# ISO 12122-6:2017

(Main)## Timber structures — Determination of characteristic values — Part 6: Large components and assemblies

## Timber structures — Determination of characteristic values — Part 6: Large components and assemblies

ISO 12122-6:2017 specifies methods of determination of characteristic values for a defined population of large components and assemblies, calculated from test values. It establishes two methods for the determination of characteristic values: a) direct calculation from test values; b) calculation from a resistance model, which is firstly calibrated from test results, including calculation of error terms.

## Structures en bois — Détermination des valeurs caractéristiques — Partie 6: Composants assemblés

### General Information

### Standards Content (Sample)

INTERNATIONAL ISO

STANDARD 12122-6

First edition

2017-07

Timber structures — Determination

of characteristic values —

Part 6:

Large components and assemblies

Structures en bois — Détermination des valeurs caractéristiques —

Partie 6: Composants assemblés

Reference number

ISO 12122-6:2017(E)

©

ISO 2017

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ISO 12122-6:2017(E)

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© ISO 2017, Published in Switzerland

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form

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ISO 12122-6:2017(E)

Contents Page

Foreword .iv

Introduction .v

1 Scope . 1

2 Normative references . 1

3 Terms and definitions . 1

4 Symbols . 1

5 Reference population . 2

5.1 General . 2

5.2 Prediction of test results . 3

6 Sampling . 3

7 Sample conditioning . 4

8 Test data . 4

8.1 Loading specifications . 4

8.2 Testing arrangement . 4

8.3 Test measurements . 4

9 Evaluation of characteristic values for structural properties . 4

9.1 General principles . 4

9.2 Direct evaluation of characteristic value . 5

9.2.1 Sampling factor k .

n 5

9.2.2 Normal distribution . 5

9.2.3 Log-normal distribution . 6

9.3 Statistical determination of resistance models . 6

9.3.1 General. 7

9.3.2 Procedure . 7

9.3.3 Use of prior test data .11

10 Reporting .12

Annex A (informative) Commentary .13

Annex B (informative) Example of calculation according to 9.2 and 9.3 .21

Bibliography .23

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ISO 12122-6:2017(E)

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO’s adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following

URL: w w w . i s o .org/ iso/ foreword .html.

This document was prepared by Technical Committee ISO/TC 165, Timber structures.

A list of all parts in the ISO 12122 series can be found on the ISO website.

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ISO 12122-6:2017(E)

Introduction

This document sets out a framework for establishing characteristic values from test results on a

sample drawn from a clearly defined reference population of large components and assemblies. The

characteristic value is an estimate of the property of the reference population with a consistent level of

confidence prescribed in the standard.

This document is to be used in conjunction with ISO 12122-1.

Since this document is dedicated to large components and assemblies, it has to deal with a specific

statistical issue, namely that the characteristic values are to be derived from a very small number of

test results.

In some cases, characteristic values determined in accordance with this document may be modified to

become a design value.

Annex A presents a commentary on the provisions in this document.

Annex B presents examples of the use of the statistical methods.

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INTERNATIONAL STANDARD ISO 12122-6:2017(E)

Timber structures — Determination of characteristic

values —

Part 6:

Large components and assemblies

1 Scope

This document specifies methods of determination of characteristic values for a defined population of

large components and assemblies, calculated from test values.

It establishes two methods for the determination of characteristic values:

a) direct calculation from test values;

b) calculation from a resistance model, which is firstly calibrated from test results, including

calculation of error terms.

2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 12122-1, Timber structures — Determination of characteristic values — Part 1: Basic requirements

3 Terms and definitions

For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— IEC Electropedia: available at http:// www .electropedia .org/

— ISO Online browsing platform: available at http:// www .iso .org/ obp

3.1

large components and assemblies

parts of a timber structure consisted of at least two members, assembled together by connections

4 Symbols

E(.) mean value of (.)

Var(.) variance of (.)

V coefficient of variation [V = (standard deviation)/(mean value)]

V coefficient of variation of X

X

V estimator for the coefficient of variation of the error term δ

δ

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ISO 12122-6:2017(E)

array of j basic variables X … X

X 1 j

array of mean values of the basic variables

X

m

array of nominal values of the basic variables

X

n

resistance function (of the basic variables X) used as the resistance model

gX

()

rt

k characteristic fractile factor

n

m mean of the n sample results

X

n number of experiments or numerical test results

r resistance value

r experimental resistance value

e

r extreme (maximum or minimum) value of the experimental resistance

ee

[i.e. value of r that deviates most from the mean value r ]

e em

r experimental resistance for specimen i

ei

r mean value of the experimental resistance

em

r characteristic value of the resistance

k

r

m

resistance value calculated using the mean values X of the basic variables

m

r nominal value of the resistance

n

r

t

theoretical resistance determined from the resistance function gX

()

rt

r

theoretical resistance determined using the measured parameters X for specimen i

ti

s estimated value of the standard deviation σ

s estimated value of σ

δ δ

δ error term

δ observed error term for test specimen i obtained from a comparison of the experimental

i

resistance r and the mean value corrected theoretical resistance br

ei ti

η reduction factor applicable in the case of prior knowledge

k

σ

standard deviation σ = variance

5 Reference population

5.1 General

The reference population is the population of large components or assemblies that the test program

is designed to represent. Prior to the carrying out of tests, a test plan shall be documented. It shall

contain the objectives of the test and all specifications necessary for the selection or production of the

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ISO 12122-6:2017(E)

test specimens, the execution of the tests and the test evaluation. The test plan shall cover the following

details of the reference population, including structural context for the loading of the specimens:

— objectives and scope;

— prediction of test results;

— specification of test specimens and sampling;

— description of expected restraint and boundary conditions in normal service;

— loading specifications;

— testing arrangement;

— measurements;

— evaluation and reporting of the tests.

The objective of the tests shall be clearly stated, e.g. the required properties, the influence of certain

design parameters varied during the test and the range of validity. Limitations of the test and required

conversions (e.g. scaling effects) shall be specified.

5.2 Prediction of test results

All properties and circumstances that can influence the prediction of test results should be taken into

account, including:

— geometrical parameters and their variability;

— geometrical imperfections;

— material properties;

— parameters influenced by fabrication and execution procedures;

— scale effects of environmental conditions taking into account, if relevant, any sequencing.

The expected modes of failure and/or calculation models, together with the corresponding variables,

should be described. If there is a significant doubt about which failure modes can be critical, then the

test plan should be developed on the basis of accompanying pilot tests.

Attention shall be given to the fact that a structural assembly can possess a number of fundamentally

different failure modes.

6 Sampling

Test specimens shall be constructed, or obtained by sampling, in such a way as to represent the

conditions of the real structure.

Factors that shall be taken into account include:

— dimensions and tolerances;

— material and fabrication of prototypes;

— number of test specimens;

— sampling procedures;

— restraints.

The objective of the sampling procedure is to obtain a statistically representative sample.

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ISO 12122-6:2017(E)

Attention should be drawn to any difference between the test specimens and the product population

that could influence the test results.

7 Sample conditioning

Test samples shall be conditioned to represent the reference population as detailed in ISO 12122-1.

8 Test data

8.1 Loading specifications

The loading and environmental conditions to be specified for the test shall include:

— loading points;

— expected loading time history;

— restraints;

— temperatures;

— relative humidity;

— loading by deformation or force control, etc.

Load sequencing shall be selected to represent the anticipated use of the structural assembly, under

both normal and severe conditions of use. Interactions between the structural response and the

apparatus used to apply the load shall be taken into account where relevant.

Where structural behaviour depends upon the effects of one or more actions that will not be varied

systematically, then those effects shall be specified by their representative values.

8.2 Testing arrangement

The test equipment shall be relevant for the type of tests and the expected range of measurements.

Special attention shall be given to measures to obtain sufficient strength and stiffness of the loading

and supporting rigs, and clearance for deflections, etc.

8.3 Test measurements

Prior to the testing, all relevant properties to be measured for each individual test specimen shall

be listed.

9 Evaluation of characteristic values for structural properties

9.1 General principles

Two methods are described in this document:

— direct evaluation of characteristic values from test results (see 9.2);

— evaluation of characteristic values from a model including error calculation (see 9.3).

NOTE 1 Both methods are acceptable, but if there are less than 10 test results, the second method is preferred,

since the first method can lead to conservative characteristic values with a low number of test results.

When evaluating test results, the behaviour of test specimens and failure modes should be compared

with theoretical predictions. When significant deviations from the predicted behaviour occur, an

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ISO 12122-6:2017(E)

explanation shall be sought: this might involve additional testing, perhaps under different conditions,

or modification of the theoretical model.

The result of a test evaluation shall be considered valid only for the specifications and load characteristics

considered in the tests. If the results are to be extrapolated to cover other design parameters and

loading, additional information from previous tests or from theoretical bases shall be used.

The derivation of a characteristic value from tests (see 9.2) should take into account:

a) the scatter of test data;

b) statistical uncertainty associated with the number of tests;

c) prior statistical knowledge.

NOTE 2 Annex A gives additional explanation about variability of test results.

If the response of large components or assemblies depends on influences not sufficiently covered by the

tests such as

— time and duration effects,

— scale and size effects,

— different environmental, loading and boundary conditions, and

— resistance effects,

then a behaviour model shall be derived and shall take such influences into account as appropriate

(see 9.3).

9.2 Direct evaluation of characteristic value

9.2.1 Sampling factor k

n

A sampling factor is used in the evaluation of characteristic value detailed in both 9.2 and 9.3. The

values for this factor shall be drawn from Table 1.

Where using the direct evaluation of the characteristic value from the test results, the 5 percentile

value of a property, X, shall be found by using either a normal distribution fitted through the test data

as indicated in 9.2.1 or a log-normal distribution fitted through the test data as indicated in 9.2.2.

Table 1 — Values of k for the 5 % characteristic value

n

n 1 2 3 4 5 6 8 10 20 30 ∞

V known 2,31 2,01 1,89 1,83 1,80 1,77 1,74 1,72 1,68 1,67 1,64

X

V unknown̶̶3,37 2,63 2,33 2,18 2,00 1,92 1,76 1,73 1,64

X

9.2.2 Normal distribution

The characteristic value shall be calculated using Formula (1).

Xm=−1 kV (1)

{}

kX nX

The value of k shall be obtained from Table 1 using either of the following two cases:

n

— The row “V known” shall be used if the coefficient of variation of the structural property of the

X

reference population, V , or a realistic upper bound of it, is known from prior knowledge.

X

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ISO 12122-6:2017(E)

— The row “V unknown” shall be used if the coefficient of variation V is not known from prior

X X

knowledge and so, needs to be estimated from the sample using Formulae (2) and (3):

n

2

1

s = xm− (2)

()

∑

Xi X

n−1

i=1

s

X

V = (3)

X

m

X

9.2.3 Log-normal distribution

The characteristic value shall be calculated using Formulae (4) and (5).

Xm=−exp ks (4)

kY nY

where:

1

m = ln x (5)

()

∑

Yi

n

i

The value of k shall be obtained from Table 1 using either of the following two cases:

n

— The row “V known” shall be used if the coefficient of variation of the structural property of the

X

reference population, V , or a realistic upper bound of it, is known from prior knowledge with s as

X Y

given in Formula (6).

2

sV=+ln 1 ≈V (6)

( )

YX X

— The row “V unknown” shall be used if the coefficient of variation V is not known from prior

X X

knowledge and so s is estimated from the sample as given in Formula (7).

Y

2

1

s = lnxm− (7)

()

∑

Yi Y

n−1

i

9.3 Statistical determination of resistance models

In 9.3, the procedures (methods) for calibrating resistance models and for deriving characteristic values

from tests are defined. Use will be made of available prior information (knowledge or assumptions).

Based on the observation of actual behaviour in tests and on theoretical considerations, a “resistance

model” shall be developed, leading to the derivation of a resistance function. The validity of this model

shall be then checked by means of a statistical interpretation of all available test data. If necessary,

the resistance model shall be adjusted until sufficient correlation is achieved between the theoretical

values and the test data.

Deviation in the predictions obtained by using the resistance model shall also be determined from

the tests. This deviation shall be combined with the deviations of the other variables in the resistance

function in order to obtain an overall indication of deviation. These other variables shall include:

— deviation in material strength and stiffness;

— deviation in geometrical properties.

The characteristic resistance shall be determined by taking account of the deviations of all the variables.

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ISO 12122-6:2017(E)

9.3.1 General

For this evaluation procedure, the following assumptions are made:

a) the resistance function is a function of a number of independent variables X;

b) a sufficient number of test results is available;

c) all relevant geometrical and material properties are measured;

d) there is no correlation (statistical dependence) between the variables in the resistance function;

e) all variables follow either a normal or a log-normal distribution.

NOTE Adopting a log-normal distribution for a variable has the advantage that no negative values can occur.

9.3.2 Procedure

a) Step 1: Develop a resistance model.

Develop a resistance model for the theoretical resistance, r , of the large components or assemblies

t

considered, represented by the resistance function given in Formula (8):

rg= X (8)

()

trt

The resistance function shall cover all relevant basic variables, X, that affect the resistance at the

relevant limit state.

All basic parameters shall be measured for each test specimen, I, and shall be available for use in the

evaluation.

b) Step 2: Compare experimental and theoretical values.

Substitute the actual measured properties into the resistance function to obtain theoretical values r

ti

and to form the basis of a comparison with the experimental values, r , from the tests.

ei

The points representing pairs of corresponding values, (r , r ), shall be plotted on a diagram, as

ti ei

indicated in Figure 1.

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ISO 12122-6:2017(E)

Figure 1 — Experimental resistance versus theoretical resistance (r , r ) diagram

ti ei

π

If the resistance function is exact and complete, then all of the points will lie on the line θ = . In

4

practice, the points will show some scatter but the causes of any systematic deviation from that line

should be investigated to check whether this indicates errors in the test procedures or in the resistance

function.

c) Step 3: Estimate the mean value correction factor b.

1) Represent the probabilistic model of the resistance, r, in the format given in Formula (9):

rb= r δ (9)

t

where

b is the “least squares” best-fit to the slope, given by Formula (10):

rr

∑

ei ti

i

b= (10)

2

r

∑

ti

i

2) The mean value of the theoretical resistance function, calculated using the mean values, X , of

m

the basic variables, shall be obtained from Formula (11):

r

= br X δ

()

m

tm

(11)

= bg X δ

()

rt m

d) Step 4: Estimate the coefficient of variation of the errors.

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ISO 12122-6:2017(E)

The error term, δ , for each experimental value, r , shall be determined from Formula (12):

i ei

r

ei

δ = (12)

i

br

ti

e) Step 5: Analyse compatibility.

1) The compatibility of the test population with the assumptions made in the resistance function

shall be analysed.

2) If the scatter of the (r , r ) values is too high to give economical design resistance functions,

ti ei

this scatter shall be reduced in one of the following ways:

i) by correcting the resistance model to take into account parameters which had previously

been ignored;

ii) by modifying b and V by dividing the total test population into appropriate subsets for

δ

which the influence of such additional parameters may be considered to be constant.

NOTE 1 Annex A gives a suitable check to indicate whether the resistance model gives economical results.

3) To determine which parameters have most influence on the scatter, the test results shall be

split into subsets with respect to these parameters.

NOTE 2 The purpose is to improve the resistance function per subset by analysing each subset using the

standard procedure. The disadvantage of splitting the test results into subsets is that the number of test

results in each subset can become very small.

4) When determining the fractile factors k (see step 7), the k value for the subsets shall be

n n

determined on the basis of the total number of the tests in the original series.

NOTE 3 Attention is drawn to the fact that the frequency distribution for resistance can be better

described by a bi-modal or a multi-modal function. Special approximation techniques can be used to

transform these functions into a uni-modal distribution.

f) Step 6: Determine the coefficients of variation, V , of the basic variables.

Xi

If it can be shown that the test population is fully representative of the variation in the reference

population, then the coefficients of variation, V , of the basic variables in the resistance function shall

Xi

be determined from the test data.

Since this is not generally the case, the coefficients of variation, V , will normally need to be determined

Xi

on the basis of some prior knowledge.

g) Step 7: Determine the characteristic value, r , of the resistance.

k

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ISO 12122-6:2017(E)

The coefficient of variation of δ is given by Formula (13):

Var δ

V = (13)

δ

E δ

The coefficient of variation of r is given by Formula (14):

t

Varg X

()

rt

V = (14)

rt

Eg X

()

rt

The coefficient of variation of r is given by Formula (15):

Varg X Vargδ X

() ()

r rt

V = = (15)

r

Eg X Egδ X

() ()

r rt

From these expressions, the characteristic resistance r shall be obtained from Formulae (16), (17)

k

and (18):

2

rb= gX exp −−kQααkQ −05, Q (16)

()

( )

krtm ∞ rt rt n δδ

with:

2

QV==σ ln +1

( )

rt ln()rt rt

2

(17)

QV==σ ln +1

( )

δδln() δ

2

QV==σ ln +1

( ))

ln()rr

and

Q

rt

α =

rt

Q

(18)

Q

δ

α =

δ

Q

where

k is the characteristic fractile factor from Table 1 for the case V unknown;

n X

k is the value of k for n → ∞ [k = 1,64];

∞ n ∞

α is the weighting factor for Q ;

rt rt

α is the weighting factor for Q .

δ δ

NOTE 4 The value of V is to be estimated from the test sample under consideration.

δ

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ISO 12122-6:2017(E)

9.3.3 Use of prior test data

If the validity of the resistance function r and an upper bound (conservative estimate) for the coefficient

t

of variation V are already known from a significant number of previous tests, the following simplified

r

procedure may be adopted when further tests are carried out.

a) If only one further test is carried out, the characteristic value r may be determined from the result

k

r of this test by using Formula (19):

e

rr=η (19)

kk e

where

η is a reduction factor applicable in the case of prior knowledge that may be obtained from

k

Formula (20):

2

η =−09,,exp 2310VV− ,5 (20)

( )

kr r

where

V is the maximum coefficient of variation observed in previous tests.

r

b) If two or three further tests are carried out, the characteristic value r may be determined from the

k

mean value r of the test results by using Formula (21):

em

rr=η (21)

kk em

where

η is a reduction factor applicable in the case of prior knowledge that may be obtained from

k

Formula (22):

2

η =−exp2,,00VV− 5 (22)

)

(

kr r

wher

**...**

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