (Section 277).

3. R.E.E.F.-58 (Volume I, page 603).

4

.

Manuel des Industries Thermiques ( Thermal Industries

Handbook) , Volume I

.

Canada

England

5. G.O.Handegord "Wall Surface Temperatures", ASHAE

journal Section Heating Piping and air Conditionning

(June 1957)

.

6. N.S.Billington "Thermal properties of Building".

Germany

Publications of the Technical Institute of Stuttgart.

M.Reiher, D.V .Sodem, H.Kunzel "Warme-und

Feuchtigkeitsschutz in Wohnbauten" (Heat and Moisture

Protection in Housing Structures) , (1958)

.

Cahier 29 (1954). W.Schiile, H.Schacke "Warmebrucken im

Wohungsbau'' (Thermal bridges in Housing Structures) , (Translation by C.S.T.B.

Cahier 29 (1954). W.Schiile, H.Kiinzel "Modelluntersuchungen iiber die Wirkung von Warmebriicken in Wanden"

(Model Analysis on the Effect of Thermal Bridges in

Walls), Translation by C.S.T.B.

59
Figure 1. Study of thermal bridges

With

diffusion slab Total

Partial bridges

externally in- sulated

Partial bridges

internally in- sulated

INT.

20 H£i^lj/-5 WA^V-J

N", INT. <<, INT.J:

7.5. . ,12.5 ft

INT.

gJS 5„IS

A

Vertical sections showing horizontal thermal bridges

Interior view, condensation on the reactive paint

m m, scasawaj ssaaq

Horizontal section showing the vertical thermal bridge

60
[

1 flillilm

f

i

1

dm

Ti

6c

Figure 2. Distribution of temperature at the

surface of a heterogeneous wall

Figure 3 Plan of thermal room ®

®

A — Introduction of wall

B — Wall under test C — Ventilation ducts D — Air conditioning unit — hot cold — humidity

X — Thermometers • —Thermocouples

61
Figure 10. — p< D» curves for interior (D.,) or exterior (D 3

) insulation

Porous concrete

u

?- \\\

4 >s^^v

6

8

10

12

1/, 16 18 20

Temperature of interior wall surface in C

Figure 11. Distribution of temperatures at the surface of a wall near a thermal bridge produced by the corner

of a wall and an attic floor and the beam

between them(8)

62
o

o

.c8

3aI

20

1816

141210a

West wall o North wall

1—»—i—i—i—

'

—i—i—i—p—i 50cm

T/.-20'

dc.13.5

dm : 8.5

Te-7"

Pm= 1.8 50cm

Figure 12. Temperature curves at the corner between two homogeneous external walls'''

Te = - 5 C

30-

I

i "> mmmm i

I \M

i i

\ WWMWMt, l

4

io

77= ^s^c

Sl=25.5°c

ep.mc

\/°m s 4.9 | /ju= 0.55J

Figure 13. Light wall — Total bridge — Metal frame

63
Coating Thermal bridge

20 cm

Figure 14. Distribution of temperatures on the interior surface of a wall close to a thermal bridge

produced by a metal frame in the interior of a light panel. Note the diffusion obtained by the interior coating. Never- theless the thermal bridge is very

evident'"'

Mineral wool Cellular concrete Air film Plaster

01

v.'-

1 /-'

^-."^•v>>;r.

o

o

$

3

5I

0)

30

Figure 15.

«? - ^

lb

1Z. /»12 - /\

lum / \ f \* R -

' I ~i_ \ f: s \

£. - p

i

20 10 10 20 30 cm

Distribution of temperatures on the interior surface of the exterior wall, lower curve; and on the interior surface of the interior wall, upper curve. Note the good cor- rection of the thermal bridge by complete

interruption of the two frames by a good

insulator**' 64
0.6 r

0.5

04

0.3 40 4 2 1

<J~ en cm2 per meter

Figure 16. Interrupted bridge. Value of is in terms of the path cross-sectional area

Figure 17. Light wall. Total bridge with fin

65
Figure 18. Liqht wall. Total bridge. Practical example of correction by interruption of the cold bridge and

by interior moulding

Unbroken OJ Perforated 03 Slotted hi Slotted co 2 rows of slots 3 rows of slots

(1) - (2) (3) (4) (5)

i-7 Unbroken thin CO J^ Unbroken thick CO

v? Perforated CO Q Slotted CO 2 rows of s/ofs

/Rj Slotted CO 3 rows of s/ors

4. _

f /

***

•s N

/ \

3.5 \

/ < ••*' H "*'.i V / / / s \ \ /

\ » \ /

". i ^ eaa. / \ \ V / /

i: ' > j - Hi \ :» Y -/ 1! ! \ V

2.5

' i i 1

» '.

i i I \ \

7 /•

1 V

*\

/•• 1 I 2.0 t

• / V

/", k t // \ /• \

t

•,\

>'.' <V '%>

,<• ?£> r*1 ^.> ^^

fffr5»«

Cr ^^?^>j

it,-^*» a*^ a*

**** 0^— fS '"

, e/nX 75 ;o 2 / ; ^ 70 75 Xcm

cmX 15 42-334

/©Slotted thick CO with 2 rows /^ wooden moulding of slots ^Slotted CO with expanded 3 rows p polystyrene moulding of slots

2.i

°°"

: • /

2.C

.• t a . r H f-V i

.• • 1 \ \

p** / /" i \

f > 5 ^ZZ ^ \ N, •.

m

• > > „•• ••. \

T t

6. ,

1 » .• \ ''n

,. "' K s

'«*

fc X -. —— .« ^

:>' !.-••

* --•*w sj*w u

70 2 1 12 10 15 Xcm

2

66
Figure 19. Light walls. Metal frame. Practical example of correction by interior and exterior moulding

nte r nal moulding

1 Joint by itself 2 Filled with glass wool

3 With insulation at A:

67
Fig. 20 — Total bridge. Curve of temperatures given by the elementary theory.

--Te

Fia. 21. —.Total bridge.

Temperature profiles in the thickness of the wall given by the elementary theory.

68
Exterior Central Interior insulation insulation insulation

Ti- TiL-Te

Ti-

-Te -Te

Fig. 22. — Corrected bridge.

Temperature profiles through

the thickness of the wall

Fig. 23. — Left, flux lines of elementary theory

right, true flux iines.

69
-or,

— Te

Plane (C)

Fig. 24. — Example for the calculation of L Convention of signs

f—Te Fig. 25. — Total bridge.

Temperature profiles

70
CD03 73h

CO

03X

LU

CDCT 73n c

o

CO

CO

+-» 3

co m

D_ c

'i O CTj C£ l\ (o IO ^t (^ C\| is

*-" O' Ci C3 C> Cf O' C5 C C5

3u

CDo> a

t~. C\j O} n» LO (Q N. ^D C5 Q- CJ Q C>* C5 C3* C$ iii i i

i i

i

71
Z in centimeters

Fig. 27 — Heavy wall. Total bridge Pm (Z) curve with coatings.

72
=N>

CD s

E

c

CD

CJ

0^ QD l\ CQ *0 \* CV) C\

3 sjaiaumuao ui ssau^oim

73
(DE

co

i- Ha> *J

a)

*_uco . U V

T3

73 .-

CP to O ,_ o o

>- 0) £ £

"O a. £ -E

CD *- >- c c ° o -a

o) a) ro t; . E «! ^ g in o> £ (l) -i <u -—• . O) = "O 5

CD i- 3 -=> > "to .<r n

CD £ CO 41 CD ( ( 1 asCM

S2ec

I\ Co io ** Co C\j 3 sjeieuijiuso in ssau^ojiji

74
i

SB

s\\\ 3

i

1

H — o pi %

CD3

(0c — ^

A

c \

a

oo

c c^S

^v

0)c

(0Q. <^

^s — rete 3ridg ty

o

o <5 w U §-— e

=CD5 "O£ r\""s <P

^>^

avy

\

ffuse aph < S>

I Q (J

I ! 1 ^

©

CO V, V^ >^

0)

Li. 0/

>

8

io

10

k-05

CDE

cu

lO

O

3 sjaieujuuao u; ssainpiiji

75
>||mmwi[i ii m'»

|

iii miii

|

i i MMiiMBt A

acn2 m

Fig. 31. — Concrete wall incorporating light insulation joint between two panels.

J

Fig. 32. — Corner of two exterior walls incorporating a post case of light masonry

Fig. 33. — Correction of the thermal bridge

in the corner

76
J

m

Fig. 34. — Partition, Floor. Case of concrete panels incorporating light insulation.

toAx

X>2-8

a) Partition.

b) Floor.

Fig. 35. — Corrected bridges.

77
Fig. 36. — Partition. Floor.

e

W$m$WX§M$SS$MM!m

M

i>±

Partial bridge. Exterior insulation

Combined exterior insulation and interior insulation

s§" ^££^£££a££^£tt£Sk

1

i..

78
3.5

2.5

6

Q.

1.5

l

I

3^m W

1

T 1

*-70

Width in centimeters £

Fig. 37. — Light wall. Total bridge. Wood framing curve P m ( £)

79
Fig. 38. — Light wall. Example of correction

of a thermal bridge produced by internal framing

o) Interior diffusion

15

m

m

b) Interior insulation

Fig. 39. — Two equivalent solutions. P m =a 1.5

80
Table I

Heavy walls: Reinforced concrete frame - Light masonry filling or large panel of light masonry

HH Compact concrete mm®wm

Reinforcement i I Plaster

TOTAL BRIDGES

A,

o

Cellular concrete

IMIMIM1 Expanded Polystrene

7.5 Te.- - 4.8 22.5

I At?.- 7.95 1 Pc.ZA \Pm = 2.20

dp 20.5

TOTAL BRIDGES

7.5 Te: .4.5 | 22.5

A2

to

|

I I—

Ti:

Gc

Bp

' H I

"""" *>.

i

I

I

1

5.5

0.1

u ! Jc—

a> 264 ——^ „ 6c 2 NA lU \ / \ a

b 21 \

CD dp 2

|

i Pm = 2.15 Pc = 2.4 Pm=2.40

81
B

o

3129 c

27

0} 25

im3 23

(D 21

a.F 19

o> i- 17

Table I (cont'd)

BRIDGES WITH INTERIOR DIFFUSION LAYER

22.5

Exterior

Interior

PmJ.8

Ti:31.3

0c: 25.7

8p:21.2

T.e:-4.6

B, Pm= 1.40 \ Pc = 2.4 \ Pm= 1J0

7.5 10

Te.- - 4.6 22.5 JO

Q

' '

' ^ -

' J ,-,,r„

B2

o 7-/, 30.-? c

3 ©c2<5

IB01 Op 22.6

0.

03

Ti:30.5

Be 24.9

dp 21.5

82
Table I (cont'd)

BRIDGES WITH INTERIOR DIFFUSION LAYER (cont'd)

7.5 20 22.5 20

O

o

B3

6c 25.1 -

Gp23A

B4

Pm= 1.30 Pc= ZA \pm= 1.45

7.5 T.e-48

O Tl 31 TJ. 30.9

Pm=1.35 Pc = 2.4 Pm = 1.65

Te: - 4.8

% \

O

oc Ti:30.4

CD

l.35 0c25.<9

cua

H 6»o2Q7

22. 5

f

i |_^

7"/, 30.4

9c 25.9

Op 20.7

B5 Pm=l90 Pc,2.4 \Pm.2.15

83
Table I (cont'd)

PARTIAL BRIDGES

7.5"

Te : -4.5

>o ^o

22.5 T

fm

^mmm^fmm^

o° r#:3Qfi=

<D

w

a.Eo

c,

Pm-_ 1.25 PcJ.85 Pm- 1.65

Ti: 30.4

dc 25.9

dp 23

7.5 Te:-4.5 22.5 —

Pm, 1.25 PcJ.65 Pm= 1.50

84
Table I (cont'd)

PARTIAL BRIDGES (cont'd)

7.5 Te:-4.8 22.5 T <o

O Ti:30.8 c«

I.3

(0

|HQ.

6c26^:

%eP 20.9\

Pm = 2.15 Pc= 1.85 Pm = 7.55

Ti: 31

dc26.3

9p21.8

7.5 Te:-4.8 fc3

22.5

S

o° ft 30.3

= Bc25.7

I ©/>2/./

A*=2.0 PcJ.65 Pm=1.8

= 7"/.-30.4

C4

85
Table I (cont'd)

CORRECTED BRIDGES

7.5 L=HI

22.5 , Te:-7.5

«fr

T/.-267

8c 22

9p 17.5 Pm= 155 PcJ Pm=1.95

7.5

Te : -7.5

22.5

! ilWffl.

',)M«i r

I?

22.5 67.5 O

o

Ti:26.8

9- Be 22.2 % 9p21.1

== r/^&s

^225

£27.3

Ai.3L25 A:.; Pm.0.87

86
Table I (cont'd)

CORRECTED BRIDGES (cont'd)

D3

u

c

d>3

ts

1-<0Q.E

0) H

-l 1

7.6

Te, - 5

22.5 L l\ _ 1—1—

-

\m. f mmmm ~

i_JL_

.....,.....1.1.1.1.1 —

1

8

T,

e

j'2SL6

te24.9

p20

23.3^=^ ~

„, ^ *~v v r~*^\ /~**^^. f- :24.8 —«^ \ / \ \ / \ /

\ / \ / v / \ LT / \ / v^\S n 12U °

PcJ

1 Pm = 2.05 Pm = 2.05

22.5 £7.5

Pm-1.65 PcJ Pm. 150 D4

87
-ao

o

-aW

in0) ac

CD

c

0) oO

o

0) D

I >

uu

_l

CQ<

<o

U/3f00 <\J <\j M" ti 8? R* ^ <£ & £:

3

p° cr> <\l "O tO KJ 83 R> $ <§ ii C5 eg

-

e

c5 1-

8'2°d eujejj uepoo/w ri =3 d eiueJj poom pessejd

90
TABLE V. - Light walls: Metal frame (interior space is to the left)

I I Polystyrene

Iron

TOTAL

BRIDGES

Jfl_

4

5.4 0.603.1 0.35

7.2

w////M.

30 _38_ i

4.9 0.80 0.55

TOTAL BRIDGES

WITH

EXTERNAL

FIN

WMM%?WM!>M Wbfflb

30

36

.ML.

3.6 0.40

ML

ML

_fi4_

5.4 0.60

. 3035

15

_«_

4.9 0.55

INTERRUPTED

BRIDGES

Uninterrupted

web o = 40 cm2 per meter of section

4.9 0.55

1 screw every 4 cm

o = 4 cm2/m

3.9 0.44

H=_4---

T

\_^Q 1*. 38

1 screw every 8 cm

o = 2 cm2 /m

3.4 0.38

-l.-J^-"4-

.20. K.

je

1 screw every 16 cm

a = 1 cm2 /m

3.1 0.35

* U. S. GOVERNMENT PRINTING OFFICE : 1 973 —51 1 -326/25 1*

91
FORM NBS-114A (1-71) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. Technical Note 710-7

2. Gov't Accession No.3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Building Research Translation

Weak Thermal Points or Thermal Bridges

5. Publication Date May 1973

6. Performing Organization Code

7. AUTHOR(S)

J. Berthier

8. Performing Organization

10. Project/Task/Work Unit- No. 4633104

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Same as item 9

13. Type of Report & Period Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Translated By National Science Library

National Research Council,

Ottawa, Ontario, flanarla

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

Uniformity of temperature on the internal face is one of the essential hygro<-

thermal qualities for a wall.

Cold bridges, which are the cause of uneven temperatures, constitute a weakness which ought to be corrected.

The author describes a large number of tests carried out with -various types

of wall (dense walls and lightweight panels) in order to assess the importance of

cold bridges and to determine the effectiveness of possible remedies; he shows that

the accepted theory used in the calculation of U-coefficients is unsatisfactory

when estimating surface temperatures. The results obtained can be explained, however

by means of two simple hypotheses; on the basis of these there are practical rules

which can be used in establishing the importance of cold bridges, and recommendations

for reducing them.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Floors and panels; moisture condensation; thermal bridges; thermal insulation;

U-values of walls.

18. AVAILABILITY STATEMENT

PH UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

96

22. Price

$1.25 Domestic postpaid $1.00 G.P.0. Bookstore

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