ISO 10211:2017

INTERNATIONAL ISO
STANDARD 10211
Second edition
2017-06
Thermal bridges in building
construction — Heat flows and surface
temperatures — Detailed calculations
Ponts thermiques dans les bâtiments — Flux thermiques et
températures superficielles — Calculs détaillés
Reference number
©
ISO 2017
© ISO 2017, Published in Switzerland
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ii © ISO 2017 – All rights reserved

Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2  Normative references . 1
3  Terms and definitions . 2
4 Symbols and subscripts . 7
4.1 Symbols . 7
4.2 Subscripts . 7
5  Description of the method . 8
5.1 Output . 8
5.2 General description . 8
6 Output data and input data . 8
6.1 Output data . 8
6.2 Calculation time intervals . 9
6.3 Input data . 9
7  Modelling of the construction . 9
7.1 Dimension systems . 9
7.2 Rules for modelling . 9
7.2.1 General. 9
7.2.2 Cut-off planes for a 3-D geometrical model for calculation of total heat
flow and/or surface temperatures . 9
7.2.3 Cut-off planes for a 2-D geometrical model .11
7.2.4 Cut-off planes in the ground .12
7.2.5 Periodic heat flows via the ground .13
7.2.6 Adjustments to dimensions .13
7.2.7 Auxiliary planes .15
7.2.8 Quasi-homogeneous layers and materials .15
7.3 Conditions for simplifying the geometrical model .15
7.3.1 General.15
7.3.2 Conditions for adjusting dimensions to simplify the geometrical model .16
7.3.3 Conditions for using quasi-homogeneous material layers to simplify the
geometrical model .17
8  Input data specifications .20
8.1 General .20
8.2 Thermal conductivities of materials .21
8.3 Surface resistances .21
8.4 Boundary temperatures .21
8.5 Thermal conductivity of quasi-homogeneous layers .21
8.6 Equivalent thermal conductivity of air cavities .21
8.7 Determining the temperature in an adjacent unheated room .22
9 Calculation method .22
9.1 Solution technique .22
9.2 Calculation rules .22
9.2.1 Heat flows between material cells and adjacent environment .22
9.2.2 Heat flows at cut-off planes .22
9.2.3 Solution of the formulae .22
9.2.4 Calculation of the temperature distribution .23
10  Determination of thermal coupling coefficients and heat flow rate from 3-D calculations 23
10.1 Two boundary temperatures, unpartitioned model .23
10.2 Two boundary temperatures, partitioned model .23
10.3 More than two boundary temperatures .24
11  Calculations using linear and point thermal transmittances from 3-D calculations .25
11.1 Calculation of thermal coupling coefficient .25
11.2 Calculation of linear and point thermal transmittances .25
12  Determination of thermal coupling coefficient, heat flow rate and linear thermal
transmittance from 2-D calculations .26
12.1 Two boundary temperatures .26
12.2 More than two boundary temperatures .26
12.3 Determination of the linear thermal transmittance .27
12.4 Determination of the linear thermal transmittance for wall/floor junctions .27
12.4.1 All cases .27
12.4.2 Option A .27
12.4.3 Option B .29
12.5 Determination of the external periodic heat transfer coefficient for ground floors .31
13  Determination of the temperature at the internal surface .32
13.1 Determination of the temperature at the internal surface from 3-D calculations .32
13.1.1 Two boundary temperatures .32
13.1.2 More than two boundary temperatures .32
13.2 Determination of the temperature at the internal surface from 2-D calculations .33
13.2.1 Two boundary temperatures .33
13.2.2 Three boundary temperatures .33
14 Report .33
14.1 Input data .33
14.2 Output data .34
14.2.1 General.34
14.2.2 Calculation of the heat transmission using the thermal coupling coefficient .34
14.2.3 Calculation of the surface temperatures using weighting factors .34
14.2.4 Additional output data .34
14.2.5 Estimate of error .35
Annex A (normative) Input and method selection data sheet — Template .36
Annex B (informative) Input and method selection data sheet — Default choices .38
Annex C (normative) Validation of calculation methods .40
Annex D (normative) Examples of the determination of the linear and point
thermal transmittances.47
Annex E (normative) Determination of values of thermal coupling coefficient and
temperature weighting factor for more than two boundary temperatures .50
Bibliography .55
iv © ISO 2017 – All rights reserved

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO 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.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www. iso. org/d irectives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www. iso. org/p atents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO’s adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following
URL: w w w . i s o. org/i so/f oreword. html.
ISO 10211 was prepared by ISO Technical Committee ISO/TC 163, Thermal performance and energy use
in the built environment, Subcommittee SC 2, Calculation methods, in collaboration with the European
Committee for Standardization (CEN) Technical Committee CEN/TC 89, Thermal performance of
buildings and building components, in accordance with the Agreement on technical cooperation between
ISO and CEN (Vienna Agreement).
This second edition cancels and replaces the first edition (ISO 10211:2007), which has been technically
revised.
The changes in the second edition are mostly editorial. The standard has been re-drafted according
to CEN/TS 16629:2014.
Introduction
This document is part of a series aimed at the international harmonization of the methodology for
assessing the energy performance of buildings. Throughout, this series is referred to as a “set of EPB
standards”.
All EPB standards follow specific rules to ensure overall consistency, unambiguity and transparency.
All EPB standards provide a certain flexibility with regard to the methods, the required input data and
references to other EPB standards, by the introduction of a normative template in Annex A and Annex B
with informative default choices.
For the correct use of this document, a normative template is given in Annex A to specify these choices.
Informative default choices are provided in Annex B.
The main target groups for this document are architects, engineers and regulators.
Use by or for regulators: In case the document is used in the context of national or regional legal
requirements, mandatory choices may be given at national or regional level for such specific
applications. These choices (either the informative default choices from Annex B or choices adapted to
national/regional needs, but in any case following the template of Annex A) can be made available as
national annex or as separate (e.g. legal) document (national data sheet).
NOTE 1 So in this case:
— the regulators will specify the choices;
— the individual user will apply the document to assess the energy performance of a building, and thereby use
the choices made by the regulators.
Topics addressed in this document can be subject to public regulation. Public regulation on the same
topics can override the default values in Annex B. Public regulation on the same topics can even, for
certain applications, override the use of this document. Legal requirements and choices are in general
not published in standards but in legal documents. In order to avoid double publications and difficult
updating of double documents, a national annex may refer to the legal texts where national choices
have been made by public authorities. Different national annexes or national data sheets are possible,
for different applications.
It is expected, if the default values, choices and references to other EPB standards in Annex B are not
followed due to national regulations, policy or traditions, that:
— national or regional authorities prepare data sheets containing the choices and national or regional
values, according to the model in Annex A. In this case a national annex (e.g. NA) is recommended,
containing a reference to these data sheets;
— or, by default, the national standards body will consider the possibility to add or include a national
annex in agreement with the template of Annex A, in accordance to the legal documents that give
national or regional values and choices.
Further target groups are parties wanting to motivate their assumptions by classifying the building
energy performance for a dedicated building stock.
More information is provided in the Technical Report accompanying this document (ISO/TR 52019-2).
The subset of EPB standards prepared under the responsibility of ISO/TC 163/SC 2 cover inter alia:
— calculation procedures on the overall energy use and energy performance of buildings;
— calculation procedures on the internal temperature in buildings (e.g. in case of no space heating or
cooling);
— indicators for partial EPB requirements related to thermal energy balance and fabric features;
vi © ISO 2017 – All rights reserved

— calculation methods covering the performance and thermal, hygrothermal, solar and visual
characteristics of specific parts of the building and specific building elements and components, such
as opaque envelope elements, ground floor, windows and facades.
ISO/TC 163/SC 2 cooperates with other technical committees for the details on appliances, technical
building systems, indoor environment, etc.
This document sets out the specifications for a geometrical model of a thermal bridge for the numerical
calculation of linear thermal transmittances, point thermal transmittances and internal surface
temperatures.
Table 1 shows the relative position of this document within the set of EPB standards in the context of
the modular structure as set out in ISO 52000-1.
NOTE 2 In ISO/TR 52000-2 the same table can be found, with, for each module, the numbers of the relevant
EPB standards and accompanying technical reports that are published or in preparation.
NOTE 3 The modules represent EPB standards, although one EPB standard could cover more than one module
and one module could be covered by more than one EPB standard, for instance, a simplified and a detailed method
respectively. See also Tables A.1 and B.1.
Table 1 — Position of this document (in casu M2–5) within the modular structure of the set of
EPB standards
Building
Overarching Technical Building Systems
(as such)
Building
Ven- Dehu- PV,
Sub- Descrip- Heat- Cool- Humidi- Domestic automa-
Descriptions Descriptions tila- midifi- Lighting wind,
module tions ing ing fication hot water tion and
tion cation .
control
sub1 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11
1 General General General
Common
terms and
definitions; Building en-
a
2 Needs
symbols, ergy needs
units and
subscripts
(Free)
indoor Maximum
3 Applications conditions load and
without power
systems
Ways to
Ways to ex- Ways to ex-
express
4 press energy press energy
energy per-
performance performance
formance
Building
Heat trans-
categories ISO Emission and
5 fer by trans-
and building 10211 control
mission
boundaries
a
The shaded modules are not applicable.
Table 1 (continued)
Building
Overarching Technical Building Systems
(as such)
Building
Ven- Dehu- PV,
Sub- Descrip- Heat- Cool- Humidi- Domestic automa-
Descriptions Descriptions tila- midifi- Lighting wind,
module tions ing ing fication hot water tion and
tion cation .
control
sub1 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11
Building oc- Heat trans-
cupancy and fer by infil- Distribution
operating tration and and control
conditions ventilation
Aggregation
of energy
Internal Storage and
7 services
heat gains control
and energy
carriers
Building Solar heat Generation
zoning gains and control
Building Load dis-
Calculated
dynamics patching and
9 energy per-
(thermal operating
formance
mass) conditions
Measured Measured Measured
10 energy per- energy per- Energy Per-
formance formance formance
11 Inspection Inspection Inspection
Ways to ex-
12 press indoor BMS
comfort
External
13 environment
conditions
Economic
calculation
a
The shaded modules are not applicable.
viii © ISO 2017 – All rights reserved

INTERNATIONAL STANDARD ISO 10211:2017(E)
Thermal bridges in building construction — Heat flows
and surface temperatures — Detailed calculations
1 Scope
This document sets out the specifications for a three-dimensional and a two-dimensional geometrical
model of a thermal bridge for the numerical calculation of
— heat flows, in order to assess the overall heat loss from a building or part of it, and
— minimum surface temperatures, in order to assess the risk of surface condensation.
These specifications include the geometrical boundaries and subdivisions of the model, the thermal
boundary conditions, and the thermal values and relationships to be used.
This document is based upon the following assumptions:
— all physical properties are independent of temperature;
— there are no heat sources within the building element.
This document can also be used for the derivation of linear and point thermal transmittances and of
surface temperature factors.
NOTE  Table 1 in the Introduction shows the relative position of this document within the set of EPB standards
in the context of the modular structure as set out in ISO 52000-1.
2  Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 6946, Building components and building elements — Thermal resistance and thermal transmittance —
Calculation method
ISO 7345, Thermal insulation — Physical quantities and definitions
ISO 13370, Thermal performance of buildings — Heat transfer via the ground — Calculation methods
ISO 13788, Hygrothermal performance of building components and building elements — Internal surface
temperature to avoid critical surface humidity and interstitial condensation — Calculation methods
ISO 10456, Building materials and products — Hygrothermal properties — Tabulated design values and
procedures for determining declared and design thermal values
ISO 13789, Thermal performance of buildings — Transmission and ventilation heat transfer coefficients —
Calculation method
ISO 52000-1:2017, Energy performance of buildings — Overarching EPB assessment — Part 1: General
framework and procedures
NOTE 1 Default references to EPB standards other than ISO 52000-1 are identified by the EPB module code
number and given in Annex A (normative template in Table A.1) and Annex B (informative default choice in
Table B.1).
EXAMPLE EPB module code number: M5–5, or M5–5,1 (if module M5–5 is subdivided), or M5–5/1 (if
reference to a specific clause of the standard covering M5–5).
NOTE 2 In this document, there are no choices in references to other EPB standards. The sentence and note
above is kept to maintain uniformity between all EPB standards.
3  Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 7345, ISO 52000-1, and the
following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http:// www .electropedia .org/
— ISO Online browsing platform: available at http:// www .iso .org/ obp
3.1
thermal bridge
part of the building envelope where the otherwise uniform thermal resistance is significantly changed
by full or partial penetration of the building envelope by materials with a different thermal conductivity,
and/or a change in thickness of the fabric, and/or a difference between internal and external areas,
such as occur at wall/floor/ceiling junctions
3.2
linear thermal bridge
thermal bridge (3.1) with a uniform cross-section along one of the three orthogonal axes
3.3
point thermal bridge
localized thermal bridge (3.1) whose influence can be represented by a point thermal transmittance (3.20)
3.4
three-dimensional geometrical model
3-D geometrical model
geometrical model, deduced from building plans, such that for each of the orthogonal axes, the cross-
section perpendicular to that axis changes within the boundary of the model
Note 1 to entry: See Figure 1.
3.5
three-dimensional flanking element
3-D flanking element
part of a 3-D geometrical model (3.4) which, when considered in isolation, can be represented by a
2-D geometrical model (3.7)
Note 1 to entry: See Figure 1 and Figure 2.
3.6
three-dimensional central element
3-D central element
part of a 3-D geometrical model (3.4) which is not a 3-D flanking element (3.5)
Note 1 to entry: See Figure 1.
Note 2 to entry: A central element is represented by a 3-D geometrical model (3.4).
2 © ISO 2017 – All rights reserved

3.7
two-dimensional geometrical model
2-D geometrical model
geometrical model, deduced from building plans, such that for one of the orthogonal axes, the cross-
section perpendicular to that axis does not change within the boundaries of the model
Note 1 to entry: See Figure 2.
Note 2 to entry: A 2-D geometrical model is used for two-dimensional calculations.
3.8
two-dimensional flanking element
2-D flanking element
part of a 2-D geometrical model (3.7) which, when considered in isolation, consists of plane, parallel
material layers
Note 1 to entry: The plane, parallel material layers can be homogeneous or non-homogeneous.
3.9
two-dimensional central element
2-D central element
part of a 2-D geometrical model (3.7) which is not a 2-D flanking element (3.8)
3.10
construction plane
plane in the 3-D geometrical model (3.4) or 2-D geometrical model (3.7) which separates different
materials, and/or the geometrical model from the remainder of the construction, and/or the flanking
elements from the central element
Note 1 to entry: See Figure 3.
3.11
cut-off plane
construction plane (3.10) that is a boundary to the 3-D geometrical model (3.4) or 2-D geometrical model
(3.7) by separating the model from the remainder of the construction
Note 1 to entry: See Figure 3.
3.12
auxiliary plane
plane which, in addition to the construction planes (3.10), divides the geometrical model into a number
of cells
3.13
quasi-homogeneous layer
layer which consists of two or more materials with different thermal conductivities, but which can be
considered as homogeneous with an equivalent thermal conductivity
Note 1 to entry: See Figure 4.
3.14
temperature factor at the internal surface
difference between internal surface temperature and external temperature, divided by the difference
between internal temperature and external temperature, calculated with a surface resistance R at the
si
internal surface
3.15
temperature weighting factor
weighting factor which states the respective influence of the temperatures of the different thermal
environments upon the surface temperature at the point under consideration
3.16
external boundary temperature
external air temperature, assuming that the air temperature and the radiant temperature seen by the
surface are equal
3.17
internal boundary temperature
operative temperature, taken as the arithmetic mean value of internal air temperature and mean
radiant temperature of all surfaces surrounding the internal environment
3.18
thermal coupling coefficient
heat flow rate per temperature difference between two environments which are thermally connected
by the construction under consideration
3.19
linear thermal transmittance
heat flow rate in the steady-state compared to a reference heat flow rate calculated disregarding the
thermal bridge (3.1), divided by length and by the temperature difference between the environments on
either side of a linear thermal bridge (3.2)
Note 1 to entry: The linear thermal transmittance is a quantity describing the influence of a linear thermal bridge
on the total heat flow.
3.20
point thermal transmittance
heat flow rate in the steady-state compared to a reference heat flow rate calculated disregarding the
thermal bridge (3.1), divided by the temperature difference between the environments on either side of
a point thermal bridge (3.3)
Note 1 to entry: The point thermal transmittance is a quantity describing the influence of a point thermal bridge
on the total heat flow.
3.21
EPB standard
[5]
standard that complies with the requirements given in ISO 52000-1, CEN/TS 16628 and
[6]
CEN/TS 16629
Note 1 to entry: These three basic EPB documents were developed under a mandate given to CEN by the
European Commission and the European Free Trade Association and support essential requirements of EU
Directive 2010/31/EU on the energy performance of buildings. Several EPB standards and related documents
are developed or revised under the same mandate.
[SOURCE: ISO 52000-1:2017, 3.5.14]
4 © ISO 2017 – All rights reserved

Key
F1, F2, F3, F4, F5 3-D flanking elements
C 3-D central element
NOTE 3-D Flanking elements have constant cross-sections perpendicular to at least one axis; the 3-D central
element is the remaining part.
Figure 1 — 3-D geometrical model with five 3-D flanking elements and one 3-D central element
Key
F1, F2, F3, F4, F5 3-D flanking elements
NOTE F2 to F5 refer to Figure 1.
Figure 2 — Cross-sections of the 3-D flanking elements in a 3-D geometrical model
treated as 2-D geometrical models
Key
C construction planes perpendicular to the x-axis
x
C construction planes perpendicular to the y-axis
y
C construction planes perpendicular to the z-axis
z
NOTE Cut-off planes are indicated with enlarged arrows; planes that separate flanking elements from
central element are encircled.
Figure 3 — Example of a 3-D geometrical model showing construction planes
Figure 4 — Example of a minor point thermal bridge giving rise to three-dimensional heat flow,
incorporated into a quasi-homogeneous layer
6 © ISO 2017 – All rights reserved

4 Symbols and subscripts
4.1 Symbols
For the purposes of this document, the symbols given in ISO 52000-1 and the following apply.
Symbol Quantity Unit
A area m
B characteristic dimension of floor m
b width m
d thickness m
f temperature factor at the internal surface —
g temperature weighting factor —
h height m
L thermal coupling coefficient W/(m·K)
L thermal coupling coefficient from two-dimensional calculation W/(m·K)
2D
L thermal coupling coefficient from three-dimensional calculation W/K
3D
l length m
N number —
q density of heat flow rate W/m
R thermal resistance m ·K/W
T thermodynamic temperature K
t time month
U thermal transmittance W/(m ·K)
V volume m
w wall thickness m
z depth of floor surface below ground level m
Φ heat flow rate W
λ thermal conductivity W/(m·K)
θ Celsius temperature °C
Δθ temperature difference K
χ point thermal transmittance W/K
Ψ linear thermal transmittance W/(m·K)
4.2 Subscripts
For the purposes of this document, the subscripts given in ISO 52000-1 and the following apply.
Subscript Definition
b basement, below ground level
c component
e external
f floor
g air layer, air gap (8.6)
g ground (12.4)
ie from internal to external
iu from internal to unheated
int internal
Subscript Definition
min minimum
pe external periodic heat transfer coefficient
se external surface
si internal surface
t including thermal bridge (total)
tb thermal bridge
ue from unheated to external
w wall
0 without thermal bridge
5  Description of the method
5.1 Output
The output of this document is the linear thermal transmittances, point thermal transmittances and
internal surface temperatures. The formulae for doing so are provided in Clause 10 to Clause 13.
5.2 General description
The temperature distribution within, and the heat flow through, a construction can be calculated if the
boundary conditions and constructional details are known. For this purpose, the geometrical model is
divided into a number of adjacent material cells, each with a homogeneous thermal conductivity. The
criteria which shall be met when constructing the model are given in Clause 7.
In Clause 8, instructions are given for the determination of the values of thermal conductivity and
boundary conditions.
The temperature distribution is determined either by means of an iterative calculation or by a direct
solution technique, after which the temperature distribution within the material cells is determined by
interpolation. The calculation rules and the method of determining the temperature distribution are
described in Clause 9.
NOTE Specific procedures for window frames are given in ISO 10077-2.
6 Output data and input data
6.1 Output data
The output data are listed in Table 2.
Table 2 — Output data
Destination mod- Validity
Description Symbol Unit Varying
ule (Table 1) interval
linear thermal transmittance Ψ W/(m·K) M2-5 — No
thermal coupling coefficient from >0 No
L W/(m·K) M2-5
2D
two-dimensional calculation
thermal coupling coefficient from >0 No
L W/K M2-5
3D
three-dimensional calculation
temperature factor at the internal
f — M2-5 >0 No
Rsi
surface
point thermal transmittance χ W/K M2-5 >0 No
8 © ISO 2017 – All rights reserved

6.2 Calculation time intervals
In most cases, the calculations described in this document are steady-state and do not have time
intervals.
Where calculations are being undertaken to obtain periodic heat transfer coefficients (see 7.2.5), the
time interval shall be 1 h or less.
6.3 Input data
Tables 3 and 4 list identifiers for input data required for the calculation.
Table 3 — Identifiers for geometric characteristics
Name Symbol Unit Value Range Origin Varying
Area A m — >0 — No
Width of building component b m — >0 — No
Thickness of building component d m — >0 — No
Length l m — >0 — No
Volume V m — >0 — No
Characteristic dimension of floor B m — >0 ISO 13370 No
Table 4 — Identifiers for thermal characteristics of building component
Name Symbol Unit Value Range Origin Varying
design thermal conductivity λ W/(m·K) — 0 to 200 ISO 10456 No
thermal resistance R m ·K/W — >0 ISO 6946 No
external surface resistance R m ·K/W 0,04 — ISO 6946 No
se
internal surface resistance R m ·K/W — 0,1 to 0,2 ISO 6946 No
si
thermal transmittance U W/(m ·K) — >0 ISO 6946 No
temperature θ °C — −50 to +50 — No
7  Modelling of the construction
7.1 Dimension systems
Lengths are measured using internal dimensions, overall internal dimensions or external dimensions,
according to the dimension system being used for the building (see ISO 13789).
7.2  Rules for modelling
7.2.1 General
It is not usually feasible to model a complete building using a single geometrical model. In most cases,
the building is partitioned into several parts (including the subsoil, where appropriate) by using cut-
off planes. This partitioning shall be performed in such a way that all differences are avoided in the
results of calculation between the partitioned building and the building when treated as a whole. This
partitioning into several geometrical models is achieved by choosing suitable cut-off planes.
7.2.2  Cut-off planes for a 3-D geometrical model for calculation of total heat flow and/or
surface temperatures
The geometrical model includes the central element(s), the flanking elements and, where appropriate,
the subsoil. The geometrical model is delimited by cut-off planes.
Cut-off planes shall be positioned as follows:
— at a symmetry plane if this is less than d from the central element (see Figure 5);
min
— at least d from the central element if there is no nearer symmetry plane (see Figure 6);
min
— in the ground, in accordance with 7.2.4
where d is the greater of 1 m and three times the thickness of the flanking element concerned.
min
A geometrical model can contain more than one thermal bridge. In such cases, cut-off planes need to be
situated at least d from each thermal bridge, or need to be at a symmetry plane (see Figure 6).
min
Dimensions in millimetres
Key
a
Arrows indicate the symmetry planes.
Figure 5 — Symmetry planes which can be used as cut-off planes
10 © ISO 2017 – All rights reserved

Dimensions in millimetres
a) b)
Key
1 1 000 mm or at a symmetry plane
A thermal bridge at the corner of the internal room
B thermal bridge around the window in the external wall
NOTE Thermal bridge B does not fulfil the condition of being at least d (= 1 m) from a cut-off plane
min
[Figure 6 a)]. This is corrected by extending the model in two directions [Figure 6 b)].
Figure 6 — 3-D geometrical model containing two thermal bridges
7.2.3  Cut-off planes for a 2-D geometrical model
The same rules as given in 7.2.2 apply to a 2-D geometrical model. Examples are shown in Figure 7 and
Figure 8. In Figure 8, the left-hand drawing may be used if the thermal bridge is symmetrical.
≥ d
min
Key
d minimum thickness
min
Figure 7 — Location of cut-off planes at least d  from the central element in a 2-D
min
geometrical model
Key
d minimum thickness
min
l fixed distance
W
Figure 8 — Example of a construction with linear thermal bridges at fixed distances, l ,
W
showing symmetry planes which can be used as cut-off planes
7.2.4  Cut-off planes in the ground
Where the calculation involves heat transfer via the ground (foundations, ground floors, basements),
the cut-off planes in the ground shall be positioned as indicated in Table 5. This includes ground below
the internal walls in contact with ground.
12 © ISO 2017 – All rights reserved
≥ d ≥ d
min min
Table 5 — Location of cut-off planes in the ground
Distance to central element
Direction Purpose of the calculation
Heat flow and surface
Surface temperatures only
a
temperatures
Horizontal distance to vertical plane, inside the at least three times wall
b
0,5 × floor dimension
building thickness
Horizontal distance to vertical plane, outside the at least three times wall
c,d
2,5 × floor width
building thickness
Vertical distance to horizontal plane below
c
at least 3 m 2,5 × floor width
ground level
Vertical distance to horizontal plane below floor
c
level (applies only if the level of the floor under con- at least 1 m 2,5 × floor width
sideration is more than 2 m below the ground level)
a
See Figure 9 and Figure 10.
b
In a 3-D geometrical model, the floor dimensions (length and width) inside the building are to be considered separately
in each direction (see Figure 9).
c
In a 3-D geometrical model, the distance outside the building and below ground is to be based on the smaller dimension
(width) of the floor (see Fi
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