BS EN 13381-3:2015 BSI Standards Publication Test methods for determining the contribution to the fire resistance of structural members Part 3: Applied protection to concrete members BS EN 13381-3:2015 BRITISH STANDARD National foreword This British Standard is the UK implementation of EN 13381-3:2015 It supersedes DD ENV 13381-3:2002 which is withdrawn The UK participation in its preparation was entrusted to Technical Committee FSH/22/-/12, Fire resistance tests For Protection Systems A list of organizations represented on this committee can be obtained on request to its secretary This publication does not purport to include all the necessary provisions of a contract Users are responsible for its correct application © The British Standards Institution 2015 Published by BSI Standards Limited 2015 ISBN 978 580 78055 ICS 13.220.50; 91.060.01; 91.080.40 Compliance with a British Standard cannot confer immunity from legal obligations This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 April 2015 Amendments issued since publication Date Text affected BS EN 13381-3:2015 EN 13381-3 EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM April 2015 ICS 13.220.50; 91.080.40 Supersedes ENV 13381-3:2002 English Version Test methods for determining the contribution to the fire resistance of structural members - Part 3: Applied protection to concrete members Méthodes d'essai pour déterminer la contribution la résistance au feu des éléments de construction - Partie 3: Protection appliquée aux éléments en béton Prüfverfahren zur Bestimmung des Beitrages zum Feuerwiderstand von tragenden Bauteilen - Teil 3: Brandschutzmaßnahmen für Betonbauteile This European Standard was approved by CEN on November 2014 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 CEN-CENELEC 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 CEN-CENELEC Management Centre has the same status as the official versions CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom EUROPEAN COMMITTEE FOR STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels © 2015 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members Ref No EN 13381-3:2015 E BS EN 13381-3:2015 EN 13381-3:2015 (E) Contents Page Foreword Scope Normative references 3.1 3.2 Terms and definitions, symbols and units Terms and definitions Symbols and units 4.1 4.2 4.3 Test equipment 10 General 10 Furnace 10 Loading equipment 10 5.1 5.2 5.2.1 5.2.2 5.3 Test conditions 10 General 10 Support and restraint conditions 11 Standard support and restraint conditions 11 Other support and restraint conditions 11 Loading conditions 11 6.1 6.1.1 6.1.2 6.2 6.2.1 6.2.2 6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5 6.4 6.4.1 6.4.2 6.4.3 6.5 6.5.1 6.5.2 6.5.3 6.5.4 6.6 Test specimens 12 Type and number of test specimens 12 Type of test specimens 12 Number of test specimens 12 Size of test specimens 13 Concrete slabs 13 Concrete beams 13 Construction of concrete test specimens 14 Concrete slab test members 14 Concrete beam test members 14 Fabrication of concrete test members 14 Application of fire protection material (except ceiling) to concrete test member 15 Installation of a ceiling below the concrete slab 15 Composition of test specimen component materials 16 Concrete 16 Steel reinforcement 16 Fire protection system 16 Properties of test materials 16 General 16 Concrete 16 Steel reinforcement 17 Fire protection materials 17 Verification of the test specimen 17 7.1 7.2 7.3 Installation of the test construction 18 Concrete large slab test specimens 18 Concrete small slab test specimens 18 Concrete beam test specimens 18 Conditioning 18 BS EN 13381-3:2015 EN 13381-3:2015 (E) 9.1 9.2 9.2.1 9.2.2 9.3 9.3.1 9.3.2 9.3.3 9.3.4 9.4 9.5 9.6 Application of instrumentation 19 General 19 Instrumentation for measurement of furnace temperature 19 Slab specimens 19 Beam specimens 19 Instrumentation for the measurement of test specimen temperature 19 General 19 Large and small concrete slab test specimens 20 Beams 20 Equivalent locations as referred to in 11.2 are: 21 Instrumentation for the measurement of pressure 22 Instrumentation for the measurement of deformation 22 Instrumentation for the measurement of applied load 22 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 Test procedure 22 General 22 Furnace temperature and pressure 22 Application and control of load 22 Temperature of test specimen 23 Deformation 23 Observations 23 Termination of test 23 11 11.1 11.2 Test results 23 Acceptability of test results 23 Presentation of test results 24 12 Test report 25 13 13.1 13.2 13.3 13.4 13.5 13.6 Assessment 25 General 25 Concrete slabs 26 Concrete beams 26 Insulation 27 Stickability 27 Equivalent thickness of concrete 27 14 Report of the assessment 27 15 Limits of applicability of the results of the assessment 28 16 Additional limits of applicability of the results of the assessment for suspended ceilings used as protection system 30 Height of the cavity 30 Exposed width of test specimen 30 Properties of the horizontal protective membrane 30 Size of panels within the horizontal protective membrane 30 Fixtures and fittings 30 Gaps between grid members and test frame or walls 31 16.1 16.2 16.3 16.4 16.5 16.6 Annex A (normative) Test method to the smouldering fire or slow heating curve 44 A.1 Introduction 44 A.2 Evaluation of the results 44 Annex B (normative) Measurement of properties of fire protection materials 46 B.1 General 46 B.2 Thickness of fire protection materials 46 B.3 Density of applied fire protection materials 47 BS EN 13381-3:2015 EN 13381-3:2015 (E) B.3.1 General 47 B.4 Moisture content of applied fire protection materials 48 Annex C (normative) Equivalent thickness of concrete 49 C.1 General 49 C.1.1 General 49 C.1.2 Equivalent thickness of concrete slabs - preliminary data collection 49 C.1.3 Equivalent thickness of concrete beams - preliminary data collection 49 C.2 Equivalent thickness of concrete slabs and beams - assessment methodology 50 Annex D (normative) Calculation of stresses in standard concrete structures 58 D.1 General 58 D.2 Relevant concrete structures 58 D.3 Distribution of stresses across the section of the concrete structures 58 D.4 Mechanical study 59 D.4.1 Equilibrium of external forces 59 D.4.2 Determination of the position of the neutral axis (x) 59 D.4.3 Determination of the quadratic modulus 60 D.4.4 Determination of stresses in reinforcement bars and concrete 60 Annex E (informative) Calculation of the load to apply on concrete member 63 E.1 Remind and scheme 63 E.2 Calculation of the force of the spring for a loaded beam 63 E.3 Calculation of the force of the spring for a loaded large slab 64 Bibliography 66 BS EN 13381-3:2015 EN 13381-3:2015 (E) Foreword This document (EN 13381-3:2015) has been prepared by Technical Committee CEN/TC 127 “Fire safety in buildings”, the secretariat of which is held by BSI 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 October 2015 and conflicting national standards shall be withdrawn at the latest by October 2015 Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights This document supersedes ENV 13381-3:2002 This document has been prepared under a mandate given to CEN by the European Commission and the European Free Trade Association, and supports essential requirements of 89/106/EEC The dimension tolerances regarding the manufacturing of the specimen indicated in the ENV 13381-3:2002 led to tensile stress values of 290 +/- 30 N/mm² in the reinforcement bars depending on the type of structural member In order to harmonize the mechanical constraint applied on the structural member, the bending moment has been modified to produce the same tensile stress on reinforcement bars equal to 300 N/mm² This value is corresponding to 60 % of the grade of the steel to be used Due to this approach, the result of tests carried out according to ENV 13381-3:2002 can be taken into account for assessment according to the present document In comparison with ENV 13381-3:2002, the following significant changes have been made: — the bending moment has been modified to be adapted to the thickness of the slab; — the location of thermocouple used within beams for the calculation of equivalent thickness of concrete is now at 25 mm away from the beam bottom corner instead of 55 mm; — the graphs to be used for the determination of equivalent concrete thickness for slabs has been improved and extended and is directly available in the standard This European Standard is one of a series of standards for evaluating the contribution to the fire resistance of structural members by applied fire protection materials The other parts of this standard are: — Part 1: Horizontal protective membranes — Part 2: Vertical protective membranes — Part 4: Applied protection to steel members — Part 5: Applied protection to concrete/profiled sheet steel composite members — Part 6: Applied protection to concrete filled hollow steel columns — Part 7: Applied protection to timber members — Part 8: Applied reactive protection to steel members Annexes A, B and C are normative BS EN 13381-3:2015 EN 13381-3:2015 (E) Caution: The attention of all persons concerned with managing and carrying out this fire resistance test is drawn to the fact that fire testing can be hazardous and that there is a possibility that toxic and/or harmful smoke and gases can be evolved during the test Mechanical and operational hazards can also arise during the construction of test elements or structures, their testing and the disposal of test residues An assessment of all potential hazards and risks to health should be made and safety precautions should be identified and provided Written safety instructions should be issued Appropriate training should be given to relevant personnel Laboratory personnel should ensure that they follow written safety instructions at all times The specific health and safety instructions contained within this standard should be followed According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom BS EN 13381-3:2015 EN 13381-3:2015 (E) Scope This European Standard specifies a test method for determining the contribution of fire protection systems to the fire resistance of structural concrete members, for instance slabs, floors, roofs and walls and which can include integral beams and columns The concrete can be lightweight, normal weight or heavyweight concrete and of all strength classes (e.g 20/25 to 50/60 for normal strength concrete and for high strength concrete 55/67 to 90/105) The member is to contain steel reinforcing bars The test method is applicable to all fire protection materials used for the protection of concrete members and includes sprayed materials, reactive coatings, cladding protection systems and multi-layer or composite fire protection materials, with or without a gap between the fire protection material and the concrete member This European Standard specifies the tests which are to be carried out to determine the ability of the fire protection material to remain coherent and fixed to the concrete and to provide data on the temperature distribution throughout the protected concrete member, when exposed to the standard temperature time curve In special circumstances, where specified in national building regulations, there can be a need to subject the protection material to a smouldering curve The test for this and the special circumstances for its use are detailed in Annex A The fire test methodology makes provision for the collection and presentation of data which can be used as direct input to the calculation of fire resistance of concrete members in accordance with the procedures given in EN 1992-1-2 This European Standard also contains the assessment which prescribes how the analysis of the test data is to be made and gives guidance to the procedures by which interpolation is to be undertaken The limits of applicability of the results of the assessment arising from the fire test are defined together with permitted direct application of the results to different concrete structures, densities, strengths, thicknesses and production techniques over the range of thicknesses of the applied fire protection system tested The test method, the test results and the assessment method are not applicable to structural hollow concrete members Normative references The following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application For dated references, only the edition cited applies For undated references, the latest edition of the referenced document (including any amendments) applies EN 206, Concrete - Specification, performance, production and conformity EN 823, Thermal insulating products for building applications - Determination of thickness EN 1363-1, Fire resistance tests - Part 1: General Requirements EN 1363-2, Fire resistance tests - Part 2: Alternative and additional procedures EN 1992-1-1, Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings EN 1992-1-2, Eurocode 2: Design of concrete structures - Part 1-2: General rules - Structural fire design EN 10080, Steel for the reinforcement of concrete - Weldable reinforcing steel - General BS EN 13381-3:2015 EN 13381-3:2015 (E) EN 12467, Fibre-cement flat sheets - Product specification and test methods EN ISO 13943, Fire safety - Vocabulary (ISO 13943) ISO 8421-2, Fire protection - Vocabulary - Part 2: Structural fire protection Terms and definitions, symbols and units 3.1 Terms and definitions For the purposes of this document, the terms and definitions given in EN 1363-1, EN ISO 13943, ISO 8421-2 and EN 206 and the following apply 3.1.1 concrete member element of building construction which is loadbearing and is fabricated from concrete, defined according to EN 206 and shall contain steel reinforcing bars 3.1.2 fire protection material material or combination of materials applied to the surface of a concrete member for the purpose of increasing its fire resistance 3.1.3 passive fire protection materials materials which not change their physical form upon heating and which provide fire protection by virtue of their physical or thermal properties and may include materials containing water which, on heating, evaporates to produce cooling effects 3.1.4 reactive fire protection materials materials which are specifically formulated to provide a chemical reaction upon heating such that their physical form changes and in so doing provide fire protection by thermal insulation and cooling effects 3.1.5 fire protection system fire protection material together with a prescribed method of attachment to the concrete member 3.1.6 fire protection protection afforded to the concrete member by the fire protection system such that the temperature throughout the depth of the structural member and upon any steel reinforcing bars within it is limited throughout the period of exposure to fire 3.1.7 test specimen concrete slab or beam test member plus the fire protection system under test 3.1.8 fire protection thickness thickness of a single layer fire protection system or the combined thickness of all layers of a multilayer fire protection system, excluding the width or height of supporting profiles, clips and other fixings BS EN 13381-3:2015 EN 13381-3:2015 (E) Key A temperature within concrete B equivalent thickness of concrete Figure C.7 — Temperatures inside concrete versus equivalent thickness for beam Table C.2 — Temperature at location with additional equivalent thickness of concrete Exposure duration Additional equivalent thickness of concrete (mm) (min) 20 40 60 80 100 120 140 160 180 200 30 464 233 120 63 35 25 21 20 20 20 20 60 691 444 272 166 107 68 43 31 25 22 21 90 818 588 399 267 179 123 86 59 41 31 25 120 904 695 503 356 251 177 128 94 68 48 36 180 1015 847 664 506 380 286 214 162 124 96 73 240 1087 952 784 625 491 382 298 232 181 143 114 NOTE The column headed in the Additional Equivalent thickness part of the table refers to location in Figure with zero protection Other columns represents the temperature at location with additional concrete protection This enables the equivalent concrete protection provided by the actual protection material to be established C.2.2 For a given thickness of fire protection, inclusion of measured data for characteristic temperature θ(dcp, t) obtained at a specific concrete thickness dcp, into selected curves from Figure C.5 (slab) as shown in Figure C.8 (slab) permits the determination by interpolation of the depth dcc in an unprotected concrete slab at which that same temperature θ(dcp, t) would be found 54 BS EN 13381-3:2015 EN 13381-3:2015 (E) Key X time (min) X concrete depth dcc (mm) Y characteristic temperature inside concrete slab at 15 mm o deep ( C) Y temperature inside concrete slab ( C) Characteristic temperature recorded at 15 mm deep inside a concrete slab protected by x mm of a protective material,at 120 of a fire test o Temperature evolution inside an unprotected concrete slab at 120 exposure under EN 1363-1 Figure C.8 — Characteristic temperature versus depth for slab The equivalent thickness of concrete ε, corresponding to x mm of protective material applied under a concrete slab and after 120 mm under EN 1363-1 thermal program, is given by: ε = [dcc (unprotected) - dcp (protected)] i.e in the example ε(x, 120min) = [56 – 15] = 41 mm C.2.3 For a given thickness of fire protection, inclusion of measured data for characteristic temperature θ(dcp, t) obtained at a specific concrete thickness dcp, into selected curves from Figure C.7 (beam) as shown in Figure C.9 (beam) permits the determination by interpolation of the depth dcc in an unprotected concrete beam at which that same temperature θ(dcp, t) would be found 55 BS EN 13381-3:2015 EN 13381-3:2015 (E) Key Key X time (min) X equivalent thickness of concrete (mm) Y characteristic temperature inside concrete beam at o [25,25] mm deep ( C) Y temperature inside concrete beam ( C) Characteristic temperature recorded at [25,25] mm deep inside a concrete beam 150 mm x 450 mm protected by x mm of a protective material o Temperature evolution recorded at [25,25] mm deep inside a concrete beam 150 mm x 450 mm protected by x mm of concrete at 30 min, 60 and 90 exposure under EN 1363-1 Figure C.9 — Characteristic temperatures versus equivalent thickness of concrete for beam The equivalent thicknesses of concrete, corresponding to x mm of protective material applied on a concrete beam at 30, 60 and 90 minutes under EN 1363-1 thermal program, are given by the X value corresponding to the temperature and duration, i.e in the example: — at 30 ε(x, 30min) = 42 mm — at 60 ε(x, 60min) = 50 mm — at 90 ε(x, 90min) = 46 mm 56 BS EN 13381-3:2015 EN 13381-3:2015 (E) C.2.4 The values of equivalent concrete thickness ε can be plotted for each thickness of fire protection tested permitting interpolation of the result as a function of fire duration according to Figure C.10 Key thicknesses tested [t = 120 minutes] 2 thicknesses (max/min) tested [t = 120 minutes] thicknesses (max/min) tested [t = 90 minutes] ε = equivalent thickness (mm) dp = fire protection thickness (mm) Figure C.10 — Equivalent thickness versus fire protection thickness for different exposure times (slab or beam) 57 BS EN 13381-3:2015 EN 13381-3:2015 (E) Annex D (normative) Calculation of stresses in standard concrete structures D.1 General Minimal dimensions for standard concrete structures to be used for assessment of a protective material are indicated in 6.2 as well as their construction details in 6.3 Dimensional tolerances are accepted for each type of standard structure Consequently, the loading conditions shall be defined according to actual dimensions of standard structure on which the protective material to assess is applied The relevant procedure to achieve such adequate loading conditions is described hereafter D.2 Relevant concrete structures The procedure is dealing with: — large and small dimensions slabs; — rectangular beams D.3 Distribution of stresses across the section of the concrete structures The distribution of stresses across the section of a rectangular section can be presented as follows: Key neutral axis NOTE Parameters of this figure are defined in D.4.1 and D.4.2 Figure D.1 — Distribution of stresses across the section of the concrete structures 58 BS EN 13381-3:2015 EN 13381-3:2015 (E) D.4 Mechanical study D.4.1 Equilibrium of external forces The equilibrium of external forces developed on a rectangular cross section and due to bending can be expressed as follows : Fb + Fsc − Fst = (D.1) ( ) ' ∑ M tensilesteel = M − Fb × Z − Fsc × d − d = (D.2) where Fst, Fsc forces in reinforcement bars respectively in tensile and compressed parts (N); Fb force in compressed concrete (N); M bending moment (N.m) Fb = b x (D.3) σ bc Fst = Ast s st (D.4) σ = and ε = (D.5) D.4.2 Determination of the position of the neutral axis (x) The position of the neutral axis (x) where σ and ε are equal to can be determined by solving Formula (D.8), on the basis of Formulae (D.6) and (D.7) : x Fb + Fsc − Fst = b × × s bc + Asc × sc − Ast × st s n bc x = (d − x ) = st =0 (D.6) sc n x−d' ( ) (D.7) i.e : b × x2 + n × Asc × x − d ' − n × Ast × (d − x ) = ( ) (D.8) where b width of the section (m); x position of the neutral axis (m); d position of the reinforcement bars in the tensile part of the concrete section (m); ’ d position of the reinforcement bars in the compressed part of the concrete section (m); 59 BS EN 13381-3:2015 EN 13381-3:2015 (E) Ast total steel section of the reinforcement bars in the tensile part of the concrete section (m²); Asc total steel section of the reinforcement bars in the compressed part of the concrete section (m²); s st s sc stress in the reinforcement bars in the tensile part (N/m²); stress in the reinforcement bars in the compressed part (N/m²); σ bc stress in the concrete in the compressed part (N/m²); n ratio between Young modulus of steel for reinforcement bars and Young modulus of concrete for class C considered For a class C25/30 concrete, coefficient n= Esteel 210.000 = = 6.325 Econcrete 33.200 D.4.3 Determination of the quadratic modulus The quadratic modulus of the cross section is equal to : I = I b + I st + I sc (D.9) where Compressed concrete Tensile reinforcement bars Compressed reinforcement bars = Ib b × x3 b × x3 x + b× x × = 12 2 I st = mstbars × π × Dst I sc = mscbars × 64 π × Dsc 64 + n × Ast × (d − x ) ≈ n × Ast × (d − x ) ( + n × Asc × x − d ' ) ( ≈ n × Asc × x − d ' ) where Dst is the diameter of the rebar located in tensile part of the concrete section (m); Dsc is the diameter of the rebar located in compressed part of the concrete section (m); i.e : I= b × x3 + n × Ast × (d − x ) + n × Asc × x − d ' (m4) ( ) (D.10) D.4.4 Determination of stresses in reinforcement bars and concrete The stress at any position (y) varying along the vertical cross section of the concrete structure can be expressed according to general Formula (D.11): σ (y) = 60 M ×y I (D.11) BS EN 13381-3:2015 EN 13381-3:2015 (E) For standard concrete structures, Formula (D.11) leads to following values in reinforcement bars and concrete : • In tensile reinforcement bars s st = nì ã In compressed reinforcement bars ã In compressed concrete s sb = s sc M × (d − x ) I (N/m²) = n× M × x −d' I (N/m²) ( ) M ×x I (N/m²) (D.12) (D.13) (D.14) The following tables indicate the bending moment to be produced within slabs and beams prepared with C25/30 strength class concrete and steel reinforcement bars which are ribbed and are of grade B500 (to EN 10080) Table D.1 — Bending moment to apply on large dimensions concrete test slabs Slab thickness Bending moment corresponding to a tensile stress of 300 MPa in the reinforcement bars 120 mm 14 250 Nm/m width 130 mm 16 000 Nm/m width 140 mm 17 750 Nm/m width 150 mm 19 500 Nm/m width Table D.2 — Bending moment to apply on small dimensions concrete test slabs Slab thickness Bending moment corresponding to a tensile stress of 300 MPa in the reinforcement bars 120 mm 500 Nm/m width 130 mm 10 500 Nm/m width 140 mm 11 500 Nm/m width 150 mm 12 500 width 61 BS EN 13381-3:2015 EN 13381-3:2015 (E) Table D.3 — Bending moment to apply on concrete test beams Bending moment corresponding to a tensile stress of 300 MPa in the reinforcement bars Width of concrete beam Height of concrete beam 140 mm 150 mm 160 mm 440 mm 28 000 Nm 28 000 Nm 28 250 Nm 450 mm 28 750 Nm 28 750 Nm 28 750 Nm 460 mm 29 500 Nm 29 500 Nm 29 250 Nm The moment to apply on test structures designed with relevant dimensions between the values indicated in Tables D.1 to D.3 shall be linear interpolated 62 BS EN 13381-3:2015 EN 13381-3:2015 (E) Annex E (informative) Calculation of the load to apply on concrete member E.1 Remind and scheme Key P is the applied load on each of the two points of the beam (N) q is the dead weight per running meter of the beam (N/m) RA and RB are reactive forces at the beam supports (N) Here RA = RB = R L is the span (distance between the supports) (m) a is the distance between the support and the point of application of the force P (m) Maximal bending moment (N.m): Mo= P.a +q L Figure E.1 — Localization of forces E.2 Calculation of the force of the spring for a loaded beam Maximal bending moment Mo= P.a +q L where The force P is applied at each of both loading points of the beam P = (Force of the spring + weight of the articulation piece + weight of the repartition beam) / The mass per running meter q shall take into account the dead weight of the beam, the dead weight of its cover in cellular concrete and the dead weight of the protective system 63 BS EN 13381-3:2015 EN 13381-3:2015 (E) q= r concrete hbeam lbeam g + r aeratedconcrete eslab lslab g + r protection e protection cbeam g where h height (m); l width (m); ρ density (kg/m ); e thickness (m); g acceleration (9,81 m/s²); c perimeter of the beam where the product is applied EXAMPLE will be: When the standard requires to generate a bending moment of M=25kN.m, for a standard beam the result q= 2350 0,45 0,15 9,81+650.0 ,125.0,6.9,81+~0 L= 4,9 m a= 1,1 m Mass of the articulation = 14 kg Linear Mass of the repartition beam= 83,2 kg/ml Length of the repartition beam = 3,1 m Example of resulting force if the protection product mass is neglected (e.g intumescent paint) F= 31686 N E.3 Calculation of the force of the spring for a loaded large slab Maximal bending moment Mo= P.a +q L where The force P is applied at each of both loading of the beam P = (Force of the spring + weight of the articulation piece + weight of the repartition beam + times the weight of the transverse beam) / The linear mass q shall take into account the dead weight of the slab and the dead weight of the protective system 64 BS EN 13381-3:2015 EN 13381-3:2015 (E) q = r concrete hslab lslab g + r protection e protection lslab g where h height (m); l width (m); ρ density (kg/m ); e thickness (m); g acceleration (9,81 m/s²) EXAMPLE When the standard requires to generate a bending moment of M=14 kN.m/m of width For m width of a standard slab: q= 2350 0,14 9,81+ ~0 and P = (Force of the spring + weight of the articulation piece + weight of the repartition beam + times the weight of the transverse beam) / L= 4,9 m a= m Mass of the articulation = 14 kg Linear Mass of the repartition beam= 83,2 kg/ml Length of the repartition beam = 3,1 m Linear Mass of one transverse beam = 26,7 kg/ml Length of the transverse beam = 2,9 m Example of resulting force if the protection product mass is neglected (e.g intumescent paint) F= 21695 N 65 BS EN 13381-3:2015 EN 13381-3:2015 (E) Bibliography EN 13381-1, Test methods for determining the contribution to the fire resistance of structural members – Part 1: Horizontal protective membranes EN 13381-2, Test methods for determining the contribution to the fire resistance of structural members – Part 2: Vertical protective membranes 66 This page deliberately left blank NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAW British Standards Institution (BSI) BSI is the national body responsible for preparing British Standards and other standards-related publications, information and services BSI is incorporated by 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