CEN/TC129/WG8 – N252E CEN TC33 WG6 n. 0109
EUROPEAN STANDARD DRAFT NORME EUROPÉENNE EUROPÄISCHE NORM
prEN 13474-3 June 2008
ICS Descriptors : English version Glass in building - Determination of the strength of glass panes - Part 3: General method of calculation and determination of strength of glass by testing
Verre dans la construction -
Glas im Bauwesen -
This draft European Standard is submitted to the CEN members members for CEN enquiry. It has been drawn up by Technica Technicall Committ Committee ee CEN/TC CEN/TC129. 129. If this draft becomes a European Standard. 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. This draft European Standard was established by CEN in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member member into its own language and notified to the Central Secretariat has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom. CEN European Committee for Standardisation Comité Européen de Normalisation Europäisches Komitee für Normung Central Secretariat: rue de Stassart 36, B-1050 Brussels ______________ _______ _____________ _____________ ______________ ______________ _____________ _____________ ______________ ______________ _____________ _____________ _________ __ c CEN 1991 Copyright reserved to CEN members Ref. No. prEN 13474-3:2008
Page 2 CEN/TC129/WG8 - N252E Contents list
Foreword Introduction 1
Scope
2
Normative references
3
Definitions
4
Symbols and abbreviations
5
Requirements 5.1 Basis of determination of glass strength 5.2 General requirements 5.3 Material partial factor 5.4 Process of determining the load resistance of glass
6
Mechanical and physical properties of glass 6.1 Values 6.2 Approximate values
7
Actions 7.1 Assumptions related to the actions and combinations of actions 7.2 Combinations of actions 7.3 Wind action
8
Strength and stress 8.1 Allowable stress for annealed glass 8.2 Allowable stress for prestressed glass
9
Calculation principles and conditions 9.1 General method of calculation 9.2 Calculation method for laminated glass and laminated safety glass 9.3 Calculation method for insulating glass units
Annex A (normative): Principles of determining the load resistance of glass by testing Annex B (informative): Calculation formulae for stress and deflection for large deflections of rectangular panes supported on all edges Annex C (informative): Procedure for obtaining the simplified method used in prEN 13474-1 from the four edge supported non-linear method given in prEN 13474-3 Annex D (informative): Calculation process for insulating glass units Annex YN (informative): Proposal for a model of a National Annex (informative) Annex ZN (informative): Proposal for a model of a National Annex (informative)
Page 3 CEN/TC129/WG8 - N252E Foreword
This draft European Standard has been prepared by the Technical Committee CEN TC 129 ‘Glass in Building’, the secretariat of which is held by IBN. CEN/TC 129/WG 8 ‘Mechanical Strength’ prepared the draft ‘Glass in building Determination of the strength of glass panes - Part 3: General method of calculation and determination of strength of glass by testing’. CEN/TC 129 has decided to submit Part 3 of this draft European Standard to the CEN enquiry.
Page 4 CEN/TC129/WG8 - N252E
Introduction European Standard prEN 13474 gives the principles of determining the strength of glass for resistance to loads. Part 1 of this European Standard gives simple methods for determining by calculation the resistance to load of glass used in fenestration. Part 2 of this European Standard gives simple methods for determining by calculation the resistance to load of glass used in common non-structural applications other than fenestration. Part 3 of this European Standard gives the general method of calculation of the strength and load resistance of glass and determination of the load resistance of glass by testing. The principles of determining the strength of glass to resist loads are based on the structural Eurocode EN 1990: Basis of structural design. The actions are determined in accordance with the structural Eurocode series EN 1991: Basis of structural design - Actions on structures, including the National annexes. In the design processes, the safety aspect is part of national competency. For that reason this European Standard foresees that, to conform the rules applied by the Eurocodes, the material partial factor M is subject to nationally to determine parameters: – –
a first value for the th e ultimate limit state (ULS); a second value for the serviceability servicea bility limit state.
Those values can be found in an informative (National) annex to this European Standard. When a Member State does not use its prerogative and no values for the material partial factor has been determined, the recommended values given in this European Standard should be used.
Page 5 CEN/TC129/WG8 - N252E
1
Scope
This European Standard gives the principles of determining the strength of glass to resist loads. It gives:
the general method of calculation, and determination of load resistance by testing for any application.
For simple calculation of the load resistance of glass products for fenestration or for common applications other than fenestration, refer to prEN 13474-1 and prEN 13474-2. This European Standard does not determine suitability for purpose. Resistance to applied loads is only one part of the design process, which may also need to take into account: environmental factors (e.g. sound insulation, thermal properties), safety characteristics (e.g. fire performance, breakage characteristics in relation to human safety, security)
2
Norma mattive ref references
This European Standard incorporates, by dated or undated reference, provisions from other publications. publication s. These normative references re ferences are cited c ited at the appropriate approp riate places in the th e text and the publicationss are listed hereafter. For dated references, publication referenc es, subsequent subsequen t amendments to or revisions of any of these publications apply to this European Standard only when incorporated by amendment or revision. For undated references, the latest edition of the publication referred to applies. EN 572 EN 572-1 EN 1036 EN 1096 EN 1296 EN 1748-1 EN 1748-1-1 EN 1748-2 EN 1748-2-1 EN 1863 EN 1863-1 EN 1990 EN 1991 EN 1991-1-4 EN 1997 EN 1998 EN 12150
Glass in Building - Basic soda lime silicate glass products Glass in Building - Basic soda lime silicate glass products - Part 1: Definitions and general physical and mechanical properties Glass in building - Mirrors from silver coated float glass for internal use Glass in building - Coated glass Glass in building - Insulating glass units Glass in Building - Basic borosilicate glass products Glass in Building - Basic borosilicate glass products - Part 1: Definitions and general physical and mechanical properties Glass in Building - Basic glass ceramics products Glass in Building - Basic glass ceramics products - Part 1: Definitions and general physical and mechanical properties Glass in building - Heat strengthened soda lime silicate glass Glass in building - Heat strengthened soda lime silicate glass - Part 1: Definition and description Eurocode – Basis of structural design Actions on structures Wind actions Geotechnical design Design of structures for earthquake Glass in building - Thermally toughened soda lime silicate safety glass
Page 6 CEN/TC129/WG8 - N252E EN 12150-1 EN 12337 EN 12337-1 EN ISO 12543 EN ISO 12543-1 EN 13024 EN 13024-1 prEN 13474-1 prEN 13474-2 EN 14178 EN 14178-1 EN 14179 EN 14179-1 EN 14321-1 EN 14321-1 EN 14449
3 3.1
Glass in building - Thermally toughened soda lime silicate safety glass Part 1: Definition and description Glass in building - Chemically strengthened soda lime silicate glass Glass in building - Chemically strengthened soda lime silicate glass - Part 1: Definition and description Glass in building - Laminated and laminated safety glass Glass in building - Laminated and laminated safety glass - Part 1: Definitions and description of component parts Glass in building - Thermally toughened borosilicate safety glass Glass in building - Thermally toughened borosilicate safety glass - Part 1: Definition and description Glass in building - Determination of the strength of glass panes - Part 1: Glass and glass products for fenestration Glass in building - Determination of the strength of glass panes - Part 2: Common glass applications other than fenestration Glass in Building - Basic alkaline earth silicate glass products Glass in Building - Basic alkaline earth silicate glass products - Part 1: Definitions and general physical and mechanical properties Glass in building - Heat soaked thermally toughened soda lime silicate safety glass Glass in building - Heat soaked thermally toughened soda lime silicate safety glass - Part 1: Definition and description Glass in building - Thermally toughened alkaline earth silicate safety glass Glass in building - Thermally toughened alkaline earth silicate safety glass - Part 1: Definition and description Glass in building - Laminated glass and laminated safety glass Evaluation of conformity/Product Standard
Definitions annealed glass
Glass which has been treated during manufacture to minimise the residual stress in the glass, allowing it to be cut by scoring and snapping. Examples are float glass, drawn sheet glass, patterned glass and wired glass. 3.2
effective thickness (of laminated glass)
A thickness calculated for laminated glass which, when used in place of the glass thickness in an engineering formula, will result in a reasonably accurate determination of the deflection of and / or stress in the laminated glass. 3.3
prestressed glass
Glass which has been subjected to a strengthening treatment, by heat or chemicals, which induces a compressive surface stress into the whole surface of the glass, balanced by a tensile stress within the body of the glass. Examples are thermally toughened safety glass, heat strengthened glass and chemically strengthened glass.
Page 7 CEN/TC129/WG8 - N252E 3.4
3.4.1
structures and infill panels
main Structure
The beams, the columns, the floor forming the main structure of the building (see figure 1). Note. These are structural for so far that they carry themselves and secondary structures, and, in case of failure, endanger the fundamental stability of the building. The main structural elements must have a safety and a reliability appropriate to their design use and larger factor of safety than the one applicable to the secondary structure or to the non structural infill elements. These main structures are the reference structure and constitute the point of reference for the coefficients determined hereafter. 3.4.2
Infill panel Secondary structure
Main structure
secondary structure (e.g. glass fins)
Windows assembly frames, which are secondary structures insofar as their stability is their own. Note. A failure of these secondary structures only affects the infill panels or the non-structural elements carried by this secondary structure and in no case has any effects on the main structure of the building. The secondary structures can be replaced independently of the main structures. 3.4.3
Figure 1. Identification of structure
infill panels
Elements placed in structures in order to close a building and which do not contribute in any manner to the stability of the main structure. Note. 3.4.4
classes of consequence
Classes which allow for the fact that the failure of the secondary structures or the infill panels does not have the same economic and/or human consequences of that of the failure of the main structures. Note. A reduced factor of safety is thus acceptable on the actions. The coefficient of class of consequence, k FI , expresses the reduction of safety applicable to the secondary structures and infill panels compared to that applicable for the main structures according to the EN 1990 appendix B. This coefficient is integrated in the partial coefficients relating to the actions, Q and G, except in the case where the action has a favourable effect in a combination of actions. The coefficient of class of consequence does not apply to the partial coefficients relating to materials.
Page 8 CEN/TC129/WG8 - N252E 3.5
unfactored load
an action as obtained from EN 1991 (e.g. wind load, snow load), including all the factors relevant for determining the action, but before applying the partial factors for actions Q, G and/or
4
Symbols and abbreviations
A a a* b C d c H c prob² cT E E d E SLS;d E ULS;d E { F SLS;d } E { F ULS;d } F d F d; 1 F d; 2 F SLS;d F ULS;d f b;k f g;d f g;k G H H P h h1 h2 h3 hef;w hef; ;j
Surface area of the pane ( = a x b) Shorter dimension of the pane Characteristic length of an insulating glass unit Longer dimension of the pane Limiting design value of the relevant serviceability criterion Coefficient for the effect of altitude change on isochore pressure (=0,12 kPa/m) Probability factor applied to the wind pressure for different return periods Coefficient for the effect of cavity temperature change on isochore pressure (=0,34 kPa/K) Young’s modulus Effect of the action(s) Serviceability limit state design value of the effect of the action(s) Ultimate limit state design value of the effect of the action(s) Calculation of the effect of the serviceability limit state design value Calculation of the effect of the ultimate limit state design value Design value of the action Design value of the action on pane 1 of an insulating glass unit Design value of the action on pane 2 of an insulating glass unit Serviceability limit state design value of a single action or of a combination of actions. Ultimate limit state design value of a single action or of a combination of actions. Characteristic value of the bending strength of prestressed glass Allowable maximum stress for the surface of glass panes Characteristic value of the bending strength of annealed glass Value of self weight load Altitude Altitude of production of insulating glass unit Nominal thickness of the pane Nominal thickness of pane 1 of an insulating glass unit or ply 1 of a laminated glass Nominal thickness of pane 2 of an insulating glass unit or ply 2 of a laminated glass Nominal thickness of pane 3 of an insulating glass unit or ply 3 of a laminated glass Effective thickness of a laminated glass for calculating out-of-plane bending deflection Effective thickness of a laminated glass for calculating out-of-plane bending stress of ply j
Page 9 CEN/TC129/WG8 - N252E
hi h j hm;1 hm;2 hm;3 hm;j k 1 k 4 k 5 k FI
k mod k mod;c k sp k v p p0 pC ;0 p H ;0 p P p* Qk,1 Qk,i Rd s T T P t V wd wmax z 1 z 2 z 3 z 4 1 2 G M
Nominal thickness of pane i of an insulating glass unit or ply i of a laminated glass Nominal thickness of pane j of an insulating glass unit or ply j of a laminated glass the distance of the mid-plane of the glass ply 1 from the mid-plane of the laminated glass, ignoring the thickness of the interlayers the distance of the mid-plane of the glass ply 2 from the mid-plane of the laminated glass, ignoring the thickness of the interlayers the distance of the mid-plane of the glass ply 3 from the mid-plane of the laminated glass, ignoring the thickness of the interlayers the distance of the mid-plane of the glass ply j from the mid-plane of the laminated glass, ignoring the thickness of the interlayers Coefficient used in the calculation of large deflection stresses Coefficient used in the calculation of large deflection deflections Coefficient used in the calculation of large deflection volume changes Coefficient of class of consequence expressing the reduction of safety applicable to the secondary structures and infill panels compared to that applicable for the main structures Factor for the load duration Factor for the load duration when there are combined loads Factor for the glass surface profile Factor for strengthening of prestressed glass Air pressure Isochore pressure for an insulating glass unit Isochore pressure due to the effect of change in cavity temperature and air pressure Isochore pressure due to the effect of change in altitude Air pressure at the time of production of insulating glass unit Non-dimensional uniformly distributed load Value of the single action or dominant action Values of the actions which are not dominant Design value of the resistance to the actions Nominal cavity width of a double glazed insulating glass unit Insulating glass unit cavity temperature Temperature of production of insulating glass unit Load duration (in hours) Volume change in an insulating glass unit cavity due to the deflection of one of the panes Allowable deflection Maximum deflection calculated for the design load Coefficient used in the approximate calculation of k 4 Coefficient used in the approximate calculation of k 1 Coefficient used in the approximate calculation of k 1 Coefficient used in the approximate calculation of k 1 Stiffness partition for pane 1 of an insulating glass unit Stiffness partition for pane 2 of an insulating glass unit Partial factor for permanent actions, also accounting for model uncertainties and dimensional variations Material partial factor
Page 10 CEN/TC129/WG8 - N252E
max 0,i 1
Material partial factor for annealed glass Material partial factor for surface prestress Partial factor for variable actions, also accounting for model uncertainties and dimensional variations Insulating glass unit factor Aspect ratio of the pane ( a b ) Poisson number Glass density Maximum stress calculated for the design load Coefficient for the shear transfer of an interlayer in laminated glass Combination factors for the actions Combination factors for the actions which are not dominant Partial factor for a frequent value of a variable action
2
Note. This value is determined - in so far as it can be fixed on statistical bases so that either the total time, within the reference period, during which it is exceeded is only a small given part of the reference period, or the frequency of it being exceeded is limited to a given value. It may be expressed as a determined part of the characteristic value by using a factor 1 1 Combination factor for a quasi-permanent value of a variable action
2,i
Note. This value is determined so that the total period of time for which it will be exceeded is a large fraction of the reference period. It may be expressed as a determined part of the characteristic value by using a factor 2 1 Combination factor for a quasi-permanent value of a variable action
M;A M;v Q
Note. This value is determined so that the total period of time for which it will be exceeded is a large fraction of the reference period. It may be expressed as a determined part of the characteristic value by using a factor 2;i 1
5 5.1
Requirements Basis of determination of glass strength
The process shall conform to EN 1990: Eurocode – Basis of structural design. The determination of actions shall be in accordance with the relevant parts of EN 1991: Actions on structures. Where relevant or required, the following shall also be taken into account. EN 1997: Geotechnical design, and EN 1998: Design of structures for earthquake design.
Page 11 CEN/TC129/WG8 - N252E 5.2
General requirements Table 1: Table of requirements for the various limit states
Ultimate limit state E ULS ;d Rd
Requirement
(1.a)
Serviceability limit state (1.b) E SLS ;d C d
where the effect of the E ULS ;d E F ULS ;d (2.a) E SLS ;d E F SLS ;d (2.b) actions is: in which: F ULS;d is the Ultimate Limit F SLS;d is the Serviceability State design value of a single Limit State design value of a action or of a combination of single action or of a actions. combination of actions. and is the design value of the effect of the action(s), expressed as E ULS;d where: calculated stress, caused by the action(s). is the design value of the corresponding resistance, expressed Rd as maximum ultimate limit state allowable stress f g;d , taking into account the material partial factor for the ultimate limit state M (see 5.3). is the design value of the effect of the action(s), expressed as E SLS;d calculated stress or deflection, caused by the action(s). is the limiting design value of the relevant serviceability C d criterion, expressed as maximum serviceability limit state allowable stress f g;d , or limit on deflection, wd , taking into account the material partial factor for the serviceability limit state M (see 5.3). 5.3
Material partial factor
The recommended values of the material partial factor are given in table 2. Table 2: Recommended values of the material partial factor
Ultimate limit state Serviceability limit state Annealed glass M;A = 1,8 M;A = 1,0 Surface prestress M;v = 1,2 M;v = 1,0 Note (1). The material partial factor for annealed glass is also applied to a component of the strength of prestressed glass - see equation (7). (1)
For specific National values, see Annex ZN. 5.4
Process of determining the load resistance of glass
For any calculation or test, the mechanical and physical properties of glass shall be determined in accordance with clause 6. The design value of the actions shall be determined in accordance with clause 7.
Page 12 CEN/TC129/WG8 - N252E The allowable stresses for the glass, for the ultimate limit state and for the serviceability limit state (if required), shall be determined in accordance with clause 8. Where a design deformation limit applies for the serviceability limit state, such a value shall be determined in accordance with EN 1990. Where no other standard specifies a design deformation limit, this shall be determined in accordance with 9.1.4. For calculations, the principles and conditions shall be in accordance with clause 9. Determination of load resistance by testing, or assisted by testing, shall be in accordance with annex A.
6
Mechanical and physical properties of glass
6.1
Values
The values of the mechanical and physical properties needed for calculation, such as Young's modulus E , the Poisson number µ, and the density of glass , are obtained from the following product standards: EN 572-1, EN 1748-1-1, EN 1748-2-1, EN 1863-1, EN 12150-1, EN 12337-1, EN ISO 12543-1, EN 13024-1, EN 14178-1, EN 14179-1, EN 14321-1. 6.2
Approximate values
When (e.g. for assembling different glass materials) no distinction between the various differences in mechanical and physical properties can be taken into account, or when it is not necessary, the following values may be used: – – –
glass density Young’s modulus Poisson number
= 2 500 kg/m³; E = 70 000 MPa; = 0,22;
These values are applicable approximations for glasses with: – – –
a density between a Young’s modulus between a Poisson number between
2 250 and 2 750 kg/m³; 63 000 MPa and 77 000 MPa 0,20 and 0,25
These ranges cover the following glass materials (the list not exhaustive):
Basic soda lime silicate glass products conforming to EN 572 and processed glass products made from these basic glass products such as heat strengthened glass conforming to EN 1863, chemically strengthened glass conforming to EN 12337, thermally toughened soda lime silicate safety glass conforming to EN 12150 and heat soaked thermally toughened soda lime silicate safety glass conforming to EN 14179.
Page 13 CEN/TC129/WG8 - N252E
Basic borosilicate glass conforming to EN 1748-1, and processed glass products made of this basic glass such as thermally toughened borosilicate safety glass conforming to EN 13024. Basic glass ceramics conforming to EN 1748-2, and processed glass products made of this basic glass. Basis alkaline earth silicate glass conforming to EN 14178-1, and processed glass products made of this basic glass such as thermally toughened alkaline earth silicate safety glass in accordance with EN 14321. Coated glass conforming to EN 1096 made using one of the above types of glass Mirror glass conforming to EN 1036 made using one of the above types of glass Assembled glass made of one or more of the glass types listed above such as laminated glass and laminated safety glass conforming to EN 14449 and EN 12543. Assembled glass made of one or more of the glass types listed above such as insulating glass units conforming to EN 1279.
7 7.1
Actions Assumptions related to the actions and combinations of actions
With regard to actions and combinations of actions in the service limit state, the frequent combination applies. (see EN 1990 clauses 6.5.3 and 4.1.3) With regard to the combination of the actions in an ultimate limit state, the fundamental combination applies. (See EN 1990 clauses 6.5.3 and 4.1.3) 7.2
Combinations of actions
The values of the actions shall be determined in accordance with the appropriate parts of EN 1991. The design value of the action (design load) shall be: for ultimate limit state
F d
G .G"" Q .Qk ,1 "" Q 0,i Qk ,i
(3.a)
G"" 1 .Qk ,1 "" 2,i Qk ,i
(3.b)
i
for serviceability limit state
F d
i
where: the design value of the combination of actions; F d is G is the value of permanent actions (e.g. self-weight load, permanent equipment); Qk,1 is the characteristic value of the leading variable action (e.g. imposed load on floor, wind, snow), Qk,i is the characteristic value of the accompanying variable action (e.g. wind, snow) 0,i are factors for combination value of accompanying variable actions 1 is the factor for frequent value of a variable action 2,i:is the factor for quasi-permanent value of a variable action G is the partial factor for permanent actions, also accounting for model uncertainties and dimensional variations
Page 14 CEN/TC129/WG8 - N252E Q: is the partial factor for variable actions, also accounting for model uncertainties and dimensional variations The recommended values of the partial load factors, , are given in table 3. Table 3: Partial load factors
Type of element to be calculated (1)
Main structure (1)
(3)
G
Q see Eurocodes 1,3 1,1
favourable see Eurocodes 1,0 1,0
unfavourable see Eurocodes 1,2 1,1
Secondary structure Infill panel(2) Notes. (1) Structural construction covered by Eurocodes (2) Non structural element not covered by Eurocodes (3) The lower value is used when the permanent action has a favourable effect in combination with other actions. The higher value is used when the permanent action is considered acting alone or has a unfavourable effect in combination with other loads. For specific National values, see Annex YN. The recommended values of the partial factors, , are given in table 4. Table 4: (1)
Wind
Snow
Other
0 1 2 0 1 2 0 1 2
Main structure see Eurocodes see Eurocodes see Eurocodes see Eurocodes see Eurocodes see Eurocodes
factors
See Eurocodes or national annexes
Notes. (1) Structural construction covered by Eurocodes (2) Non structural element not covered by Eurocodes For specific National values, see Annex YN.
(1)
Secondary structure 0,6 0,9 0,2 0,6 1,0 0,2
(2)
Infill panel 0,6 0,9 0,2 0,6 1,0 0,2
Page 15 CEN/TC129/WG8 - N252E 7.3
Wind action
The wind actions calculated using EN 1991-1-4 are characteristic values (See EN 1990, 4.1.2). They are determined from the basic values of wind velocity or the velocity pressure. In accordance with EN 1990 4.1.2 (7)P, the basic values are characteristic values which are exceeded with an annual probability of 0,02, which is equivalent to a mean return period of 50 years. NOTE: All coefficients or models used to derive wind actions from basic values are chosen so that the probability of the calculated wind actions does not exceed the probability of these basic values. A probability factor, c prob², can be applied to the design wind pressure allowing for a different wind return period. Values are given in table 5. Table 5: cprob² values Years 1 5 10 15 20 25
8
c prob² 0,241222 0,702303 0,795309 0,847782 0,884522 0,912822
Years 30 40 50 60 65 70
c prob² 0,935845 0,972028 1 1,022806 1,032807 1,042061
Strength and stress
8.1
8.1.1
Allowable stress for annealed glass
Formulae
The allowable stress for annealed glass material, whichever composition, is
f g ;d
where f g;k M;A k sp k mod
k mod k sp f g ;k M ; A
(4) 2
is the characteristic value of the bending strength (f g;k = 45 N/mm ). is the material partial factor for annealed glass (see 5.3 and Annex ZN). is the factor for the glass surface profile (see 8.1.2). is the factor for the load duration(see 8.1.3).
NOTE 1. CEN report CR rrr explains the origin of the value of f g;k .
Page 16 CEN/TC129/WG8 - N252E 8.1.2
Glass surface profile factor
The factor for the glass surface profile is given in table 6. Table 6: Factor for the glass surface profile
Glass material Factor for the glass surface profile k sp (whichever glass composition) Float glass 1,0 Drawn sheet glass 1,0 (1) Enamelled float or drawn sheet glass (1,0) Patterned glass 0,75 (1) Enamelled patterned glass (0,75) Polished wired glass 0,75 Patterned wired glass 0,6 Note 1. These glass types are not generally available as annealed glass, but the values of k sp are also required in the formulae for prestressed glass (see 8.2). 8.1.3
Factor for duration of load
The factor for the load duration of annealed glass is
k mod
1
0,663t 16
(5)
where t is the load duration in hours. The factor k mod has a maximum value of k mod = 1 and a minimum value of k mod = 0,25. Typical values of k mod are given in table 7.
Page 17 CEN/TC129/WG8 - N252E Table 7: Factors for load duration Action Load duration k mod (1) personnel loads short, single 0,85 wind short, multiple 0,74 (2) snow intermediate 0,44 daily temperature variation intermediate 0,57 11 hours extreme peak duration barometric pressure variation intermediate 0,50 yearly temperature variation intermediate 0,39 6 month extreme mean value duration dead load, self weight permanent 0,29 Notes: (1) The value of k mod=0,85 is based on a personnel load of 1 minute duration. Other values may be considered depending on the type of personnel load being evaluated and also the building use. (2) k mod=0,44 can be considered representative for snow loads lasting between 1 week (k mod=0,48) and 3 months (k mod=0,41). Other values of k mod may be appropriate depending on local climate.
Where loads with different durations need to be treated in combination, the appropriate factor for load duration for the combined loads, kmod;c, is determined from the following equation.
k mod;c
E ULS ;G E ULS ;1
8.2.1
ULS ;i
i
E ULS ;G k mod;G
8.2
E
E ULS ;1 k mod;1
E ULS ;i
i
(6)
k mod;i
Allowable stress of prestressed glass
Formula
The allowable stress of prestressed glass material, whichever composition is
f g ;d
k mod k sp f g ;k M ; A
k v f b;k f g ;k M ;v
(7)
where f g;k , M;A, k mod and k sp are described in 8.1. M;v is the material partial factor for surface prestress (see 5.3 and Annex ZN). is the characteristic value of the bending strength of prestressed glass (see f b;k 8.2.2). is the factor for strengthening of prestressed glass (see 8.2.3). k v 8.2.2
Characteristic bending strength
The values of characteristic bending strength for prestressed glass are given in table 9.
Page 18 CEN/TC129/WG8 - N252E Table 9: Values of characteristic strength and strengthening factors for prestressed glass
Glass material per product (whichever composition)
Values for characteristic bending strength f b;k for prestressed glass processed from: thermally toughened safety glass, heat strengthened chemically and glass strengthened glass heat soaked thermally toughened safety glass
float glass or drawn sheet glass patterned glass enamelled float or drawn sheet glass enamelled patterned glass 8.2.3
120 N/mm2
70 N/mm2
2
55 N/mm
2
45 N/mm
2
45 N/mm
90 N/mm
75 N/mm
75 N/mm
150 N/mm2
2
2
150 N/mm
2
2
Strengthening factor
The presence of tong marks in vertically toughened glass reduces the effectiveness of the prestressing locally compared with horizontally toughened glass which has no tong marks. The strengthening factor for method of manufacture is given in table 10. Table 10: Strengthening factor
Manufacturing process Horizontal toughening (or other process without the use of tongs or other devices to hold the glass) Vertical toughening (or other process using tongs or other devices to hold the glass)
9
Strengthening factor, k v 1,0
0,6
Calculation principles and conditions
9.1
9.1.1
General method of calculation
Design load
The characteristic value of the design load, F d , shall be determined in accordance with clause 7.
Page 19 CEN/TC129/WG8 - N252E
Note: If glass is used in an application where there is no specific design load from standards or regulations, consideration should be given to using a glass thickness sufficient to resist an unfactored short duration uniformly distributed load of 500 N/m2. 9.1.2
Stress and deflection calculation
The design load shall be used for calculating the tensile or tensile bending stress in the glass and the deflection of the glass. The method used for the determination shall be an engineering formula or method appropriate to the load distribution, the shape of the glass and the support conditions. For common applications of glass, Part 1 and Part 2 of this European Standard give simple methods. In general, the maximum stress and the maximum deflection, wmax, shall be calculated according to linear theory. Where the deflection induced by the actions exceeds half the glass thickness, linear theory of plate bending may excessively overestimate the stresses and maximum deflection. In this case the stress distribution and maximum deflection can be calculated according to non-linear plate theory. Annex B gives formulae for non-linear calculations for four-edge supported rectangular panes.
Note: For fenestration, Part 1 of this European Standard gives an approximate method using glass factors to compensate for the use of l inear plate bending theory in fenestration, where the effect of actions is generally non-linear. The derivation of this is given in Annex C. For laminated glass, the stress in each ply shall be calculated. For insulating glass units, the stress in each pane shall be calculated. A method for determining the loads applied to each pane of an insulating glass unit is given in Annex D. 9.1.3
Allowable stress
The allowable stress, f g;d , shall be determined according to clause 8. The value of the load duration factor used to calculate the allowable stress shall be appropriate to the anticipated duration of the single load (or the dominant load where there are combined loads). 9.1.4
Allowable deflection
There is no specific requirement of glass to limit the deflection of the glass under load. Other standards or regulations may require deflection limits for particular applications. If required, the allowable deflection, wd , shall be in accordance with the appropriate standard or regulation. Consideration should be given to ensuring the glass is not excessively flexible when subjected to applied loads, as this can cause alarm to building users. In the absence of any specific requirement, deflections shall be limited to Span/65 or 50 mm, whichever is the lower value.
Page 20 CEN/TC129/WG8 - N252E 9.1.5
Comparisons of stress and deflection
The maximum stress calculated for the design load shall not exceed the allowable stress: max f g;d (8) If there is a requirement for limitation of the glass deflection, the maximum deflection calculated for the most onerous load condition shall not exceed the allowable deflection:
wd
wmax
(9)
If there are combinations of loads to be considered, it may be necessary to perform the procedures in 9.1.1 to 9.1.5 more than once, taking alternative loads as the dominant load, in order to determine the most onerous condition. The most onerous condition is either: - the highest value of the effective stress, in relation to the allowable stress based on the duration of the dominant load; or - the largest value of maximum deflection.
Note: The most onerous condition may differ for stress and deflection. 9.2
Calculation method for laminated glass and laminated safety glass
9.2.1
Calculation method
In cases where shear stress is developed in laminated glass parallel with the interlayer, the interlayer can be considered as having some shear resistance. This can be taken into account in evaluating resistance to bending of the laminated glass using a suitable engineering formula in combination with the shear resistance of the interlayer. The following approach, using the concept of ‘effective thickness’ can be used. The effective thickness for calculating bending deflection is:
hef ;w
3 1 i hi3 i hi
3
(10)
and the effective thickness for calculating the stress of glass ply number j is:
h
3
hef ; ; j
ef ;w
h 2 h j
where
(11)
m; j
is a coefficient between 0 and 1 representing no shear transfer (0) and full shear transfer (1), hi, h j are the thicknesses of the glass plies (see figure 2), and hm;j is the distance of the mid-plane of the glass ply j from the mid-plane of the laminated glass, ignoring the thickness of the interlayers (see figure 2).
Page 21 CEN/TC129/WG8 - N252E h1
h2
hm;1 hm;2
1 hm;3
2
h3
1 Mid-plane of each glass ply 2 Mid-plane of laminated glass Figure 2. Example of laminated glass thickness dimensions The effective thicknesses for calculating stresses and deflection in laminated glass comprising two plies of the same thickness using a value of = 0.25 are given in table 11. Table 11. Effective thicknesses of laminated glass with two plies of the same thickness and = 0.25
Glass thickness mm 3+3 4+4 5+5 6+6 8+8 10 + 10 9.2.2
Short duration loads ( = 0.25) hef;w mm hef; ;j mm 4.55 5.02 6.07 6.69 7.59 8.37 9.11 10.04 12.15 13.39 15.18 16.73
Long duration loads ( = 0.05) hef;w mm hef; ;j mm 3.96 4.44 5.28 5.92 6.60 7.40 7.92 8.88 10.56 11.84 13.20 14.80
Determination of
The value of to be used for a specific interlayer and a particular load case depends on the interlayer stiffness family to which the interlayer belongs for that particular load case. The interlayer stiffness families and the equivalent values of are given in table 12. Table 12. Value of
Interlayer stiffness family 3 2 1 0
associated with interlayer stiffness family
Value of 0.6 ? 0.25 ? 0.1 ? 0
Page 22 CEN/TC129/WG8 - N252E Each interlayer has its interlayer stiffness family assigned for a number of different load cases according to the test method and evaluation from EN vwxyz. The load cases are given in table 13. Table 13. Load cases
Load case Wind load Personnel loads - normal duty Personnel loads - crowds Snow load - external canopies Snow load - roofs Permanent
Load duration 3 seconds 30 seconds 5 minutes 3 weeks 3 weeks 50 years
Temperature range o o 0 C < < 20 C o o 0 C < < 30 C o o 0 C < < 30 C o o -20 C < < 0 C o o -20 C < < 20 C o o -20 C < < 40 C
Editorial note: The above are examples. The load cases, durations and temperature ranges are to be determined by the CEN/TC129/WG8 full committee. 9.3
Calculation method for insulating glass units
The calculation method for insulating glass units conforming to EN 1279 shall take into account the consequences arising from the presence of the hermetically sealed and fixed quantity of gas within the cavity or cavities of the insulating glass unit. This shall take into account:
the presence of the fixed quantity of gas causing actions which are applied to only one pane to develop effects in all the panes in the insulating glass unit (a phenomenon also known as load sharing); changes in ambient barometric pressure conditions relative to the barometric pressure at the time of sealing the insulating glass unit causing actions (internal actions) which develop effects in all the panes; changes in the temperature of the gas in the cavity causing actions (internal actions) which develop effects in all the panes.
A method is given in Annex D for determining the proportions of the loads applied to the individual panes of a double glazed insulating glass unit. If insulating glass units conform to EN 1279-5, then the stresses generated in the seal when the units are subjected to normally expected loads in service - e.g. wind, snow, self-weight, personnel, or climatic, but excluding exceptional loads such as explosion pressures - will not cause premature failure of the hermetic seal, provided the deflection of the glass is not excessive.
Page 23 CEN/TC129/WG8 - N252E
Annex A (normative) Principles of determining the load resistance of glass by testing A.1
General
Testing of glass as a construction element or part thereof shall preferably be performed on full scale models. Where models different from full scale are used, appropriate techniques shall be used to:
verify that calculated and measured values for the model used do not differ significantly; evaluate the expected deformations and stresses for the considered construction element with a reliable degree of accuracy and confidence.
For the ultimate limit state the following requirement applies.
E d Rd
(A.1)
where E d is the effect of the action(s), expressed: – as measured stress; – or as an evaluated stress on the basis of the measured stress when no 1 to 1 scale model has been used; caused by the action(s), which shall be determined in accordance with clause 7 of this European Standard. Rd is the design value of the corresponding resistance, expressed; – as the maximum allowable stress, f g;d , determined in accordance with this European Standard. For the serviceability limit state the following requirement applies
E d C d
(A.2)
where E d is the effect of the action(s), expressed: – as measured stress; – or as an evaluated stress on the basis of the measured stress when no 1 to 1 scale model has been used; – or as deformation; caused by the action(s), which shall be determined in accordance with clause 7 of this European Standard. the limiting design value, expressed; C d is – as the maximum allowable stress, f g;d , determined in accordance with this European Standard; – or as the maximum allowable deformation in accordance with this European Standard.
Page 24 CEN/TC129/WG8 - N252E A.2
Factors affecting load resistance
Glass is a homogeneous isotropic material having almost perfect linear-elastic behaviour over its tensile strength range. Glass has a very high compressive strength and theoretically a very high tensile strength, but the surface of the glass has many irregularities which act as weaknesses when glass is subjected to tensile stress. These irregularities are caused by attack from moisture and by contact with hard materials (e.g. grit) and are continually modified by moisture which is always present in the air. Tensile strengths of around 10 000 N/mm2 can be predicted from the molecular structure, but 2 bulk glass normally fails at stresses considerably below 100 N/mm . The presence of the irregularities and their modification by moisture contributes to the properties of glass which need consideration when performing tests of strength. Because of the very high compressive strength, glass always fails under tensile stress. Since glass in buildings is very rarely used in direct tension, the most important property for load resistance is the tensile bending strength. The major influences on the bending strength and load resistance of glass are the following factors: a) rate and duration of loading; b) area of surface stressed in tension; c) the surface condition. The bending strength and load resistance of laminated glass is also influenced by the following factors affecting the interlayer properties: d) rate and duration of loading giving rise to creep of the interlayer; e) temperature affecting the stiffness of the interlayer. The influence exerted by factors a) to e) on bending strength and load resistance should be taken into account in the testing method and/or subsequent analysis. A.3
Effect of rate and duration of loading
Since glass is linearly elastic, altering the rate or duration of load does not affect stresses or deflections if all the other components are also linearly elastic. However the duration of the load has a significant effect on the ultimate strength. In particular, if the design load is long duration, it is not sensible to test to ultimate failure in a short duration test. Better is to measure the induced stress (e.g. by the use of strain gauges) and compare it with the allowable long duration stress.
Page 25 CEN/TC129/WG8 - N252E For laminated glass there is no simple way to measure the stresses in a short duration test to obtain an estimate of long duration stresses, since the greater shear transfer over short duration can develop significantly different stresses in the glass plies. The test and the analysis model need to take this into account. A.4
Effect of stressed surface area
There is an area effect on glass strength depending on the specimen size. On average, smaller sizes will break at higher stresses than larger sizes. This can be overcome by using test specimens of sizes representative of the application. It affects only the breakage stress, not the stress generated by a specific load. The interlaminar shear transfer in laminated glass is size dependent. Larger pane sizes have greater shear transfer than smaller pane sizes. The test specimen sizes should be representative of the application. A.5
Surface condition
The variation in microscopic flaws in glass surfaces means that the load resistance obtained in a test to ultimate failure of nominally identical glass specimens can vary by a factor of 4. Caution should be used in assessing factors of safety related to ultimate strength tests unless a large number have been performed (more than 10 to obtain a reliable mean strength and more than 20 in order to obtain a reliable characteristic strength). A.6
Temperature
Variations of temperature within the range normally obtained in buildings have negligible effect on the reaction of glass to load and stress. Temperature can have a major effect on the properties of laminated glass interlayers. Where possible tests on laminated glass should be conducted at a temperature representative of service.
Page 26 CEN/TC129/WG8 - N252E
Annex B (informative) Calculation formulae for stress and deflection for large deflections of rectangular panes supported on all edges. Of the dimensions a and b of the pane, a shall be taken as the shorter dimension. The aspect ratio is given by = a/b and the area is given by A = ab For practical determination of the stress, the deflection and the change in volume (for the cavity of insulating glass units), formulae are given as follows: Maximum tensile bending stress
Deflection
Volume
max
wmax
k 1 k 4
V k 5
A h2
F d
A2 F d h 3 E
A 3 F d h 3 E
(B1)
The values of the coefficients are given in tables B.1 to B.3.
(B2)
(B3)
Page 27 CEN/TC129/WG8 - N252E In case of four-edge supported panes, the dimensionless coefficients k 1 and k 4, depend on the aspect ratio, , and the non-dimensional load. 2
A F p* 2 d 4h E
Non-dimensional load
(B4)
The coefficients in tables B.1 to B.3 are valid for a Poisson number in the range 0,20 to 0,24. They can be interpolated linearly. For small deflections (linear theory) the values for p* = 0 apply. Table B.1: Coefficient k 1 for calculation of the maximum stress 0 1 2 =a/b 1,0 0.268 0.261 0.244 0,9 0.287 0.278 0.258 0,8 0.304 0.295 0.273 0,7 0.314 0.306 0.285 0,6 0.314 0.309 0.294 0,5 0.300 0.298 0.290 0,4 0.268 0.268 0.266 0,3 0.217 0.217 0.217 0,2 0.149 0.149 0.149 0,1 0.075 0.075 0.075 For the purposes of calculation:
k 1
where
3
5
p* 10
20
50
0.223 0.234 0.247 0.261 0.274 0.279 0.262 0.216 0.149 0.075
0.190 0.197 0.205 0.218 0.235 0.253 0.252 0.215 0.149 0.075
0.152 0.155 0.159 0.165 0.176 0.197 0.221 0.208 0.149 0.075
0.135 0.137 0.138 0.140 0.143 0.151 0.171 0.189 0.148 0.075
0.130 0.131 0.131 0.130 0.129 0.128 0.129 0.141 0.140 0.075
1
1 p *2 4 2 2 2 z 2 z 3 z 4 p *
0.5
1.073 1 z 2 24 0.0447 0.0803 1 exp 1.17 1 2
1 z 3 4.5 1 4.5 1 z 4 0.585 0.05 1
100
200
300
0.129 0.130 0.130 0.129 0.127 0.124 0.119 0.116 0.123 0.075
0.128 0.129 0.130 0.129 0.126 0.123 0.116 0.107 0.100 0.074
0.128 0.129 0.130 0.129 0.126 0.122 0.116 0.105 0.091 0.073
Page 28 CEN/TC129/WG8 - N252E Table B.2: Coefficient k 4 for calculation of the maximum deflection 0 1 2 =a/b 1,0 0.0461 0.0414 0.0354 0,9 0.0452 0.0409 0.0351 0,8 0.0437 0.0399 0.0346 0,7 0.0404 0.0377 0.0333 0,6 0.0354 0.0339 0.0309 0,5 0.0287 0.0281 0.0267 0,4 0.0208 0.0207 0.0204 0,3 0.0128 0.0128 0.0127 0,2 0.0059 0.0059 0.0059 0,1 0.0015 0.0015 0.0015 For the purposes of calculation:
3
5
p* 10
0.0310 0.0309 0.0305 0.0297 0.0281 0.0251 0.0199 0.0127 0.0059 0.0015
0.0255 0.0254 0.0253 0.0248 0.0240 0.0222 0.0187 0.0125 0.0059 0.0015
0.0189 0.0188 0.0188 0.0186 0.0183 0.0176 0.0159 0.0119 0.0059 0.0015
0.5 1 1 2 4 4 p * 2 z 1 z 1 2 k 4
20 0.0137 0.0136 0.0136 0.0136 0.0134 0.0132 0.0125 0.0105 0.0058 0.0015
50 0.0088 0.0088 0.0087 0.0087 0.0087 0.0086 0.0085 0.0079 0.0055 0.0015
100
200
300
0.0062 0.0062 0.0062 0.0062 0.0062 0.0062 0.0061 0.0059 0.0048 0.0015
0.0044 0.0044 0.0044 0.0044 0.0044 0.0044 0.0044 0.0043 0.0038 0.0015
0.0036 0.0036 0.0036 0.0036 0.0036 0.0036 0.0036 0.0035 0.0033 0.0015
0.5
16 p *
where
Note:
z 1 192 1
For p*=0,
k 4
2
2
1.097 1 0.00406 0.00896 1 exp 1.123 1
z 1 16
Table B.3: Coefficient k 5 for calculation of the volume change 1,0 0,9 0,8 =a/b 0,0190 0,0186 0,0181 k 5 E. Dupont 0,0196 0,0192 0,0186 For the purposes of calculation :-
k 5 where
0,7 0,0169
0,6 0,0150
0,5 0,0124
0,4 0,0094
0,3 0,0061
0,2 0,0031
0,1 0,00086
0,0174
0,0153
0,0126
0,0094
0,0061
0,0031
0,00086
z 1 0.4198 0.22 exp 6.8 1.33 16
z 1 is given in table B.2
Page 29 CEN/TC129/WG8 - N252E
Annex C (Informative) Procedure for obtaining the simplified method used in prEN 13474-1 from the four edge supported non-linear method given in prEN 13474-3 Proposed to insert the contents of document CEN/TC129/WG8 - N186 (to be revised) here
Page 30 CEN/TC129/WG8 - N252E
Annex D (Informative) Calculation process for insulating glass units D.1
General
In case of double glazing, with panes of thickness h1 and h2, the distribution (partition) of external uniformly distributed loads (e.g. wind, snow, self weight) is essentially determined by the distribution (partition) of the stiffness of the panes, that is: Stiffness partition for pane 1 with thickness h1: Stiffness partition for pane 2 with thickness h2:
1 2
h13 h13 h23
h23 h13
h23
(D1)
1 1
(D2)
Additionally, the distribution (partition) of external loads as well as the effect of internal loads is determined by the insulating unit factor :
1 1 ( a / a*) 4
(D3)
The length a gives the actual dimension of the unit (e.g. in case of a rectangular unit the length of the short edge) while a* is the characteristic length of the unit, depending on the thickness of the glass panes and the gas space, s, and the shape of the unit.
sh13 h23 a* 28,9 3 3 h h k 1 2 5
0, 25
(D4)
The coefficient of volume, k 5, depends on the shape of the unit (see table B.3 in Annex B) D.2
Distribution (partition) of external loads (load sharing)
By means of the internal pressure the external loads (e.g. wind on pane 1) are distributed to both panes. Table D.1: Load partition for external loads
Load External load F d acting on pane 1
External load F d acting on pane 2 D.3
Partition of load carried by pane 1 F d ;1 1 2 F d
F d ;1
Effect of internal loads
D.3.1 Internal loads applied to the panes
1 1 F d
Partition of load carried by pane 2 F d ; 2 1 2 F d
F d ; 2
1 2 F d
Page 31 CEN/TC129/WG8 - N252E The internal loads given by the isochore pressure are reduced by the flexibility of the panes described by the insulating glass unit factor, . Table D.2: Internal loads
Isochore pressure p0
Load carried by pane 1 p0
Load carried by pane 2 p0
D.3.2 Isochore pressure
The isochore pressure generated by a difference of altitude is: p H ;0 where c H
c H ( H H P )
(D5)
0,012 kPa/m
Isochore pressure generated by a difference of temperature and/or air pressure is: pC ;0 where cT
cT (T T P ) ( p p P )
(D6)
0,34 kPa/K
The isochore pressure is: p0
p H ;0 pC ;0
(D7)
Page 32 CEN/TC129/WG8 - N252E
Annex YN (informative) Proposal for a model of a National Annex (informative) The values of the partial load factors for glass to be used on the territory of [Member State] are: Table YN1. partial factors Type of element to be calculated
G(3)
Q
favourable unfavourable (1)
Main structure (1) Secondary structure Infill panel(2) Notes. (1) Structural construction covered by Eurocodes (2) Non structural element not covered by Eurocodes (3) The lower value is used when the permanent action has a favourable effect in combination with other actions. The higher value is used when the permanent action is considered acting alone or has a unfavourable effect in combination with other loads. Table YN2. partial factors Main structure Wind
Snow
Other
0 1 2 0 1 2 0 1 2
(1)
Secondary structure
(1)
Infill panel
(2)
See Eurocodes or national annexes
Notes. (1) Structural construction covered by Eurocodes (2) Non structural element not covered by Eurocodes When not filled in, the recommended values in this European Standard should be used (see 7.2). Probability factor for wind return period:
c prob² = 1,0.
Page 33 CEN/TC129/WG8 - N252E
Annex ZN (informative) Proposal for a model of a National Annex (informative) Nationally determined material partial factors by [Member State]
The values of the material partial factor for glass to be used on the territory of [Member State] are: Ultimate limit state Serviceability limit state Annealed glass M;A = ……. M;A = ……. Surface prestress M;v = ……. M;v = ……. Note (1). The material partial factor for annealed glass is also applied to a component of the strength of prestressed glass - see equation (7). (1)
When not filled in, the recommended values in this European Standard should be used (see 5.3).
CEN/TC129/WG8 - NxxxE
EUROPEAN STANDARD
prEN
thstr
NORME EUROPÉENNE EUROPÄISCHE NORM
October 2007
_____________________________________________________________________ ICS
Descriptors : English version Glass in building - Thermal Stress Calculation Method
Verre dans la construction -
Glas im Bauwesen -
This draft European Standard is submitted to the CEN members for CEN enquiry. It has been drawn up by Technical Committee CEN/TC129. If this draft becomes a European Standard. 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. This draft European Standard was established by CEN 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 Central Secretariat has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom. CEN European Committee for Standardisation Comité Européen de Normalisation Europäisches Komitee für Normung Central Secretariat: rue de Stassart 36, B-1050 Brussels __________________________________________________________________________________ c CEN 2007. Copyright reserved to CEN members Ref. No. prEN thstr : 2007
Page 2 CEN/TC129/WG8 - N199E Contents Foreword Introduction 1
Scope
2
Normative references
3
Definitions
2
Page 3 CEN/TC129/WG8 - N199E Foreword
To be completed later
Page 4 CEN/TC129/WG8 - N199E
1 Scope To be added later.
2 References EN 410 EN 673
To be completed later
3 Definitions Backup: an area of solid material, behind and in close proximity to the glass, which will reflect heat back into the glass and / or trap hot air behind the glass and / or insulate the rear surface of the glass. Thermally safe: the risk of thermal stress cracks originating from a good quality glass edge is sufficiently low to be acceptable.
To be completed later
4 Symbols To be added later
5 Calculation Method 5.1 General
Thermal stress in glass panes in buildings is caused by the central area of the glass heating up, when the sun shines on it and when ambient temperatures rise, more quickly and to a higher temperature than the edges of the glass, which are concealed within a frame, and may be subjected to a shadow from its direct environment. The warmer central area expands relative to the cooler edges and causes tensile stress to be developed in the edges of the glass. If the temperature difference between the warmer centre and the cooler edges is sufficiently high, the stress can cause cracks to develop from the edges of the glass. For each pane submitted to a cast shadow, three zones are considered: - the central zone directly hit by the sun - the shaded part of the central zone - the edges of the pane in the shaded part.
4
Page 5 CEN/TC129/WG8 - N199E The calculation of the edges temperature takes into account the effect of the inertia of the rebate, together with the influence of the spacer between the panes, generally metallic, that tends to equalize the temperatures of the two adjacent glass panes edges. The temperature difference to be considered for each pane is the greater difference between the first, and alternatively the second or third zone temperatures. 5.2 Principles
It is stated in the following that any glazing in a building shall be able to withstand the effect of a cast shadow, resulting from permanent or temporary external obstacles, for all possible climatic conditions of the site. Thus the instantaneous temperature difference for each glass shall be calculated in the worst condition for that glass. The temperature differences between two points of one glass depend on: -
climatic conditions of the site (solar flow, daily amplitude, façade orientation, altitude, season…) Nature and constitution of the glazing (number of panes, solar characteristics, U value) Thermal inertia of the framing Presence and nature of a blind or a backup, or eventually of a radiator
In the case of mobile blinds or awnings, the temperature difference shall be calculated taking into account different positions of the blind (Retracted, half retracted, extended), or of the lathes of a venetian blind (closed, open at 45°, open). The value of the thermal stress is proportional to the temperature difference. The calculated thermal stress shall be less than the allowable thermal stress. The allowable thermal stress depends on the nature of the glass and its treatment, but also of its position and settlement: if the edges of the glass may be subjected to mechanical stresses, the allowable thermal stress is reduced. Due to the probabilistic character of thermal breakage, the allowable thermal stress considered is higher for non permanent shadow risks (e.g. smooth façade) than for permanent shadowing condition (window masonry framing, balconies, etc…)
6 Characteristics of the glazing 6.1 General
The sides of the panes in a glazing are numbered from exterior to interior. The slope of the glazing shall be specified. The treatment of the edges of the glass is defined in Annex….
Page 6 CEN/TC129/WG8 - N199E 6.2 Solar characteristics
Each glass, monolithic or laminated, is defined by its solar characteristics (transmission, absorption, reflection) calculated according to EN 410, for each side. For an insulating glazing, the characteristics have to be known for each component individually. The global characteristics of the glazing, with or without a blind, are calculated from those of each component, according to EN 13363. Note: The use of the solar characteristics of the component constitutes an admissible simplification, which generally overestimates the absorptions and thus is on the safe side concerning glass warming up under the sun. If the spectral characteristics of the components are known, they can be used in a more precise calculation. 6.3 Glass with high thermal resistance
The glass products offering a high resistance to thermal shock are: -
heat strengthened soda lime silicate glass (EN 1863) or toughened (EN 12150 or EN 14179) or chemically strengthened (EN 12337) glass with low expansion coefficient, such as borosilicate that are generally thermally toughened, or glass ceramics (EN 1748-2), or alkaline earth silicate glass (EN 14178).
6.4 Treatment of edges
Treatments of glass edges increasing the thermal shock resistance are described in Annex 1.
7 Surrounding of the glazing 7.1 Rebates
Three types of rebates are considered, from their thermal inertia. 7.1.1
Light inertia rebates
Enter in this category: (sketches to be given) - Wood or PVC frames - Aluminium frames, with or without thermal break - Thin steel frames, in openings or without contact to the structure - Mix frames using wood and aluminium or PVC. - Structural sealant glazing - Point fixed glazing 7.1.2
Medium inertia rebates
Enter in this category: (sketches to be given) - Heavy steel framings (hot laminated)
6
Page 7 CEN/TC129/WG8 - N199E 7.1.3
Fixed frames of aluminium of steel in direct contact to a masonry or a heavy metal structure, even on one side only Mix frames using steel and aluminium High inertia rebates
Enter in this category: (sketches to be given) - Mineral rebates - Metallic rebates engraved in masonry This is mainly the cases of showroom glazing. 7.2 Openings
The type of opening shall be precised (side-hung casement, sliding sash, galandage). As a general case, the window will be considered in its closed position. For sliding sashes, the opened position shall also be considered. This type of opening may lead to the total or partial superposition of two double glazings, and thus a greater temperature rise in the space between the two glazings, with increased breakage risks if this space is not ventilated, and moreover if there is a cast shadow from the reveal wall. 7.3 Cast shadows
The presence of solar screens, top boards, loggias, reveals, or any masks, may induce temporarily or permanently a cast shadow on the glazing. Presence of one or more of these elements shall be indicated by the building owner. Glazing set at the inner side of the wall present systematically a cast shadow. Glazing at the outer side of the façade or of the roofing, and not subjected usually to the shadow of a neighbour obstacle are termed without cast shadow. Vertical or horizontal pivot casements are systematically subjected to cast shadows. 7.4 Blinds or solar protections, shutters 7.4.1
Characteristics
The blind characteristics are defined according to EN 14501, from: - its type (fabric, Venetian blind) - its solar characteristics (transmission, reflexion, absorption) - its permeability, or openness factor The characteristics of shutters are defined according to Annex H of EN ISO 10077-1. The position of the solar protection or shutter (interior, exterior or incorporated into the glazing) shall be indicated. In the case of glazing equipped with blinds of mobile solar protections (interior, exterior or incorporated into the glazing), the solar protection is supposed to be half extended. Calculation shall then be performed, for the central part, for shaded and not shaded zones, alternatively with and without the solar protection.
Page 8 CEN/TC129/WG8 - N199E When incorporated in a glazing, a Venetian blind shall be considered successively as closed, then opened at 45°. 7.4.2
Ventilation
A blind or a solar protection may be ventilated or not, and partially permeable to infra-red radiation. Ventilation of the space between blind or shutter and the glass results from several factors: - porosity of current part - ventilation through the peripheral gaps between the blind and wall or window. (see sketch)
Blind or shutter
Outdoors
Indoors
Outdoors
Indoors
Provision should be taken so that the blind do not remain in direct contact with the glass. If the interior blind in retracted position does not escape completely the glazing light, it has to be considered as an opaque backup if it meets the conditions explained in paragraph 7.5.
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Page 9 CEN/TC129/WG8 - N199E
7.5 Opaque backups 7.5.1
Dimensions and geometry
The figures xx and xy below define the conditions where a glazing is considered as in front of an opaque backup. On a vertical cross section, the glazing is in front of a backup if : d1 < 0,80 m and h1 0.5 d1 + 0.10 (m) or d2 < h2 and h2 0.10 m
Wall or opaque parts
Glazing
Wall or opaque parts
On a horizontal cross section, the glazing is in front of a backup if: d3 < h3 and h3 0.10 m Wall or opaque parts
Glazing
Page 10 CEN/TC129/WG8 - N199E For a glazing located partially in front of a backup, the calculation of the temperatures includes the following steps: - Higher temperature: - Lower temperatures
7.5.2
in frond of the backup, not shaded central zone far from backup, shaded glass edges far from backup, shaded
Solar and thermal characteristics
The opaque backup is defined through its thermal resistance, as a function of the thickness and thermal conductivity of the constitutive material(s), and of its solar absorption or reflexion. In the case of a concrete floor abutment, or of a thick mullion, the thermal resistance of the obstacle is evaluated grossly considering a backup thickness equal to its width. Examples of backup characteristics are given in Annex 2. 7.6 Glazing in front of a radiator
The glazing should not be exposed to a local concentrated energy flow. If the glazing is submitted to thermal flows from radiating or air pulsating systems (high intensity spotlights, radiating heater, radiator, pulsed air convector), it is necessary: - either to use a high thermal shock resistance product (defined in 6.2) - or to make sure that the radiator is distant at least of 20 cm from the glass In this latter case, a verification of the temperature difference between: -
the zone of the glazing facing the radiator, and hit by the sun, a zone far from the radiator, shaded the glass edges in this shaded zone
The surface temperature of the radiator can be estimated as 70°C during the colder seasons. In summer, the radiator is to be considered as a static backup.
8 Climatic data 8.1 General
The temperature difference on the panes of insulating glazing depends on the external temperature, mainly because of the thermal coupling of the edge temperatures by the spacer. For a given orientation and slope of the glazing, the maximal incident solar flow and associated temperature conditions depend on the season. For these reasons the calculations will be performed in the four seasons : - Winter, cold temperature, higher solar flow on south façades - Spring, with high solar flow on South-East and South-West façades, supposed low temperatures - Summer, high temperatures, high solar flow on East and West façades - Autumn, with high solar flow on South-East and South-West façades, supposed warm temperatures 10
Page 11 CEN/TC129/WG8 - N199E
This satisfies the requirement of “all year round” verification towards thermal shock. Common sense considerations apply naturally to some cases: -
a radiator will be supposed turned off in summer and autumn Sliding sashes are not supposed to be completely open in winter
8.2 Temperatures
A given geographic site is characterized by: -
the maximum temperature in summer the minimum daily temperature in winter the maximal temperature amplitude on clear days.
These figures can be obtained from available meteorological data using the following rules. 8.2.1
Meteorological data
For a given location, the following data are generally available: -
Record maximum temperature Record minimum temperature Mean monthly maximum temperature Mean monthly minimum temperature
Rules : -
8.2.2
maximum temperature in summer Tmax,s= record maximum temperature less 2 ° minimum daily temperature in winter Tmin,w= record minimum temperature plus 5° maximal amplitude is obtained from the difference between mean maximum and mean minimum temperatures, plus 5°. Basic outdoor temperatures for each season
Basic values of outdoor temperatures are obtained as: -
Te,summer = Tmax,s Te,autumn = 2/3.Tmax.s + 1/3.Tmin,w + ½ Amplitude Te,winter = Tmin,w Te,spring = 1/3.Tmax,s + 2/3.Tmin,w
A more refined temperature analysis taking into account the façade orientation is given in Annex 3.
Page 12 CEN/TC129/WG8 - N199E 8.2.3
Indoor temperatures
The indoor temperature of building zones in exploitation is supposed constant and given in table 1 below. Table 1 – Indoor temperatures Vertical glazing Sloping glazing ( 60°) ( < 60°) Summer – air conditioned zone Ti = 25°C 30°C Summer – non air conditioned Ti = 25°C Ti = Tmax,s 35°C Other seasons Ti = 20°C Ti = 20°C Winter, no heating Ti = 5°C Ti = 5°C 8.3 Solar radiation intensity 8.3.1
General
The maximum solar radiation intensity, I , which may be incident on the glass can be calculated using any appropriate method which takes into account:
the latitude of the site, the orientation of the glazing, the slope of the glazing, the altitude of the site, the haze factor, the ground reflectance, and the time of year.
Detailed solar radiation data may be obtained for each European city from the website: re.jrc.ec.europa.eu/pvgis
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Page 13 CEN/TC129/WG8 - N199E
8.3.2
Maximal solar radiation on vertical glazing
Figure 1 - Maximal solar irradiation on vertical walls at sea level
(to be discussed) The above figure shows the maximum solar radiation intensity on vertical wall for Europe: - in regions with altitude 500 m - in the open land Corrections for urban situation and altitude are introduced according to the following table. Let Io be the solar radiation intensity at low altitude in the open land from the above map. Table 2 – Corrections for altitude and urban zones Altitude (m) Radiation intensity (W/m²) Rural zone Urban zone 0 - 500 Io Io-50 500 - 1000 Io + 50 Io > 1000 Io + 150 Io + 100 Note: provision shall be made for temporary or local increase of the solar radiation due to reflecting surfaces (snow, reflective glass roofing below a part of the building,etc…) 8.3.3
Sloping glazing
For sloping glazing, the above values are to be multiplied by a coefficient Ci, depending on the slope of the glazing to horizontal, and given by table…
Page 14 CEN/TC129/WG8 - N199E
Table 3 - Factors for maximal solar radiation on sloping glazing (Latitude 42 to 48°N) Slope Ci summer Ci winter
90° 1,00 1,00
75° 1,15 1,15
60° 1,20 1,15
45° 1,25 1,05
30° 1,25 0,95
15° 1,25 0,75
0° 1,20 0,50
Note: these coefficients depend on latitude 8.3.4
Diffuse and reflected radiation
The shaded zones of the glazing receive however the diffused and reflected parts of the solar radiation. These are estimated at 10% of the global incident radiation, without being less than 75 W/m².
9 Heat transfer coefficients 9.1 External heat transfer coefficient
The value of the external heat transfer coefficient, he, shall be obtained from table 4. Table 4 -. External heat transfer coefficient
Slope
90o (vertical) o 0 (horizontal)
External heat transfer coefficient, he (W/m².K) Winter, Summer, Spring Autumn 11 13 12 14
For slopes between vertical and horizontal, the external heat transfer coefficient can be estimated by linear interpolation. 9.2 Internal heat transfer coefficient
The value of the internal heat transfer coefficient, hi, shall be obtained from table 5. Table 5. Internal heat transfer coefficient
Slope o
90 (vertical) o 0 (horizontal)
Internal heat transfer coefficient, hi 2 8 W/m K 2 6,7 W/m K
For slopes between vertical and horizontal, the internal heat transfer coefficient can be estimated by linear interpolation.
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Page 15 CEN/TC129/WG8 - N199E 9.3 Cavity heat transfer coefficient
The value used for the cavity (gas space) heat transfer coefficient, h s, shall be calculated according to EN 673 for vertical glazing. Calculation of h s proceeds normally using the calculated values of the adjacent pane temperatures
Page 16 CEN/TC129/WG8 - N199E
10 Allowable temperature difference 10.1 Principle
The allowable temperature difference for a glass is obtained from the comparison between the thermal stress th resulting from a temperature difference on a glass, and the allowable thermal stress adm:
adm = k v.k a.vm th = k t.E.. < adm 10.2 Coefficient k t
The shadow coefficient, k t, represents the fact that the glazing is submitted or not to a cast shadow, together as the rebate inertia: if the rebate inertia is high, the peripheral zone of the glazing may remain cold on the four sides, increasing the thermal stress. The values of k t are given in the table 6.
With cast shadow Without cast shadow
Table 6 – Values of k t Low inertia, Medium inertia Structural sealant 0.90 1.00 0.80 0.95
10.3 Working stress of glass ,
High inertia 1.10 1.10
vm
The table 7 gives, as a function of the glass nature, the allowable working stress for glass in vertical position towards thermal stresses. Table 7 – Working stress vm Glass type Float or sheet glass Patterned glass Wired patterned glass or polished wired glass Heat strengthened glass (all types) Toughened glass (all types) Laminated glass
vm (MPa) 20 18 16 35 50 Smallest value of the component panes
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Page 17 CEN/TC129/WG8 - N199E 10.4 Coefficient k v
The coefficient k v represents the sensitivity of the glass to thermal shocks. It depends on the nature of the glass and on its transformation. It applies to monolithic and laminates, with edges worked as defined in XXX. Table 8 – Values of coefficient k v Sawed glass As cut or arrissed
Nature Monolithic glass 12 mm 15 or 19 mm 25 mm Symmetric laminate Non symmetric laminate Wired glass Patterned glass
-
0.75 0.70 -
1.00 0.85 0.75 1.00 0.75 0.80 1.00
Smooth ground or polished 1.20
1.20 1.00 1.00
10.5 Coefficient k a
The coefficient k a depends on the slope of the glazing and on its setting conditions. Stresses due to the self weight of the glass may develop at the edges and be added to the thermal stresses, and particularly if the glass is not settled on its whole periphery. Table 9 gives the values of the coefficient k a. Table 9 – Values of coefficient k a Angle with horizontal 60° > 30° 60° 1.00 0.90 0.90 0.8
Glazing settled on All sides Other cases
< 30° 0.80 0.70
10.6 Values of allowable temperature difference
The allowable temperature difference for a glass is given by :
adm =
kv.ka. vm kt . E .
Some typical cases for adm are given below. Example : For a vertical glass 12 mm settled on 4 sides, as cut, in aluminium rebate
adm =
1 * 1 * 20
0.9 * 70000 * 0.9e 6 (To be completed)
= 35°
Page 18 CEN/TC129/WG8 - N199E
11 Temperature difference calculations 11.1 General process a) Calculate the maximal temperatures of the sunlit panes tot
T1
T2
If there is presence of movable blind, backup, radiator, etc… the temperatures are calculated with it. b) Calculate the temperatures of the shaded panes
dif T10
T20
If there is presence of movable blind, backup, radiator, etc… the temperatures are calculated without it. c) Take into account the cold bridge effect The cold bridge effect due to the metallic spacer has to be taken into account. The temperatures of the two pane edges in rebate are equalized to a value To.
dif
T10
T20
T0 For glass panes in a metallic rebate: T0 #
T0
T10 T 20 2
d) Select the worst case of temperature difference for each pane
Tb1 = Max{(T1 – T10), (T1-T0)} = (T1-T10) + Max{T10-T0, 0} Tb2 = Max{(T2 – T20), (T2-T0)} = (T2-T20) + Max {T20-T0, 0)
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Page 19 CEN/TC129/WG8 - N199E 11.2 Example of a double glazing without blind or backup
a) Temperatures in the sunlit part T1 =
hs.(hi.Ti I . e2) (hi hs).(he.Te I . e1) (hi.he hi.hs he.hs)
T2 =
hs.(he.Te I . e1) ( he hs).(hi.Ti I . e2) ( hi.he hi.hs he.hs)
b) Temperatures of the shaded part T10 =
hs.(hi.Ti 0.1 I . e2) ( hi hs).(he.Te 0.1 I . e1) (hi.he hi.hs he.hs)
T20 =
hs.(he.Te 0.1 I . e1) (he hs).(hi.Ti 0.1 I . e2) ( hi.he hi.hs he.hs)
c) Cold bridge effect T0 =
hi.he.(Ti Te) 2hs.(hi.Ti he.Te) 0.1 I .( 1.(hi 2hs) 2.(he 2hs)) 2(hi.he hi.hs he.hs)
The temperature differences may be expressed in a simpler form as : Outer pane:
I e1 hi h s I e 2 ha he hi he h s hi h s
T b;1 T 1 T 10 0.9
(2)
Inner pane:
I e 2 he h s he hi he h s hi h s
I e1h s
T b;2 T 2 T 20 0.9
(3)
Cold bridge effect T10-T0 = T20-T0 =
(Te Ti )[ he.hi ] 2(he.hs hi.hs he.hi) (Ti Te)[ he.hi ] 2(he.hs hi.hs he.hi)
>0 if Te>Ti
(summer)
>0 if Ti>Te
(winter)
. d) Worst case : Tb1 = Max{(T1 – T10), (T1-T0)} = (T1-T10) + Max{T10-T0, 0} Tb2 = Max{(T2 – T20), (T2-T0)} = (T2-T20) + Max {T20-T0, 0)
Page 20 CEN/TC129/WG8 - N199E 11.3 General equations
For any case, the temperatures in the components of a glazing can be obtained by solving a system of equations, for both situations (sunlit and shaded part of the glazing), following the principles described in chapter 11.1. The components considered may be a glass pane, a blind, a backup, a gas layer ventilated or not. The corresponding systems of equations are given in Annex 5. Other cases may be easily derived from those given.
11.4 Influence of rebate inertia
For medium and high inertia framing, the effect of increased inertia is taken into account by increasing the temperature differences of each pane, depending on the season, with a temperature difference Tri calculated as :
Tri = 0.05.kri.Amp Where : Amp the maximal daily temperature amplitude defined in 8.2.2 kri coefficient defined in table xx below (kri is the increase in temperature difference for a daily amplitude of 20°) Season
Winter Spring Summer Autumn
Coefficient kri increase in temperature difference due to rebate inertia Medium High 4 5 2.5 3 0.5 1 1.5 2
This addition occurs after all the operations described in chapter 11.1. 11.5 Internal temperature rise
The room temperature usually does not vary sufficiently to affect the temperature difference of the glass. However, there may be factors (e.g. air heaters blowing air past the glass, heat build up under an unventilated glazed roof), where the temperature of room air in the vicinity of the glass changes rapidly or by a large amount. The effect of this can be evaluated by including an internal temperature rise, T i, which is the difference between the heated air and o the average ambient temperature of the room (usually taken as 21 C). Where there is no obvious heating of the air near the glass, the internal temperature rise shall be taken as 0 K.
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Page 21 CEN/TC129/WG8 - N199E List of Annexes Annex 1 – Treatment of glass edges to improve the resistance to thermal shocks Annex 2 – Characteristics of current backups Annex 3 – Outdoors temperatures in function of façade orientation Annex 4 – Tables for solar irradiation Annex 5 – General equations Annex 6 – Calculation of coefficient kx – heat transfer through air exchange Annex 7 – Special cases of calculation: Sliding sashes…
Page 22 CEN/TC129/WG8 - N199E
Annex 5
A5 General equations In order to face any situation – triple glazing with blind, ventilated glazing, backup, etc…the following equations are given. They represent the thermal equilibrium of each component in the glazing. Each component is represented by a node, even the air spaces because they may be ventilated. A5.1 Glass pane in a glazing
1
3
2
5
4
Pane 1 Pane 3 Pane 5
he.(e-1)+ hr13.(3-1)+hc2(2-1) + e1.I = 0 hr13.(1-3)+ hr35.(5-3)+hc2.( 2-3)+hc4.(4-3)+ e3.I =0 hi.(i-5)+ hr35.(3-5)+hc4(4-5) + e5.I = 0
Space 2 Space 4
hc2.( 1-2)+hc2.(3-2) = 0 hc4.( 3-4)+hc4.(5-4) = 0
A5.2 Blind behind a glazing
1
3
2
5
4
Blind 5
he.(e-1)+ hr13.(3-1)+hc2(2-1) + e1.I = 0 hr13.(1-3)+ hr35.(1- ).(5-3)+hc2.( 2-3)+hc4.(4-3)+ e3.I +hr35. .( 5- i) =0 hi.(i-5)+ hr35.(3-5)+hc4(4-5) + e5.I = 0
Space 2 Space 4
hc2.( 1-2)+hc2.(3-2) = 0 hc4.( 3-4)+hc4.(5-4) + hx.(i-4) = 0
Pane 1 Pane 3
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Page 23 CEN/TC129/WG8 - N199E is the air porosity of the blind (openness factor) hx is the heat transfer coefficient by air exchange between interior and space 4.
(Calculation of hx is detailed in Annex 6) A5.3 Blind inside a glazing
1
3
2
5
4
Pane 1 Blind 3 Pane 5
he.(e-1)+ hr13.(1- ).(3-1)+ .hr15. (5-1)+hc2(2-1) + e1.I = 0 hr13.(1- ).(1-3)+ hr35.(1- ).(5-3)+hc2.( 2-3)+hc4.(4-3)+ e3.I =0 hi.(i-5)+ hr35.(1-).(3-5)+ .hr15.(1-5)+ hc4(4-5) + e5.I = 0
Space 2 Space 4
hc2.( 1-2)+hc2.(3-2) + hx.(4-2) = 0 hc4.( 3-4)+hc4.(5-4) + hx.(2-4) = 0
A5.4 Backup behind a glazing
1
3
2
6
5
4 R
hx Pane 1 Pane 3 Backup 5 Backup 6
he.(e-1)+ hr13.(3-1)+hc2(2-1) + e1.I = 0 hr13.(1-3)+ hr35.(5-3)+hc2.( 2-3)+hc4.(4-3)+ e3.I =0 1/R.(6-5)+ hr35.(3-5)+hc4(4-5) + e5.I = 0 1/R.(5-6) + hi.(i-6) = 0
Space 2 Space 4
hc2.( 1-2)+hc2.(3-2) = 0 hc4.( 3-4)+hc4.(5-4) + hx.(i-4)= 0
Page 24 CEN/TC129/WG8 - N199E
A5.5 Glazing ventilated from outside
1
3
2
5
4
Pane 1 Pane 3 Pane 5
he.(e-1)+ hr13.(3-1)+hc2(2-1) + e1.I = 0 hr13.(1-3)+ hr35.(5-3)+hc2.( 2-3)+hc4.(4-3)+ e3.I =0 hi.(i-5)+ hr35.(3-5)+hc4(4-5) + e5.I = 0
Space 2 Space 4
hc2.( 1-2)+hc2.(3-2) + hx.(i-2) = 0 hc4.( 3-4)+hc4.(5-4) = 0
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Page 25 CEN/TC129/WG8 - N199E
A.6 Evaluation of factor K x
The factor of heat transfer through air flow K depends on the dimensions of the glazing, of peripheral gaps , on the air permeability of the blind, and on the temperature difference between the two air layers separated by the blind. x
A.6.1 General case
Let b, h the width and the height of the glazing, d , d et d the width of respectively lower, lateral and high peripheral gaps, and the porosity of the blind. 1
2
3
Let (1) represent the zone between blind and glazing, and (2) the connected ambiance.
Figure 1.1 — Ventilated blind - Notations
Between the two zones separated by the blind, respectively at absolute temperatures T et T (k), a pressure difference builds itself due to the difference in specific air weigth between the two ambiances. It depends linearly on the height z: p(z) 1 (z) - 2 (z) 0 - 1 - 2 . g . z (Pa) 1
2
1 0 . T0 T 1 2 0 . T0 T 2
0 1,293 (kg/m3)
T0 273 (K)
If T > T , so > , let = ( - ) 1
2
2
1
2
1
T 0 T0 Tl - Tl 0 T 0T 1 2 2 1 In this case, the air enters zone 1 through the lower part, and exits in the higher part as figured on the sketch. The elementary air flow dQ entering through a hole of section dS located at the height z may be calculated as:
dQ 0,85 dS
(z)
Let z be the height of neutral axis ((zn) = 0). Setting :x = z /h n
n
3
(m /s)
