# BS EN 14358-2016

BS EN 14358:2016 Timber structures — Calculation and verification of characteristic values BSI Standards Publication WB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06BS EN 14358:2016 BRITISH STANDARD National foreword This British Standard is the UK implementation of EN 14358:2016. It supersedes BS EN 14358:2006 which is withdrawn. The UK participation in its preparation was entrusted to Technical Committee B/518, Structural timber. 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 2016. Published by BSI Standards Limited 2016 ISBN 978 0 580 83527 8 ICS 79.040; 91.080.20 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 June 2016. Amendments/corrigenda issued since publication Date T e x t a f f e c t e dBS EN 14358:2016EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM EN 14358 June 2016 ICS 79.040; 91.080.20 Supersedes EN 14358:2006 English Version Timber structures - Calculation and verification of characteristic values Structures en bois - Détermination et vérification des valeurs caractéristiques Holzbauwerke - Berechnung und Kontrolle charakteristischer Werte This European Standard was approved by CEN on 23 January 2016. 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 © 2016 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN 14358:2016 EBS EN 14358:2016 EN 14358:2016 (E) 2 Contents Page European foreword . 3 1 Scope 4 2 Symbols . 4 3 Calculation of characteristic properties from test results in the frame of initial type testing 5 3.1 General 5 3.2 Calculation of 5 and 95 percentiles values. 5 3.2.1 General 5 3.2.2 Parametric calculation 5 3.2.3 Non parametric calculation . 7 3.3 Calculation of characteristic mean values . 7 4 Calculation of characteristic properties from test results in the frame of internal factory production control 9 4.1 General 9 4.2 Calculation of characteristic strength, density or resistance properties (5- percentile) . 9 4.3 Calculation of characteristic stiffness properties (mean values) . 11 5 Acceptance procedure for verification of a lot 12 5.1 General . 12 5.2 Verification of mean values (e.g. mean modulus of elasticity) 12 5.2.1 Method keeping the consumer’s risk at 10 % 12 5.2.2 Alternative method limiting the sample size for large COVs 13 5.3 Verification of 5-percentile values (e.g. characteristic strength) . 13 5.3.1 Method with consumer s risk equal to 10 % 13 5.3.2 Alternative method limiting the sample size for large COVs 14 Bibliography . 15 BS EN 14358:2016 EN 14358:2016 (E) 3 European foreword This document (EN 14358:2016) has been prepared by Technical Committee CEN/TC 124 “Timber structures”, the secretariat of which is held by AFNOR. 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 December 2016, and conflicting national standards shall be withdrawn at the latest by December 2016. 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 EN 14358:2006. This document is based on Annex D of EN 1990:2002, Eurocode – Basis of structural design. Compared to EN 14358:2006, the following modifications have been made: — integration of normal distributions, and non parametric estimation; — proposals for simplified equations to evaluate correction factors; — estimation of mean values; — acceptance procedure for verification of a lot (taken from EN 384: 2010). 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 14358:2016 EN 14358:2016 (E) 4 1 Scope This standard gives statistical methods for the determination of characteristic values from test results on a sample drawn from a clearly defined reference population of e.g. solid wood, fasteners, connectors and wood-based products. The characteristic value is an estimate of the property of the reference population and can be based on a 5-percentile value of strength, resistance or density as well as on a mean value for stiffness. Parametric methods are given for the determination of lower and upper 5-percentiles. The upper 5- percentile is the 95-percentile. This standard is suitable for use with any structural product in the frame of type testing as well as factory production control. Sampling is not covered by this document, but reference is made to the relevant product standards. This standard also provides the acceptance procedure for verification of a lot. Depending on the product, characteristic values determined in accordance with this standard may be used directly or may need additional adjustments specified in the relevant product standards. Note: For example, in the case of solid timber, specific adjustment factors for calculation of characteristic values are given in EN 384. 2 Symbols s () kn Factor used to calculate characteristic properties for initial type testing (see Tables 1 and 2) () kn Factor used to calculate characteristic properties for factory production control (see Tables 3 and 4) m i Individual test value i of stochastic variable m m k 5-percentile value of stochastic variable m mean m Population mean value of stochastic variable m n Number of test values s y Standard deviation u x x-percentile in the standardised normal distribution y Sample mean value — y = m for normally distributed variable — y = ln m for logarithmically normally distributed variable 5 . 0 y Sample 5-percentile from the test data α Confidence level (%) BS EN 14358:2016 EN 14358:2016 (E) 5 3 Calculation of characteristic properties from test results in the frame of initial type testing 3.1 General The characteristic value of a material parameter or a resistance shall be determined at a confidence level of α = 75 %, where the confidence level α is defined as the probability of which the characteristic value is greater than the estimator on the characteristic value. NOTE The confidence level α = 75 % corresponds to the value recommended in EN 1990. 3.2 Calculation of 5 and 95 percentiles values 3.2.1 General a) The characteristic value k m for a material strength parameter or a resistance m modelled as a stochastic variable is defined as the p -percentile in the distribution function for m , corresponding to an assumed infinitely large test series; b) p = 5 % shall be assumed. 3.2.2 Parametric calculation a) The parametric approach shall not be used on test data not fitting the assumed distribution. In that case, a non-parametric method should be used; b) It is assumed that n test values are available and that these may be assumed to originate from a statistically homogeneous population. The test values, which are assumed to be logarithmically normally distributed or normally distributed and independent, are denoted 12 , ,, n mm m . The n test values constitute the sample; c) Strength parameters should be assumed as logarithmically normally distributed unless analysis of the data shows that a normal distribution is more appropriate. Density shall be assumed as normally distributed; NOTE Some product standards define the statistical distribution to be used. d) The mean value y and the standard deviation s y shall be determined as: logarithmically normally distributed normally distributed = = ∑ 1 1 ln n i i ym n(1) = = ∑ 1 1 n i i ym n(2) = − = − ∑ 2 1 1 (ln ) max 1 0,05 n i y i my s n(3) = − = − ∑ 2 1 1 () max 1 0,05 n i y i my s n y(4) The sample coefficient of variation shall not be taken as less than 0,05. For logarithmically normally distributed test values, the standard deviation s y shall not be less than ( ) +≈ 2 ln 1 0,05 0,05 . BS EN 14358:2016 EN 14358:2016 (E) 6 For normally distributed test values, the standard deviation s y shall not be less than 0,05 y . e) The characteristic value of the sample shall be determined as follows: percentile logarithmically normally distributed normally distributed 5-percentile ( ) = − k syexp ( ) m y k ns (5) = − k sy() m y k ns (6) 95-percentile ( ) = + k syexp ( ) m y k ns (7) = + k sy() m y k ns (8) f) s () kn shall be taken as: α = s () () kn kn n(9) where α () kn is the α-percentile in a non-central t-distribution with n – 1 degrees of freedom and the non-centrality parameter λ − = ⋅ 1p un . whereby u 1-p is the (1 – p)-percentile of the standardised normal distribution function. The following simplified expression may be used to evaluate s () kn + = − s 6,5 6 () 3,7 3 n kn n(10) Some values of s () kn calculated according to Formula (9) are given in Table 1. Table 1 — ( ) s kn values for strength properties for p = 5 % and α = 75 % Number of test specimens Factor n s () kn 3 3,15 5 2,46 10 2,10 15 1,99 20 1,93 30 1,87 50 1,81 100 1,76 500 1,69 ∞ 1,64 For other numbers of test specimens, one should take the value corresponding to the next smallest value of n listed in this table. BS EN 14358:2016 EN 14358:2016 (E) 7 3.2.3 Non parametric calculation a) Non parametric calculation shall not be applied if the sample size is less than = 40 n ; b) The 5-percentile of the test data shall be evaluated by ranking the test data and determining the 5- percentile of the ranked data; To rank the data, any p-percentile value f p shall be linearly interpolated from the empirical cumulative frequency distribution of the test data ranked in ascending order. The i-th data point in the empirical cumulative frequency distribution of the test data (ranked in ascending order) shall be taken to be the percentile (p) given by the following equation: = i p n(11) where n sample size i i-th data point ranked in ascending order c) The 5-percent lower tolerance limit with 75 % confidence shall be evaluated from Formula (12): − = n V k y m k 75 . 0 , 5 . 0 5 . 0 1 (12) where n is the number of test values k m is the 5-percent lower tolerance limit with 75 % confidence 5 . 0 y is the 5-percentile from the test data V is the coefficient of variation of the test data found by dividing the standard deviation of the test data by the average of the test data k 0.5,0.75 is a multiplier to give the 5-percent lower tolerance limit with 75 % confidence: 1 , 7 28 , 0 17 49 , 0 75 . 0 , 5 . 0 + + = n n k (13) 3.3 Calculation of characteristic mean values a) The characteristic value mean m for a material stiffness m modelled as a stochastic variable is defined as the mean value in the distribution function for m, corresponding to an assumed infinitely large test series; b) It is assumed that n test values are available and that these may be assumed to originate from a homogeneous population. The test values, which are assumed to be normally distributed and independent, are denoted 12 n , ,, mm m . The n test values constitute the sample; BS EN 14358:2016 EN 14358:2016 (E) 8 c) The sample mean value y and the sample standard deviation s y for the stochastic variable y = m shall be determined as: = = ∑ i 1 1 n i ym n(14) = − = − ∑ 2 i y 1 1 () max 1 0,05 n i my s n y(15) d) For stiffness properties, the characteristic mean value shall be taken as the sample mean value y as given in Formula (14); e) When it is required to make use of confidence intervals, the characteristic mean value m mean shall be determined as. = − mean s y() m y k ns (16) where α− = ,n 1 s () t kn n(17) α− ,n 1 t is the α percentile in a central t-distribution with n-1 degrees of freedom. Some values of s () kn are given in Table 2. For other numbers of test specimens, one should either interpolate or take the safer value for s () kn , i.e. the one which is larger. The following simplified equation may also be used to evaluate. = s 0,53 0,78 () kn n(18) BS EN 14358:2016 EN 14358:2016 (E) 9 Table 2 — ( ) s kn values for stiffness properties Number of test specimens Factor n () s kn 3 0,471 5 0,331 10 0,222 15 0,179 20 0,154 30 0,125 50 0,096 100 0,068 500 0,030 ∞ 0,000 4 Calculation of characteristic properties from test results in the frame of internal factory production control 4.1 General If a variable control method is applied to control the material parameters or resistance, such control method shall be composed with a significance level of α = 75 %, where the significance level α is defined as the probability of not accepting a batch having the required characteristic value. NOTE The significance level α = 75 % corresponds to the value required in Clause 3. 4.2 Calculation of characteristic strength, density or resistance properties (5-percentile) a) It is assumed that n test values are available and that these may be assumed to be derived from a homogeneous population described by the stochastic variable m. The test values which are assumed to be logarithmically normally distributed or normally distributed, are denoted 12 n , ,, mm m . The n test values constitute the sample; b) Strength parameters shall be assumed as logarithmically normally distributed. Density shall be