EN ISO 10211-2:2001

SLOVENSKI STANDARD
SIST EN ISO 10211-2:2002
01-marec-2002
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Thermal bridges in building construction - Calculation of heat flows and surface
temperatures - Part 2: Linear thermal bridges (ISO 10211-2:2001)
Wärmebrücken im Hochbau - Berechnung der Wärmeströme und
Oberflächentemperaturen - Teil 2: Linienförmige Wärmebrücken (ISO 10211-2:2001)
Ponts thermiques dans les bâtiments - Calcul des flux thermiques et des températures
superficielles - Partie 2: Ponts thermiques linéaires (ISO 10211-2:2001)
Ta slovenski standard je istoveten z: EN ISO 10211-2:2001
ICS:
91.120.10
SIST EN ISO 10211-2:2002 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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EUROPEAN STANDARD
EN ISO 10211-2
NORME EUROPÉENNE
EUROPÄISCHE NORM
March 2001
ICS 91.120.00
English version
Thermal bridges in building construction - Calculation of heat
flows and surface temperatures - Part 2: Linear thermal bridges
(ISO 10211-2:2001)
Ponts thermiques dans les bâtiments - Calcul des flux Wärmebrücken im Hochbau - Berechnung der
thermiques et des températures superficielles - Partie 2: Wärmeströme und Oberflächentemperaturen - Teil 2:
Ponts thermiques linéaires (ISO 10211-2:2001) Linienförmige Wärmebrücken (ISO 10211-2:2001)
This European Standard was approved by CEN on 21 July 1999.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the Management Centre has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece,
Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2001 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 10211-2:2001 E
worldwide for CEN national Members.

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EN ISO 10211-2:2001
Page
CONTENTS
Foreword 3
Introduction 3
1 Scope 4
2 Normative references 4
3 Definitions, symbols and units 4
4 Rules for modelling 6
5 Calculation values 10
6 Calculation method 10
7 Input and output data 12
Annex A(informative) Determination of temperature weighting factors for three
boundary temperatures 14
Annex B(informative) Simplified method for the calculation of internal surface
temperatures at intersecting linear thermal bridges 15

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EN ISO 10211-2:2001
Foreword
The text of EN ISO 10211-2:2001 has been prepared by Technical Committee CEN/TC 89
"Thermal performance of buildings and building components", the secretariat of which is held by
SIS, in collaboration with Technical Committee ISO/TC 163 "Thermal insulation",
subcommittee 2 "Calculation methods".
This European Standard shall be given the status of a national standard, either by publication of
an identical text or by endorsement, at the latest by September 2001, and conflicting national
standards shall be withdrawn at the latest by December 2001.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of
the following countries are bound to implement this European Standard: Austria, Belgium, Czech
Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg,
Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom.
This standard consists of two parts. The title of part 1 is "Thermal bridges in building
construction - Calculation of heat flows and surface temperatures - Part 1: General methods".
This standard is one of a series of standards on calculation methods for the design and
evaluation of the thermal performance of buildings and building components.
Introduction
Part 1 of this standard gives general methods for the calculation of heat flows and surface
temperatures of thermal bridges of arbitrary shape and with an arbitrary number of boundary
conditions. This part deals with linear thermal bridges bounded by two different thermal
environments. For the calculation of surface temperatures, a third boundary temperature applies
only if the thermal bridge is in thermal contact with the ground.
A linear thermal bridge can be represented by its cross-section, which provides the basis for a
two-dimensional geometrical model.
As the two-dimensional model is a simplification of the real construction, the calculation results
are approximations of the results calculated with a three-dimensional model according to EN ISO
10211-1:1995. The errors due to this simplification are related to the length of the linear thermal
bridge which is often not specified. The calculation methods given in part 2 are termed "Class B"
methods in order to distinguish them from the "Class A" methods given in part 1.
Although similar calculation procedures are used, the procedures are not identical for the
calculation of heat flows and of surface temperatures.
Part 2 of this standard lays down criteria which have to be satisfied in order that a calculation
method for linear thermal bridges can be described as being "Class B".
Part 2 can be used for the calculation of the linear thermal transmittance of the linear thermal
bridge.
Part 2 does not provide reliable results for the assessment of surface condensation. Although
accurate internal surface temperatures can be calculated with a two dimensional model, the
actual minimum surface temperature can be lower,as a result of other linear or point thermal
bridges in the vicinity.

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EN ISO 10211-2:2001
At the intersection of two or three linear thermal bridges a drop of the internal surface
temperature occurs. A method to calculate the lower limiting value of the temperature factor at
the intersection is given in annex B.
1 Scope
This part 2 of the standard gives the specifications for a two-dimensional geometrical model of a
linear thermal bridge for the numerical calculation of:
- the linear thermal transmittance of the linear thermal bridge;
- the lower limit of the minimum surface temperatures.
These specifications include the geometrical boundaries and subdivisions of the model, the
thermal boundary conditions and the thermal values and relationships to be used.
The standard is based upon the following assumptions:
- steady-state conditions apply;
- all physical properties are independent of temperature;
- there are no heat sources within the building element;
- only one internal thermal environment applies;
- one or two external thermal environments apply.
A second external thermal environment only applies when surface temperatures are calculated
and the soil is a part of the geometrical model. In that case the temperature at the horizontal cut-
off plane in the soil is the second external thermal environment.
2 Normative references
This European Standard incorporates, by dated or undated reference, provisions from other
publications. These normative references are cited at the appropriate places in the text and the
publications are listed hereafter. For dated references, subsequent amendments to or revisions
of any of these publications apply to this standard only when incorporated in it by amendment or
revision. For undated references the latest edition of the publication referred to applies
(including amendments).
EN ISO 7345 Thermal insulation - Physical quantities and definitions (ISO7345:1987)
EN ISO 10211-1:1995 Thermal bridges in building construction - Heat flows and surface
temperatures - Part 1: General calculation methods (ISO 10211-1:1995)
3 Terms, definitions, symbols and units
3.1 Terms and definitions
For the purposes of this standard the terms and definitions given in
EN ISO 7345, EN ISO 10211-1:1995 and the following apply.
3.1.1
linear thermal bridge
thermal bridge with a uniform cross-section along one of the three orthogonal axes

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EN ISO 10211-2:2001
3.1.2
2-D flanking element
part of a two-dimensional (2-D) geometrical model which, when considered in isolation, consists
of plane, parallel material layers
3.1.3
2-D central element
part of a 2-D geometrical model which is not a 2-D flanking element

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EN ISO 10211-2:2001
F1 to F4 have constant cross-sections. C is the remaining part.
Figure 1 - 2-D model with four flanking elements and a central element

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EN ISO 10211-2:2001
3.2 Symbols and units
Symbol Physical quantity Unit
2D
L linear thermal coupling coefficient W/(m⋅K)
R surface to surface thermal resistance m²⋅K/W
t
R external surface resistance m²⋅K/W
se
R internal surface resistance m²⋅K/W
si
U thermal transmittance W/(m²⋅K)
b ground floor width m
3D
ƒ temperature factor at the intersection of linear thermal
Rsi
bridges -
2D
ƒ temperature factor of a linear thermal bridge -
Rsi
1D
ƒ temperature factor of a plane building element with
Rsi
uniform thermal resistance -
g temperature weighting factor -
l length m
q density of heat flow rate W/m²
qCelsius temperature °C
lthermal conductivity W/(m⋅K)
ztemperature difference ratio -
Rsi
heat flow rate W
linear thermal transmittance W/(m⋅K)
Subscripts
external
e
i internal
s surface
l length
Superscripts
1D refers to a one-dimensional geometrical model
2D refers to a two-dimensional geometrical model
3D refers to a three-dimensional geometrical model
4 Rules for modelling
4.1 Cut-off planes of the geometrical model
The geometrical model includes the 2-D central element, the 2-D 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 least 1 m from the central element if there is no nearer symmetry plane (see Figure 2);
- at a symmetry plane if this is less than 1 m from the central element (see Figure 3);
- in the ground according to Table 1 (see Figure 4).

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EN ISO 10211-2:2001
Dimensions in millimetres
Figure 2 - Location of cut-off planes at least 1 m from the central element
Dimensions in millimetres
Figure 3 - Example of a construction with linear thermal bridges at fixed distances W,
showing symmetry planes which can be used as cut-off planes

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EN ISO 10211-2:2001
Table 1 - Location of cut-off planes in the subsoil
(foundations, ground floors, basements)
Direction Distance to central element
Surface temperature Heat flow
calculations, calculations,
see Figure 4a) see Figure 4b)
1)
Horizontal inside the building at least 1 m 0,5 b
1)
Horizontal outside the building same distance as 2,5 b
inside the building
1)
Vertical below ground level 3 m 2,5 b
2)
Vertical below floor level 1 m -
1) If the value of b is not given the default value b = 8 m shall be applied.
2) This value applies only if the level of the floor under consideration is more
than 2 m below the ground surface.
Dimensions in millimetres Dimensions in metres
Figure 4a) - Soil dimensions for Figure 4b) - Soil dimensions for
     calculation of surface           calculation of heat flow
     temperatures

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EN ISO 10211-2:2001
4.2 Adjustments to dimensions
Adjustments to the dimensions of the geometrical model with respect to the geometry as
specified in the architectural drawing are only allowed if they have no significant influence on the
result of the calculation; this can be assumed if the conditions of 5.2.1 of
EN ISO 10211-1:1995 are satisfied.
Point thermal bridges that may be part of the architectural drawing (e.g. screws) should be
ignored. The thermal effect of distributed point thermal bridges should be incorporated into the
thermal conductivity of the material layers according to clause 5 of EN ISO 10211-1:1995.
4.3 Auxiliary planes
Planes which are necessary to separate blocks of different materials are called construction
planes. Planes which are neither construction planes nor cut-off planes are called auxiliary
planes.
The number of auxiliary planes in the model shall be such that doubling the number of
subdivisions does not change the linear coupling coefficient by more than 2 %, otherwise further
subdivisions shall be made until this criterion is met.
Dimensions in millimetres
Figure 5 - Example of construction planes supplemented with auxiliary planes

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EN ISO 10211-2:2001
NOTE this requirement is in many cases fulfilled when the distance between adjacent parallel planes

does not exceed the following values
(see Figure 5):
- within the central element 25 mm;
- within the flanking elements, measured from the construction plane which separates the central element
 from the flanking element: 25, 25, 50, 50, 50, 100, 200, 500, 1000, 2000 and 4000 mm.
For construc
...