ISO 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)

Contents

Page

1 Scope ... 1

2 Normative references ... 1

3 Definitions and symbols ... 1

4 Principles ...

3

5 Thermal resistances ... 4

6 Total thermal resistance ... 9

7 Thermal transmittance ... 12

Annexes

A

Surface resistance ... 13

B Thermal resistance of unventilated airspaces ...

15

C Calculation of the thermal transmittance of components with tapered layers ... . ... 18

D Corrections to thermal transmittance ... 21

E

Examples of corrections for air gaps ... 23

0 IS0 1996

All rights reserved. Unless otherwise specified, no part of this publication may be repro- duced or utilized in any form or by any means, electronic or mechanical, including photo- copying 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

Foreword

IS0 (the International Organization for Standardization) is a worldwide fed- eration 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 rep- resented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. IS0 col- laborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

Draft International Standards adopted by the technical committees are cir- culated 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 Commit- tee for Standardization KEN) in collaboration with ISO/TC 163, Thermal in- sulation, 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 Standard. Annex E is for information only.

. . III

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 tem- peratures:

- _{internal: dry resultant temperature;} - _{external: air temperature.}

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 or design thermal resistances of the materials and products involved.

The method applies to components and elements consisting of thermally homogeneous layers (which can include air layers).

The standard also gives an approximate method that can be used for inhomogeneous layers, except cases where an insulating layer is bridged by metal.

2

Normative

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 - Building materials and products - Determination of declared and design thermal values.

IS0 7345:1987, Thermal insulation - Physical quantities and definitions.

3

Definitions

and symbols

3.1

Definitions

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.

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 or environmental conditions.

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

A R R9 R se Rsi RT 6 RY R” u d h a

Quantity

area

design thermal resistance thermal resistance of airspace external surface resistance internal surface resistance

total thermal resistance (environment to environment) upper limit of total thermal resistance

lower limit of total thermal resistance thermal resistance of unheated space thermal transmittance

thickness

heat transfer coefficient design thermal conductivity

Unit

m* m2WW m*K/W m*K/W m*K/W m*K/W m*K/W m*K/W m*K/W W/(m*.K) m W/(m*.K) W/( m+K)

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 and/or the total thermal resistance according to annex C.

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 between the environments on either side of the

component concerned, for example internal and external environments, two internal environments in the case of an internal partition, internal environment and an unheated space. Simplified procedures are given in 5.4 for treating an unheated space as a thermal resistance.

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

r

Upwards

Horizontal

Downwards

I I

1 %i 1 0~10 ( 0,13 1 OS17 (

I I

R se 0,04 _I 0,04 _I 0,04 _I

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.

5.3

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 to the direction of heat flow} 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;

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 with the internal environment.

If the above conditions do not apply, use the procedures in annex B.

53.1

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 air layers:

high emissivity surfaces

Thickness

of air layer

Direction of heat flow

mm

Upwards

Horizontal

Downwards

0

0,oo

0,oo

0,oo

5

0,ll 0,ll 0,ll 7 0,13 0,13 0,13 10 0,15 0,15 0,15 15 0,16 0,17 0,17 25 0,16 0,18 0,19 50 0,16 0,18 0,21 100 0,16 0,18 0,22 300 0,16 0,18 0,23

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 as the area of openings per metre length. For horizontal air layers it is expressed as the area of openings per square metre area.

5.4

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).

5.4.2

Other spaces

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;

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)

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.

6

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; R se 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 for the purposes of evaluating the risk of condensation.

6.2.1

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.

1CI

lb

lc

Figure 1 - Sections and layers of a thermally inhomogeneous component

The component (figure la) is considered cut into sections (figure 1 b) and into layers (figure lc).

The section m (m = a, b, c, . . . 9) perpendicular to the surfaces of the component has fractional area f,,,. The layerj(j= 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.

6.2.2

Upper limit of the total thermal resistance

(R; )

The upper limit of the total thermal resistance, is determined by assuming one-dimensional heat flow perpendicular to the surfaces of the component. It is given by the following expression:

l fa+fa+...+

-=

₆

rs

RTa RTb RT9

(5)

where

&a, &by .-., &9 are the total thermal resistances from environment to environment for each

section, calculated using equation (3);

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 by assuming that all planes parallel to the surfaces of the component are isothermal surfaces.*)

Calculate an equivalent thermal resistance Rj, for each thermally inhomogeneous layer using the following expression:3)

La+-+...+- f fb 6

Rj Raj Rbj Rqj (6)

*) If there is a non-planar surface adjacent to an air layer, the calculation should be undertaken as if it were planar, by considering the narrower sections extended (but without alteration to thermal resistance):

or projecting parts removed (so reducing the thermal resistance):

3, An alternative method is by means of an equivalent thermal conductivity of the layer:

where the equivalent thermal conductivity hi of layer j is: hi = haj fa + hbj fb+e. a+hQi 4

If an air layer is part of an inhomogeneous layer, it may be treated as a material with an equivalent thermal conductivity hi = dj /F$ where F$ is the thermal resistance of the air layer determined in accordance with annex B.

The lower limit is then determined using equation (3) i.e. RF = Rsi + RI + R2+eam+Rn + Rse

6.2.4

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

2RT

(7)

(8)

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

- 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.}

7

Thermal

transmittance

The thermal transmittance is given by:

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.

(9)

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.

Annex

A (normative)

Surface

resistance

A.1

Plane surfaces

The surface resistance is given by4)

where

R,=L

hc +hr

hc is the convective coefficient; hr is the radiative coefficient; and

where

h, = Ehro h,=4oT;

& 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 constant (567 x 10-s W/(m2.K4));

T?l is the mean thermodynamic temperature of the surface and of its surroundings.

Table A.1 - Values of the black-body radiative coefficient I?,,

I

Temperature

I

h

ro I “C W/(mz.K) -10 -10 0 0 10 10 20 20 30 30 491 496 571 597 63

61)

(A-2) (A.3)

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.

At internal surfaces h, = hci, where

- for heat flow upwards: hci = 5,0 W/(m2.K) - for heat flow horizontal: hci = 2,5 W/(mz.K) - for heat flow downwards: hci = 0,7 W/(m2.K) 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

Wind speed

R _{R se se} m/s m/s m2K/W m2K/W 1 1 2 2 3 3 4 4 5 5 7 7 10 10 0,08 0,08 0,06 0,06 0,05 0,05 0‘04 0‘04 0,04 0,04 0,03 0,03 0,02 0,02

A.2

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:

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.

Equation (A.5) applies to both internal and external surface resistance.

Figure A.1 - Actual and projected areas

Annex

B (normative)

Thermal

resistance

of unventilated

airspaces

B.l

General

This annex applies to airspaces in building components other than glazing. A more precise treatment is necessary for glazing and window frames.

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.

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.+/+ where

44 is the thermal resistance of the airspace; ha is the conduction/convection coefficient; hr is the radiative 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 emittance;

h ro is the radiative coefficient for a black-body surface (see table A.2); and

E= I

1/&,+1/&p-1

where ~1, ~2 are the hemispherical emissivities of the surfaces bounding the airspace. The design value of emissivity should allow for any effects of tarnishing with time.

(B-1)

(B.3)

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.

B.3

Small or divided unventilated airspaces (air voids)

,

0

-7

I

; 0

; heat 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- d ! b) U3.4)

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)

C.l

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:

Symbol

Quantity

Unit

Xl design thermal conductivity of the tapered part (having zero W/( m-K) thickness at one end)

RO design thermal resistance of the remaining part, including surface m24VW resistances on both sides of the component

RI maximum thermal resistance of the tapered layer m%/W

4 maximum thickness of the tapered layer m

and In denotes natural logarithm.

+ 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 of common shapes shall be calculated by equations (C.l) to (C.3) for pitches not exceeding 5%.

NOTE - Numerical methods can be used for greater pitches.

C.2.1

Rectangular area

C.2.2

Triangular area, thickest at apex

dl- A r’ i.)ln(I+?)-I]

HI L\

1 I ,’ ,’ -- =?

(C-1)

(C.2)

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 of each individual part (UJ according to the relevant equation in C.2.

5) Calculate the overall thermal transmittance for the whole area A using

If total thermal resistance of a component with tapered layers is required then

(C.5)

RT = l/U

20

Annex D (normative)

Corrections

to thermal transmittance

D.l

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

AUg is the correction for air gaps;

AlJf is the correction for mechanical fasteners; A”, is the correction for inverted roof@).

D.2

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)

Description of air gap

0,oo

0,Ol

0,04

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.

This correction is adjusted according to equation (D.3): 4 ( 1 2 A",=A"" - RT 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 where

a is a coefficient (see table D.2);

h is the thermal conductivity of the fastener; nf is the number of fasteners per square metre; 4 is the cross-sectional 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: - wall ties across an empty cavity;

- wall ties between a masonry leaf and timber studs;

(D-3)

P-4)

- when the thermal conductivity of the fastener, or par-t of it, is less than 1 W/(m.K).

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

for air gaps

A non-exhaustive list of possible configurations is shown in a) to h).

Correction level 0

4

Continuous insulation in multiple layers with staggered joints

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 /+)

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

ICS 91.120.10

Descriptors: thermal insulation, buildings, components, building elements, thermal properties, heat transfer, determination, thermal resistance, thermal transmittance, rules of calculation.