INTERNATIONAL STANDARD
IS0 6946 First edition 1996-08-I 5
Building components and building elements - Thermal resistance and thermal transmittance - Calculation method Composants et parois de bitiments - RBsistance thermique et coefficient de transmission thermique - M&hode de calcul
This material is reproduced from IS0 documents under international Grganization for Standardization (ISO) Copyright License number lHSllCC11996. Not for resale. No part of these IS0 documents may be reproduced in any form, electronic retrieval system or otherwise, except as allowed in the copyright law of the country of use, or with the prior written consent of IS0 (Case postale 56,121l Geneva 20, Switzerland, Fax +41 22 734 10 79), IHS or the IS0 Licenser’s members.
Reference number IS0 6946:1996(E)
IS0 6946:1996( E)
Contents
Page
1
Scope ................................................................................................
2
Normative references
3
Definitions
and symbols
4
Principles
..........................................................................................
5
Thermal resistances
6
Total thermal resistance
7
Thermal transmittance
1
.......................................................................
1
...................................................................
1
3
.........................................................................
4
...................................................................
9
...................................................................
12
..........................................................................
13
Annexes A
Surface resistance
B
Thermal resistance of unventilated
C
Calculation of the thermal transmittance of components with tapered 18 layers ....................................... .......................................................
D
Corrections to thermal transmittance
.............................................
21
E
Examples of corrections for air gaps ..............................................
23
airspaces
................................
15
0 IS0 1996 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from the publisher. International Organization for Standardization Case Postale 56 l CH-1211 Geneve 20 l Switzerland Printed in Switzerland
ii
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IS0 6946:1996(E)
Foreword IS0 (the International Organization for Standardization) is a worldwide federation of national standards bodies (IS0 member bodies). The work of preparing international Standards is normally carried out through IS0 technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. IS0 collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. International Standard IS0 6946 was prepared by the European Committee for Standardization KEN) in collaboration with ISO/TC 163, Thermal insulation, Subcommittee SC 2, Calculation methods, in accordance with the Agreement on technical cooperation between IS0 and CEN (Vienna Agreement). This first edition cancels and replaces IS0 6946-l :1986. IS0 6946-2:1986 was withdrawn in 1995. Annexes A, B, C and D form an integral part of this International Annex E is for information only.
Standard.
.. III
IS0 6946:1996(E)
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Introduction The thermal transmittance calculated according to this standard is suitable for determining heat flow through building components that are within the scope of this standard. For most purposes heat flows can be calculated with the following peratures: -
internal: dry resultant temperature;
-
external: air temperature.
iv
tem-
IS0 6946:1996(E)
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1
Scope
This standard gives the method of calculation of the thermal resistance and thermal transmittance of building components and building elements, excluding doors, windows and other glazed units, components which involve heat transfer to the ground, and components through which air is designed to permeate. The calculation method is based on the appropriate design thermal conductivities resistances of the materials and products involved.
or design thermal
The method applies to components and elements consisting of thermally homogeneous include air layers). The standard also gives an approximate method that can be used for inhomogeneous cases where an insulating layer is bridged by metal.
2
Normative
layers (which can
layers, except
references
The following standards contain provisions which, through reference in this text, constitute provisions of this International Standard. At the time of publication, the editions indicated were valid. All standards are subject to revision, and parties to agreements based on this International Standard are encouraged to investigate the possibility of applying the most recent editions of the standards indicated below. Members of IEC and IS0 maintain registers of currently valid International Standards. IS0 10456:--11, Thermal insulation and design thermal values.
Building materials and products -
IS0 7345:1987,
Physical quantities and definitions.
3
Definitions
3.1
Definitions
Thermal insulation -
Determination
of declared
and symbols
For the purposes of this standard, the following definitions and those given in IS0 7345 apply.
3.1 .l building element: Major part of a building such as a wall, floor or roof.
1)
To be
published.
IS0 6946:1996(E)
3.1.2 building component: Building element or a part of it. NOTE - In this standard the word “component”
is used to indicate both element and component.
3.1.3 design thermal value: Design thermal conductivity or design thermal resistance. NOTE - A given product can have more than one design value, for different applications environmental conditions.
or
3.1.4 design thermal conductivity:
Value of thermal conductivity of a building material or product under specific external and internal conditions which can be considered as typical of the performance of that material or product when incorporated in a building component.
3.1.5 design thermal resistance: Value of thermal resistance of a building product under specific external and internal conditions which can be considered as typical of the performance of that product when incorporated in a building component. 3.1.6 thermally homogeneous
layer: Layer of constant thickness having thermal properties which are uniform or which may be regarded as being uniform.
3.2
Symbols and units Symbol
Quantity
Unit
A
area
m*
R
design thermal resistance
m2WW
R9
thermal resistance of airspace
m*K/W
Rse
external surface resistance
m*K/W
Rsi
internal surface resistance
m*K/W
RT
total thermal resistance (environment
6
upper limit of total thermal resistance
m*K/W
RY
lower limit of total thermal resistance
m*K/W
R” u
thermal resistance of unheated space
m*K/W
thermal transmittance
W/(m*.K)
d
thickness
m
h
heat transfer coefficient
W/(m*.K)
a
design thermal conductivity
W/( m+K)
to environment)
m*K/W
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4
Principles
The principle of the calculation
method is to:
a) obtain the thermal resistance of each thermally homogeneous
part of the component;
b) combine these individual resistances so as to obtain the total thermal resistance of the component, including (where appropriate) the effect of surface resistances. Thermal resistances of individual parts are obtained according to 5.1. The values of surface resistance given in 5.2 are appropriate in most cases. Annex A gives detailed procedures for low-emissivity surfaces, specific external wind speeds, and non-planar surfaces. Air layers may be regarded as thermally homogeneous for the purposes of this standard. Values of the thermal resistance of large air layers with high-emissivity surfaces are given in 5.3, and annex B gives procedures for other cases. The resistances of the layers are combined as follows: a) for components consisting of thermally homogeneous layers, obtain the total thermal resistance according to 6.1 and the thermal transmittance according to clause 7; b) for components having one or more thermally inhomogeneous layers, obtain the total thermal resistance according to 6.2 and the thermal transmittance according to clause 7; c) for components containing a tapered layer, obtain the thermal transmittance thermal resistance according to annex C.
and/or the total
Finally, corrections are applied to the thermal transmittance if appropriate according to annex D, to allow for the effects of air gaps in insulation, mechanical fasteners penetrating an insulation layer, and precipitation on inverted roofs. The thermal transmittance so calculated applies component concerned, for example internal and case of an internal partition, internal environment given in 5.4 for treating an unheated space as a
between the environments on either side of the external environments, two internal environments in the and an unheated space. Simplified procedures are thermal resistance.
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IS0 6946: 1996(E)
5
Thermal
resistances
5.1
Thermal resistance of homogeneous layers
Design thermal values can be given as either design thermal conductivity or design thermal resistance. if thermal conductivity is given, obtain the thermal resistance of the layer from:
where d
is the thickness of the material layer in the component;
a
is the design thermal conductivity of the material, either calculated according to ISO/DIS 10456.2 or obtained from tabulated values. NOTE - The thickness d may be different from the nominal thickness (e.g. when a compressible product is installed in a compressed state, d is less than the nominal thickness). If relevant, d should also make appropriate allowance for thickness tolerances (e.g. when they are negative).
Thermal resistance values used in intermediate calculations shall be calculated to at least 3 decimal places.
5.2
Surface resistances
Use the values in table 1 for plane surfaces in the absence of specific information on the boundary conditions. The values under “horizontal” apply to heat flow directions +30” from the horizontal plane. For non-planar surfaces or for specific boundary conditions use the procedures in annex A.
Table 1 - Surface resistances (in m2WW) Direction of heat flow Upwards r
Horizontal I
Downwards I
1 %i
1
0~10
(
0,13
1
OS17
(
I
I
0,04
I
0,04
I
0,04
I
Rse
NOTE - The values in table 1 are design values. For the purposes of declaration of the thermal transmittance of components and other cases where values independent of heat flow direction are required, it is recommended that the values for horizontal heat flow are used.
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5.3
IS0 6946:1996(E)
Thermal resistance of air layers
The values given in this subclause apply to an air layer which: -
is bounded by two faces which are effectively parallel and perpendicular and which have emissivities not less than 0,8;
-
has a thickness (in the direction of heat flow) of less than 0,i times each one of the other two dimensions, and not greater than 0,3 m;
to the direction of heat flow
NOTE - A single thermal transmittance should not be calculated for components containing air layers thicker than 0,3 m. Rather, heat flows should be calculated by performing a heat balance (see ISO/DIS 13789, Thermal performance of buildings - Transmission heat loss coefficient Calculation method). -
has no air interchange
If the above conditions
53.1
with the internal environment.
do not apply, use the procedures in annex B.
Unventilated air layer
An unventilated air layer is one in which there is no express provision for air flow through it. Design values of thermal resistance are given in table 2. The values under “horizontal” apply to heat flow directions *30” from the horizontal plane.
Table 2 - Thermal resistance (in m2XAIV) of unventilated high emissivity surfaces Thickness of air layer mm
0 5 7 10 15 25 50 100 300
air layers:
Direction of heat flow Upwards
Horizontal
Downwards
0,oo
0,oo
0,oo
0,ll 0,13 0,15 0,16 0,16 0,16 0,16 0,16
0,ll 0,13 0,15 0,17 0,18 0,18 0,18 0,18
0,ll 0,13 0,15 0,17 0,19 0,21 0,22 0,23
NOTE - Intermediate values may be obtained by linear interpolation.
IS0 6946: 1996(E)
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An air layer having no insulation layer between it and the external environment but with small openings to the external environment shall also be considered as an unventilated air layer, if these openings are not arranged so as to permit air flow through the layer and they do not exceed: -
500 mm2 per m length for vertical air layers 500 mm2 per m2 of surface area for horizontal air layers.‘) NOTE - Drain openings (weep holes) in the form of open vertical joints in the outer leaf of a masonry cavity wall are not regarded as ventilation openings.
5.3.2
Slightly ventilated air layer
A slightly ventilated air layer is one in which there is provision for limited air flow through it from the external environment by openings within the following ranges: -
> 500 mm2 but 5 1500 mm2 per m length for vertical air layers > 500 mm2 but 5 1500 mm2 per m2 of surface area for horizontal air layers.‘)
The design thermal resistance of a slightly ventilated air layer is one half of the corresponding value in table 2. If, however, the thermal resistance between the air layer and the external environment exceeds 0,15 m2WW, it shall be replaced by the value 0,15 m2WW.
5.3.3
Well ventilated air layer
A well ventilated air layer is one for which the openings between the air layer and the external environment exceed: -
1500 mm2 per m length for vertical air layers 1500 mm2 per m2 of surface area for horizontal air layers.‘)
The total thermal resistance of a building component containing a well-ventilated air layer shall be obtained by disregarding the thermal resistance of the air layer and all other layers between the air layer and external environment, and including an external surface resistance corresponding to still air (i.e. equal to the internal surface resistance of the same component).
‘1 For vertical air layers the range is expressed the area of openings per square metre area.
as the area of openings per metre length. For horizontal air layers it is expressed
as
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5.4
IS0 6946:1996(E)
Thermal resistance of unheated spaces
When the external envelope of the unheated space is not insulated the following simplified procedures, treating the unheated space as a thermal resistance, may be applied. NOTE - ISO/DIS 13789, Thermal performance of buildings - Transmission heat loss coefficient Calculation method, gives general, and more precise, procedures for the calculation of heat transfer from a building to the external environment via unheated spaces, and should be used when a more accurate result is required. For crawl spaces below suspended floors see ISO/DIS 13370, Thermal performance of buildings - Heat transfer via the ground - Calculation method.
5.4.1
Roof spaces
For a roof structure consisting of a flat, insulated ceiling and a pitched roof, the roof space may be regarded as if it were a thermally homogeneous layer with thermal resistance as given in table 3.
Table 3 - Thermal resistance of roof spaces Characteristics
of roof
RU m*XM
1
Tiled roof with no felt, boards or similar
0,06
2
Sheeted roof, or tiled roof with felt or boards or similar under the tiles
02
3
As 2 but with aluminium cladding or other low emissivity surface at underside of roof
093
4
Roof lined with boards and felt
093
NOTE - The values in table 3 include the thermal resistance of the ventilated space and the thermal resistance of the (pitched) roof construction. They do not include the external surface resistance (Rse).
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IS0 6946:1996(E)
Other spaces
5.4.2
When the building has a small unheated space attached to it, the thermal transmittance between the internal and external environments can be obtained by treating the unheated space together with its external construction components as if it were an additional homogeneous layer with thermal resistance R,, given by: R, = 0,09 + 94;
(2) U
subject to RU IO,5 m2-WW, where
4
is the total area of all components between the internal environment and the unheated space;
4
is the total area of all components between the unheated space and the external environment. NOTES 1 Examples of small unheated spaces include garages, store rooms and conservatories. 2 If there is more than one component between the internal environment and the unheated space, R, should be included in the calculation of the thermal transmittance of each such component.
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IS0 6946: 1996(E)
Total
thermal
resistance
If the total thermal resistance is presented as a final result, it shall be rounded to two decimal places.
6.1
Total thermal resistance of a building component consisting of homogeneous
layers
The total thermal resistance RT of a plane building component consisting of thermally homogeneous layers perpendicular to the heat flow shall be calculated by the following expression:
RT = &j + Rl + & + ........ Rn + Rse
(3)
where hii
is the internal surface resistance;
Rl, R-J . ... . Rn
are the design thermal resistances of each layer;
Rse
is the external surface resistance.
In the case of calculation of the resistance of internal building components (partitions etc.), or an component between the internal environment and an unheated space, R,i applies on both sides. NOTE - The surface resistances should be omitted in equation (3) when the resistance of a component from surface to surface is required.
6.2
Total thermal resistance of a building component consisting of homogeneous and inhomogeneous layers
This subclause gives a simplified method to calculate the thermal resistance of building components consisting of thermally homogeneous and inhomogeneous layers, except in cases where an insulation layer is bridged by metal. NOTES 1 A more precise result will be obtained by using a numerical method conforming to IS0 10211, Thermal bridges in building construction - Heat flows and surface temperatures - Part I: General calculation methods, or Part 2 (under preparation): Calculation of linear thermal bridges. 2 The procedure described in 6.2 is not suitable to compute surface temperatures purposes of evaluating the risk of condensation.
for the
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IS0 6946: 1996(E)
6.2.1
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Total thermal resistance of an component
The total thermal resistance, RT, of an component consisting of thermally homogeneous and thermally inhomogeneous layers parallel to the surface is calculated as the arithmetic mean of the upper and lower limits of the resistance: R /r+dr T
2
(4)
where Fir
is the upper limit of the total thermal resistance, calculated according to 6.2.2;
R;
is the lower limit of the total thermal resistance, calculated according to 6.2.3.
Calculation of the upper and lower limits shall be carried out by considering the component split into sections and layers, as shown in figure 1, in such a way that the component is divided into parts mj, which are themselves thermally homogeneous.
lc
lb
1CI
Figure 1 - Sections and layers of a thermally inhomogeneous
component
The component (figure la) is considered cut into sections (figure 1b) and into layers (figure lc). The section m (m = a, b, c, ... 9) perpendicular The layerj(j=
to the surfaces of the component has fractional area f,,,.
1,2, .. . n) parallel to the surfaces has thickness c$.
The part mj has thermal conductivity
hmj, thickness c$, fractional area fm and thermal resistance R,Q.
The fractional area of a section is its proportion of the total area. Thus fa + fb + ... . + f, = 1.
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6.2.2
IS0 6946:1996( E)
Upper limit of the total thermal resistance (R; )
The upper limit of the total thermal resistance, is determined by assuming one-dimensional perpendicular to the surfaces of the component. It is given by the following expression:
heat flow
rs -= l6 fa+fa+...+ RTa
RTb
(5)
RT9
where are the total thermal resistances from environment section, calculated using equation (3); &a,
&by
.-., &9
to environment
for each
fa fb, . ... f9 are the fractional areas of each section.
6.2.3
Lower limit of the total thermal resistance (RT )
The lower limit is determined isothermal surfaces.*)
by assuming that all planes parallel to the surfaces of the component
Calculate an equivalent thermal resistance Rj, for each thermally inhomogeneous expression:3) f La+-+...+Rj Raj
fb
6
Rbj
Rqj
layer using the following
(6)
*) If there is a non-planar surface adjacent to an air layer, the calculation should be undertaken the narrower sections extended (but without alteration to thermal resistance):
or projecting
are
as if it were planar, by considering
parts removed (so reducing the thermal resistance):
3, An alternative
method is by means of an equivalent
where the equivalent
thermal conductivity
hi
thermal conductivity
of the layer:
of layer j is:
hi = haj fa + hbj fb+e. a+hQi4 If an air layer is part of an inhomogeneous dj /F$ where F$ is the thermal resistance
layer, it may be treated as a material with an equivalent of the air layer determined
in accordance
thermal conductivity
hi
=
with annex B.
11
IS0 6946: 1996(E)
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The lower limit is then determined using equation (3) i.e. RF = Rsi + RI + R2+eam+Rn+ Rse
6.2.4
(7)
Estimation of error
This method of estimating the maximum relative error may be used when the calculated thermal transmittance is required to meet specified accuracy criteria. The maximum relative error, e, as a percentage when using this approximation
is:
eJ~-R;xlOO
(8)
2RT
EXAMPLE - If the ratio of the upper limit to the lower limit is 1,5, the maximum possible error is 20%. The actual error is usually much less than the maximum. This error may be evaluated to decide whether the accuracy obtained through the procedure described in 6.2 is acceptable, having regard to
7
-
the purpose of the calculation;
-
the proportion of the total heat flow through the building fabric that is transmitted through the components the thermal resistance of which is evaluated through the procedure described in 6.2;
-
the accuracy of the input data.
Thermal
transmittance
The thermal transmittance
is given by:
(9) Corrections shall be applied to the thermal transmittance, as appropriate, according to annex D. If, however, the total correction is less than 3% of U, the corrections need not be applied. If the thermal transmittance is presented as a final result, it shall be rounded to two significant figures, and information shall be provided on the input data used for the calculation.
12
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IS0 6946:1996(E)
Annex
A (normative)
Surface A.1
resistance
Plane surfaces
The surface resistance is given by4)
R,=L hc+hr
61)
where hc
is the convective
coefficient;
hr
is the radiative coefficient;
and h, = Ehro
(A-2)
h,=4oT;
(A.3)
where &
is the emissivity of the surface;
h ro
is the radiative coefficient for a black-body surface (see table A.l);
0
is the Stefan-Boltzmann
T?l
is the mean thermodynamic
constant (567 x 10-s W/(m2.K4)); temperature
of the surface and of its surroundings.
Table A.1 - Values of the black-body radiative coefficient I?,,
I
Temperature
I
h ro
“C
W/(mz.K)
-10 0 10 20 30
491 496 571 597 63
I
4, This is an approximate treatment of surface heat transfer. Precise calculations of heat flow can be based on the internal and external environmental temperatures (in which the radiant and air temperatures are weighted according to the respective radiative and convective coefficients, and which can also take account of room geometry effects and air temperature gradients). If, however, the internal radiant and air temperatures are not markedly different, the internal dry resultant temperature (equal weighting of air and radiant temperatures) may be used. At external surfaces it is conventional to use the external air temperature, based on an assumption of overcast sky conditions so that external air and radiant temperatures are effectively equal. This also ignores any effect of short-wave solar radiation on external surfaces.
13
IS0 6946:1996(E)
At internal surfaces h, = hci, where -
hci = 5,0 W/(m2.K) hci = 2,5 W/(mz.K) hci = 0,7 W/(m2.K)
for heat flow upwards: for heat flow horizontal: for heat flow downwards:
At external surfaces hc = hce, where hce=4 +4 v
(A-4)
and v is the wind speed adjacent to the surface in m/s. Values of the external surface resistance, f&e, for various wind speeds are given in table A.2. NOTE - The values given in 5.2 for internal surface resistance were calculated for E = 0,9 and with h, evaluated at 20°C. The value given in 5.2 for external surface resistance was calculated for E = 0,9, hro evaluated at O”C, and for v = 4 m/s.
Table A.2 : Values of R,, at various wind speeds Wind speed
A.2
m/s
Rse m2K/W
1 2 3 4 5 7 10
0,08 0,06 0,05 0‘04 0,04 0,03 0,02
Components with non-planar surfaces
Parts which protrude from otherwise plane surfaces, such as structural columns, shall be disregarded in the calculation of the total thermal resistance if composed of material having thermal conductivity not more than 2 W/(m.K). If the part that protrudes is composed of material having thermal conductivity greater than 2 W/(m.K) and is not insulated, the surface resistance shall be modified by the ratio of the projected area to the actual surface area of the protruding part (see figure A.1):
where:
14
Rs
is the surface resistance of a plane component according to A.1 ;
AP
is the projected area of the protruding part;
A
is the actual surface area of the protruding part.
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IS0 6946:1996(E)
Equation (A.5) applies to both internal and external surface resistance.
Figure A.1 - Actual and projected areas
Annex
B (normative)
Thermal B.l
resistance
of unventilated
airspaces
General
This annex applies to airspaces in building components necessary for glazing and window frames.
other than glazing. A more precise treatment is
The term airspace includes both air layers (which have a width and length both 10 times the thickness, with thickness measured in the heat flow direction) and air voids (which have width or length comparable to thickness). If the thickness of the air layer varies, its average value should be used to calculate the thermal resistance. NOTE - Airspaces can be treated as media with thermal resistance because the radiation and convection heat transfer across them is approximately proportional to the temperature difference between the bounding surfaces.
15
IS0 6946:1996(E)
B.2
Unventilated airspaces with length and width both more than 10 times thickness
The thermal resistance of an airspace is given by: 1 Rg= ha.+/+
(B-1)
where 44
is the thermal resistance of the airspace;
ha
is the conduction/convection
hr
is the radiative coefficient.
coefficient;
ha is calculated as follows: - for heat flow horizontal:
ha is the larger of I,25 W/(m2+K) and 0,025/d W/(m2+K);
- for heat flow upwards:
ha is the larger of I,95 W/(m’.K) and 0,025/d W/(m2.K);
- for heat flow downwards:
ha is the larger of 0,12~f-~j~~ W/(m2.K) and 0,025/dW/(m2.K);
where d is the thickness of the airspace (in heat flow direction). hr is given by hr = E hro
03.2)
where E
is the intersurface
h ro
is the radiative coefficient for a black-body surface (see table A.2);
emittance;
and E=
I 1/&,+1/&p-1
where ~1, ~2 are the hemispherical
(B.3) emissivities
of the surfaces bounding the airspace.
The design value of emissivity should allow for any effects of tarnishing with time. NOTE - The values in table 2 were calculated using equation (B.l) with ~1 = 0,9, r2 = 0,9, and hro evaluated to 10°C.
16
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B.3
IS0 6946:1996(E)
Small or divided unventilated
airspaces (air voids)
-70 I ;; heat0
, flow
Figure B.l - Dimensions of small airspace Figure B.l illustrates a small airspace with width less than 10 times its thickness. Its thermal resistance is given by: 1 Rg = ha + % Eh,(l
+ ,/m-
U3.4)
d ! b)
where 63
is the thermal resistance of the airspace;
d
is the thickness of the airspace;
b
is the width of the airspace;
E, ha and hro are calculated as in B.2.5) NOTE - Equation(B.4) is appropriate for the calculation of heat flow through building components for any thickness of air void, and for the calculation of temperature distributions in building components having air voids whose thickness d less than or equal to 50 mm. For thicker air voids, the equation gives an approximate temperature distribution. For an air void that is not rectangular in shape, take its thermal resistance as equal to that of a rectangular void which has the same area and aspect ratio as the actual void.
5, h, depends on d but is independent
0; b. Obtain E using the emissivities
of the hot and cold faces in equation (6.3)
17
Annex
C (normative)
Calculation C.l
of the thermal
transmittance
of components
with tapered
layers
General
When a component has a tapered layer (e.g. in external roof insulation layers to establish fall) the total thermal resistance varies over the area of the component. Such components
are built up as shown in figure C.l.
NOTE - For tapered air layers see annex B.
Figure C.l - Principle of build-up of component
The thermal transmittance
is defined by an integral over the area of the relevant component.
The calculation shall be carried out separately for each part (e.g. of a roof) with different pitch and/or shape as shown in figure C.2. In addition to those in clause 3, the following symbols are used in this annex:
Quantity
Xl
design thermal conductivity thickness at one end)
RO
design thermal resistance of the remaining part, including surface resistances on both sides of the component
m24VW
RI
maximum thermal resistance of the tapered layer
m%/W
4
maximum thickness of the tapered layer
m
and In denotes natural logarithm.
18
Unit
Symbol
of the tapered part (having zero
W/( m-K)
IS0 6946:1996(E)
+
indicates direction of pitch (which can be in either direction)
---
indicates alternative
(supplementary)
subdivision
to enable use of equations (C.l) to (C.3)
Figure C.2 - Examples of how to subdivide roofs into individual parts
C.2
Calculation for common shapes
The thermal transmittance not exceeding 5%.
of common shapes shall be calculated by equations (C.l) to (C.3) for pitches
NOTE - Numerical methods can be used for greater pitches.
C.2.1
Rectangular area
(C-1)
C.2.2
Triangular area, thickest at apex
A r’
HIL\ dl- 1
I
,’
,’
-=?
i.)ln(I+?)-I]
(C.2)
IS0 6946:1996(E)
C.2.3
Triangular area, thinnest at apex
(C.3)
C.3
Calculation procedure
The calculation
shall be carried out as follows:
1) Calculate Ro as the total thermal resistance of the component excluding the tapered layer, using equation (3) if all layers are thermally homogeneous, or the procedure in 6.2 if there are inhomogeneous layers. 2) Subdivide the area with tapered layers into individual parts as necessary (see figure C.2). 3) Calculate RI for each tapered layer using
4) Calculate the thermal transmittance in C.2.
of each individual part (UJ according to the relevant equation
5) Calculate the overall thermal transmittance
for the whole area A using (C.5)
If total thermal resistance of a component with tapered layers is required then RT = l/U
20
(C.6)
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IS0 6946:1996(E)
Annex D (normative) Corrections D.l
to thermal
transmittance
General
The thermal transmittance obtained by the procedures given in this standard shall be corrected where relevant to allow for the effects of: -
air gaps in insulation;
-
mechanical fasteners penetrating an insulation layer;
-
precipitation
on inverted roofs6).
The corrected thermal transmittance
UC is obtained by adding a correction term AU:
“,=“+A”
(D-1)
AU is given by A” = A”,
-I-A”f + A”,
(D-2)
where
D.2
AUg
is the correction for air gaps;
AlJf
is the correction for mechanical fasteners;
A”,
is the correction for inverted roof@).
Correction for air gaps
There are three levels of correction, depending on the extent and position of the gaps, as given in table D.1.
Table D.l - Correction for air gaps Level
AU” W/(m*.K)
0,oo
0,Ol
0,04
Description of air gap Insulation installed in such a way that no air circulation is possible on the warm side of the insulation. No air gaps penetrating the entire insulation layer. Insulation installed in such a way that no air circulation is possible on the warm side of the insulation. Air gaps may penetrate the insulation layer. Air circulation possible on the warm side of the insulation. Air gaps may penetrate the insulation.
6, An inverted roof is one having an insulation layer above the waterproof membrane. Correction procedures for inverted roofs are not included in the present edition of the standard, but are under preparation for incorporation by revision or amendment.
21
IS0 6946:1996(E)
This correction is adjusted according to equation (D.3): 2
-4
A",=A""
(D-3)
( RT 1 where RI
is the thermal resistance of the layer containing gaps, as obtained in 5.1;
RT
is the total thermal resistance of the component, as obtained in clause 6.
NOTE - Examples of corrections for air gaps are given in annex E.
D.3
Correction for mechanical fasteners
When an insulation layer is penetrated by mechanical fasteners the correction to the thermal transmittance is given by: AUf=cxhfnfAf
P-4)
where a
is a coefficient
(see table D.2);
h
is the thermal conductivity
nf
is the number of fasteners per square metre;
4
is the cross-sectional
of the fastener;
area of one fastener.
Table D.2 - Values of the coefficient a Type of fastener
a m-l
Wall tie between masonry leaves
6
Roof fixing
5
No correction shall be applied in the following cases:
22
-
wall ties across an empty cavity;
-
wall ties between a masonry leaf and timber studs;
-
when the thermal conductivity
of the fastener, or par-t of it, is less than 1 W/(m.K).
@ IS0
IS0 6946:1996(E)
This procedure does not apply when both ends of the fastener are in contact with metal sheets. NOTE - The methods in IS0 1021 l-1, Thermal bridges in building construction - Heat flows and surface temperatures - Part 7: General calculation methods, can be used to obtain correction factors for cases where both ends of the fastener are in contact with metal sheets.
Annex
E (informative)
Examples
of corrections
A non-exhaustive
for air gaps
list of possible configurations
is shown in a) to h).
Correction level 0
4
Continuous insulation in multiple layers with staggered joints
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IS0 6946:1996(E)
b)
Continuous insulation, single layer, with shiplap, tongue-and-groove or sealed joints
cl
Continuous insulation, single layer with butt joints, provided that the length, width and squareness tolerances and the dimensional stability of the insulation are such that any gaps do not exceed 5 mm. This requirement is deemed to be satisfied if the sum of either length or width tolerances and dimensional changes is less than 5 mm, and the deviation from rectangularity for boards is less than 5 mm.
d)
Two layers of insulation, one between rafters, studs, joists or similar constructional components, the other as a continuous layer covering the first layer
6
Single layer of insulation in a construction, where the thermal resistance of the construction excluding that of the insulation layer is at least 50% of the total thermal resistance (ie RI I 0,5 /+)
24
0 IS0
IS0 6946:1996(E)
Correction level 1
f)
Insulation entirely between rafters, joists, studs or similar constructional components
9)
Continuous insulation, single layer with butt joints, where the length, width and squareness tolerances plus the dimensional stability of the insulation are such that gaps exceed 5 mm. This condition is assumed if the sum of either length or width tolerances and dimensional changes is more than 5 mm, or if the deviation from rectangularity for boards is more than 5 mm.
Correction level 2
t-4
Construction with the possibility for air circulation on the warm side of the insulation due to insufficient fastening or sealing at top or bottom
25
IS0 6946:1996(E)
ICS 91.120.10 Descriptors: thermal insulation, buildings, components, resistance, thermal transmittance, rules of calculation. Price based on 25 pages
building elements,
thermal properties,
heat transfer,
determination,
thermal
